https://kbwiki.ercoftac.org/w/api.php?action=feedcontributions&user=David.Fowler&feedformat=atom
KBwiki - User contributions [en]
2021-05-12T05:19:52Z
User contributions
MediaWiki 1.33.0
https://kbwiki.ercoftac.org/w/index.php?title=The_Semantic_Web_and_the_QNET_Wiki&diff=12109
The Semantic Web and the QNET Wiki
2009-11-12T12:08:51Z
<p>David.Fowler: /* Introduction: The Semantic Web */</p>
<hr />
<div>== Introduction: The Semantic Web ==<br />
First of all, one has to consider what the Semantic Web is intended to be. At the risk of venturing a crude definition, the Semantic Web is a means of linking together different information resources on the Internet so that they can be accessible to machine reasoning systems. 'Link' here is certainly not meant in the sense of a hyperlink. Rather, the concept of a link here is more relevant to 'relationships'- something that ordinary hyperlinks do not necessarily express. By means of these relationships between say, web pages, associations can be made between information that endows it with meaning. <br />
<br />
The Semantic Web deals with resources represented by Uniform Resource Indicators. <br />
<br />
http://www.complico.org/joe_bloggs<br />
<br />
[Please don't click it if you don't want to disappoint your web browser...]<br />
<br />
Clearly one is left with a great deal of ambiguity about what these 'resources' actually are. <br />
<br />
In the example above, the possibilities are:<br />
* it could be a regular web page address- eg, the home page of someone called Joe Bloggs<br />
* perhaps an abstract URI of a person called joe bloggs who works for an organisation called 'complico'<br />
* a network device attached to a cat cheekily called 'joe bloggs'<br />
* a sensor in a non-network location<br />
* a reference to a special interest group where JOE_BLOGS is an acronym for 'Joint Optimisation of Engineering Buildings and Leisure OrGanisation Group'<br />
* etc etc<br />
<br />
To find out more about 'joe bloggs' we would have to be given some attributes or properties about him or it. That is, we need to know its relationships to other entities to get a better understanding of what it actually '''is'''. These entities could be either typed constants (strings, integers etc), collections, or references to other web resources.<br />
<br />
Using these kind of formal data models can lead to a more rigorous and accurate search and retrieval mechanism for data on the Internet than is possible by keyword association alone. In this way, a higher degree of confidence and trust can be placed in the results from this machine reasoning that is based on these formally defined relationships. Compare this to Google where keyword searches are used to find the relevant data and a human agent is required to sort the results out.<br />
<br />
As an example - here is some RDF code that could express the fact that Joe Bloggs is a person, and that they have a specific email address, web page, that they know some other people, etc. (I apologise for the code - this is how the data might be stored electronically, but semantic wikis allow people to express this in a less painful manner). With enough of these people descriptions, you could find all the people that Joe Bloggs knows, and build up a network of his contacts - something that would be next to impossible with keyword searches.<br />
<br />
<rdf:RDF xmlns:foaf="http://xmlns.com/foaf/0.1/" <br />
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"<br />
xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"><br />
<foaf:Person rdf:about="http://www.complico.org/joe_bloggs"><br />
<foaf:name>Joe Bloggs</foaf:name><br />
<foaf:mbox rdf:resource="mailto:jbloggs@complico.org" /><br />
<foaf:homepage rdf:resource="http://www.joebloggs.com/" /><br />
<foaf:nick>Joe</foaf:nick><br />
<foaf:depiction rdf:resource="http://www.joebloggs.com/joebloggs.jpg" /><br />
<foaf:knows><br />
<foaf:Person><br />
<foaf:name>Dave Golby</foaf:name> <br />
</foaf:Person><br />
</foaf:knows><br />
</foaf:Person><br />
</rdf:RDF><br />
<br />
Some of the issues with this approach are:<br />
<br />
* Getting enough annotated data - users may be discouraged from doing annotations, as the benefits may not be immediately obvious.<br />
* Getting people to agree on a common vocabulary - the "foaf" (Friend Of A Friend) in the example above is a standard vocabulary, but other people might choose to use their own, which will cause problems.<br />
<br />
== The Semantic Web Stack ==<br />
A (possibly oversimplified) description is that one starts with 'data models'. A data model formally expresses the relations between different data entities, eg, as in a traditional database schema. At this stage, no inference can necessarily be made on these descriptions. Indeed, the data model tends to be worked with by specific applications in which these associations are treated with much greater significance than is apparent to an external observer. So for example, one could conceive of a relational database of data that links a product to the datasets that have various analyses of it under certain flow regimes or operating conditions. This database would be used by a web site to search and retrieve this information, using application back-end code, eg, written in Java, PHP or a .NET language. In a certain sense, the knowledge of types and relations between the data entities is hidden in the application itself and is not visible to outsiders. Finally, the data models tend to be 'brittle' and easily break as different business needs arise.<br />
<br />
So, as a consequence of this 'hidden knowledge' in the application two things arise:<br />
* a great deal of logic is re-implemented across different applications<br />
* more critically, this knowledge is hidden from, eg, collaborators or even the same organisation who may wish to exploit it.<br />
<br />
== QNET and the Semantic Web ==<br />
Getting back to Wikis, a particular challenge is organising the information they contain in a way that makes sense to the user of the site. A common solution, as used in this first version of the QNET Wiki, is to 'stove-pipe' the articles into categories from some top-level downwards. So one has AC and UFR articles belonging to higher categories and so on. <br />
<br />
The problem with this approach is the following:<br />
* the administrative overheads: administrators have to be very dilligent in order to classify and organise articles, inserting links into tables etc in order to make the articles accessible<br />
* it fixes a particular view of the articles that may not be appropriate for certain users. <br />
* it overlooks other very interesting relationships that may be submerged within the articles. <br />
<br />
Ideally, one would prefer to annotate the articles themselves, ie, assign them properties that can be used for automatic categorisation.</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Abstr:RAE_M2155_Wing&diff=9197
Abstr:RAE M2155 Wing
2009-04-28T15:08:28Z
<p>David.Fowler: /* Abstract */</p>
<hr />
<div>{{AC|front=AC 1-02|description=Description_AC1-02|testdata=Test Data_AC1-02|cfdsimulations=CFD Simulations_AC1-02|evaluation=Evaluation_AC1-02|qualityreview=Quality Review_AC1-02|bestpractice=Best Practice Advice_AC1-02|relatedUFRs=Related UFRs_AC1-02}}<br />
<br />
== Application Area 1: External Aerodynamics ==<br />
<br />
=== Application Challenge AC1-02 ===<br />
<br />
<br />
<br />
==== Abstract ====<br />
The wing RAE M2155 is a low aspect-ratio (3.27) swept wing that has been tested at the DERA 8ft x 6ft transonic wind tunnel in the Mach number range 0.6 - 0.87. The wing was mounted directly on the wall of the tunnel, so that the wall boundary layer and wing boundary layer interact. Tunnel wall interference effects have been measured, and were found to be significant especially for the higher Mach number test conditions. The computational studies, therefore have been performed as internal flow calculations, making tunnel corrections unnecessary.<br />
<br />
At the design conditions (Mach number 0.86, lift coefficient 0.5, Reynolds number 4x10<sup>6</sup>, based on geometric mean chord) the wing has the following characteristics: attached boundary layer everywhere; high rear loading, providing a difficult test of the calculation of boundary layer growth; and a triple shock structure on the upper surface. At off design conditions, flow separations occur. <br />
<br />
Wing and tunnel wall pressure measurements are available for several combinations of Mach number and incidences. A set of 4 conditions (named as case 1-4) have also oil flow pictures, boundary layer measurements, and skin friction coefficient. Normal force coefficients have been calculated from the measured pressure distribution at several span stations and integrated on the whole wing.<br />
<br />
The wing RAE M2155 has been the subject of many numerical simulations, and has been chosen to validate and assess turbulence models in E.C. funded project AVTAC.<br />
<br />
Computations have been performed at QINETIQ for the case 1,2,3, and 4 by using the following turbulence models :<br />
<br />
* A κ-g based variant of the Menter SST scheme<br />
<br />
* A κ-g based EARSM utilizing a novel calibration and incorporating explicitly the variable ratio of turbulence production to dissipation rate.<br />
<br />
* A tensorially linear version of the κ-g based EARSM model (only case 3).<br />
<br />
and at CIRA, for the case 2, by employing the following turbulence models :<br />
<br />
* Spalart-Allmaras <br />
<br />
* Myong-Kasagi κ-ε<br />
<br />
* Non-Linear κ-ε (Myong-Kasagi κ-ε + 2nd order constitutive relation by Shih)<br />
<br />
* Standard Wilcox κ-ω <br />
<br />
* Kok TNT κ-ω <br />
<br />
* Menter SST κ-ω <br />
<br />
The numerical results consist of pressure and skin friction coefficients as well as velocity profiles at several stations along the wing span.<br />
<br />
The M2155 test cases were specifically intended for the validation of CFD methods, as aeronautical design tools. The test geometry, consisting of a wing attached to a wind-tunnel wall, is akin to a wing-body configuration, although the test flow is clearly an internal one. The importance of such configurations for aeronautical applications is obvious. The wing is swept and is of low aspect ratio, as is common in military applications. The low aspect ratio of the wing ensures that the resulting flow is strongly three-dimensional. Inappropriate modeling in the wing-wall junction, for instance, can affect the computed flow over a significant fraction of the span. The wing design and test conditions probe the buffet and separation boundaries at the edge of the flight envelope, these boundaries being of importance in both civil and military aircraft design, and providing a considerable challenge to numerical flow solvers. The flows are complex with three-dimensional separations and triple shock structures. The boundary layers are subjected to strong adverse pressure gradients (the trailing edges being heavily loaded), a regime which is difficult for numerical methods but of great importance in wing design. <br />
<br />
The simulation of this kind of flow represents a severe and relevant test to assess the ability of the computational methods. The prediction of the shock waves system, of the separation and reattachment lines and of the pressure recovery behind the shock and in the trailing edge zone are the challenges for the turbulence models.<br />
<br />
The design and assessment parameter are the aerodynamic coefficients.<br />
<br />
Normal force coefficients have been calculated from the measured pressure distributions and integrated on the whole wing. It is therefore possible to determine inviscid values of the aerodynamic coefficients.<br />
<br><br />
<br><br />
----<br />
''Contributors: Pietro Catalano - CIRA; QinetiQ''<br />
<br />
{{AC|front=AC 1-02|description=Description_AC1-02|testdata=Test Data_AC1-02|cfdsimulations=CFD Simulations_AC1-02|evaluation=Evaluation_AC1-02|qualityreview=Quality Review_AC1-02|bestpractice=Best Practice Advice_AC1-02|relatedUFRs=Related UFRs_AC1-02}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC1-05&diff=9196
CFD Simulations AC1-05
2009-04-28T15:04:31Z
<p>David.Fowler: /* =Solution strategy CFD5 */</p>
<hr />
<div>{{AC|front=AC 1-05|description=Description_AC1-05|testdata=Test Data_AC1-05|cfdsimulations=CFD Simulations_AC1-05|evaluation=Evaluation_AC1-05|qualityreview=Quality Review_AC1-05|bestpractice=Best Practice Advice_AC1-05|relatedUFRs=Related UFRs_AC1-05}}<br />
<br />
='''Ahmed body'''=<br />
<br />
'''Application Challenge 1-05''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of CFD Simulations'''==<br />
<br />
CFD simulations have developed rapidly during the writing of the present document, during the MOVA consortium and in the frame of the 9th and 10th ERCOFTAC-IAHR Workshop on Refined Turbulence Modeling organized in Darmstad, Germany and Poitiers, France, in 2001 and 2002, respectively. These workshops were organized under the auspices of the Special Interest Group 15 on Turbulence Modeling of ERCOFTAC. The proceedings of the 10th ERCOFTAC-IAHR Workshop can be found at:<br />
<br />
[http://www.ercoftac.nl/workshop10/index.html http://www.ercoftac.nl/workshop10/index.html]<br />
<br />
For the 10th ERCOFTAC-IAHR Workshop, several recommendations were made to the groups participating in the CFD calculations. Among them the recommendation to extend the computational domain up to 5 times the car length downstream of the body, and the possibility to omit the stilts.<br />
<br />
Many of the CFD results are considered by the authors themselves as preliminary computations and were therefore not inserted into the knowledge base.<br />
<br />
The geometry is simple enough to be satisfactorily represented.<br />
<br />
=='''Simulation Case CFD1'''==<br />
<br />
==='''Solution strategy CFD1'''===<br />
<br />
RANS modelling.<br />
<br />
Commercial FLUENT 4.2 code, based on unstructured finite volume discretization.<br />
<br />
Reynolds number: 4.29x106 (see EXP1). Steady state computation.<br />
<br />
The slant angle is varied from 0 to 50 degrees.<br />
<br />
<br />
==='''Computational Domain CFD1'''===<br />
<br />
Symmetry is used to compute half the domain.<br />
<br />
Domain: [-3L;5L]x[0;2L]x[0;2L]<br />
<br />
Mesh : 450,000 cells<br />
<br />
Approximate value of y+ on solid surfaces : 30.<br />
<br />
<br />
==='''Boundary Conditions CFD1'''===<br />
<br />
Inlet: turbulence level 0.5% with a mixing length of 5x10-3m.<br />
<br />
Outlet: constant pressure.<br />
<br />
Solid boundaries: wall functions<br />
<br />
Symmetry plane: symmetry<br />
<br />
Other boundaries: no details<br />
<br />
<br />
==='''Application of Physical Models CFD1'''===<br />
<br />
Standard K-ε model with standard wall functions.<br />
<br />
<br />
==='''Numerical Accuracy CFD1'''===<br />
<br />
Mesh refinement is performed until the drag reaches a constant value.<br />
<br />
Convection scheme : 2nd order.<br />
<br />
<br />
==='''CFD Results CFD1'''===<br />
<br />
Friction lines, pressure iso-contours at the model surface, velocity vector fields, drag coefficient.<br />
<br />
=='''References CFD1'''==<br />
<br />
'''Modelling of stationnary three-dimensional separated flows around an Ahmed reference model.'''<br />
<br />
P. Gilliéron, F. Chometon, ESAIM proc., vol 7, 173-182, 1999<br />
<br />
<br />
=='''Simulation Case CFD2'''==<br />
<br />
==='''Solution strategy CFD2'''===<br />
<br />
RANS modeling.<br />
<br />
Commercial FLUENT 5 code based on unstructured finite volume discretization.<br />
<br />
Reynolds number: 4.29x106 (see EXP1). Steady state computation.<br />
<br />
Slant angle: 30°.<br />
<br />
==='''Computational Domain CFD2'''===<br />
<br />
Symmetry is used to compute half the domain. Stilts are included.<br />
<br />
Domain: no details.<br />
<br />
Mesh : 704,000 cells.<br />
<br />
y+ at the first grid point from the wall of order of 50 - 350.<br />
<br />
==='''Boundary Conditions CFD2'''===<br />
<br />
No details.<br />
<br />
==='''Application of Physical Models CFD2'''===<br />
<br />
- Standard k-ε model with non-equilibrium wall functions.<br />
<br />
- RSM (no details) with non-equilibrium wall functions.<br />
<br />
==='''Numerical Accuracy CFD2'''===<br />
<br />
No details.<br />
<br />
==='''CFD Results CFD2'''===<br />
<br />
Pathlines and velocities.<br />
<br />
Aerodynamic drag coefficient.<br />
<br />
=='''References CFD2'''==<br />
<br />
Advances in external-aero simulation of ground vehicles using the steady RANS equation.<br />
<br />
Makowski F.T and Kim S.E., SAE Conf 2000-01-0484<br />
<br />
<br />
=='''Simulation Case CFD3'''==<br />
<br />
==='''Solution strategy CFD3'''===<br />
<br />
'''Large-eddy simulation.'''<br />
<br />
In house code PRICELES, based on unstructured second-order finite-element discretization.<br />
<br />
Reynolds number= 4.29 x106<br />
<br />
Slant angle: 28°.<br />
<br />
==='''Computational Domain CFD3'''===<br />
<br />
Domain: [-3L;5L]x[-L;L]x[-LxL] (the ground plate is NOT included: the body is suspended in the middle of the domain).<br />
<br />
Mesh: 1.6x106 cells.<br />
<br />
y+ at the first grid point from the wall is about 80 (averaged value).<br />
<br />
==='''Boundary Conditions CFD3'''===<br />
<br />
Inlet: constant velocity.<br />
<br />
Outlet: constant pressure conditions.<br />
<br />
Solid boundaries: wall functions<br />
<br />
Other boundaries : symmetry.<br />
<br />
==='''Application of Physical Models CFD3'''===<br />
<br />
Sub-grid model: standard Smagorinsky.<br />
<br />
==='''Numerical Accuracy CFD3'''===<br />
<br />
Second-order convection scheme and time marching (CFL number=3).<br />
<br />
==='''CFD Results CFD3'''===<br />
<br />
'''Pressure, pressure coef., velocity, drag coef, Q-criterion contours, vorticity.'''<br />
<br />
=='''References CFD3'''==<br />
<br />
Large eddy simulation of an Ahmed reference model.<br />
<br />
R.J.A. Howard, M. Pourquie.<br />
<br />
Journal of Turbulence, 2002<br />
<br />
<br />
=='''Simulation Case CFD4'''==<br />
<br />
==='''Solution strategy CFD4'''===<br />
<br />
RANS modelling.<br />
<br />
Commercial AVL SWIFT code, based on unstructured finite volume discretization.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25° and 35°.<br />
<br />
==='''Computational Domain CFD4'''===<br />
<br />
Symmetry is used to compute half the domain.<br />
<br />
Domain: Inlet at -1.5L. No other details.<br />
<br />
Mesh : 530,000 cells.<br />
<br />
y+ on solid surfaces < 100.<br />
<br />
==='''Boundary Conditions CFD4'''===<br />
<br />
Inlet: interpolated experimental profile at –1.4L used at –1.5L.<br />
<br />
Solid boundaries: wall functions<br />
<br />
Symmetry plane: symmetry<br />
<br />
Other boundaries: no details<br />
<br />
==='''Application of Physical Models CFD4'''===<br />
<br />
- Standard k-ε model with standard wall functions.<br />
<br />
- SSG Reynolds stress model with standard wall functions<br />
<br />
- Hybrid k-ε/Reynolds stress model (coefficient Cm of the k-ε model obtained from Reynolds stress transport equations) with standard wall functions<br />
<br />
==='''Numerical Accuracy CFD4'''===<br />
<br />
Grid sensitivity study.<br />
<br />
Study of the influence of the convection scheme.<br />
<br />
==='''CFD Results CFD4'''===<br />
<br />
Cp, velocity profiles in the boundary layer over the slant part.<br />
<br />
=='''References CFD4'''==<br />
<br />
B. Basara, S. Jakirlic, Flow Around a simplified car body (Ahmed body) : description of numerical methodology, in : S. Jakirlic, R. Jester-Zürker, C. Tropea, editors, 9th ERCOFTAC/IAHR/COST Workshop on Refined Turbulence Modelling, Oct. 4-5, 2001, Darmstadt University of Technology, Germany.<br />
<br />
<br />
=='''Simulation Case CFD5'''==<br />
<br />
=='''Solution strategy CFD5'''==<br />
<br />
RANS modelling.<br />
<br />
In-house code Saturne, based on unstructured finite volume discretization.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25° and 35°.<br />
<br />
==='''Computational Domain CFD5'''===<br />
<br />
Full body (no symmetry used)<br />
<br />
Domain: no details<br />
<br />
Mesh : 300,000 cells<br />
<br />
y+ on solid surfaces : no details.<br />
<br />
==='''Boundary Conditions CFD5'''===<br />
<br />
Inlet: no details.<br />
<br />
Solid boundaries: wall functions<br />
<br />
Other boundaries: no details<br />
<br />
==='''Application of Physical Models CFD5'''===<br />
<br />
- Standard k-ε model with standard wall functions<br />
<br />
- Launder, Reece, Rodi (IP) Reynolds stress model with standard wall functions<br />
<br />
- Linearized production k-ε model with standard wall functions<br />
<br />
<br />
==='''Numerical Accuracy CFD5'''===<br />
<br />
Convection scheme : 80% central differencing (2nd order), 20% upwind differencing (1st order).<br />
<br />
==='''CFD Results CFD5'''===<br />
<br />
Cp, velocity profiles in the boundary layer over the slant part.<br />
<br />
Vector plots, turbulent energy contours, streamlines.<br />
<br />
=='''References CFD5'''==<br />
<br />
S. Tekam, D. Laurence, T. Buchal, Flow around the Ahmed body, in : S. Jakirlic, R. Jester-Zürker, C. Tropea, editors, 9th ERCOFTAC/ IAHR/ COST Workshop on Refined Turbulence Modelling, Oct. 4-5, 2001, Darmstadt University of Technology, Germany.<br />
<br />
<br />
=='''Simulation Case CFD6'''==<br />
<br />
==='''Solution strategy CFD6'''===<br />
<br />
RANS modelling.<br />
<br />
Commercial FLUENT code, based on unstructured finite volume discretization.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25°.<br />
<br />
==='''Computational Domain CFD6'''===<br />
<br />
Domain: no details<br />
<br />
Mesh : 2.3x106 cells<br />
<br />
y+ on solid surfaces : no details<br />
<br />
==='''Boundary Conditions CFD6'''===<br />
<br />
Solid boundaries:<br />
<br />
- non-equilibrium wall functions for the k-ε model<br />
<br />
- no slip walls for the SST model<br />
<br />
<br />
<br />
Inlet, outlet and other boundaries: no details<br />
<br />
==='''Application of Physical Models CFD6'''===<br />
<br />
- Realizable k-ε model with non-equilibrium wall functions<br />
<br />
- SST model<br />
<br />
==='''Numerical Accuracy CFD6'''===<br />
<br />
No details<br />
<br />
==='''CFD Results CFD6'''===<br />
<br />
Cp, velocity profiles in the boundary layer over the slant part.<br />
<br />
=='''References CFD6'''==<br />
<br />
M. Lanfrit, M. Braun, D. Cokljat, Contribution to case 9.4: Ahmed body, in : S. Jakirlic, R. Jester-Zürker, C. Tropea, editors, 9th ERCOFTAC/ IAHR/ COST Workshop on Refined Turbulence Modelling, Oct. 4-5, 2001, Darmstadt University of Technology, Germany.<br />
<br />
<br />
=='''Simulation Case CFD7'''==<br />
<br />
==='''Solution strategy CFD7'''===<br />
<br />
RANS modelling in unsteady mode.<br />
<br />
In-house X-Stream code, based on finite volume solver for multi block structured non-orthogonal, curvilinear grid with collocated data arrangement. The convection terms are discretized using hybrid scheme with more than 60% central differencing. The diffusion terms are approximated with central differences. The SIMPLE method is used for the pressure-velocity coupling.<br />
<br />
Reynolds number: 2.78x106 (see EXP2).<br />
<br />
Slant angle: 35°<br />
<br />
==='''Computational Domain CFD7'''===<br />
<br />
Full body (no symmetry condition used).<br />
<br />
Domain: [-2L;5L]x[-1.2;1.2L]x[0;1.3L]<br />
<br />
9th ERCOFTAC workshop: 500,000 cells<br />
<br />
10th ERCOFTAC workshop: 2 meshes: 490,000 and 820,000 cells (fine mesh used for the k-ε model only)<br />
<br />
Approximate value of y+ on solid surfaces:<br />
<br />
- 9th workshop: 60<br />
<br />
- 10th workshop: 17 (coarse mesh) and 11 (fine mesh).<br />
<br />
==='''Boundary Conditions CFD7'''===<br />
<br />
Inlet: turbulence intensity=2,5%<br />
<br />
Solid boundaries: wall functions<br />
<br />
Outlet: no details<br />
<br />
Other boundaries: no details<br />
<br />
==='''Application of Physical Models CFD7'''===<br />
<br />
9th ERCOFTAC workshop:<br />
<br />
- Standard k-ε model with standard wall functions<br />
<br />
- SSG Reynolds stress model with standard wall functions<br />
<br />
- SSS Reynolds stress model with non-equilibrium wall functions<br />
<br />
- V2F model with wall functions<br />
<br />
- Elliptic blending model (Reynolds stress model) with wall functions<br />
<br />
<br />
<br />
10th ERCOFTAC workshop:<br />
<br />
- Standard k-ε model with wall functions<br />
<br />
- V2F model with wall functions<br />
<br />
- SSG Reynolds stress model with modified ε equation (Hanjalic, Jakirlic) and standard wall functions<br />
<br />
==='''Numerical Accuracy CFD7'''===<br />
<br />
Convection scheme : 60% 2nd order central differencing, 40% 1st order upwind differencing.<br />
<br />
==='''CFD Results CFD7'''===<br />
<br />
Cp contours on the slant part, velocity profiles in the boundary layer over the slant part, vectors plots in 13 planes (see EXP2).<br />
<br />
==''References CFD7'''==<br />
<br />
O. Ouhlous, W. Khier, Y. Liu, K. Hanjalic, in: S. Jakirlic, R. Jester-Zürker, C. Tropea, editors, 9th ERCOFTAC/ IAHR/ COST Workshop on Refined Turbulence Modelling, Oct. 4-5, 2001, Darmstadt University of Technology, Germany.<br />
<br />
<br />
<br />
M. Hadziabdic, K. Hanjalic, W. Khier, Y. Liu, O. Ouhlous, Flow around a simplified car body (Ahmed car model), in: R. Manceau, J.-P. Bonnet, editors, 10th ERCOFTAC (SIG-15)/IAHR/QNET-CFD Workshop on Refined Turbulence Modelling, Oct. 10-11, 2002, Laboratoire d’études aérodynamiques, UMR CNRS 6609, Université de Poitiers, France.<br />
<br />
<br />
=='''Simulation Case CFD8'''==<br />
<br />
==='''Solution strategy CFD8'''===<br />
<br />
RANS modelling.<br />
<br />
In-house code STREAM, which is a finite volume solver which uses a structured, non-orthogonal curvilinear, multi block grid and a fully collocated arrangement. The SIMPLE pressure correction method and Rie & Chow interpolation are used to prevent unrealistic pressure fluctuations. The convection terms are discretized using an upwind scheme or a TVD scheme based on the third-order QUICK scheme.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25° and 35°.<br />
<br />
==='''Computational Domain CFD8'''===<br />
<br />
Symmetry is used to compute half the domain. Stilts not included.<br />
<br />
Domain: [-2L;4L]x[0;L]x[0;L]<br />
<br />
Mesh : 300,000 cells<br />
<br />
Approximate value of y+ on solid surfaces : between 55 and 550.<br />
<br />
==='''Boundary Conditions CFD8'''===<br />
<br />
Inlet:<br />
<br />
- U=38.51 m/s (based on the experimental profile at –1.4L in order to account for the flow deceleration in front of the body)<br />
<br />
- K=6.58x10-3 m2 s-2<br />
<br />
- nt/n=10 (influence tested)<br />
<br />
<br />
<br />
Outflow: zero gradients for all variables<br />
<br />
Solid boundaries: wall functions<br />
<br />
Symmetry plane: symmetry<br />
<br />
Other boundaries: symmetry<br />
<br />
==='''Application of Physical Models CFD8'''===<br />
<br />
- Standard k-ε model with Yap correction and SCL wall functions (see below)<br />
<br />
- Standard k-ε model with Yap correction and UMIST-N wall functions<br />
<br />
- Linear realizable k-ε model with SCL wall functions<br />
<br />
- Linear realizable k-ε model with UMIST-A wall functions<br />
<br />
- Nonlinear k-ε model (Craft et al.) with SCL wall functions<br />
<br />
- Nonlinear k-ε model (Craft et al.) with UMIST-A wall functions<br />
<br />
<br />
<br />
Wall functions:<br />
<br />
- SCL = Simplified Chieng and Launder<br />
<br />
- UMIST-A = UMIST Analytical<br />
<br />
- UMIST-N = UMIST Numerical<br />
<br />
==='''Numerical Accuracy CFD8'''===<br />
<br />
Convection scheme : 3rd order Quick scheme (UMIST) or 1st order upwind scheme in case of numerical instability.<br />
<br />
Tests were made to assess iteration convergence. Some unsteady calculations were made too. A coarser grid was used to obtain some information on grid dependency.<br />
<br />
==='''CFD Results CFD8'''===<br />
<br />
Cp contours on the slant part, velocity profiles in the boundary layer over the slant part, vectors plots in 13 planes (see EXP2).<br />
<br />
=='''References CFD8'''==<br />
<br />
T.J. Craft, S.E. Gant, H. Iacovides, B.E. Launder, C.M.E. Robinson, Computational methods applied to the study of flow around a simplified “Ahmed” car body, in: R. Manceau, J.-P. Bonnet, editors, 10th ERCOFTAC (SIG-15)/IAHR/QNET-CFD Workshop on Refined Turbulence Modelling, Oct. 10-11, 2002, Laboratoire d’études aérodynamiques, UMR CNRS 6609, Université de Poitiers, France.<br />
<br />
<br />
=='''Simulation Case CFD9'''==<br />
<br />
==='''Solution strategy CFD9'''===<br />
<br />
LES.<br />
<br />
In-house code LESOCC2, based on block-structured finite volume discretization. A collocated cell arrangement was used employing the Rhie and Chow momentum interpolation procedure. The SIMPLE scheme was used for the pressure-velocity coupling, and the pressure correction equation was solved using the SIP method. Fluxes were discretized in space using a second order central difference scheme. The equations were integrated in time using a second order Runge Kutta scheme with an adaptive time step, employing a maximum CFL number of 0.6.<br />
<br />
Reynolds number: 2.78x106 (see EXP2).<br />
<br />
Slant angle: 25°.<br />
<br />
==='''Computational Domain CFD9'''===<br />
<br />
Domain: [-2.2L;4.8L]x[-0.9L;0.9L]x[0;1.35L]. Ground plate and stilts included.<br />
<br />
Mesh :18.5x106 cells<br />
<br />
y+ on solid surfaces : no details<br />
<br />
==='''Boundary Conditions CFD9'''===<br />
<br />
Inlet: constant velocity<br />
<br />
Outlet: convective outlet.<br />
<br />
Solid boundaries: wall functions<br />
<br />
Other boundaries: slip walls<br />
<br />
==='''Application of Physical Models CFD9'''===<br />
<br />
Subgrid scale model: Smagorinky<br />
<br />
==='''Numerical Accuracy CFD9'''===<br />
<br />
2nd order convection scheme and time marching (CFL number < 0.6)<br />
<br />
==='''CFD Results CFD9'''===<br />
<br />
Cp contours on the slant part, velocity profiles in the boundary layer over the slant part, vectors plots in 13 planes (see EXP2).<br />
<br />
=='''References CFD9'''==<br />
<br />
C. Hinterberger, M. Garcia-Villalba, W. Rodi, Flow around a simplified car body. LES with wall functions, in: R. Manceau, J.-P. Bonnet, editors, 10th ERCOFTAC (SIG-15)/IAHR/QNET-CFD Workshop on Refined Turbulence Modelling, Oct. 10-11, 2002, Laboratoire d’études aérodynamiques, UMR CNRS 6609, Université de Poitiers, France.<br />
<br />
<br />
=='''Simulation Case CFD10'''==<br />
<br />
==='''Solution strategy CFD10'''===<br />
<br />
RANS modelling.<br />
<br />
Commercial HEXANS CFD code, based on unstructured finite volume discretization. The convective fluxes are discretized using a centered scheme with 2nd and 4th order artificial dissipation. Diffusive fluxes are computed on pyramidal elements. The equations are integrated in time using the explicit Runge Kutta scheme. Local time stepping, multi grid and low-mach number preconditioning are used to accelerate the convergence to steady state. A mesh adaptation procedure is used in which the grid cells are refined by splitting it in 2, 4 or 8 subcells. The mesh adaptation is governed by criteria based on the flow physics, geometry or error estimates.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25°.<br />
<br />
==='''Computational Domain CFD10'''===<br />
<br />
Symmetry is used to compute half the domain. Ground plate included, no stilts.<br />
<br />
Domain: [-2L;5L]x[0;0.9L]x[0;1.35L]<br />
<br />
Final Mesh : 815,000 cells<br />
<br />
Approximate value of y+ on solid surfaces : 1<br />
<br />
==='''Boundary Conditions CFD10'''===<br />
<br />
Inflow: turbulence level 1%. nt/n = 1.<br />
<br />
Solid boundaries: no-slip walls<br />
<br />
Symmetry plane: symmetry<br />
<br />
Other boundaries: no details<br />
<br />
==='''Application of Physical Models CFD10'''===<br />
<br />
Low-Reynolds number K-ε model (Yang-Shih).<br />
<br />
==='''Numerical Accuracy CFD10'''===<br />
<br />
Mesh adaptation applied.<br />
<br />
Convection scheme : 2nd order.<br />
<br />
==='''CFD Results CFD10'''===<br />
<br />
Cp contours on the slant part, velocity profiles in the boundary layer over the slant part, vectors plots in 13 planes (see EXP2).<br />
<br />
=='''References CFD10'''==<br />
<br />
B. Leonard, Ch. Hirsch, K. Kovalev, M. Elsden, K. Hillewaert, A. Patel, Flow around a simplified car body (Ahmed body), in: R. Manceau, J.-P. Bonnet, editors, 10th ERCOFTAC (SIG-15)/IAHR/QNET-CFD Workshop on Refined Turbulence Modelling, Oct. 10-11, 2002, Laboratoire d’études aérodynamiques, UMR CNRS 6609, Université de Poitiers, France.<br />
<br />
<br />
=='''Simulation Case CFD11'''==<br />
<br />
==='''Solution strategy CFD11'''===<br />
<br />
RANS modelling.<br />
<br />
Commercial CFX-5 code, based on an unstructured, vertex based finite volume method. Co-located variables are used. The solver is second order accurate in space and time. The Rhie-Chow velocity pressure coupling is used. An implicit solver with algebraic multi grid is used to converge the equations to steady state.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Transient computation (steady solution obtained).<br />
<br />
Slant angle: 25° and 35°.<br />
<br />
==='''Computational Domain CFD11'''===<br />
<br />
Symmetry is used to compute half the domain. No stilts included.<br />
<br />
Domain: [-3L;6L]x[0;0.9L]x[0;1.15L]<br />
<br />
The ground plate starts 2L in front of the body in order that the boundary layer approaching the body matches the experimental profile.<br />
<br />
Mesh : 2,5x106 cells<br />
<br />
Approximate value of y+ on solid surfaces : 1<br />
<br />
==='''Boundary Conditions CFD11'''===<br />
<br />
Inlet: turbulence intensity=1%, nt/n=1.<br />
<br />
Solid boundaries:<br />
<br />
- SST model: no slip walls<br />
<br />
- Others: scalable wall functions<br />
<br />
Outlet: constant pressure<br />
<br />
Other boundaries: opening boundary conditions.<br />
<br />
==='''Application of Physical Models CFD11'''===<br />
<br />
- Standard k-ε model with scalable wall functions<br />
<br />
- SST model<br />
<br />
- SSG Reynolds stress model with scalable wall functions<br />
<br />
==='''Numerical Accuracy CFD11'''===<br />
<br />
Convection scheme: 2nd order.<br />
<br />
Studies of the influence of the following parameters are performed:<br />
<br />
Mesh refinement, formulation of the boundary conditions (opening vs. slip walls), advection scheme.<br />
<br />
==='''CFD Results CFD11'''===<br />
<br />
The same quantities (except for triple correlations) as for experiment EXP2 are available in the Knowledge Base : results for the mean velocities U, V, W, Reynolds stresses [[Image:Image23.gif]] [[Image:Image24.gif]] [[Image:Image25.gif]] [[Image:Image26.gif]] [[Image:Image27.gif]] in some planes and profiles in the boundary layer above the slant part:<br />
<br />
<br />
<br />
<br />
<br />
'''k-epsilon model'''<br />
<br />
25° slant angle:<br />
<br />
planes: [http://qnetkb.cfms.org.uk/TA1/AC1-05/C/CFD11/KEPS/Ahmed_25_y=0.dat y=0]; [http://qnetkb.cfms.org.uk/TA1/AC1-05/C/CFD11/KEPS/Ahmed_25_y=100.dat y=100]; [http://qnetkb.cfms.org.uk/TA1/AC1-05/C/CFD11/KEPS/Ahmed_25_y=180.dat y=180];<br />
<br />
[http://qnetkb.cfms.org.uk/TA1/AC1-05/C/CFD11/KEPS/Ahmed_25_y=195.dat y=195]; [http://qnetkb.cfms.org.uk/TA1/AC1-05/C/CFD11/KEPS/Ahmed_25_z=360.dat z=360]<br />
<br />
[http://qnetkb.cfms.org.uk/TA1/AC1-05/C/CFD11/KEPS/Ahmed_25_x=-794.dat x=-794] x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
<br />
<br />
35° slant angle:<br />
<br />
planes: y=0; y=100; y=180;<br />
<br />
y=195; z=360<br />
<br />
x=-794; x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
<br />
<br />
'''SST model'''<br />
<br />
25° slant angle:<br />
<br />
planes: y=0; y=100; y=180;<br />
<br />
y=195; z=360<br />
<br />
x=-794; x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
<br />
<br />
35° slant angle:<br />
<br />
planes: y=0; y=100; y=180;<br />
<br />
y=195; z=360<br />
<br />
x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
=='''References CFD11'''==<br />
<br />
L. Durand, M. Kuntz, F. Menter, Validation of CFX-5 for the Ahmed car body (synopsis), in: R. Manceau, J.-P. Bonnet, editors, 10th ERCOFTAC (SIG-15)/IAHR/QNET-CFD Workshop on Refined Turbulence Modelling, Oct. 10-11, 2002, Laboratoire d’études aérodynamiques, UMR CNRS 6609, Université de Poitiers, France.<br />
<br />
<br />
<br />
L. Durand, M. Kuntz, F. Menter, Validation of CFX-5 for the Ahmed car body, CFX Validation report (florian.menter@ansys.com)<br />
<br />
<br />
=='''Simulation Case CFD12'''==<br />
<br />
==='''Solution strategy CFD12'''===<br />
<br />
RANS modelling.<br />
<br />
In-house code CFL3D, compressible flow solver employing multi block structured grids. An upwind finite volume formulation is used for the space discretization. An implicit approximate factorization method is used to integrate the equations in time. Local time stepping, grid sequencing, multi grid and low Mach number preconditioning are used to accelerate convergence to steady state.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25° and 35°.<br />
<br />
==='''Computational Domain CFD12'''===<br />
<br />
Symmetry is used to compute half the domain. No stilts included.<br />
<br />
Domain: [-3L;6L]x[0;0.9L]x[0;1.15L]<br />
<br />
Mesh : 1.3x106 cells<br />
<br />
Approximate value of y+ on solid surfaces : 1.5<br />
<br />
==='''Boundary Conditions CFD12'''===<br />
<br />
Inlet: no details<br />
<br />
Solid boundaries: no-slip walls<br />
<br />
Symmetry plane: symmetry<br />
<br />
Other boundaries: farfield Riemann-invariant conditions<br />
<br />
==='''Application of Physical Models CFD12'''===<br />
<br />
- SST model<br />
<br />
- Explicit Algebraic Stress Model with ω-equation<br />
<br />
==='''Numerical Accuracy CFD12'''===<br />
<br />
Convection scheme : 1st order.<br />
<br />
==='''CFD Results CFD12'''===<br />
<br />
The same quantities (except for triple correlations) as for experiment EXP2 are available in the Knowledge Base : results for the mean velocities U, V, W, Reynolds stresses [[Image:Image23.gif]] [[Image:Image24.gif]] [[Image:Image25.gif]] [[Image:Image26.gif]] [[Image:Image27.gif]] in some planes and profiles in the boundary layer above the slant part:<br />
<br />
<br />
<br />
'''SST model'''<br />
<br />
25° slant angle:<br />
<br />
planes: y=0; y=100; y=180;<br />
<br />
y=195; z=360<br />
<br />
x=-794; x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
<br />
<br />
35° slant angle:<br />
<br />
planes: y=0; y=100; y=180;<br />
<br />
y=195; z=360<br />
<br />
x=-794; x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
<br />
<br />
'''EASM model'''<br />
<br />
25° slant angle:<br />
<br />
planes: y=0; y=100; y=180;<br />
<br />
y=195; z=360<br />
<br />
x=-794; x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
<br />
<br />
35° slant angle:<br />
<br />
planes: y=0; y=100; y=180;<br />
<br />
y=195; z=360<br />
<br />
x=-794; x=-178; x=-138; x=-88; x=-38; x=0; x=80; x=200; x=500<br />
<br />
profiles in the boundary layer: x=-243, -223, -203, -183, -163, -143, -123, -103, -83, -63, -43, -23, -3<br />
<br />
Pressure coefficients on the rear of the body: Cp<br />
<br />
<br />
<br />
=='''References CFD12'''==<br />
<br />
C.L. Rumsey, Application of CFL3D to case 9.4 (Ahmed Body), in: R. Manceau, J.-P. Bonnet, editors, 10th ERCOFTAC (SIG-15)/IAHR/QNET-CFD Workshop on Refined Turbulence Modelling, Oct. 10-11, 2002, Laboratoire d’études aérodynamiques, UMR CNRS 6609, Université de Poitiers, France.<br />
<br />
<br />
=='''Simulation Case CFD13'''==<br />
<br />
==='''Solution strategy CFD13'''===<br />
<br />
RANS modelling.<br />
<br />
In-house code STREAM, which is a finite volume solver which uses a structured, non-orthogonal curvilinear, multi block grid and a fully collocated arrangement. The SIMPLE pressure correction method and Rie & Chow interpolation are used to prevent unrealistic pressure fluctuations. The convection terms are discretized using an upwind scheme or a TVD scheme based on the third-order QUICK scheme<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25°.<br />
<br />
==='''Computational Domain CFD13'''===<br />
<br />
Symmetry is used to compute half the domain. No stilts included.<br />
<br />
Domain: [-3L;6L]x[0;0.9L]x[0;1.15L]<br />
<br />
Mesh : 1.3x106 cells<br />
<br />
Approximate value of y+ on solid surfaces : 1<br />
<br />
==='''Boundary Conditions CFD13'''===<br />
<br />
Inlet: no details<br />
<br />
Solid boundaries: no-slip walls<br />
<br />
Other boundaries: symmetry<br />
<br />
===''''Application of Physical Models CFD13'''===<br />
<br />
All are low-Reynolds number models<br />
<br />
- Linear k-ε model (Launder-Sharma)<br />
<br />
- Linear k-ω model (Wilcox)<br />
<br />
- Cubic k-ε model (Apsley, Leschziner)<br />
<br />
- Quadratic k-ω model (Abe, Jang, Leschziner)<br />
<br />
- Quadratic k-ε model (Abe, Jang, Leschziner)<br />
<br />
- SSG + Chen (Abe, Jang, Leschziner)<br />
<br />
==='''Numerical Accuracy CFD13'''===<br />
<br />
No details<br />
<br />
==='''CFD Results CFD13'''===<br />
<br />
Cp contours on the slant part, velocity profiles in the boundary layer over the slant part, vectors plots in 13 planes (see EXP2).<br />
<br />
=='''References CFD13'''==<br />
'''Y.J. Jang, M. Leschziner, Contribution of Imperial College to Test Case 9.4: Flow around a simplified car body, In: R. Manceau, J.-P. Bonnet, editors, '''''10th ERCOFTAC (SIG-15)/IAHR/QNET-CFD Workshop on Refined Turbulence Modelling, Oct. 10-11, 2002, Laboratoire d’études aérodynamiques, UMR CNRS 6609, Université de Poitiers, France.'''''<br />
<br />
<br />
=='''Simulation Case CFD14'''==<br />
<br />
==='''Solution strategy CFD14'''===<br />
<br />
RANS modelling.<br />
<br />
In-house code ISIS, based on unstructured finite volume discretization.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25° and 35°.<br />
<br />
==='''Computational Domain CFD14'''===<br />
<br />
Symmetry is used to compute half the domain.<br />
<br />
Domain: [-4L;5L]x[0;0.9L]x[0;1.35L]<br />
<br />
Mesh : 3.8x106 cells<br />
<br />
Approximate value of y+ on solid surfaces: 0.5<br />
<br />
==='''Boundary Conditions CFD14'''===<br />
<br />
Solid boundaries: no slip wall<br />
<br />
Symmetry plane: symmetry<br />
<br />
Other boundaries: no details<br />
<br />
==='''Application of Physical Models CFD14'''===<br />
<br />
SST model<br />
<br />
==='''Numerical Accuracy CFD14'''===<br />
<br />
No details<br />
<br />
==='''CFD Results CFD14'''===<br />
<br />
Velocity profiles in the boundary layer over the slant part, streamlines, turbulent energy contours.<br />
<br />
=='''References CFD14'''==<br />
<br />
E. Guilmineau, Numerical simulation of flow around a simplified car body, Proc. ASME JSME Joint Fluids Engineering Conference, July 6-10, 2003, Honolulu, Hawaii, USA<br />
<br />
<br />
=='''Simulation Case CFD15'''==<br />
<br />
==='''Solution strategy CFD15'''===<br />
<br />
RANS modelling.<br />
<br />
Commercial StarCD code, based on unstructured finite volume discretization.<br />
<br />
Reynolds number: 2.78x106 (see EXP2). Steady state computation.<br />
<br />
Slant angle: 25°.<br />
<br />
==='''Computational Domain CFD15'''===<br />
<br />
Symmetry is used to compute half the domain. No stilts included. The ground plate starts 2L upstream of the body in order to reproduce the experimental boundary layer.<br />
<br />
Domain: [-5.75L;5.75L]x[0;L]x[0;1.35L]<br />
<br />
Mesh : 1.6x106 cells<br />
<br />
Approximate value of y+ on solid surfaces : < 3<br />
<br />
==='''Boundary Conditions CFD15'''===<br />
<br />
Inlet: turbulence level 0.1%, nt/n=10.<br />
<br />
Outlet: convective outlet.<br />
<br />
Solid boundaries: no-slip walls<br />
<br />
Symmetry plane: symmetry<br />
<br />
Other boundaries: symmetry<br />
<br />
==='''Application of Physical Models CFD15'''===<br />
<br />
Rescaled V2F model (Manceau, Carlson, Gatski)<br />
<br />
==='''Numerical Accuracy CFD15'''===<br />
<br />
No details.<br />
<br />
==='''CFD Results CFD15'''===<br />
<br />
Vector plots.<br />
<br />
=='''References CFD15'''==<br />
<br />
R. Manceau, Computation of the flow around a simplified car using the rescaled v2f model, ''Proc. ASME JSME Joint Fluids Engineering Conference, July 6-10, 2003, Honolulu, Hawaii, USA''<br />
<br />
<br />
<br />
<br />
{| align="center" width="700" border="1"<br />
|+ align="bottom" | Table CFD-A Summary Description of All Test Cases<br />
! NAME<br />
! Re x 10<sup>-6</sup><br />
! width="90" | Slant angle (degrees)<br />
! colspan="2" | [[DOAPs#SPs:_Simulated_Parameters|SPs]]<br />
|-<br />
|<br />
|<br />
|<br />
! width="80" | Detailed Data<br />
! [[DOAPs#DOAPs:_Design_or_Assessment_Parameters|DOAP]]<br />
|-<br />
! align="left" | CFD1<br />
| align="center" | 4.29<br />
| align="center" | 0, 10, 12, 20, 25, 30, 40, 50<br />
| align="center" | Pressure&nbsp;Tomographies<br />
| align="center" | C<sub>d</sub>, Streamlines, Friction&nbsp;Lines<br />
|-<br />
! align="left" | CFD2<br />
| align="center" | 4.29<br />
| align="center" | 30<br />
| align="center" | Effective&nbsp;Viscosity<br />
| align="center" | C<sub>D</sub>, Velocities<br />
|-<br />
! align="left" | CFD3<br />
| align="center" | 4.29<br />
| align="center" | 28<br />
| align="center" | Pressure&nbsp;Coefficient, Q-criterion&nbsp;Contours<br />
| align="center" | C<sub>d</sub>, Velocities, Vorticity&nbsp;Contours<br />
|-<br />
! align="left" | CFD4<br />
| align="center" | 2.78<br />
| align="center" | 25, 35<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles<br />
|-<br />
! align="left" | CFD5<br />
| align="center" | 2.78<br />
| align="center" | 25, 35<br />
| align="center" | C<sub>P</sub>, Turbulent&nbsp;Energy&nbsp;Contours<br />
| align="center" | Velocity&nbsp;Profiles, Vector&nbsp;Plots, Streamlines<br />
|-<br />
! align="left" | CFD6<br />
| align="center" | 2.78<br />
| align="center" | 25<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles<br />
|-<br />
! align="left" | CFD7<br />
| align="center" | 2.78<br />
| align="center" | 35<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles, Vector&nbsp;Plots<br />
|-<br />
! align="left" | CFD8<br />
| align="center" | 2.78<br />
| align="center" | 25, 35<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles, Vector&nbsp;Plots<br />
|-<br />
! align="left" | CFD9<br />
| align="center" | 2.78<br />
| align="center" | 25, 35<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles, Vector&nbsp;Plots<br />
|-<br />
! align="left" | CFD10<br />
| align="center" | 2.78<br />
| align="center" | 25<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles, Vector&nbsp;Plots<br />
|-<br />
! align="left" | CFD11<br />
| align="center" | 2.78<br />
| align="center" | 35<br />
| align="center" | C<sub>P</sub><br />
| align="center" | C<sub>d</sub>, Velocity&nbsp;Profiles, Vector&nbsp;Plots<br />
|-<br />
! align="left" | CFD12<br />
| align="center" | 2.78<br />
| align="center" | 25, 35<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles, Vector&nbsp;Plots<br />
|-<br />
! align="left" | CFD13<br />
| align="center" | 2.78<br />
| align="center" | 25<br />
| align="center" | C<sub>P</sub><br />
| align="center" | Velocity&nbsp;Profiles, Vector&nbsp;Plots<br />
|-<br />
! align="left" | CFD14<br />
| align="center" | 2.78<br />
| align="center" | 25, 35<br />
| align="center" | Turbulent&nbsp;Energy&nbsp;Contours<br />
| align="center" | Velocity&nbsp;Profiles, Streamlines<br />
|-<br />
! align="left" | CFD15<br />
| align="center" | 2.78<br />
| align="center" | 25<br />
|<br />
| align="center" | Vector&nbsp;Plots<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
<br />
Contributors: Remi Manceau; Jean-Paul Bonnet - Université de Poitiers<br />
<br />
Site Design and Implementation:[[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 1-05|description=Description_AC1-05|testdata=Test Data_AC1-05|cfdsimulations=CFD Simulations_AC1-05|evaluation=Evaluation_AC1-05|qualityreview=Quality Review_AC1-05|bestpractice=Best Practice Advice_AC1-05|relatedUFRs=Related UFRs_AC1-05}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=UFR_4-06_Description&diff=6819
UFR 4-06 Description
2009-03-27T14:50:40Z
<p>David.Fowler: /* Introduction */</p>
<hr />
<div><br />
{{UFR|front=UFR 4-06|description=UFR 4-06 Description|references=UFR 4-06 References|testcase=UFR 4-06 Test Case|evaluation=UFR 4-06 Evaluation|qualityreview=UFR 4-06 Quality Review|bestpractice=UFR 4-06 Best Practice Advice|relatedACs=UFR 4-06 Related ACs}}<br />
<br />
<br />
{{Status|checked=no|by= |date= }}<br />
<br />
<br />
<br />
= Swirling diffuser flow =<br />
<br />
Underlying Flow Regime 4-06 <font size="-2" color="#888888"> © copyright ERCOFTAC 2004</font><br />
<br />
<br />
<br />
= Description =<br />
<br />
== Introduction ==<br />
<br />
A diffuser is a component of a fluid flow system designed to reduce the flow velocity and hence increase the fluid pressure without causing significant pressure loss. Most turbomachines and many other flow systems incorporate diffusers. These include:<br />
<br />
*The duct between the compressor and burner of a gas turbine engine<br />
*The duct at exit from a gas turbine connected to the jet pipe<br />
*The duct following the impellor of a centrifugal compressor<br />
*Closed circuit wind tunnels<br />
*Draft tubes of water turbines<br />
*And many more.<br />
<br />
Clearly, therefore, the design of the diffuser can have a significant impact on the performance of many of these applications and this is recognised in application challenge AC6-01 Planar Diffuser Flow and application challenge AC6-07 Draft Tube. Many other application challenges include the same underlying flow regimes.<br />
<br />
In relative terms the geometric design of a diffuser is simple, however, the duration over which research into diffuser design has been and continues to be carried out would suggest that the fluid flow phenomena in diffusers are complex. A simple 2D section through a conical diffuser is shown in Figure 1.<br />
<br />
[[Image:UFR4-06.gif|centre|thumb|628px|'''Figure 1.''' A 2D section through a simple diffuser.]]<br />
<br />
The pressure loss that occurs as flow passes through a diffuser depends on the angle of divergence and on the ratio of the upstream to the downstream flow area (the area ratio) and can be considered to be caused by two different effects. Firstly there is a contribution to the pressure loss from wall friction. For a given area ratio, this loss decreases as the angle of divergence is increased as the larger angle results in a shorter length of diffuser. Secondly, with the exception of small angles of divergence, energy is dissipated by eddies caused by the separation of the flow from the walls. For a given area ratio, this loss increases as the angle of divergence is increased. For each area ratio there is therefore an optimum angle of divergence where the sum of the two loss components is minimised.<br />
<br />
The loss of head in a diffuser may be expressed as[[UFR_4-06_References#ref2| [2]]]:<br />
<br />
<center><math><br />
\text{Head Loss}=k{\left(1-\frac{A_1}{A_2}\right)}^2 \frac{{u_1}^2}{2g}<br />
</math></center><br />
where u<sub>1</sub> is the mean velocity in the upstream section and k can be considered a loss coefficient.<br />
The relationship between k and the angle of divergence (&theta;) for three different area ratio<br />
diffusers is shown in Figure 2. Similar curves can be derived that show pressure efficiency as a<br />
function of diffuser angle.<br />
<br />
<br />
<br />
[[Image:UFR4-06_Fig2.gif|centre]]<br />
<center>Angle &theta; between diverging sides of a diffuser</center><br />
<br />
<center><b>Figure 2. Loss of Head in a Conical Diffuser [[UFR_4-06_References#ref2|[2]]]</b></center><br />
<br />
<br />
Research has shown that the inclusion of a swirling flow component in the flow entering the diffuser can prevent the occurence of separation in a diffuser in which separation would occur without the swirling component. This implies therefore that near optimum pressure recovery may be obtained from smaller, lighter diffusers. However, an excessive amount of swirl may cause the centre line axial velocity to drop so much that reversal at the centreline occurs thus leading to reduced pressure recovery.<br />
<br />
Some common devices where swirling flows in diffusers are encountered are combusters and draft tubes. In a combuster the swirl helps to carry out mixing and the stabilisation of the flame. The main function of the swirl in a draft tube is to reduce flow separation and thus increase pressure recovery.<br />
<br />
In most practical engineering applications the swirling flow through a diffuser is turbulent.<br />
<br />
Computational Fluid Dynamics (CFD) has been used by several researchers to simulate swirling diffuser flow. The underlying flow physics that need to be captured by CFD modelling include:<br />
<br />
*Turbulence (and the effect of swirl on turbulence)<br />
*Boundary layer flow and separation<br />
<br />
This document presents a brief review of CFD studies of swirling diffuser flow which have included comparisons of the CFD results with experimental data and then focuses on one study in more detail. The document concludes with best practice advice for CFD modelling of swirling diffuser flow.<br />
<br />
== Review of UFR studies and choice of test case ==<br />
<br />
Numerical simulations of diffuser flow have been performed and reported by several researchers and some of these were identified by Armfield et al [[UFR 4-06 References#ref4|[4]]] and are summarised as follows. Okhio et al. [[UFR 4-06 References#ref5|[5]]] used a Prandtl mixing length model to predict mean velocities in a 16.5&deg; diffuser with a tail pipe. Armfield and Fletcher [[UFR 4-06 References#ref6|[6]]] predicted the mean velocity field in a 7&deg; diffuser using a reduced form of the Navier Stokes equations with a mixing length turbulence model. Habib and Whitelaw [[UFR 4-06 References#ref7|[7]]] applied the k-&epsilon; turbulence model to the simulation of swirling recirculating flows in 40-90&deg; wide angle diffusers with tail pipes longer than the diffuser section. The mean velocities and turbulence quantities were compared with experimental data. Hah [[UFR 4-06 References#ref8|[8]]] used an algebraic Reynolds stress model to solve 8 and 16&deg; diffuser flows.<br />
<br />
More recently Page et al [[UFR 4-06 References#ref9|[9]]] compared the predictions made using the commerical CFD code FIDAP with the experimental results of Clausen et al. [[UFR 4-06 References#ref10|[10]]].<br />
<br />
For the purpose of this document the CFD study described by Armfield et al [[UFR 4-06 References#ref4|[4]]] is considered in more detail in conjuction with the work reported by EDF [[UFR 4-06 References#ref11|[11]]]. In these studies the prediction of turbulence quantities and velocity profiles for swirling flow in conical diffusers were considered. The results of the studies have been compared with the experimental results of Clausen et al. [[UFR 4-06 References#ref10|[10]]]. These experimental data can be found on the [http://tmdb.ws.tn.tudelft.nl/database/test60/test60.html ERCOFTAC database] and were carried out as a complementary study to the work of Armfield et al [[UFR 4-06 References#ref4|[4]]].<br />
<br />
The work reported by EDF [[UFR 4-06 References#ref11|[11]]] provides a summary of the updated and corrected results submitted to an ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) workshop entitled Data Bases and Testing of Calculation Methods for Turbulent Flows held in Karlsruhe from April 3 to 7, 1995. As a summary document little specific detail on each simulation result is presented, however, further details can be found in the workshop proceedings, Rodi et al [[UFR 4-06 References#ref12|[12]]].<br />
<br />
<font size="-2" color="#888888">© copyright ERCOFTAC 2004</font><br /><br />
----<br />
<br />
<br />
Contributors: Chris Carey - Fluent Europe Ltd<br />
<br />
<br />
{{UFR|front=UFR 4-06|description=UFR 4-06 Description|references=UFR 4-06 References|testcase=UFR 4-06 Test Case|evaluation=UFR 4-06 Evaluation|qualityreview=UFR 4-06 Quality Review|bestpractice=UFR 4-06 Best Practice Advice|relatedACs=UFR 4-06 Related ACs}}<br />
<br />
<br />
[[Category:Underlying Flow Regime]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Evaluation_AC2-01&diff=6818
Evaluation AC2-01
2009-03-27T14:35:01Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 2-01|description=Description_AC2-01|testdata=Test Data_AC2-01|cfdsimulations=CFD Simulations_AC2-01|evaluation=Evaluation_AC2-01|qualityreview=Quality Review_AC2-01|bestpractice=Best Practice Advice_AC2-01|relatedUFRs=Related UFRs_AC2-01}}<br />
<br />
='''Bluff body burner for CH4-HE turbulent combustion'''=<br />
<br />
'''Application Challenge 2-01''' © copyright ERCOFTAC 2004<br />
<br />
<br />
==''Evaluation''==<br />
<br />
<br />
=='''CFD results and Comparison against Experiments'''==<br />
<br />
The bluff-body burner here considered has been suggested and investigated experimentally by Masri, 1985. It is centred in a coflowing stream of air and consists of a circular bluff-body with an orifice at its centre for the main fuel Fig. 14. The diameters are 3.6 mm for the fuel nozzle and 50mm for the bluff-body. The main fuel jet composition is 50% CH4 and 50% H2 for a bulk Jet velocity of 118 m/s. The outer flowing air has a 40m/s velocity. The jet flame can be extinguished in a region downstream the recirculation zone where turbulence is well developed and the finite rate chemistry effects are significant. The flame may also reignite further downstream where turbulent mixing rates are relaxed. It should therefore be noted that, as observed by Masri, both the piloted and the bluff-body jet flames discussed here consist, generally, of three main zones: stabilization, extinction and reignition zones. The computation of this complex flow structure has been here addressed considering a more flexible unstructured grid. As for the pilot-jet flame, the axial symmetry of the problem is considered solving a single tangential sector of the cylindrical flow.<br />
<br />
<br />
[[Image:Image78.gif]]<br />
<br />
<br />
<br />
<br />
Figure 9:zoom of the unstructured mesh at inlet section<br />
<br />
<br />
<br />
[[Image:Image075.jpg]] [[Image:Image79.gif]]<br />
<br />
<br />
<br />
Figure 10: measured and computed recirculation streaklines<br />
<br />
In this case, the elements on the plane section (Fig. 9) are triangles, which allow an easy clustering close to the bluff-body walls and especially at the sharp leading edges with the fuel and air jets. Being D the bluff-body external diameter, a total number of 11000 elements have been used for the discretization grid which has a 2.5xD radial dimension while the outlet plane is placed 5xD downstream the inlet section. The boundary conditions are specified with the same approach described in the previous test. The Flamelet database is obtained from the same reduced mechanism of the previous application.<br />
<br />
[[Image:Image82.gif]] [[Image:Image80.gif]]<br />
<br />
<br />
<br />
Figure 11a:axial velocity Y/D=0.6 Figure 11b: axial velocity Y/D=0.9<br />
<br />
<br />
[[Image:Image81.gif]]<br />
<br />
<br />
<br />
Figure 11c: axial velocity Y/D=1.3<br />
<br />
The steady convergence of the computation has not been obtained for the present case. In fact going on with the computation after the residual level of 10E-6 is firstly reached, then a cyclic behaviour of the convergence is observed. This effect has been associated to a pseudo-unsteady evolution of the flow field behind the bluff-body, which is apparently caused by the numerical discretization. The recirculation zone seems to be not numerically stable and periodically detaches from the bluff-body moving downstream towards the outlet section. Beside the downstream motion of this main recirculation vortex, a new one starts to develop at the bluff-body wall restarting the original flow pattern. It has to be pointed out that the present computation is not time-accurate. Moreover since no mention has been done of a similar phenomenon in the experiments results then this behaviour has to be considered a spurious numerical effect. Despite this fact, the minimum value of 10E-6 for the residual is reached when a single recirculation vortex is attached to the bluff-body wall as observed in the field from the experimental investigation. All the data shown in the following therefore refers to this condition.<br />
<br />
In Fig. 11, the velocity profiles are compared with experiments for three cross sections after the inlet. The accordance with measures is reasonably accurate showing that the main recirculation is correctly predicted by the numerical computation. This is qualitatively shown also comparing the flow pattern of Fig. 10. From computation it is also noticeable a small second vortex close to the fuel jet core as mentioned by Masri. The accurate simulation of the flow pattern reflects at the same instance a realistic representation of the turbulence field and therefore of the mixing properties behind the bluff-body which are to be expected in good agreement with experiments. As well known the conserved scalar approach is highly dependent on the turbulent mixing experienced by the reactants in the flow. The realistic simulation of this feature allows the correct prediction of the flame evolution and the accurate placement of the stoichiometric front. This can be observed in the following figures where the conserved scalar and temperature profiles are compared against experiments at several cross sections. Starting from the first section plane at Y/D=0.3 after the inlet, a peak is observed in the T profile inside the outer edge of the hot recirculation zone. This peak seems not present in the experiments and it is probably caused by the entrainment of unburned air flowing close to the bluff-body wall from the coflow stream directly into the main vortex core (Fig. 10).<br />
<br />
<br />
[[Image:Image83.gif]] [[Image:Image84.gif]]<br />
<br />
<br />
<br />
Figure 12a: T profile Y/D=0.3 Figure 12b:scalar profile Y/D=0.3<br />
<br />
<br />
[[Image:Image85.gif]] [[Image:Image86.gif]]<br />
<br />
<br />
<br />
Figure 13a: T profile Y/D=0.6 Figure 13b:scalar profile Y/D=0.6<br />
<br />
[[Image:Image87.gif]] [[Image:Image88.gif]]<br />
<br />
<br />
Figure 14a: T profile Y/D=0.9Figure 14b:scalar profile Y/D=0.9<br />
<br />
<br />
[[Image:Image89.gif]] [[Image:Image90.gif]]<br />
<br />
<br />
Figure 15a: T profile Y/D=1.3Figure 15b:scalar profile Y/D=1.3<br />
<br />
[[Image:Image91.gif]] [[Image:Image92.gif]]<br />
<br />
<br />
Figure 16a: T profile Y/D=1.8Figure 16b:scalar profile Y/D=1.8<br />
<br />
<br />
[[Image:Image93.gif]] [[Image:Image94.gif]]<br />
<br />
<br />
Figure 17a: T profile Y/D=2.4Figure 17b:scalar profile Y/D=2.4<br />
<br />
<br />
[[Image:Image95.gif]] [[Image:Image96.gif]]<br />
<br />
<br />
Figure 18a: T axial r/D=0.12 Figure 18b: T axial r/D=0.8<br />
<br />
<br />
This effect slightly reduces the mixture fraction concentration observed inside the vortex and for r»18 the presence of more air enhance the combustion producing the peak observed in the temperature. At the same instance the vortex outer branch seems to be more stretched by the entrainment of more fresh air in the core and again an overshoot of scalar mixture fraction, this time due to the excess of fuel, is observed from r»20 to r»24. Considering downstream sections the agreement with experiments is generally satisfying although a noticeable lower value of temperature is seen on the flame centreline for Y/D=1.3. Here a higher velocity of the fuel jet (observed from Fig. 11c) still maintains an efficient convective transport for the scalar field, which attains on the centreline a richer fuel-air ratio. This lag in the fuel jet spreading is probably due to the turbulence model response and it is soon recovered by the computation on the following sections as shown from the improved agreement of Fig. 14 and 18. A similar effect was above reported for the pilot-jet flame computation and seems to arise also for the present test concerning the turbulent field behaviour. In fact, although here less pronounced, the computation soon recovers from the under prediction of the scalar diffusion with a strong turbulent production which finally leads to a downstream excess of diffusion. This overdiffusion is clearly shown in Fig. 18 from the axial profile of the flame downstream about Y/D=120. In this case, the increased diffusion slightly reduces the level of the scalar mixture fraction crossing the flame front. Conversely, since quite lower turbulence production is expected within the fuel jet core then an accurate agreement is observed in Fig. 18 close to the flame centreline. This turbulence lag followed by a steep overproduction, although not pronounced as for the previous test, seems to be an intrinsic characteristic of the adopted turbulence model which becomes more critical when the grid is not enough refined and accurate as in the pilot-jet computation and as it starts to be for the section of Fig. 15. It has to be reminded that the large density fluctuations due to the combustion are here accounted in the flow computation simply through the density weighted averaging and no modifications were included into the original turbulent model suggested by Wilcox for inert conditions. Also the application of the eddy-viscosity approach becomes incapable of reproducing some important aspects of the physical flow such as the variable density-mean pressure gradients influence. Despite this evidence, the temperature and scalar profiles resulting from the present computation generally compare accurately with experiments.<br />
<br />
<br />
[[Image:Image97.gif]] [[Image:Image98.gif]]<br />
<br />
<br />
<br />
[[Image:Image99.gif]] [[Image:Image100.gif]]<br />
<br />
<br />
Figure 19: radial distribution for species mass fraction, Y/D=0.3<br />
<br />
<br />
The average levels of main species are reported in Fig. 19, 20 and 21. A good agreement is shown for the O2 and H2 mass fractions in all sections considered. Conversely, a well-pronounced underproduction of CO and CO2 levels is characterising all the numerical prevision. The profiles are reproduced but the mass fraction levels are well below the experiments. This result for CO is to some extend surprising as it is known (Jones, 1994) that the fast chemistry assumption generally overestimates CO emissions especially on the rich side of the flame front.<br />
<br />
This chemical mechanism is considered enough accurate for computing CO levels and therefore the source of the inaccuracy observed is more realistically though to be lying in the non-equilibrium effects associated with CO oxidation. In fact, CO is particularly dependent on the local stretch applied by the turbulent field on the laminar flame front.<br />
<br />
[[Image:Image101.gif]] [[Image:Image102.gif]]<br />
<br />
<br />
<br />
[[Image:Image103.gif]] [[Image:Image104.gif]]<br />
<br />
<br />
Figure 20: radial distribution for species mass fraction, Y/D=0.9<br />
<br />
<br />
Since an accurate prevision has been obtained for both the mixture fraction and the temperature of the flame then this effect has to be attributed to the chemical mechanism and to the Flamelet database computation. As far as the chemical reaction a 22-steps mechanism of CH4 involving 20 species has been considered.<br />
<br />
<br />
[[Image:Image105.gif]] [[Image:Image106.gif]]<br />
<br />
<br />
<br />
[[Image:Image107.gif]] [[Image:Image108.gif]]<br />
<br />
<br />
Figure 21: radial distribution for species mass fraction, Y/D=2.4<br />
<br />
<br />
The turbulent-chemistry interaction is only approximately accounted in the present model through a constant flame stretch for the whole field. This parameter is enforced during the counterflowing Flamelet computation imposing the relative reactants velocity. An increasing value for the flame stretch reduces considerably the amount of equilibrium species found at high temperatures. This explains why for CO the under prediction appears more relevant in the first sections and generally where higher temperatures are found in the hot burning gases. Having no priori information about the level of stretching to be expected in the flow field then it has been guessed using clearly a too high value. Although this effect has a little impact on the temperature profiles, it has a strong influence for CO and CO2 prediction.<br />
<br />
Finally, in Fig. 22 the computed fields of temperature, mixture fraction and turbulent kinetic energy are reported showing the overall flame structure.<br />
<br />
<br />
[[Image:Image137.jpg]][[Image:Image139.jpg]][[Image:Image141.jpg]]<br />
<br />
<br />
Figure 22: computed contours of T,[[Image:Image109.gif]] and k<br />
<br />
<br />
The numerical CFD solver HybFlow has been briefly described for simulation of internal turbulent reacting flows. Three application of the numerical procedure have been here described for turbulent non-premixed flames. General agreement with experimental data has been obtained for the turbulent CH4 bluff body flame experimentally studied at SANDIA although some discrepancies where observed in the temperature profiles. Apparently, the reason for these inaccuracies seems to be due to the strong response of the k-w turbulence model in the burning shear layer surrounding the fuel main jet. The low mach preconditioning approach of the solver performed efficiently for this particular flow condition where inlet velocity profiles have a fairly different magnitude that are ranging from about 40 m/s in the jet down to less than 1 m/s in the coflow air.<br />
<br />
An accurate comparison against experiments has been performed for the bluff-body burner of Masri, 1985. In this test, the unstructured grid allowed a flexible disposition of the elements especially close the inlet streams and in the main recirculating vortex entraining the hot burning gases. This unstructured mesh features proved to be successfully allowing an accurate computation of the flow pattern developing behind the bluff-body as also of the mixture fraction and temperature profiles. Concerning the species mass fraction the miss prediction observed for CO and CO2 were attributed to an incorrect overestimation of the turbulent flame stretch within the Flamelet database assembly. In this regard, equilibrium phenomena resulted of considerable importance for the computation of CO emissions.<br />
<br />
Further developments are still needed for a deeper analysis and understanding of the turbulence model performances for reacting flows. More computation will be then performed extending the application of the unstructured meshes which are promising greater flexibility and efficiency for the analysis of effective internal gas combustor geometries.<br />
<br />
<br />
{{AC|front=AC 2-01|description=Description_AC2-01|testdata=Test Data_AC2-01|cfdsimulations=CFD Simulations_AC2-01|evaluation=Evaluation_AC2-01|qualityreview=Quality Review_AC2-01|bestpractice=Best Practice Advice_AC2-01|relatedUFRs=Related UFRs_AC2-01}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=UFR_3-14_Description&diff=6182
UFR 3-14 Description
2009-03-20T15:12:30Z
<p>David.Fowler: /* Review of UFR studies and choice of test case */</p>
<hr />
<div>{{UFR|front=UFR 3-14|description=UFR 3-14 Description|references=UFR 3-14 References|testcase=UFR 3-14 Test Case|evaluation=UFR 3-14 Evaluation|qualityreview=UFR 3-14 Quality Review|bestpractice=UFR 3-14 Best Practice Advice|relatedACs=UFR 3-14 Related ACs}}<br />
<br />
<br />
{{Status|checked=no|by= |date= }}<br />
<br />
<br />
<br />
= Flow over surface-mounted cube/rectangular obstacles<br /> =<br />
<br />
Underlying Flow Regime 3-14 <font size="-2" color="#888888"> © copyright ERCOFTAC 2004</font><br />
<br />
<br />
<br />
= Description =<br />
<br />
== Introduction ==<br />
<br />
Fluid flow past bluff obstacles - i.e. those whose geometry ensures that at all practical Reynolds numbers flow separation will occur somewhere on the surface - is ubiquitous. In the QNET-CFD context and, in particular, within the TA4 and TA5 themes, there are a number of Application Challenges which include flow past obstacles. For example, 4.02 concerns the atmospheric wind flow over an airport terminal building. If the obstacle has sharp-edges and corners - a common situation in the environmental field - issues of Reynolds number dependence are less significant than they are for the more classical case of, for example, flow over a circular cylinder. On the other hand, in this field the upstream flow is usually both sheared and turbulent and the obstacle is normally attached to the surface (the ground). The flow is consequently very complex, even if the geometry is not.<br />
<br />
Boundary layer flow over one of the simplest (isolated) obstacles possible, a cube, can be thought of as the most elemental of flows typical of those that occur in practice. Even this flow could be broken down conceptually into underlying flow regimes like, for example, a boundary separating from a flat surface, curved mixing layers, 3D wakes, etc. But it is helpful to consider the whole as a UFR, particularly as there have now been a few detailed experimental studies of such a situation and an increasing number of corresponding CFD investigations.<br />
<br />
We will consider here only cases in which the scale of the vertical shear is not small compared to the height of the body (e.g. the latter is a small fraction of the upstream boundary layer height). There are many features of such a flow which provide severe tests for CFD modelling. Some of these are outlined now; we reserve detailed discussion until later. First, there is the upstream region embodying a turbulent boundary layer responding to the 3D adverse pressure gradient generated by the presence of the obstacle. It is well known that standard RANS models (like ''k-&epsilon;'') do not react properly to strong adverse pressure gradients, so one expects the separation process upstream of the obstacle and, in fact, the entire region upstream of the front face of the body, to be difficult to capture accurately. Secondly, there is substantial mean flow curvature not only upstream but in the wake region also. This, too, could tax standard models. Thirdly, the interactions between the small-scale turbulence in the shear layers separating from the leading edges (assuming this process is itself captured adequately) and the distorted, larger scale structures advected from the upstream region and 'seen' by these shear layers at their outer boundaries, is quite subtle. Such interactions can determine whether or not the shear layers reattach onto the body surfaces and are thus important even for the mean flow. Fourthly, although there is no genuine periodic unsteadiness (like Karman vortex shedding), the flow is nonetheless very unsteady and some experiments have suggested a bi-modal behaviour in the wake. This would clearly not be captured at all by standard RANS methods. Fifthly, in the environmental context, the ground plane would normally be aerodynamically rough. Given that local values of surface stress (and thus friction velocity) will vary widely around the body - and indeed be zero at mean separation or attachment points - this requires considerable care in applying wall boundary conditions. The surface of the body itself may well be smooth but, in any case, there is little likelihood of genuine log-law regions being present in the region immediately upstream or in the near wake; it is not yet really clear how much inappropriate boundary conditions affect the overall accuracy of the computations.<br />
<br />
== Review of UFR studies and choice of test case ==<br />
<br />
The first detailed study of boundary layer flow over a surface-mounted cube was that of Castro &amp; Robins (1977). They demonstrated the significant affects of the upstream turbulence and shear, by comparing cases for which ''h/d'' was 0.1 and 40, where ''h'' is the cube height and ''d'' is the upstream boundary layer thickness. Comprehensive cube surface pressure and mean velocity and turbulence data in the wake were obtained. Less extensive data were collected for intermediate values of ''h/d'' and these suggested that if the turbulence level in the upstream flow at the cube height exceeded about 10% then the separated shear layer reattached onto the roof of the cube. In the ''h/d''=0.1 case (having an upstream intensity of around 35%) this occurred well upstream of the centre of the roof.<br />
<br />
Similar experiments were performed later by Sakamoto &amp; Arie (1982) and Ogawa et al (1983); the latter included field studies and very recently there have been some further field measurements, reported by Hoxey ''et al'' (2002a). Some of these various experiments have provided the basis for CFD comparisons. For example, Baethe ''et al'' (1990) provided the first LES computations of the Castro &amp; Robins experiments although, a little earlier, Murakami ''et al'' (1987) described a similar calculation of their own experiment. In fact, Murakami has undertaken extensive CFD for this case, with reviews given in Murakami (1997) for example, but unfortunately their wind tunnel experiments have never been comprehensively presented in the literature so, in terms of a test case, their experiment is not satisfactory from a QNET-CFD perspective. (The experiment was described in four lines only in the Murakami ''et al'', 1990, paper and this is more than in any other related publication, as far as this reviewer can determine!). Most recently, Hoxey ''et al'' (2002b) have reported RANS computations of their field experiments. Other computations can be found in Paterson &amp; Apelt (1990), He &amp; Song (1992), Delauney ''et al'' (1995), Lee &amp; Bienkiewicz (1997) and Thomas &amp; Williams (1997), for example. In some respects many of these computations have not been entirely satisfactory. This is often because the upstream flow characteristics were not sufficiently well characterised to allow adequate inflow boundary conditions to be set up for the computations. The Castro &amp; Robins experiment is certainly less than ideal in this respect and, for this reason, there have been more recent experiments undertaken specifically to provide the necessary data for comparison with the results of numerical simulations. Tamura ''et al'' (1997), for example, report studies conducted for the Architectural Institute of Japan, but in this case for a 'low-rise' building with relative dimensions (length/width/height) of 1/1/0.5.<br />
<br />
Since in all these cases the entire boundary layer has to be modelled and also, ideally, a reasonable depth of free stream, the computational demands are more severe than they are for the flow studied by Martinuzzi &amp; Tropea (1993). In this case, the cube was mounted on the wall in a fully developed, smooth-wall channel flow and had a height of one half of the channel depth. So the flow is in detail rather different from those mentioned above, but nonetheless embodies many of the important physical effects. Although the experiments were not originally designed to produce data specifically for comparison with CFD results, a wider range of turbulence quantities were measured than in any of the previous studies and, given also the well-characterised nature of the upstream flow, it is thus particularly well suited to comparisons with detailed numerical modelling. This is no doubt why it has been the subject of considerable attention. A workshop which focussed particularly on Large-Eddy Simulation (LES) for bluff bodies was held in 1995 and the results have been reported by Rodi ''et al'' (1997). This 'cube-in-a-channel' flow was one of the test cases and the results for this case, obtained using various (steady) RANS methods as well as LES, have been recently reviewed again by Rodi (2002). Shah &amp; Ferziger (1997) provided one of the most comprehensive and useful comparisons (using LES) and one of the better (unsteady) RANS simulations has been given by Iaccarino &amp; Durbin (2000).<br />
<br />
The major disadvantage of this 'cube-in-a-channel' case in the wind engineering context is that cube surface pressures were not measured or, at least, seem not to be available. It is well known that computing accurate values for these can be difficult, particularly if the body is orientated at an angle to the free stream - the common case is a 45&deg; angle, when the two delta-wing-type vortices generated along the top leading edges can lead to very large suction pressures close to the edges. And it is these pressures (and, often, their <u>fluctuating</u> values) which are of major concern in terms of wind loading. However, it is possible to compute the overall pressure field reasonably (even if localised peaks are not captured) whilst missing the velocity field by a wide margin, as Shah &amp; Ferziger (1997) have pointed out. They have suggested that to 'validate a method solely by its ability to predict the velocity distribution about a single object may be dangerous; relying on the pressure distribution alone is almost surely of no value whatever'. Despite the limitation (no measured surface pressures) it is this 'cube-in-a-channel' case which is therefore chosen as the specific test case to be reviewed here. It also has the advantage of having been the subject of a workshop which, although not very recent (1995 - see above) included comparisons between a variety of turbulence models - mostly ''k-&epsilon;'' based - as well as LES.<br />
<br />
<font size="-2" color="#888888">© copyright ERCOFTAC 2004</font><br /><br />
----<br />
<br />
<br />
Contributors: Ian Castro - University of Southampton<br />
<br />
<br />
{{UFR|front=UFR 3-14|description=UFR 3-14 Description|references=UFR 3-14 References|testcase=UFR 3-14 Test Case|evaluation=UFR 3-14 Evaluation|qualityreview=UFR 3-14 Quality Review|bestpractice=UFR 3-14 Best Practice Advice|relatedACs=UFR 3-14 Related ACs}}<br />
<br />
[[Category:Underlying Flow Regime]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Abstr:Downward_flow_in_a_heated_annulus&diff=6072
Abstr:Downward flow in a heated annulus
2009-03-19T10:31:13Z
<p>David.Fowler: /* Abstract */</p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
<br />
==Application Area 3: Chemical & Process, Thermal Hydraulics & Nuclear Safety==<br />
<br />
===Application Challenge AC3-11===<br />
<br />
====Abstract====<br />
This AC concerns turbulent downward flow in an annulus with a uniformly heated core and an adiabatic outer casing. An investigation is made on the influence of buoyancy on mixed convection flow, heat transfer and turbulence. The Reynolds number of the flows ranges from 1000 to 6000, and the Grashof number (based on heat flux) ranges from 1.1x10<sup>8</sup> to 1.4x10<sup>9</sup>.<br />
<br />
The experimental rig is housed in the Nuclear Engineering Department, School of Engineering, University of Manchester. The experimental data collected are temperatures, velocity and turbulence.<br />
<br />
A representative set of CFD calculations have been undertaken at UMIST. The calculations undertaken at UMIST have employed the k-e turbulence model, with three different approaches to the modelling of near-wall turbulence.<br />
<br />
Most of the computations of the flow were three-dimensional with the circumferential grid covering the entire 360&deg; of the annulus cross-section. This was necessary in order to explore deviations from axi-symmetric conditions.<br />
<br />
CFD calculations of this Application Challenge are currently being undertaken at UMIST and at British Energy.<br />
<br />
This is a test case by which the competency of CFD for use in nuclear power stations can be judged. However, it only shows the validity for buoyancy influenced flows with vertical boundary layers. This AC is well understood due to the available experimental data. However, only a relatively small amount of CFD has been undertaken so far, and so a comprehensive set of CFD requirements are not yet available for this flow.<br />
<br />
The assessment parameter used to judge the competency of CFD calculations is the variation of Nusselt number on the heated core.<br />
<br><br />
<br><br />
----<br />
''Contributors: Mike Rabbitt - British Energy''<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Abstr:Downward_flow_in_a_heated_annulus&diff=6071
Abstr:Downward flow in a heated annulus
2009-03-19T10:30:51Z
<p>David.Fowler: /* Abstract */</p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
<br />
==Application Area 3: Chemical & Process, Thermal Hydraulics & Nuclear Safety==<br />
<br />
===Application Challenge AC3-11===<br />
<br />
====Abstract====<br />
This AC concerns turbulent downward flow in an annulus with a uniformly heated core and an adiabatic outer casing. An investigation is made on the influence of buoyancy on mixed convection flow, heat transfer and turbulence. The Reynolds number of the flows ranges from 1000 to 6000, and the Grashof number (based on heat flux) ranges from 1.1x10<sup>8</sup> to 1.4x10<sup>9</sup>.<br />
<br />
The experimental rig is housed in the Nuclear Engineering Department, School of Engineering, University of Manchester. The experimental data collected are temperatures, velocity and turbulence.<br />
<br />
A representative set of CFD calculations have been undertaken at UMIST. The calculations undertaken at UMIST have employed the k-e turbulence model, with three different approaches to the modelling of near-wall turbulence.<br />
<br />
Most of the computations of the flow were three-dimensional with the circumferential grid covering the entire 360o of the annulus cross-section. This was necessary in order to explore deviations from axi-symmetric conditions.<br />
<br />
CFD calculations of this Application Challenge are currently being undertaken at UMIST and at British Energy.<br />
<br />
This is a test case by which the competency of CFD for use in nuclear power stations can be judged. However, it only shows the validity for buoyancy influenced flows with vertical boundary layers. This AC is well understood due to the available experimental data. However, only a relatively small amount of CFD has been undertaken so far, and so a comprehensive set of CFD requirements are not yet available for this flow.<br />
<br />
The assessment parameter used to judge the competency of CFD calculations is the variation of Nusselt number on the heated core.<br />
<br><br />
<br><br />
----<br />
''Contributors: Mike Rabbitt - British Energy''<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=AC_3-11&diff=6069
AC 3-11
2009-03-19T10:30:14Z
<p>David.Fowler: Redirecting to Downward flow in a heated annulus</p>
<hr />
<div>#REDIRECT [[Downward flow in a heated annulus]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC3-11&diff=6068
Best Practice Advice AC3-11
2009-03-19T10:29:57Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
='''Downward flow in a heated annulus'''=<br />
<br />
'''Application Challenge 3-11''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Best Practice Advice for the AC'''==<br />
<br />
<br />
===Key Fluid Physics===<br />
<br />
In these buoyancy-opposed mixed convection flows, the buoyancy has the effect of increasing the heat-transfer relative to that which would be found in forced convection at the same Reynolds number. Heat is transferred from the heated core to the downward flowing water, and the velocity magnitude in the near-wall region is thus reduced as the buoyancy becomes stronger. At sufficiently high levels of buoyancy flow reversal can occur adjacent to the wall.<br />
<br />
The UFR associated with this AC is “Mixed Convection Boundary Layers on Vertical Heated Walls”.<br />
<br />
<br />
===Application Uncertainties===<br />
<br />
Measurement Errors<br />
<br />
The accuracy of the temperature data depends on the suitability of the sampling time and the accuracy of the thermocouples employed. A bounding estimate of the error in the temperature data is 0.5oC. This translates into an error of less than 2% on Nusselt number.<br />
<br />
There are no major sources of uncertainty, and a CFD model is straightforward to assemble.<br />
<br />
<br />
===Computational Domain and Boundary Conditions===<br />
<br />
The problem can be treated as axi-symmetric.<br />
<br />
COMPUTATIONAL BOUNDARY CONDITIONS<br />
<br />
Fully developed pipe inlet conditions were applied, although tests with uniform inlet conditions returned indistinguishable results – because the 23 diameters over which the flow can develop before the heated section of pipe ensured that fully developed flow conditions were achieved by the beginning of the heated section. Zero streamwise gradients were applied at the outlet plane.<br />
<br />
Regarding the thermal boundary conditions, adiabatic conditions were applied on the outer wall, together with the initial and end sections of the inner wall, whilst a constant heat flux was applied to the middle section of the inner wall, to match the experimental conditions.<br />
<br />
<br />
[[Image:D34_image222.gif]]<br />
<br />
<br />
<br />
Computational Domain<br />
<br />
The above figure shows the computational domain.<br />
<br />
<br />
===Discretisation and Grid Resolution===<br />
<br />
Use a higher order scheme (second order or above).<br />
<br />
For the low-Reynolds-number model a grid of 252 (streamwise) by 60 (radial) nodes was employed, which was sufficient (at these low bulk Reynolds numbers) to ensure that the value of y+ at the near-wall node was less than unity, and to produce grid-independent results. With the wall function approaches, the number of radial grids could be reduced to 12 whilst still obtaining grid-independent results. Because of the low bulk Reynolds numbers of these flows, a fairly large near-wall cell of around 10% of the annular gap width was used. This ensured that, when the algebraic wall function was employed, the first grid node lay in the fully turbulent flow region. However, with the standard wall function, even these large near-wall cells did, in some cases, result in the near-wall node still lying within the viscosity-affected region. It is worth noting at this point that the analytical wall function is, in fact, designed to be fairly insensitive to the size of the near-wall cell (and can even be applied when the near-wall node does not lie in the fully turbulent region). Predictions obtained with the standard wall function, on the other hand, are known to show a dependence on the size of the near-wall cell.<br />
<br />
<br />
===Physical Modelling===<br />
<br />
• Use the low-Reynolds number k-ε turbulence model of Launder and Sharma (1974), including property variation with temperature. It is also likely that higher order turbulence models are acceptable, but only in conjunction with an analytic wall function. However this has not been checked.<br />
<br />
• For water flows it is important to include the variation of molecular properties with temperature.<br />
<br />
• Where buoyant effects are significant the computational studies have highlighted the need for an accurate modeling of the near-wall sublayer. The usual form of wall functions, based on a universal logarithmic wall law, do not account for these buoyancy effects and hence fail to predict the enhancement of heat transfer as the buoyancy parameter is increased.<br />
<br />
• The choice of wall model is the most important consideration to obtain accurate predictions. The low-Reynolds number model equations can be solved up to the wall. However, this is an expensive approach because it requires resolution of the flow and temperature down to the wall. The alternative is to use an analytical wall function that captures the important physical phenomena, in conjunction with the solution of the low-Reynolds number model equations outside the wall layer. The analytic wall function incorporates the effects of;<br />
<br />
(a) convection parallel and normal to the wall,<br />
<br />
(b) fluid property variation across the wall layer, including a parabolic variation of molecular viscosity across the viscous sub-layer,<br />
<br />
(c) the inclusion of any pressure gradient and buoyancy force,<br />
<br />
(d) viscous sub-layer thickening and thinning,<br />
<br />
(e) a Prandtl number which may not be close to unity (e.g. water at room conditions) and its significant variation with temperature.<br />
<br />
The alternative approaches suggested above will give good results for most flows. However, if there is weak buoyancy influence and the properties vary significantly near the wall then the results would under-predict the experimental values by ~20%.<br />
<br />
<br />
===Recommendations for Future Work===<br />
<br />
Application of second order turbulence models (e.g. Reynolds stress models), in conjunction with the analytic wall function.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Mike Rabbitt - British Energy<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Evaluation_AC3-11&diff=6067
Evaluation AC3-11
2009-03-19T10:28:56Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
='''Downward flow in a heated annulus'''=<br />
<br />
'''Application Challenge 3-11''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Comparison of Test data and CFD'''==<br />
<br />
<br />
<br />
The CFD explorations have brought out several important features relevant to the prediction of vertically downward flows through an annulus with a heated core tube.<br />
<br />
• The study of Guy et al (1999) has shown that these annular flows (with the possible exception of very low Reynolds number cases) can be treated as axisymmetric, and that for water flows it is important to include the variation of molecular properties with temperature.<br />
<br />
• Where buoyant effects are significant the computational studies have highlighted the need for an accurate modeling of the near-wall sublayer. The usual form of wall functions, based on a universal logarithmic wall law, do not account for these buoyancy effects and hence fail to predict the enhancement of heat transfer as the buoyancy parameter is increased.<br />
<br />
• The analytical wall function, which accounts for buoyant forces within the viscous sublayer and mimics the effects of changes in the viscous sublayer thickness, returns results in generally good agreement with the data. It thus provides an economic alternative to low-Reynolds-number models, which would otherwise be needed in order to resolve accurately the near-wall region of these annular flows<br />
<br />
.<br />
<br />
• The present calculations have not included a lengthscale correction term in the ε equation. Earlier computations showed such a term to have some influence, particularly at high heat loadings. Further calculations using the present scheme under such conditions, particularly when reverse flow may occur, should therefore also include a correction of this form.<br />
<br />
<br />
=='''References'''==<br />
<br />
1) Cotton, M.A., Jackson, J.D., 1987, “Calculation of Turbulent Mixed Convection in a Vertical Tube using a Low-Reynolds-Number k-ε turbulence model”, Proc. 6th ''Turbulent Shear Flows Symposium'', Toulouse, France.<br />
<br />
2) Gerasimov A.V., 2002, “CFD Quality and Trust: Develoment and Validation of an Analytical Wall-Function Strategy for Modelling Forced, Mixed and Natural Convection Flows”, ''Report PM/GNSR/5106'', Department of Mechanical, Aerospace & Manufacturing Engineering, UMIST.<br />
<br />
3) Guy A., Iacovides H., Launder B.E., 1999, “Study of Downward Water Flow in a Heated Annulus, Phase 2”, ''Technical Report HTH/GNSR/5032'', Department of Mechanical Engineering, UMIST.<br />
<br />
4) Huang P.G., Leschziner M.A., 1983, “An Introduction and Guide to the Computer Code TEAM”, ''Report TFD/83/9/(R)'', Thermofluids Division, Department of Mechanical Engineering, UMIST.<br />
<br />
5) Ince, N.Z., Launder, B.E., 1989, “On the Computation of Buoyancy-Driven Turbulent Flows in Rectangular Enclosures”, ''Int. J. Heat and Fluid Flow'', '''10''', 110-117.<br />
<br />
6) Jackson, J.D., Hall, W.B., 1979, “Influences of Buoyancy on Heat Transfer to Fluids Flowing in Vertical Tubes under Turbulent Conditions”, ''In Turbulent Forced Convection in Channels and Bundles Theory and Applications to Heat Exchangers and Nuclear Reactors'', (eds. S. Kakac & D.B. Spalding), Vol 2, pp 613-640.<br />
<br />
7) Jackson J.D., He S., Xu Z., Wu T., 2000, “CFD Quality and Trust – Generic Studies of Thermal Convection”, ''Technical Report HTH/GNSR/5029'', School of Engineering, Univeristy of Manchester.<br />
<br />
8) Jones, W.P., Launder, B.E., 1972, “The Prediction of Laminarization with a Two-Equation Model of Turbulence”, ''Int. J. Heat Mass Transfer'', '''15''', 301-314.<br />
<br />
9) Launder B.E., Sharma B.I., 1974, “Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc”, ''Letters in Heat and Mass Transfer'', '''1''', pp131-138 .<br />
<br />
10) Launder, B.E., 1986, “Low-Reynolds-Number Turbulence near Walls”, ''Report TFD/86/4'', Dept of Mechanical Engineering, UMIST.<br />
<br />
11) Leonard B.P., 1979, “A stable and accurate convective modeling procedure based on quadratic upstream interpolation”, ''Comp. Meth. Appl. Mech. Eng''., '''19''', p59.<br />
<br />
12) Patankar S.V., 1980, ''“Numerical Heat Transfer and Fluid Flow”'', Hemisphere Publishing Corporation, Taylor and Francis Group, New York.<br />
<br />
13) Patankar S.V., Spalding D.B., 1972, “A Calculation Procedure of Heat, Mass and Momentum transfer in Three-Dimensional Parabolic Flows”, ''Int J. Heat and Mass Transfer'', '''15''', p1787.<br />
<br />
14) Spalding D.B, 1967, “Heat Transfer from Turbulent Separated Flows”, ''J. Fluid Mechanics'', '''27''', p97.<br />
<br />
15) Yap, C.R., 1987, “Turbulent heat and momentum transfer in recirculating and impinging flows”, PhD Thesis, Dept of Mech. Eng., Faculty of Technology, University of Manchester.<br />
<br />
<br />
<br />
=='''Figures'''==<br />
<br />
[[Image:Image323.gif]]<br />
<br />
<br />
<br />
Figure 4: Variation of Nusselt number and temperature along the heated inner wall for Re=6000, Bo=0.22.<br />
<br />
<br />
[[Image:Image325.gif]]<br />
<br />
<br />
<br />
Figure 5: Variation of Nusselt number and temperature along the heated inner wall for Re=6000, Bo=0.78.<br />
<br />
<br />
[[Image:Image327.gif]]<br />
<br />
<br />
<br />
<br />
Figure 6: Variation of Nusselt number and temperature along the heated inner wall for Re=4000, Bo=0.83.<br />
<br />
<br />
[[Image:Image329.gif]]<br />
<br />
<br />
<br />
<br />
Figure 7: Variation of Nusselt number and temperature along the heated inner wall for Re=4000, Bo=2.89.<br />
<br />
<br />
[[Image:Image331.gif]]<br />
<br />
<br />
<br />
<br />
Figure 8: Profiles of mean vertical velocity across the annular gap at a streamwise position x/deff=35.9. Upper graph: unheated case; Lower graph: buoyant case at Re=4000, Bo=2.89.<br />
<br />
<br />
<br />
[[Image:Image334.gif]]<br />
<br />
<br />
<br />
Figure 9: Normalized Mean temperature and vertical velocity profiles close to the inner heated wall at x/deff=35.9 for the buoyant case at Re=4000, Bo=2.89. (Position of main grid nodes is indicated by symbols on the wall function solutions).<br />
<br />
<br />
=='''Acknowledgement'''==<br />
<br />
This work was funded under the HSE Generic Nuclear Safety Research programme and is published with the permission of the UK Nuclear Industry Management Committee (IMC). The authors gratefully acknowledge the financial assistance provided for this investigation. The Manchester University experiments were carried out under the terms of the research Contract entitled ‘CFD Quality and Trust – Generic Studies of Thermal Convection’. The UMIST computational studies were carried out under the terms of the research Contract entitled ‘CFD Quality and Trust – Model Evaluation, Refinement and Application Advice’.<br />
<br />
<br />
<br />
=='''Appendix A'''==<br />
<br />
'''APPENDIX A: LRN MODEL (Low Reynolds Number k-ε Model)'''<br />
<br />
<br />
<br />
The model of Launder & Sharma employs transport equations for the turbulent kinetic energy and its dissipation rate, and includes effects of molecular viscosity, allowing it to be applied across the viscous sublayer to the wall.<br />
<br />
The equations for the turbulent energy and modified dissipation rate <math>\[\tilde{\varepsilon}\]</math> are:<br />
<br />
<br />
<math>\[\frac{D\kappa}{D{t}} = \frac{\partial}{\partial x_{j}}\left[{(\nu + \nu_{t})} \frac{\partial\kappa}{\partial x_{j}}\right] + P_{\kappa} + G_{\kappa} - \tilde{\varepsilon} - 2\nu\left(\frac{\partial\sqrt{\kappa}}{\partial x_{j}}\right)^2\]</math><br />
<br />
<br />
<math>\[\frac{D\tilde{\varepsilon}}{D{t}} = \frac{\partial}{\partial x_{j}}\left[{(\nu + \nu_{t}/\sigma_{\varepsilon})} \frac{\partial\tilde{\varepsilon}}{\partial x_{j}}\right] + c_\varepsilon {1} \frac{\tilde{\varepsilon}}{\kappa} {(P_{\kappa} + G_{\kappa})} - c_{\varepsilon 2} f_2 \frac{\tilde{\varepsilon}^2}{\kappa} + 2\nu\nu_{t}\left(\frac{\partial^2 U_{i}}{\partial x_{j}\partial x_{\kappa}}\right)^2\]</math><br />
<br />
<br />
<br />
where the production rates of turbulent kinetic energy due to shear and buoyancy are:<br />
<br />
<math>\[P_{\kappa} = -\overline{u_{i}u_{j}} \frac{\partial U_{i}}{\partial x_{j}}\]</math><br />
<br />
<br />
and <math>\[G_{\kappa} = -\beta g_{i}\overline{u_{i}\theta}\]</math><br />
<br />
The turbulent viscosity is then calculated as:<br />
<br />
<br />
<math>\[\nu_{t} = c_{\mu} f_{\mu}\frac{\kappa^2}{\varepsilon}\]</math><br />
<br />
<br />
The stresses and turbulent heat fluxes are modeled as:<br />
<br />
<math>\[\overline{u_{i}u_{j}} = \frac{2}{3}\kappa\partial_{j} - \nu_{t}\left(\frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}}\right)\]</math><br />
<br />
and <math>\[\overline{u_{i}\theta} = -\frac{\nu_{t}}{\sigma_{t}}\frac{\partial T}{\partial x_{i}}\]</math><br />
<br />
<br />
<br />
The various constants and function appearing in the model are:<br />
<br />
<math>\[c_{\mu} = 0.09 c_{\varepsilon 1} = 1.44 c_{\varepsilon 2} = 1.92 \sigma_{\varepsilon} = 1.3 \sigma_{t} = 0.9\]</math><br />
<br />
<math>\[f_{\mu} = exp\left[\frac{-3.4}{{(1 + Re_{t}/50)}^2}\right]f_2 = 1-0.3 exp {(-Re^2_{t})}Re_{t} = \frac{\kappa}{\nu\varepsilon}\]</math><br />
<br />
<br />
<br />
=='''Appendix B'''==<br />
<br />
'''APPENDIX B: StWF (Standard Wall Function)'''<br />
<br />
<br />
<br />
The standard wall function employs the log-laws:<br />
<br />
<math>\[U\cdot = \frac{1}{\kappa}log {(E\cdot Y\cdot)} T\cdot = \sigma_{t}{(U\cdot + P\cdot)}\]</math><br />
<br />
where<br />
<br />
<math>\[U\cdot = U\kappa^{1/2}/\nu T\cdot = \sigma C_{p}\kappa^{1/2} {(T_{w}-T)}/q_{w}Y\cdot = y\kappa^{1/2}/\nu\]</math><br />
<br />
and<br />
<br />
<br />
<math>\[P\cdot\]</math> = 9.24{(Pr/st)3/4-1}[1+0.28exp(-0.007Pr/st)] cm-1/4 <math>\[E\cdot\]</math> = 9.79 <math>\kappa</math> = 0.41 <math>\sigma_{t}</math> = 0.9<br />
<br />
<br />
<br />
In solving the k equation over the near-wall cell, the generation and dissipation terms are replaced by cell-averaged values, defined as<br />
<br />
<br />
<math>\[\overline{P_{\kappa}} = \frac{s^2_{w}}{\kappa{c}^{1/2}_{\mu} {d}\kappa^{1/2}_{p} Y_{n}} log{(Y_{n}/Y_{\nu})}\]</math><br />
<br />
<br />
<math>\[-_{\varepsilon} = \frac{1}{y_{n}}\left[\frac{2{\mu\kappa}_{p}}{y_{\nu}} + \frac{\kappa^{3/2}_{p}}{c_{l}} log {(y_{n}/y{\nu})}\right]\]</math><br />
<br />
<br />
and the dissipation rate at the near-wall node is prescribed as<br />
<br />
<math>\[\varepsilon_{p} = \kappa^{3/2}_{p}/{(c_{l}y_{p})}\]</math><br />
<br />
<br />
<br />
=='''Appendix C'''==<br />
<br />
'''APPENDIX C: AWF (Algebraic Wall Function)'''<br />
<br />
<br />
<br />
[[Image:Image335.gif]]<br />
<br />
<br />
<br />
<br />
<br />
=='''Appendix D'''==<br />
<br />
'''APPENDIX D: Experimental Temperature and Heat Transfer Results'''<br />
<br />
<br />
[[Image:Image336.gif]]<br />
<br />
<br />
[[Image:Image337.gif]]<br />
<br />
<br />
[[Image:Image338.gif]]<br />
<br />
<br />
[[Image:Image339.gif]]<br />
<br />
<br />
[[Image:Image340.gif]]<br />
<br />
<br />
[[Image:Image341.gif]]<br />
<br />
<br />
[[Image:Image342.gif]]<br />
<br />
<br />
[[Image:Image343.gif]]<br />
<br />
<br />
<br />
[[Image:Image344.gif]]<br />
<br />
<br />
<br />
[[Image:Image345.gif]]<br />
<br />
<br />
<br />
[[Image:Image346.gif]]<br />
<br />
<br />
<br />
[[Image:Image347.gif]]<br />
<br />
<br />
<br />
[[Image:Image348.gif]]<br />
<br />
<br />
<br />
[[Image:Image349.gif]]<br />
<br />
<br />
<br />
[[Image:Image350.gif]]<br />
<br />
<br />
<br />
[[Image:Image351.gif]]<br />
<br />
<br />
<br />
[[Image:Image352.gif]]<br />
<br />
<br />
[[Image:Image353.gif]]<br />
<br />
<br />
[[Image:Image354.gif]]<br />
<br />
<br />
<br />
[[Image:Image355.gif]]<br />
<br />
<br />
<br />
<br />
=='''Appendix E'''==<br />
<br />
'''APPENDIX E: Experimental Conditions and Heat Transfer Results'''<br />
<br />
<br />
[[Image:Image356.gif]]<br />
<br />
<br />
[[Image:Image357.gif]]<br />
<br />
<br />
[[Image:Image358.gif]]<br />
<br />
<br />
<br />
[[Image:Image359.gif]]<br />
<br />
<br />
<br />
[[Image:Image360.gif]]<br />
<br />
<br />
<br />
[[Image:Image361.gif]]<br />
<br />
<br />
[[Image:Image362.gif]]<br />
<br />
<br />
<br />
[[Image:Image363.gif]]<br />
<br />
<br />
<br />
[[Image:Image134.jpg]]<br />
<br />
<br />
<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Mike Rabbitt - British Energy<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC3-11&diff=6066
CFD Simulations AC3-11
2009-03-19T10:28:30Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
='''Downward flow in a heated annulus'''=<br />
<br />
'''Application Challenge 3-11''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of CFD Simulations'''==<br />
<br />
<br />
'''Introduction'''<br />
<br />
Earlier three-dimensional calculations of similar buoyancy-affected annulus flows have been reported by Guy et al (1999). One of the main objectives of this study was to establish whether buoyancy might cause the flow to become unstable, and consequently three-dimensional. The circumferential grid employed thus covered the entire 360o of the annulus cross-section. The linear k-ε scheme was employed, with three different near-wall treatments, namely standard wall functions; a low-Reynolds-number 1-equation near-wall model, and the low-Reynolds-number Launder-Sharma k-ε scheme.<br />
<br />
At Reynolds numbers greater than 3000, the use of symmetric boundary conditions was found to always result in a symmetric solution, confirming the experimental findings that the flow does not exhibit large-scale three-dimensional asymmetries. The only exception to this behaviour was for one case, at a very low Reynolds number of 2000 (for which 2-dimensional calculations suggested the flow was laminar before the heated section). In this case it proved impossible to obtain stable 3-dimensional solutions when using the low-Reynolds-number k-ε scheme. Coupled with experimental evidence, it was argued that this might indicate flow instability in this case.<br />
<br />
Three different wall treatments were tested by Guy et al. Their conclusion was that the zonal approach in which a 1-equation model was employed near the wall, or the low-Reynolds-number k-ε scheme of Launder-Sharma produced reasonable agreement with the available experimental data, whilst the wall function approach resulted in an underprediction of the Nusselt number of around 25%. It should be noted that in their low-Reynolds-number k-ε calculations, they reported that the inclusion of a lengthscale correction in the ε equation, based on that proposed by Yap (1987) or similar, was also beneficial in terms of predictive accuracy.<br />
<br />
A further important finding of the above study was the effect that the inclusion of temperature-dependent molecular viscosity and Prandtl number had on the resulting levels of heat transfer. For the one case reported, inclusion of property variations lead to an increase in Nusselt number of almost 30%, Figure 2. The conclusion was that for water flows at the heating rates studied the variation of fluid properties with temperature should not be neglected.<br />
<br />
In view of the above findings, the more recent calculations reported here have treated the problem as a two-dimensional axisymmetric flow, which obviously requires significantly less computing resources.<br />
<br />
Four of the experimental cases have been examined, covering values of the buoyancy parameter Bo ranging from 0.22 to 2.89, and details of these are summarized in Table 4. As indicated in Section 1, particular attention has been given to the modelling of the near-wall, viscosity-affected, sublayer. In principle, as noted above, the most reliable method of treating this region is with a low-Reynolds-number model, with grids fine enough to fully resolve the rapid variation of mean and turbulence quantities across the layer. However, this is not always feasible in complex industrial flows, because of the associated computational cost. Instead, wall functions are often used which are based on the assumption that across this sublayer the turbulence is in a state of simple shear where the production and dissipation rates of turbulence energy are equal. However, these idealised conditions are not generally found in the flows arising in industry, where reliable CFD predictions are sought. There, the flow physics will be highly complex, whether due to a complicated 3-dimensional strain field, or to the action of force-fields such as buoyant effects considered here. Hence the standard wall functions have a rather limited width of applicability.<br />
<br />
<br />
<br />
[[Image:Image008.jpg]]<br />
<br />
<br />
<br />
Figure 2: Effect of property variation on the predicted Nusselt number, using wall functions.<br />
<br />
<br />
<br />
Over the past three years the Turbulence Mechanics Group at UMIST has been developing a new wall function strategy that is designed to remove some of the weaknesses of the standard approach. It has primarily been developed and tuned by reference to buoyancy aided and opposed flows in vertical pipes. Subsequently, it has also proved to be successful in predicting an opposed wall jet, and the natural convection vertical boundary layer. This approach has therefore been further tested in the present cases.<br />
<br />
<br />
{|border="1" cell padding="25" cell spacing="3"<br />
!'''CFD Tests''' !! '''Re''' !! '''Bo'''!! '''Expt. Test No. (Table 1)'''<br />
|-<br />
|1 || 6000 || 0.22 || 4<br />
|-<br />
|2 || 6000 || 0.78 || 9<br />
|-<br />
|3 || 4000 || 0.83 || 2<br />
|-<br />
|4 || 4000 || 2.89 || 7<br />
|}<br />
<br />
<br />
<br />
Table 4: Summary of cases studied with CFD.<br />
<br />
<br />
=='''Numerical and Modelling Procedure'''==<br />
<br />
The computations have been carried out using the TEAM computer code (Huang & Leschziner, 1983) which is a finite-volume solver employing a staggered storage arrangement on a rectangular plane or axisymmetric Cartesian grid. The SIMPLE pressure correction scheme of Patankar (1980) is employed, whilst convection is approximated via the QUICK scheme of Leonard (1979) in equations for mean quantities, but with the PLDS scheme (Patankar, 1980) in the turbulence equations. Because the streamlines are nearly parallel with the constant-radius grid lines, false diffusion effects from using PLDS will be negligible.<br />
<br />
As noted above, it is known to be important to include property variations with temperature in these buoyancy-affected water flows, and consequently, both the molecular viscosity and Prandtl number (as well as density) were allowed to depend on temperatrure.<br />
<br />
<br />
<br />
The turbulence modelling approaches tested are:<br />
<br />
<br />
<br />
Model 1: Low-Reynolds-Number Eddy-Viscosity Scheme (LRN)<br />
<br />
The low-Reynolds-number scheme of Launder & Sharma (1974) was employed, on a grid fine enough to allow the near-wall flow to be resolved accurately. Although linear EVM’s are known to be unsuitable for many complex flows, this particular scheme has been originally developed (Jones & Launder, 1972) to account for changes in the dimensionless viscous sublayer thickness. Moreover, because the flow does closely approximate a simple shear flow, the model does actually return predictions in good agreement with experimental data for the flows considered here. Hence it provides a good modelling framework within which to test and compare the different wall function treatments. Although the earlier work of Guy et al (1999) highlighted the beneficial effects of a lengthscale correction term in the ε equation, this has not been included in the present calculations. Some initial tests were carried out which suggested that in these cases (with lower heat loadings than those simulated by Guy et al) its influence was negligible. Details of the model are given in Appendix A.<br />
<br />
<br />
<br />
Model 2: Standard Wall Function (StWF)<br />
<br />
In this case, Model 1 is applied in the main flow region. However a considerably coarser near-wall grid is employed, with the wall-adjacent node sufficiently far from the wall for it to be located in fully turbulent fluid. The widely employed wall function form of Spalding (1967) is used to obtain the wall shear stress and temperature, which assumes the near-wall flow to be a simple shear in local equilibrium. The form of equations employed in the scheme are given in Appendix B.<br />
<br />
<br />
<br />
Model 3: Algebraic Wall Function (AWF)<br />
<br />
This approach uses the same grid distribution and main flow region model as Model 2, but employs the new wall functions recently developed at UMIST to cover the near-wall cell. These wall functions are based on the analytical integration of simplified forms of the near-wall momentum and temperature equations, with a suitable assumption being made for the turbulent viscosity variation across the near wall cell. This allows buoyancy forces and fluid property variations to be taken into account. The model also includes a mechanism to account for the thickening or thinning of the viscous sublayer in non-equilibrium flows. Details of the model are summarized in Appendix C.<br />
<br />
<br />
'''Computational Grid and Boundary Conditions'''<br />
<br />
The domain employed for the calculations is shown in Figure 3, which was chosen to match the test section dimensions of the experiment. For the low-Reynolds-number model a grid of 252 (streamwise) by 60 (radial) nodes was employed, which was sufficient (at these low bulk Reynolds numbers) to ensure that the value of y+ at the near-wall node was less than unity, and to produce grid-independent results. With the wall function approaches, the number of radial grids could be reduced to 12 whilst still obtaining grid-independent results. Because of the low bulk Reynolds numbers of these flows, a fairly large near-wall cell of around 10% of the annular gap width was used. This ensured that, when the algebraic wall function was employed, the first grid node lay in the fully turbulent flow region. However, with the standard wall function, even these large near-wall cells did, in some cases, result in the near-wall node still lying within the viscosity-affected region. It is worth noting at this point that the analytical wall function is, in fact, designed to be fairly insensitive to the size of the near-wall cell (and can even be applied when the near-wall node does not lie in the fully turbulent region). Predictions obtained with the standard wall function, on the other hand, are known to show a dependence on the size of the near-wall cell.<br />
<br />
<br />
[[Image:Image322.gif]]<br />
<br />
<br />
<br />
Figure 3: Computational domain.<br />
<br />
<br />
<br />
Fully developed pipe inlet conditions were applied, although tests with uniform inlet conditions returned indistinguishable results – because the 23 diameters over which the flow can develop before the heated section of pipe ensured that fully developed flow conditions were achieved by the beginning of the heated section. Zero streamwise gradients were applied at the outlet plane. Regarding the thermal boundary conditions, adiabatic conditions were applied on the outer wall, together with the initial and end sections of the inner wall, whilst a constant heat flux was applied to the middle section of the inner wall, to match the experimental conditions.<br />
<br />
<br />
'''CFD Results and Assessment of Calculations'''<br />
<br />
As indicated in Section 1, the parameter of principal interest is the variation of Nusselt number along the annulus, and for all the cases studied, the variation of this quantity, and the corresponding wall temperature distribution, will be compared with the experimental measurements. In the figures, the predictions are labelled as LRN, StWF and AWF, corresponding to the models described above. For the low-Reynolds-number approach a set of computations were also performed where the gravitational acceleration was set to zero, allowing the effect of (principally) the buoyant term in the vertical momentum equation to be seen.<br />
<br />
Figure 4 presents results for the case where buoyant effects are weak (Bo=0.22 at a mean pipe Reynolds number of 6000, corresponding to experimental Test 4). According to the low-Reynolds-number model the buoyant terms have the effect of increasing the Nusselt number by 30% compared with the case where buoyant forces are suppressed. In this case both wall function approaches produce results which accord well with the low-Reynolds-number computations and the experimental data.<br />
<br />
However, a different picture begins to emerge when the buoyancy parameter is increased. Figure 5 shows results of simulating experimental Test 9 (Bo=0.78, Re=6000). At this level of heating, the low-Reynolds-number model still returns levels of Nu in close agreement with the measured values, and indicates that buoyant effects raise the level of Nusselt number above the level of purely forced convection by around 70%. The standard wall function calculations, however, only capture about 40% of the increase in Nusselt number relative to the non-buoyant case. The AWF predictions do much better, and are again in close agreement with the low-Reynolds-number predictions and experimental data.<br />
<br />
If the Reynolds number of the flow is reduced to 4000, whilst keeping the buoyancy parameter roughly the same, then Figure 6 shows that the AWF approach still reproduces the data with good accuracy over most of the development length, whereas the standard wall function approach now returns levels below the forced convection low-Reynolds-number scheme results.<br />
<br />
The final case computed is for the situation where Bo is increased to 2.89 (experimental Test 7), which represents a very strong buoyant effect (although still not quite enough to cause near-wall flow reversal). In this case the low-Reynolds-number results suggest that the buoyancy raises the Nusselt number by 150% relative to the non-buoyant situation (Figure 7). Even under these strong buoyant influences the AWF scheme still gives a good account of the heat transfer coefficient variation, returning levels within 10% of the measurements over most of the flow. The standard wall function approach, on the other hand, leads to predicted levels of Nusselt number in this case of less than 40% of the measured levels. This last case studied corresponds to one of the configurations for which measured velocity profiles are also available. Figure 8 shows the predicted and measured vertical velocity profiles across the annular gap for both the non-buoyant (unheated) and buoyant cases. Despite the large differences in heat transfer results seen in Figure 7, both wall function approaches appear to produce similar mean velocity profiles, which do reproduce the asymmetry of the experimental data.<br />
<br />
One reason for the large differences in heat transfer predicted by the two wall function approaches at high values of the buoyancy parameter can be traced to the importance of correctly representing the influence of buoyancy in the near-wall region of these flows. Although the velocity profiles in Figure 8 are similar, a different picture emerges if the very near-wall velocity profiles are examined. Figure 9 shows predicted profiles of the mean velocity and temperature very close to the heated wall (covering almost the width of the first two grid cells). In addition to the results returned by both wall function approaches at the main grid nodes, the figures also show the analytical near-wall profiles which the new wall function returns. As can be seen, the near-wall temperature profile returned by the analytical wall function is in reasonable agreement with the low-Reynolds-number model results. The analytical integration of the mean momentum equation in the new wall function does explicitly include buoyancy affects arising from this temperature profile, in addition to molecular property variations and other effects outlined above. As a result, the shape of the near-wall profile is again seen to mimic that returned by the full low-Reynolds-number model, with a region of significantly low velocity adjacent to the wall where the buoyancy effects act to slow down the near-wall fluid. Since the analytical wall function subsequently provides wall shear stress and temperature values from these near-wall analytical profiles, the increase in heat transfer due to buoyancy is also captured by this scheme.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Mike Rabbitt - British Energy<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC3-11&diff=6064
Test Data AC3-11
2009-03-19T10:28:08Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
='''Downward flow in a heated annulus'''=<br />
<br />
'''Application Challenge 3-11''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of Tests'''==<br />
<br />
Over 100 individual sets of data are available, with various flow and heating rates. An overview of the test cases measured is given in Table 1.<br />
<br />
<br />
{|border="1" cell padding="25" cell spacing="3"<br />
!'''No''' !! '''<math>q\left[kW/m^2\right]</math>''' !! '''Re''' !! '''Gr*'''!! '''Bo''' !! '''Water T at inlet'''<br />
|-<br />
|1 || 3.48 || 2053 || 1.13E+08 || 7.72 || 15.19<br />
|-<br />
|2 || 3.48 || 4065 || 1.24E+08 || 0.83 || 15.92<br />
|-<br />
|3 || 3.48 || 6029 || 1.24E+08 || 0.21 || 15.93<br />
|-<br />
|4 || 3.48 || 6003 || 1.23E+08 || 0.22 || 15.87<br />
|-<br />
|5 || 10.44 || 1034 || 3.67E+08 || 265.9 || 15.81<br />
|-<br />
|6 || 10.44 || 2055 || 4.06E+08 || 28.6 || 16.67<br />
|-<br />
|7 || 10.44 || 3995 || 4.02E+08 || 2.89 || 16.57<br />
|-<br />
|8 || 10.44 || 6047 || 4.01E+08 || 0.70 || 16.56<br />
|-<br />
|9 || 10.44 || 5997 || 4.28E+08 || 0.78 || 17.13<br />
|-<br />
|10 || 17.41 || 2028 || 8.35E+08 || 64.2 || 18.58<br />
|-<br />
|11 || 17.41 || 4038 || 8.34E+08 || 6.06 || 18.57<br />
|-<br />
|12 || 17.41 || 6041 || 1.02E+08 || 1.95 || 20.57<br />
|-<br />
|13 || 17.41 || 6009 || 6.77E+08 || 1.21 || 16.66<br />
|-<br />
|14 || 24.37 || 2040 || 1.12E+08 || 83.75 || 18.19<br />
|-<br />
|15 || 24.37 || 1969 || 1.13E+08 || 94.92 || 18.22<br />
|-<br />
|16 || 24.37 || 1998 || 1.19E+08 || 96.59 || 18.75<br />
|-<br />
|17 || 24.37 || 4052 || 1.44E+08 || 10.81 || 20.66<br />
|-<br />
|18 || 24.37 || 4034 || 1.12E+08 || 8.13 || 18.21<br />
|-<br />
|19 || 24.37 || 6039 || 1.42E+08 || 2.71 || 20.5<br />
|-<br />
|20 || 24.37 || 6045 || 1.02E+08 || 1.81 || 17.31<br />
|}<br />
<br />
<br />
<br />
<br />
Table 1: Summary of parameters in each test.<br />
<br />
<br />
<br />
Temperature data is obtained from an array of ninety thermocouples, which are positioned to measure the temperature of the core, and the water temperatures at inlet and outlet. Measurements of velocity and turbulence are undertaken using Laser Doppler Anemometry.<br />
<br />
The LDA system consists of a 4W Coherent Innova 70-4 Argon-ion laser generator, A DANTEC 60x40 transmitter connected by a 10 metre long fibre optic cable to a DANTEC 41x806 probe, a two component photomultiplier (PM) connected to two DANTEC 57N10 Burst Spectrum Analysers (BSA) and a computer-based data acquisition system.<br />
<br />
The laser beam from the argon-ion laser generator is divided into two pairs of beams with different frequencies in the transmitter. These are used to measure the two components of the velocity. The four beams are carried to the probe by the fibre-optic cable, separated in the probe and then focussed to a point in the test section with a lens. The light scattered backwards by the particles in the seeding flow is collected by a receiver mounted inside the probe and converted to electrical signals in the photomultiplier. A 45o arrangement of the beams was chosen to measure the velocity components in the directions ±45o off the axis of the annular tube. The vertical and horizontal velocity components were calculated from the signals of the two channels. This arrangement has two advantages over the direct vertical and horizontal velocity measurements. First, as the signals from the two channels are similar in magnitude, the effect of electronic noise during processing and transmitting are similar and relatively small. Secondly, the symmetric arrangement of the beams allowed the measurements to be made much closer to the wall. The two BSA units are used for processing the signals.<br />
<br />
<br />
<br />
Experiments were first undertaken to establish the optimum sampling time. Measurements of local mean velocity and turbulence profiles were extracted with various sampling times for isothermal flow and non-isothermal flow. For severe heating, some reversed flow is observed near the heated wall as a result of strong buoyancy influence, in which case the quality of results improves with increase of sampling time. However, problems are encountered in maintaining the experimental conditions steady for very long periods of time. It has been found that for Re>4000 the optimum sampling time was about 240 seconds. For 2000<Re<4000, it was 300 seconds; for Re<2000 and with strong influences of buoyancy it was 600 seconds.<br />
<br />
<br />
<br />
A summary of all tests, in terms of problem definition and measured parameters, is shown below in Tables 2 and 3.<br />
<br />
{|border="1" cell padding="25" cell spacing="3"<br />
!''NAME'' !! ''GNDPs'' !! ''PDPs (problem definition parameters) !! colspan="4"| ''MPs (measured parameters)'' <br />
|-<br />
|'''See Table 1 for cases''' || Re, Gr, Bo || Inlet velocity and Temperature; Wall heat flux || detailed data || [[DOAPs]] <br />
| ''U, u, T'' || Nu <br />
|}<br />
<br />
<br />
Table 2: Summary description of all test cases.<br />
<br />
<br />
{|border="1" cell padding="25" cell spacing="3"<br />
! !! MP1 ''U/V'' (m/s) !! MP2 ''u'v'' (m/s) <math>\[u'v'{(m^2/s^2)}\]</math> !! MP3 <math>\[T {(^0C)}\]</math> !! [[DOAPs]]<br />
|-<br />
|Cases in Table 1 || [[Image:Tick.gif]] || [[Image:Tick.gif]] || [[Image:Tick.gif]] || ''Nu'' obtained from <math>q_w</math> and ''T''<br />
|}<br />
<br />
<br />
<br />
Table 3: Summary description of all measured parameter.<br />
<br />
<br />
=='''Test Cases'''==<br />
<br />
<br />
'''Description of Experiments'''<br />
<br />
The experimental conditions, in terms of non-dimensional parameters, are identified in Table 1. These can be used to determine the (uniform) heat flux and the mass flow rate.<br />
<br />
<br />
'''Boundary Data'''<br />
<br />
The inlet, which is positioned 1.5m above the Test Section, is sufficiently far away from the test section (23 effective diameters, where the effective diameter is defined as the difference between the inner and outer diameters of the annular gap) for the flow to become fully developed before entering the heated section of the core. A few experiments were undertaken to confirm this, comparing results including flow conditioning grids and a flow straightener to those without flow conditioning grids and a flow straightener.<br />
<br />
The water temperature at the inlet is specified for each case in Table 1.<br />
<br />
The walls are smooth.<br />
<br />
<br />
'''Measurement Errors'''<br />
<br />
The accuracy of the temperature data depends on the suitability of the sampling time and the accuracy of the thermocouples employed. A bounding estimate of the error in the temperature data is 0.5oC. This translates into an error of less than 2% on Nusselt number.<br />
<br />
The accuracy of the velocity and turbulence data are currently unknown. It will be quantified at a later date.<br />
<br />
<br />
'''Measured Data'''<br />
<br />
For all cases, wall temperature is measured at distances of 0, 5, 10, 20, 30, 40, 50, 100, 150, 200, 250, 300 cm from the start of the heated section.<br />
<br />
The water bulk outlet temperature is also available for each case.<br />
<br />
Results for the temperature and Nusselt number are shown in the scanned images in Appendix D, and in tabular form in Appendix E.<br />
<br />
Results for the velocity and turbulence data are available in electronic form.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Mike Rabbitt - British Energy<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Description_AC3-11&diff=6063
Description AC3-11
2009-03-19T10:27:38Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
='''Downward flow in a heated annulus'''=<br />
<br />
'''Application Challenge 3-11''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Introduction'''==<br />
<br />
This AC concerns turbulent downward flow in an annulus with a uniformly heated core and an adiabatic outer casing. An investigation is made on the influence of buoyancy on mixed convection flow, heat transfer and turbulence. The Reynolds number of the flows ranges from 1000 to 6000, and the Grashof number (based on heat flux) ranges from 1.1x108 to 1.4x109. Such flows with strong buoyancy influences are found in a number of nuclear power plant situations, and pose a variety of challenges to experimentalists and CFD modellers.<br />
<br />
The experimental rig is housed in the Simon Engineering Laboratory of the School of Engineering, University of Manchester. Temperatures, velocity and turbulence data have been obtained in a water flow, using thermocouples to allow the heat-transfer rates from the inner cylinder to be mapped both axially and circumferentially, and LDA to make detailed measurements of the velocity and turbulence. The experiments are reported in Jackson et al (2000)<br />
<br />
Computational studies have been carried out at UMIST, aimed at developing and testing turbulence models for buoyancy-aided flows, with particular emphasis being placed on the representation of the near-wall region. Three-dimensional calculations with a circumferential grid covering the entire 360o of the cross-section were performed by Guy et al (1999). These, in line with experiments, showed that the flow could be treated in an axisymmetric manner, and subsequent explorations, Gerasimov (2002), have thus used the finite volume solver TEAM (Huang & Leschziner, 1983), which employs a two-dimensional or axisymmetric Cartesian geometry with a staggered grid storage arrangement.<br />
<br />
For vertical buoyancy-aided flows it has long been known (Cotton & Jackson, 1987; Ince & Launder, 1989) that the major effects of buoyancy on the flow development can be reasonably captured with the low-Reynolds-number k-ε model of Launder & Sharma (1974). However, when a high-Reynolds-number k-ε scheme is employed with standard wall functions, the effects of buoyancy in the near-wall region are poorly reproduced. New wall functions which have recently been developed at UMIST have therefore been tested. These do not rely on the traditional log-law assumptions and can account for the effects of buoyancy on the flow structure in the near-wall layer.<br />
<br />
In this particular challenge the flow direction is reversed compared with the above-cited examples, so that buoyant forces oppose the forced-convection circulation. While the geometry of the flow is simple, the strong buoyancy effects result in complex flow physics. The case thus provides a stringent test of the turbulence models’ performance in predicting buoyancy-influenced convective heat transfer.<br />
<br />
<br />
=='''Relevance to Industrial Sector'''==<br />
<br />
This is a test case by which the competency of CFD for use in nuclear power stations can be judged. However, it only shows the validity for buoyancy influenced flows with vertical boundary layers. This AC is well understood due to the available experimental data.<br />
<br />
<br />
=='''Design or Assessment Parameters'''==<br />
<br />
The main parameter of interest is the heat transfer coefficient at the inner wall, and this is particularly influenced by the flow structure of the near-wall, viscosity-affected sublayer. The modelling of this layer is thus crucial, and the computational study has therefore focused on different near-wall modeling treatments, whilst the primary parameter chosen to assess the accuracy and quality of the numerical simulations is the distribution of Nusselt number along the annulus.<br />
<br />
<br />
=='''Flow Domain Geometry'''==<br />
<br />
<br />
[[Image:Image4.jpg]]<br />
<br />
<br />
Figure 1: Experimental test rig.<br />
<br />
<br />
<br />
Figure 1 shows the arrangement of the experimental test section employed by Jackson et al (2000). The test section is a vertical passage of annular cross section which has a heated core of outside diameter 76mm and an adiabatic outer casing of internal diameter 140mm. The core is made from stainless steel which is uniformly heated by resistive means over a section of length 3m, and which is preceded by an unheated length of 1.5m and followed by a further unheated section of length 0.5m.<br />
<br />
<br />
<br />
<br />
<br />
Thermocouples distributed along the length and around the circumference of the inner core allow the surface temperature to be mapped, whilst the outer cylinder is made of perspex, to allow optical access for LDA measurements to be made.<br />
<br />
Water from a header tank flows to the top of the flow domain where it passes through a manifold and flow conditioning arrangement. It then flows downwards through the test section. On leaving the test section, the water passes through a further manifold from which it is drawn by a pump, which returns it to the header via an orifice plate flowmeter and a shell and tube cooler.<br />
<br />
<br />
=='''Flow Physics and Fluid Dynamics Data'''==<br />
<br />
In these buoyancy-opposed mixed convection flows, the buoyancy has the effect of increasing the heat-transfer relative to that which would be found in forced convection at the same Reynolds number. Heat is transferred from the heated core to the downward flowing water, and the velocity magnitude in the near-wall region is thus reduced as the buoyancy becomes stronger. At sufficiently high levels of buoyancy flow reversal can occur adjacent to the wall.<br />
<br />
The non-dimensional groups which appear when the governing equations are non-dimensionalized are the Reynolds, Prandtl and Grashof numbers, defined as:<br />
<br />
<math>\[Re = \frac{U_{b} d_{eff}}{\nu}\]</math> <br />
<br />
<br />
<math>\[Pr = \mu {C}_{p}/\kappa\]</math><br />
<br />
<br />
<math>\[Gr\cdot = \frac{\beta{g}d_{out} q\limits^4\nolimits_w}{\kappa\nu^2}\]</math><br />
<br />
where Ub is the bulk velocity, deff the effective diameter (the difference between the outer and inner diameters, doutand din, of the annular section) and qw is the heat flux.<br />
<br />
The Reynolds, Grashof and Prandtl numbers can be combined in the Buoyancy parameter Bo, identified by Jackson & Hall (1979) and Launder (1986), and defined as<br />
<br />
<math>\[Bo = \frac{8 x 10^4 Gr\cdot}{Re^{3.425} Pr^{0.8}}\]</math><br />
<br />
<br />
A high buoyancy parameter can thus either be obtained either by operating at a low flow rate (giving a low Reynolds number), or at a high heating rate (giving high Gr*).<br />
<br />
<br />
<br />
The working fluid is water, at room pressure. The thermo-physical properties of water at atmospheric pressure are well known, and are therefore not specified here. Since the temperature variation across the boundary layer is significant, to undertake CFD calculations it may be necessary to specify fluid properties that vary with temperature (see section 3.1).<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Mike Rabbitt - British Energy<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Abstr:Downward_flow_in_a_heated_annulus&diff=6062
Abstr:Downward flow in a heated annulus
2009-03-19T10:27:21Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
<br />
==Application Area 3: Chemical & Process, Thermal Hydraulics & Nuclear Safety==<br />
<br />
===Application Challenge AC3-11===<br />
<br />
====Abstract====<br />
This AC concerns turbulent downward flow in an annulus with a uniformly heated core and an adiabatic outer casing. An investigation is made on the influence of buoyancy on mixed convection flow, heat transfer and turbulence. The Reynolds number of the flows ranges from 1000 to 6000, and the Grashof number (based on heat flux) ranges from 1.1x108 to 1.4x109.<br />
<br />
The experimental rig is housed in the Nuclear Engineering Department, School of Engineering, University of Manchester. The experimental data collected are temperatures, velocity and turbulence.<br />
<br />
A representative set of CFD calculations have been undertaken at UMIST. The calculations undertaken at UMIST have employed the k-e turbulence model, with three different approaches to the modelling of near-wall turbulence.<br />
<br />
Most of the computations of the flow were three-dimensional with the circumferential grid covering the entire 360o of the annulus cross-section. This was necessary in order to explore deviations from axi-symmetric conditions.<br />
<br />
CFD calculations of this Application Challenge are currently being undertaken at UMIST and at British Energy.<br />
<br />
This is a test case by which the competency of CFD for use in nuclear power stations can be judged. However, it only shows the validity for buoyancy influenced flows with vertical boundary layers. This AC is well understood due to the available experimental data. However, only a relatively small amount of CFD has been undertaken so far, and so a comprehensive set of CFD requirements are not yet available for this flow.<br />
<br />
The assessment parameter used to judge the competency of CFD calculations is the variation of Nusselt number on the heated core.<br />
<br><br />
<br><br />
----<br />
''Contributors: Mike Rabbitt - British Energy''<br />
<br />
{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC3-11&diff=6060
CFD Simulations AC3-11
2009-03-19T10:26:59Z
<p>David.Fowler: CFD SIMulations AC3-11 moved to CFD Simulations AC3-11: Typo in title</p>
<hr />
<div>='''Downward flow in a heated annulus'''=<br />
<br />
'''Application Challenge 3-11''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of CFD Simulations'''==<br />
<br />
<br />
'''Introduction'''<br />
<br />
Earlier three-dimensional calculations of similar buoyancy-affected annulus flows have been reported by Guy et al (1999). One of the main objectives of this study was to establish whether buoyancy might cause the flow to become unstable, and consequently three-dimensional. The circumferential grid employed thus covered the entire 360o of the annulus cross-section. The linear k-ε scheme was employed, with three different near-wall treatments, namely standard wall functions; a low-Reynolds-number 1-equation near-wall model, and the low-Reynolds-number Launder-Sharma k-ε scheme.<br />
<br />
At Reynolds numbers greater than 3000, the use of symmetric boundary conditions was found to always result in a symmetric solution, confirming the experimental findings that the flow does not exhibit large-scale three-dimensional asymmetries. The only exception to this behaviour was for one case, at a very low Reynolds number of 2000 (for which 2-dimensional calculations suggested the flow was laminar before the heated section). In this case it proved impossible to obtain stable 3-dimensional solutions when using the low-Reynolds-number k-ε scheme. Coupled with experimental evidence, it was argued that this might indicate flow instability in this case.<br />
<br />
Three different wall treatments were tested by Guy et al. Their conclusion was that the zonal approach in which a 1-equation model was employed near the wall, or the low-Reynolds-number k-ε scheme of Launder-Sharma produced reasonable agreement with the available experimental data, whilst the wall function approach resulted in an underprediction of the Nusselt number of around 25%. It should be noted that in their low-Reynolds-number k-ε calculations, they reported that the inclusion of a lengthscale correction in the ε equation, based on that proposed by Yap (1987) or similar, was also beneficial in terms of predictive accuracy.<br />
<br />
A further important finding of the above study was the effect that the inclusion of temperature-dependent molecular viscosity and Prandtl number had on the resulting levels of heat transfer. For the one case reported, inclusion of property variations lead to an increase in Nusselt number of almost 30%, Figure 2. The conclusion was that for water flows at the heating rates studied the variation of fluid properties with temperature should not be neglected.<br />
<br />
In view of the above findings, the more recent calculations reported here have treated the problem as a two-dimensional axisymmetric flow, which obviously requires significantly less computing resources.<br />
<br />
Four of the experimental cases have been examined, covering values of the buoyancy parameter Bo ranging from 0.22 to 2.89, and details of these are summarized in Table 4. As indicated in Section 1, particular attention has been given to the modelling of the near-wall, viscosity-affected, sublayer. In principle, as noted above, the most reliable method of treating this region is with a low-Reynolds-number model, with grids fine enough to fully resolve the rapid variation of mean and turbulence quantities across the layer. However, this is not always feasible in complex industrial flows, because of the associated computational cost. Instead, wall functions are often used which are based on the assumption that across this sublayer the turbulence is in a state of simple shear where the production and dissipation rates of turbulence energy are equal. However, these idealised conditions are not generally found in the flows arising in industry, where reliable CFD predictions are sought. There, the flow physics will be highly complex, whether due to a complicated 3-dimensional strain field, or to the action of force-fields such as buoyant effects considered here. Hence the standard wall functions have a rather limited width of applicability.<br />
<br />
<br />
<br />
[[Image:Image008.jpg]]<br />
<br />
<br />
<br />
Figure 2: Effect of property variation on the predicted Nusselt number, using wall functions.<br />
<br />
<br />
<br />
Over the past three years the Turbulence Mechanics Group at UMIST has been developing a new wall function strategy that is designed to remove some of the weaknesses of the standard approach. It has primarily been developed and tuned by reference to buoyancy aided and opposed flows in vertical pipes. Subsequently, it has also proved to be successful in predicting an opposed wall jet, and the natural convection vertical boundary layer. This approach has therefore been further tested in the present cases.<br />
<br />
<br />
{|border="1" cell padding="25" cell spacing="3"<br />
!'''CFD Tests''' !! '''Re''' !! '''Bo'''!! '''Expt. Test No. (Table 1)'''<br />
|-<br />
|1 || 6000 || 0.22 || 4<br />
|-<br />
|2 || 6000 || 0.78 || 9<br />
|-<br />
|3 || 4000 || 0.83 || 2<br />
|-<br />
|4 || 4000 || 2.89 || 7<br />
|}<br />
<br />
<br />
<br />
Table 4: Summary of cases studied with CFD.<br />
<br />
<br />
=='''Numerical and Modelling Procedure'''==<br />
<br />
The computations have been carried out using the TEAM computer code (Huang & Leschziner, 1983) which is a finite-volume solver employing a staggered storage arrangement on a rectangular plane or axisymmetric Cartesian grid. The SIMPLE pressure correction scheme of Patankar (1980) is employed, whilst convection is approximated via the QUICK scheme of Leonard (1979) in equations for mean quantities, but with the PLDS scheme (Patankar, 1980) in the turbulence equations. Because the streamlines are nearly parallel with the constant-radius grid lines, false diffusion effects from using PLDS will be negligible.<br />
<br />
As noted above, it is known to be important to include property variations with temperature in these buoyancy-affected water flows, and consequently, both the molecular viscosity and Prandtl number (as well as density) were allowed to depend on temperatrure.<br />
<br />
<br />
<br />
The turbulence modelling approaches tested are:<br />
<br />
<br />
<br />
Model 1: Low-Reynolds-Number Eddy-Viscosity Scheme (LRN)<br />
<br />
The low-Reynolds-number scheme of Launder & Sharma (1974) was employed, on a grid fine enough to allow the near-wall flow to be resolved accurately. Although linear EVM’s are known to be unsuitable for many complex flows, this particular scheme has been originally developed (Jones & Launder, 1972) to account for changes in the dimensionless viscous sublayer thickness. Moreover, because the flow does closely approximate a simple shear flow, the model does actually return predictions in good agreement with experimental data for the flows considered here. Hence it provides a good modelling framework within which to test and compare the different wall function treatments. Although the earlier work of Guy et al (1999) highlighted the beneficial effects of a lengthscale correction term in the ε equation, this has not been included in the present calculations. Some initial tests were carried out which suggested that in these cases (with lower heat loadings than those simulated by Guy et al) its influence was negligible. Details of the model are given in Appendix A.<br />
<br />
<br />
<br />
Model 2: Standard Wall Function (StWF)<br />
<br />
In this case, Model 1 is applied in the main flow region. However a considerably coarser near-wall grid is employed, with the wall-adjacent node sufficiently far from the wall for it to be located in fully turbulent fluid. The widely employed wall function form of Spalding (1967) is used to obtain the wall shear stress and temperature, which assumes the near-wall flow to be a simple shear in local equilibrium. The form of equations employed in the scheme are given in Appendix B.<br />
<br />
<br />
<br />
Model 3: Algebraic Wall Function (AWF)<br />
<br />
This approach uses the same grid distribution and main flow region model as Model 2, but employs the new wall functions recently developed at UMIST to cover the near-wall cell. These wall functions are based on the analytical integration of simplified forms of the near-wall momentum and temperature equations, with a suitable assumption being made for the turbulent viscosity variation across the near wall cell. This allows buoyancy forces and fluid property variations to be taken into account. The model also includes a mechanism to account for the thickening or thinning of the viscous sublayer in non-equilibrium flows. Details of the model are summarized in Appendix C.<br />
<br />
<br />
'''Computational Grid and Boundary Conditions'''<br />
<br />
The domain employed for the calculations is shown in Figure 3, which was chosen to match the test section dimensions of the experiment. For the low-Reynolds-number model a grid of 252 (streamwise) by 60 (radial) nodes was employed, which was sufficient (at these low bulk Reynolds numbers) to ensure that the value of y+ at the near-wall node was less than unity, and to produce grid-independent results. With the wall function approaches, the number of radial grids could be reduced to 12 whilst still obtaining grid-independent results. Because of the low bulk Reynolds numbers of these flows, a fairly large near-wall cell of around 10% of the annular gap width was used. This ensured that, when the algebraic wall function was employed, the first grid node lay in the fully turbulent flow region. However, with the standard wall function, even these large near-wall cells did, in some cases, result in the near-wall node still lying within the viscosity-affected region. It is worth noting at this point that the analytical wall function is, in fact, designed to be fairly insensitive to the size of the near-wall cell (and can even be applied when the near-wall node does not lie in the fully turbulent region). Predictions obtained with the standard wall function, on the other hand, are known to show a dependence on the size of the near-wall cell.<br />
<br />
<br />
[[Image:Image322.gif]]<br />
<br />
<br />
<br />
Figure 3: Computational domain.<br />
<br />
<br />
<br />
Fully developed pipe inlet conditions were applied, although tests with uniform inlet conditions returned indistinguishable results – because the 23 diameters over which the flow can develop before the heated section of pipe ensured that fully developed flow conditions were achieved by the beginning of the heated section. Zero streamwise gradients were applied at the outlet plane. Regarding the thermal boundary conditions, adiabatic conditions were applied on the outer wall, together with the initial and end sections of the inner wall, whilst a constant heat flux was applied to the middle section of the inner wall, to match the experimental conditions.<br />
<br />
<br />
'''CFD Results and Assessment of Calculations'''<br />
<br />
As indicated in Section 1, the parameter of principal interest is the variation of Nusselt number along the annulus, and for all the cases studied, the variation of this quantity, and the corresponding wall temperature distribution, will be compared with the experimental measurements. In the figures, the predictions are labelled as LRN, StWF and AWF, corresponding to the models described above. For the low-Reynolds-number approach a set of computations were also performed where the gravitational acceleration was set to zero, allowing the effect of (principally) the buoyant term in the vertical momentum equation to be seen.<br />
<br />
Figure 4 presents results for the case where buoyant effects are weak (Bo=0.22 at a mean pipe Reynolds number of 6000, corresponding to experimental Test 4). According to the low-Reynolds-number model the buoyant terms have the effect of increasing the Nusselt number by 30% compared with the case where buoyant forces are suppressed. In this case both wall function approaches produce results which accord well with the low-Reynolds-number computations and the experimental data.<br />
<br />
However, a different picture begins to emerge when the buoyancy parameter is increased. Figure 5 shows results of simulating experimental Test 9 (Bo=0.78, Re=6000). At this level of heating, the low-Reynolds-number model still returns levels of Nu in close agreement with the measured values, and indicates that buoyant effects raise the level of Nusselt number above the level of purely forced convection by around 70%. The standard wall function calculations, however, only capture about 40% of the increase in Nusselt number relative to the non-buoyant case. The AWF predictions do much better, and are again in close agreement with the low-Reynolds-number predictions and experimental data.<br />
<br />
If the Reynolds number of the flow is reduced to 4000, whilst keeping the buoyancy parameter roughly the same, then Figure 6 shows that the AWF approach still reproduces the data with good accuracy over most of the development length, whereas the standard wall function approach now returns levels below the forced convection low-Reynolds-number scheme results.<br />
<br />
The final case computed is for the situation where Bo is increased to 2.89 (experimental Test 7), which represents a very strong buoyant effect (although still not quite enough to cause near-wall flow reversal). In this case the low-Reynolds-number results suggest that the buoyancy raises the Nusselt number by 150% relative to the non-buoyant situation (Figure 7). Even under these strong buoyant influences the AWF scheme still gives a good account of the heat transfer coefficient variation, returning levels within 10% of the measurements over most of the flow. The standard wall function approach, on the other hand, leads to predicted levels of Nusselt number in this case of less than 40% of the measured levels. This last case studied corresponds to one of the configurations for which measured velocity profiles are also available. Figure 8 shows the predicted and measured vertical velocity profiles across the annular gap for both the non-buoyant (unheated) and buoyant cases. Despite the large differences in heat transfer results seen in Figure 7, both wall function approaches appear to produce similar mean velocity profiles, which do reproduce the asymmetry of the experimental data.<br />
<br />
One reason for the large differences in heat transfer predicted by the two wall function approaches at high values of the buoyancy parameter can be traced to the importance of correctly representing the influence of buoyancy in the near-wall region of these flows. Although the velocity profiles in Figure 8 are similar, a different picture emerges if the very near-wall velocity profiles are examined. Figure 9 shows predicted profiles of the mean velocity and temperature very close to the heated wall (covering almost the width of the first two grid cells). In addition to the results returned by both wall function approaches at the main grid nodes, the figures also show the analytical near-wall profiles which the new wall function returns. As can be seen, the near-wall temperature profile returned by the analytical wall function is in reasonable agreement with the low-Reynolds-number model results. The analytical integration of the mean momentum equation in the new wall function does explicitly include buoyancy affects arising from this temperature profile, in addition to molecular property variations and other effects outlined above. As a result, the shape of the near-wall profile is again seen to mimic that returned by the full low-Reynolds-number model, with a region of significantly low velocity adjacent to the wall where the buoyancy effects act to slow down the near-wall fluid. Since the analytical wall function subsequently provides wall shear stress and temperature values from these near-wall analytical profiles, the increase in heat transfer due to buoyancy is also captured by this scheme.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Mike Rabbitt - British Energy<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
Top Next</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=CFD_SIMulations_AC3-11&diff=6061
CFD SIMulations AC3-11
2009-03-19T10:26:59Z
<p>David.Fowler: CFD SIMulations AC3-11 moved to CFD Simulations AC3-11: Typo in title</p>
<hr />
<div>#REDIRECT [[CFD Simulations AC3-11]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Abstr:Downward_flow_in_a_heated_annulus&diff=6059
Abstr:Downward flow in a heated annulus
2009-03-19T10:26:33Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-11|description=Description_AC3-11|testdata=Test Data_AC3-11|cfdsimulations=CFD Simulations_AC3-11|evaluation=Evaluation_AC3-11|qualityreview=Quality Review_AC3-11|bestpractice=Best Practice Advice_AC3-11|relatedUFRs=Related UFRs_AC3-11}}<br />
<br />
<br />
==Application Area 3: Chemical & Process, Thermal Hydraulics & Nuclear Safety==<br />
<br />
===Application Challenge AC3-11===<br />
<br />
====Abstract====<br />
This AC concerns turbulent downward flow in an annulus with a uniformly heated core and an adiabatic outer casing. An investigation is made on the influence of buoyancy on mixed convection flow, heat transfer and turbulence. The Reynolds number of the flows ranges from 1000 to 6000, and the Grashof number (based on heat flux) ranges from 1.1x108 to 1.4x109.<br />
<br />
The experimental rig is housed in the Nuclear Engineering Department, School of Engineering, University of Manchester. The experimental data collected are temperatures, velocity and turbulence.<br />
<br />
A representative set of CFD calculations have been undertaken at UMIST. The calculations undertaken at UMIST have employed the k-e turbulence model, with three different approaches to the modelling of near-wall turbulence.<br />
<br />
Most of the computations of the flow were three-dimensional with the circumferential grid covering the entire 360o of the annulus cross-section. This was necessary in order to explore deviations from axi-symmetric conditions.<br />
<br />
CFD calculations of this Application Challenge are currently being undertaken at UMIST and at British Energy.<br />
<br />
This is a test case by which the competency of CFD for use in nuclear power stations can be judged. However, it only shows the validity for buoyancy influenced flows with vertical boundary layers. This AC is well understood due to the available experimental data. However, only a relatively small amount of CFD has been undertaken so far, and so a comprehensive set of CFD requirements are not yet available for this flow.<br />
<br />
The assessment parameter used to judge the competency of CFD calculations is the variation of Nusselt number on the heated core.<br />
<br><br />
<br><br />
----<br />
''Contributors: Mike Rabbitt - British Energy''</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=AC_3-10&diff=6058
AC 3-10
2009-03-19T10:25:30Z
<p>David.Fowler: Redirecting to Combining/dividing flow in Y junction</p>
<hr />
<div>#REDIRECT [[Combining/dividing flow in Y junction]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC3-10&diff=6056
Best Practice Advice AC3-10
2009-03-19T10:25:09Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
='''Combining/dividing flow in Y junction'''=<br />
<br />
'''Application Challenge 3-10''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Best Practice Advice for the AC'''==<br />
<br />
<br />
===Key Fluid Physics===<br />
<br />
The application challenge on which this best practice advice is based is associated with the flow of water in a Y-junction, Reference 1. The flow is characterised by the following elements:<br />
<br />
• Steady, turbulent and incompressible flow.<br />
<br />
• Flow separation.<br />
<br />
• Mixing.<br />
<br />
• A Reynolds Number between 5x105 and 1.2x106.<br />
<br />
<br />
===Application Uncertainties===<br />
<br />
The application uncertainties associated with the Application Challenge are as follows:<br />
<br />
• Turbulence at the Y-junction inlets. It was assumed that the upstream pipework was sufficiently long for the inlet flow to the computational domain to be fully-developed.<br />
<br />
• Use of wall functions. Flow separation can occur in the Y-junction. Within separated regions and flow recirculations the standard wall function approach is unreliable.<br />
<br />
• Choice of turbulence model. The simple k-epsilon turbulence model performs less well than more sophisticated methods, e.g. Differential Stress.<br />
<br />
The sensitivity of the [[DOAP]] to these application uncertainties is relatively small.<br />
<br />
<br />
===Computational Domain and Boundary Conditions===<br />
<br />
With respect to the computational domain and boundary conditions, the following best practice advice is appropriate:<br />
<br />
• It is acceptable to model half of the Y-junction, on one side of the symmetry plane.<br />
<br />
• Use mass-flow boundaries at the inlets and exits of the Y-junction, with fully-developed velocity profiles.<br />
<br />
• For best accuracy, use the Differential Stress turbulence model, with standard wall functions.<br />
<br />
<br />
===Discretisation and Grid Resolution===<br />
<br />
With respect to discretisation and grid resolution, the following best practice advice is appropriate:<br />
<br />
• Standard (hybrid) spatial discretisation schemes are adequate.<br />
<br />
• The grid must be sufficiently fine to resolve the details of the flow. A constant near-wall cell size is recommended.<br />
<br />
<br />
===Physical Modelling===<br />
<br />
With respect to physical modelling the following BPA is appropriate:<br />
<br />
• Assume that the flow is turbulent.<br />
<br />
• Assume that the fluid is isothermal and incompressible.<br />
<br />
<br />
===Recommendations for Future Work===<br />
<br />
The following recommendations for future work are appropriate:<br />
<br />
• Do further CFD calculations using finer grids.<br />
<br />
• Perform further experiments to measure velocities and turbulence quantities within the Y-junction.<br />
<br />
<br />
=='''References'''==<br />
<br />
1. ''Combining/Dividing Flow in a Y-Junction''<br />
<br />
AC3-10 D30, July 2002<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Evaluation_AC3-10&diff=6055
Evaluation AC3-10
2009-03-19T10:24:18Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
='''Combining/dividing flow in Y junction'''=<br />
<br />
'''Application Challenge 3-10''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
<br />
=='''Comparison of Test data and CFD'''==<br />
<br />
The CFD results have been used to calculate the pressure drops between the main branch (leg 1) and each of the two secondary branches (legs 2 and 3) for each case. These are compared with the experimental data in Figures 11 to 14. The following conclusions can be drawn:<br />
<br />
<br />
<br />
• Both turbulence models predict the variation of pressure drop with flow split in the Y-junction reasonably well.<br />
<br />
<br />
<br />
• Neither turbulence model shows much sensitivity to the near-wall mesh resolution.<br />
<br />
<br />
<br />
• The ‘differential stress’ turbulence model generally gives better agreement with the experimental data.<br />
<br />
<br />
=='''Recommendations for future work'''==<br />
<br />
The following recommendations for future work are appropriate:<br />
<br />
<br />
<br />
• Do further CFD calculations using finer grids.<br />
<br />
<br />
<br />
• Perform further experiments to measure velocities and turbulence quantities within the Y-junction<br />
<br />
<br />
<br />
<br />
[[Image:Image302.gif]]<br />
<br />
<br />
<br />
[[Image:Image303.gif]]<br />
<br />
<br />
<br />
[[Image:Image304.gif]]<br />
<br />
<br />
<br />
[[Image:Image305.gif]]<br />
<br />
<br />
<br />
[[Image:Image306.gif]]<br />
<br />
<br />
[[Image:Image307.gif]]<br />
<br />
<br />
[[Image:Image308.gif]]<br />
<br />
<br />
[[Image:Image309.gif]]<br />
<br />
<br />
[[Image:Image310.gif]]<br />
<br />
<br />
[[Image:Image311.gif]]<br />
<br />
<br />
[[Image:Image1.jpg]]<br />
<br />
<br />
[[Image:Image2.jpg]]<br />
<br />
<br />
[[Image:Image312.gif]]<br />
<br />
<br />
[[Image:Image3.jpg]]<br />
<br />
<br />
<br />
[[Image:Image313.gif]]<br />
<br />
<br />
Figure 6 - Y-Junction Geometry & Block Structure<br />
<br />
<br />
[[Image:Image314.gif]]<br />
<br />
Figure 7 – Coarse mesh at z=0<br />
<br />
<br />
[[Image:Image315.gif]]<br />
<br />
Figure 8 – Coarse mesh at main branch inlet<br />
<br />
<br />
<br />
[[Image:Image316.gif]]<br />
<br />
Figure 9 – Fine mesh at z=0<br />
<br />
<br />
[[Image:Image317.gif]]<br />
<br />
Figure 10 – Fine mesh at main branch inlet<br />
<br />
<br />
[[Image:Image318.gif]]<br />
<br />
'''Figure 11 Test D - Comparison of experimental data and CFX4 predictions'''<br />
<br />
<br />
<br />
[[Image:Image319.gif]]<br />
<br />
'''Figure 12 Test D – Comparison of experimental data and CFX4 predictions'''<br />
<br />
<br />
<br />
[[Image:Image320.gif]]<br />
<br />
'''Figure 13 Test H – Comparison of experimental data and CFX4 predictions'''<br />
<br />
<br />
<br />
[[Image:Image321.gif]]<br />
<br />
'''Figure 14 Test H – Comparison of experimental data and CFX4 predictions'''<br />
<br />
<br />
<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC3-10&diff=6054
CFD Simulations AC3-10
2009-03-19T10:23:58Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
='''Combining/dividing flow in Y junction'''=<br />
<br />
'''Application Challenge 3-10''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of CFD Simulations'''==<br />
<br />
<br />
The commercially-available CFD code CFX4, version 4.3, has been used.<br />
<br />
<br />
<br />
The boundaries of the CFD model are the pressure tapping planes on each leg, located 0.457 metres from the ‘eye’ of the Y-junction. The geometry is available as an IGES file [http://qnet.cfms.org.uk/data/TA3/AC3-10/C/Yjunc.igs Yjunc.igs], and is also shown in plan view in Figure 6.<br />
<br />
<br />
<br />
CFD calculations have been performed at a Reynolds number of 1.2x107, for both converging and diverging flow (corresponding to rig tests ‘D’ and ‘H’).<br />
<br />
<br />
<br />
Two meshes were constructed, differing only in the mesh resolution near the wall. These are illustrated in Figures 7 to 10.<br />
<br />
<br />
<br />
In the ‘coarse’ mesh, the 2.176 mm thick layer adjacent to the wall was divided into three equal cells of thickness 0.725 mm. The total number of cells in this mesh was 140,544.<br />
<br />
<br />
<br />
In the ‘fine’ mesh, this 2.176 mm thick layer was divided into 8 cells, with an expansion ratio of 1.29171, so that the thickness of the cell nearest the wall was 0.1 mm, and the thickness of the eighth cell was 0.6 mm. The total number of cells in this mesh was 179,584.<br />
<br />
<br />
<br />
<br />
<br />
=='''Simulation Case'''==<br />
<br />
'''Solution strategy'''<br />
<br />
The default settings of the CFX4 solver were used throughout, as listed below:<br />
<br />
<br />
{|border="1" cell padding="25" cell spacing="3"<br />
!Parameter !! Equation Solver !! Differencing Scheme<br />
|-<br />
|u velocity || Block Stone || Hybrid<br />
|-<br />
|v velocity || Block Stone || Hybrid<br />
|-<br />
|w velocity || Block Stone || Hybrid<br />
|-<br />
|pressure || Pre-conditioned Conjungate Gradient || Central<br />
|-<br />
|k || Line Solver || Hybrid<br />
|-<br />
|epsilon || Line Solver || Hybrid<br />
|}<br />
<br />
<br />
<br />
<br />
'''Computational Domain'''<br />
<br />
The ‘coarse’ and ‘fine’ meshes were used, and the computational domain extended for a distance of 0.457 m from the eye of the Y-junction, along each branch. Upstream geometry was not modelled, and its effects were ignored.<br />
<br />
<br />
'''Boundary Conditions'''<br />
<br />
‘Mass flow boundaries’ were employed at all three legs of the Y-junction, and the flow rates were specified, i.e. any flows entering the domain were assumed to be fully developed (Neumann boundary condition). The inlet velocity profiles and turbulence parameters were therefore not specified directly – they were calculated by the code, and were those appropriate to fully developed flow in a circular pipe.<br />
<br />
<br />
<br />
The walls of the pipe were assumed to be perfectly smooth, and standard wall functions were employed. Both the ‘k-epsilon’ and ‘differential stress’ turbulence models were examined.<br />
<br />
<br />
'''Application of Physical Models'''<br />
<br />
'''Numerical Accuracy'''<br />
<br />
The computer runs were continued until the solution residuals were no longer decreasing.<br />
<br />
Reductions of 4 or 5 orders of magnitude were obtained.<br />
<br />
<br />
'''CFD Results'''<br />
<br />
‘coarse’ mesh with ‘k-epsilon’ turbulence model:<br />
<br />
case P1 (Pa) P2 (Pa) P3 (Pa)<br />
<br />
------------------------------------------------------<br />
<br />
D1 79.3 34292.9 34292.9<br />
<br />
D2 83.8 37514.7 29704.3<br />
<br />
D3 111.1 39869.0 23799.6<br />
<br />
D4 156.6 41022.7 15315.8<br />
<br />
D5 201.9 40188.5 3039.3<br />
<br />
D6 241.0 35193.8 -15266.5<br />
<br />
D7 412.3 24102.3 -43125.9<br />
<br />
D8 586.2 5315.6 -80876.0<br />
<br />
D9 669.1 -25969.7 -141872.3<br />
<br />
H1 -10.0 3088 3088<br />
<br />
H2 -10.0 11089.5 -5635.2<br />
<br />
H3 -10.0 18941.8 -16041.8<br />
<br />
H4 -10.0 27100.8 -29534.6<br />
<br />
H5 -9.9 34728.1 -46696.3<br />
<br />
H6 -9.9 41525.8 -69179.9<br />
<br />
H7 -9.9 45737.9 -99184.1<br />
<br />
H8 -10.0 45761.5 -141445.2<br />
<br />
H9 -9.9 39479.6 -201817.3<br />
<br />
<br />
<br />
‘fine’ mesh with ‘k-epsilon’ turbulence model:<br />
<br />
<br />
<br />
case P1 (Pa) P2 (Pa) P3 (Pa)<br />
<br />
------------------------------------------------------<br />
<br />
D1 65.4 34592.1 34592.1<br />
<br />
D2 68.6 37767.6 30047.6<br />
<br />
D3 93.7 40018.7 24246.7<br />
<br />
D4 137.4 40986.8 15936.5<br />
<br />
D5 176.6 39773.6 3951.6<br />
<br />
D6 213.2 34421.6 -14040.4<br />
<br />
D7 364.9 22843.1 -41507.4<br />
<br />
D8 527.0 3183.8 -79285.7<br />
<br />
D9 624.3 -28783.6 -140314.4<br />
<br />
H1 -10.1 2823.1 2823.1<br />
<br />
H2 -10.1 10815.4 -5891.2<br />
<br />
H3 -10.1 18664.6 -16311.6<br />
<br />
H4 -10.1 26814.8 -29821.4<br />
<br />
H5 -10.0 34415.0 -46999.5<br />
<br />
H6 -10.0 41140.9 -69512.1<br />
<br />
H7 -10.0 45292.9 -99600.5<br />
<br />
H8 -10.1 45228.9 -142007.1<br />
<br />
H9 -10.0 38918.6 -202729.4<br />
<br />
<br />
<br />
<br />
<br />
‘coarse’ mesh with ‘differential stress’ turbulence model:<br />
<br />
<br />
<br />
case P1 (Pa) P2 (Pa) P3 (pa)<br />
<br />
------------------------------------------------------<br />
<br />
D1 36.2 40285.3 40285.3<br />
<br />
D2 35.1 43565.7 35536.3<br />
<br />
D3 74.9 45817.0 29651.8<br />
<br />
D4 157.5 46790.8 21241.4<br />
<br />
D5 275.1 45653.5 9137.9<br />
<br />
D6 375.0 40520.1 -8844.4<br />
<br />
D7 523.3 29599.0 -35945.7<br />
<br />
D8 718.8 10976.4 -72959.6<br />
<br />
D9 888.9 -17818.0 -131989.0<br />
<br />
H1 -145.0 -1614.0 -1614.0<br />
<br />
H2 -145.5 6734.7 -10751.2<br />
<br />
H3 -145.2 14984.9 -21617.0<br />
<br />
H4 -145.6 23625.0 -35743.8<br />
<br />
H5 -144.5 31899.1 -53636.4<br />
<br />
H6 -144.7 39541.4 -77114.4<br />
<br />
H7 -144.4 44924.1 -108445.8<br />
<br />
H8 -145.2 46469.6 -152640.8<br />
<br />
H9 -144.3 41696.3 -214698.4<br />
<br />
<br />
<br />
‘fine’ mesh with ‘differential stress’ turbulence model:<br />
<br />
<br />
<br />
case P1 (Pa) P2 (Pa) P3 (Pa)<br />
<br />
------------------------------------------------------<br />
<br />
D1 89.3 39780.1 39780.1<br />
<br />
D2 88.8 42803.3 35309.6<br />
<br />
D3 128.4 44798.6 29755.0<br />
<br />
D4 213.0 45525.1 21753.9<br />
<br />
D5 332.0 44189.1 10198.0<br />
<br />
D6 399.2 38997.6 -6925.8<br />
<br />
D7 537.2 27815.0 -33068.9<br />
<br />
D8 747.4 8670.7 -69283.4<br />
<br />
D9 918.2 -20644.6 -127872.3<br />
<br />
H1 -145.5 -1648.1 -1648.1<br />
<br />
H2 -145.9 6652.6 -10735.2<br />
<br />
H3 -145.6 14791.9 -21513.9<br />
<br />
H4 -146.1 23284.9 -35535.7<br />
<br />
H5 -145.0 31363.9 -53325.9<br />
<br />
H6 -145.2 38668.3 -76656.2<br />
<br />
H7 -144.9 43462.0 -107774.1<br />
<br />
H8 -145.6 44415.9 -151711.1<br />
<br />
H9 -144.9 39438.9 -213667.7<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC3-10&diff=6052
Test Data AC3-10
2009-03-19T10:23:34Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
='''Combining/dividing flow in Y junction'''=<br />
<br />
'''Application Challenge 3-10''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of Tests'''==<br />
<br />
Experimental investigations of the flow in a ‘Y’ junction with an included angle of 50 degrees were carried out, with various distributions of flow in the minor branches, under both converging and diverging situations. The flow rates through the main branch were chosen to give nominal Reynolds numbers of (5, 7, 9 and 12) x 105.<br />
<br />
<br />
<br />
Schematic diagrams of the rig arrangement for convergent and divergent tests are shown in Figures 1 and 2 respectively. Figures 3 and 4 are photographs showing the ‘Y’ junction in the convergent arrangement. The ‘Y’ junction was manufactured from Perspex, and its internal geometry is shown in Figure 5.<br />
<br />
<br />
<br />
Each tapping plane had 4 equispaced taps around the circumference and these were connected via a ‘triple-tee’ piezometer ring (Reference 1) to an Orkney differential piston manometer. This presented an average of the pressures at the individual tappings in each plane to the manometer. The connections into the manometer were valved such that the pressures into the high and low sides of the manometer could be reversed, thus allowing the measurement of ‘negative’ differential pressures which arose at certain flow rate ratios through the branches.<br />
<br />
<br />
<br />
Water was pumped from a sump to a constant-head tank, from which it entered the suction side of a 34 bar, 335 kW (450 hp) pump. The water then discharged into a 6-inch diameter high-pressure line containing a ‘T-section’. One arm of this section led to the test-line containing the ‘Y’ junction pipework arrangement and the other acted as a bypass line to the sump. Initial flow rates and pressures were set by adjusting two matched globe valves on the arms of this ‘T-section’. Finer control of the flow rates through the two branches was achieved using the 3-inch NB valves shown in Figures 1 and 2. In the case of the converging tests, a further valve at the downstream end of the test section was also used, to ensure enough back pressure to prevent cavitation.<br />
<br />
<br />
<br />
3-inch turbine meters were installed in branches 2 and 3 to measure the flow rates, and a third 6-inch NB turbine meter was installed upstream of the installation to ease the setting up of the flow in branch 1. Prior to installation, these turbine meters were calibrated to give mean meter factors (and hence flow rates) with an uncertainty within 0.25 per cent for the 3-inch turbine meters and 0.4 per cent for the 6-inch meter over the required flow ranges.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Most of the pipework, and in particular the pipes adjacent to the ‘Y’ junction containing the tapping planes, were made of thermoplastic having smooth internal surfaces.<br />
<br />
<br />
<br />
The internal diameters of the pipes adjacent to the ‘Y’ junction were supplied by Durapipe Ltd, the pipe manufacturers, and were as follows:<br />
<br />
<br />
<br />
Branch 1 (D1) = 72.3 mm<br />
<br />
Branch 2 (D2) = 54.4 mm<br />
<br />
Branch 3 (D3) = 54.4 mm<br />
<br />
<br />
<br />
The following equation, given by the manufacturers, which is based on the modified Lamont S3 formula, was used to calculate the pressure losses between the tapping planes and the eye of the ‘Y’ junction for each branch:<br />
<br />
<br />
<br />
G = K dn hm (4)<br />
<br />
<br />
<br />
Where G = flow rate (litres/sec)<br />
<br />
K = 4.5 x 10-4<br />
<br />
d = internal diameter of pipe (mm)<br />
<br />
h = pressure loss (m head of water/m length of pipe)<br />
<br />
n = 2.6935<br />
<br />
m = 0.5645<br />
<br />
<br />
<br />
The distance from the tapping plane to the eye of the ‘Y’ junction for all branches was 0.457 m (18 inches). Hence the values of h from equation (5) were multiplied by 44.82 to convert the pressure loss to mbar for the 0.457 metre lengths.<br />
<br />
<br />
<br />
From Reference 2, the junction head loss coefficient ki,j for both convergent and divergent flows is defined as the ratio of the total head loss between branches i and j to the mean velocity head in the branch carrying the total flow. Hence, in this report, taking into account the pressure losses between the tapping planes and the eye of the junction, the following equations have been used:<br />
<br />
<br />
<br />
For convergent tests:<br />
<br />
<br />
<br />
k2,1 = (&omega;P2,1 + ½ &omega;w v22 – ½ rw v12 – h1 – h2 ) / (½ rw v12) (5)<br />
<br />
k3,1 = (&omega;P3,1 + ½ &omega;w v32 – ½ rw v12 – h1 – h3 ) / (½ rw v12) (6)<br />
<br />
<br />
<br />
<br />
<br />
For divergent tests:<br />
<br />
<br />
<br />
k1,2 = (&omega;P1,2 + ½ &omega;w v12 – ½ rw v22 – h1 – h2 ) / (½ rw v12) (7)<br />
<br />
k1,3 = (vP1,3 + ½ &omega;w v12 – ½ rw v32 – h1 – h3 ) / (½ rw v12) (8)<br />
<br />
=='''Test Cases'''==<br />
<br />
All the results are given in Tables 1 to 8, as listed below:<br />
<br />
<br />
<br />
Table 1 Convergent flow, nominal ReD = 5 x 105<br />
<br />
Table 2 Convergent flow, nominal ReD = 7 x 105<br />
<br />
Table 3 Convergent flow, nominal ReD = 9 x 105<br />
<br />
Table 4 Convergent flow, nominal ReD = 1.2 x 106<br />
<br />
Table 5 Divergent flow, nominal ReD = 5 x 105<br />
<br />
Table 6 Divergent flow, nominal ReD = 7 x 105<br />
<br />
Table 7 Divergent flow, nominal ReD = 9 x 105<br />
<br />
Table 8 Divergent flow, nominal ReD = 1.2 x 106<br />
<br />
<br />
<br />
At certain flow ratios, it was apparent that pressures within the ‘Y’ junction were giving rise to ‘negative’ differential pressures, as indicated by the minus signs in the Tables.<br />
<br />
<br />
=='''References'''==<br />
<br />
1. Blake, K. A. The design of piezometer rings. J. Fluid Mech., 1976, 78(2), pp 415-428<br />
<br />
2. Miller, D. S. Internal Flow Systems. Published by BHRA Fluid Engineering, 1978, Ch. 13.<br />
<br />
<br />
=='''Nomenclature'''==<br />
<br />
D1, D2, D3 Internal diameters of pipe branches 1, 2 and 3 m<br />
<br />
h1, h2, h3 Pressure losses for lengths of pipe between the tapping<br />
<br />
planes and ‘eye’ of junction for branches 1, 2 and 3 mbar<br />
<br />
k1,2 Head loss coefficient between branches 1 and 2 for divergent test -<br />
<br />
k1,3 Head loss coefficient between branches 1 and 3 for divergent test -<br />
<br />
k2,1 Head loss coefficient between branches 2 and 1 for convergent test -<br />
<br />
k3,1 Head loss coefficient between branches 3 and 1 for convergent test -<br />
<br />
P Absolute pressure Pa<br />
<br />
Dp1,2 Pressure difference between branches 1 and 2 for divergent test mbar<br />
<br />
Dp1,3 Pressure difference between branches 1 and 3 for divergent test mbar<br />
<br />
Dp2,1 Pressure difference between branches 2 and 1 for convergent test mbar<br />
<br />
Dp3,1 Pressure difference between branches 3 and 1 for convergent test mbar<br />
<br />
Q1, Q2, Q3 Flow rates through branches 1, 2 and 3 litre/s<br />
<br />
ReD Reynolds number, based on diameter of branch 1 -<br />
<br />
t Temperature of water °C<br />
<br />
v1, v2, v3 Mean velocities in branches 1, 2 and 3 m/s<br />
<br />
&omega;w Dynamic viscosity of water Pa s<br />
<br />
&omega; w Density of water kg/m3<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC3-10&diff=6050
Test Data AC3-10
2009-03-19T10:22:50Z
<p>David.Fowler: /* Overview of Tests */</p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
='''Combining/dividing flow in Y junction'''=<br />
<br />
'''Application Challenge 3-10''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of Tests'''==<br />
<br />
Experimental investigations of the flow in a ‘Y’ junction with an included angle of 50 degrees were carried out, with various distributions of flow in the minor branches, under both converging and diverging situations. The flow rates through the main branch were chosen to give nominal Reynolds numbers of (5, 7, 9 and 12) x 105.<br />
<br />
<br />
<br />
Schematic diagrams of the rig arrangement for convergent and divergent tests are shown in Figures 1 and 2 respectively. Figures 3 and 4 are photographs showing the ‘Y’ junction in the convergent arrangement. The ‘Y’ junction was manufactured from Perspex, and its internal geometry is shown in Figure 5.<br />
<br />
<br />
<br />
Each tapping plane had 4 equispaced taps around the circumference and these were connected via a ‘triple-tee’ piezometer ring (Reference 1) to an Orkney differential piston manometer. This presented an average of the pressures at the individual tappings in each plane to the manometer. The connections into the manometer were valved such that the pressures into the high and low sides of the manometer could be reversed, thus allowing the measurement of ‘negative’ differential pressures which arose at certain flow rate ratios through the branches.<br />
<br />
<br />
<br />
Water was pumped from a sump to a constant-head tank, from which it entered the suction side of a 34 bar, 335 kW (450 hp) pump. The water then discharged into a 6-inch diameter high-pressure line containing a ‘T-section’. One arm of this section led to the test-line containing the ‘Y’ junction pipework arrangement and the other acted as a bypass line to the sump. Initial flow rates and pressures were set by adjusting two matched globe valves on the arms of this ‘T-section’. Finer control of the flow rates through the two branches was achieved using the 3-inch NB valves shown in Figures 1 and 2. In the case of the converging tests, a further valve at the downstream end of the test section was also used, to ensure enough back pressure to prevent cavitation.<br />
<br />
<br />
<br />
3-inch turbine meters were installed in branches 2 and 3 to measure the flow rates, and a third 6-inch NB turbine meter was installed upstream of the installation to ease the setting up of the flow in branch 1. Prior to installation, these turbine meters were calibrated to give mean meter factors (and hence flow rates) with an uncertainty within 0.25 per cent for the 3-inch turbine meters and 0.4 per cent for the 6-inch meter over the required flow ranges.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Most of the pipework, and in particular the pipes adjacent to the ‘Y’ junction containing the tapping planes, were made of thermoplastic having smooth internal surfaces.<br />
<br />
<br />
<br />
The internal diameters of the pipes adjacent to the ‘Y’ junction were supplied by Durapipe Ltd, the pipe manufacturers, and were as follows:<br />
<br />
<br />
<br />
Branch 1 (D1) = 72.3 mm<br />
<br />
Branch 2 (D2) = 54.4 mm<br />
<br />
Branch 3 (D3) = 54.4 mm<br />
<br />
<br />
<br />
The following equation, given by the manufacturers, which is based on the modified Lamont S3 formula, was used to calculate the pressure losses between the tapping planes and the eye of the ‘Y’ junction for each branch:<br />
<br />
<br />
<br />
G = K dn hm (4)<br />
<br />
<br />
<br />
Where G = flow rate (litres/sec)<br />
<br />
K = 4.5 x 10-4<br />
<br />
d = internal diameter of pipe (mm)<br />
<br />
h = pressure loss (m head of water/m length of pipe)<br />
<br />
n = 2.6935<br />
<br />
m = 0.5645<br />
<br />
<br />
<br />
The distance from the tapping plane to the eye of the ‘Y’ junction for all branches was 0.457 m (18 inches). Hence the values of h from equation (5) were multiplied by 44.82 to convert the pressure loss to mbar for the 0.457 metre lengths.<br />
<br />
<br />
<br />
From Reference 2, the junction head loss coefficient ki,j for both convergent and divergent flows is defined as the ratio of the total head loss between branches i and j to the mean velocity head in the branch carrying the total flow. Hence, in this report, taking into account the pressure losses between the tapping planes and the eye of the junction, the following equations have been used:<br />
<br />
<br />
<br />
For convergent tests:<br />
<br />
<br />
<br />
k2,1 = (&omega;P2,1 + ½ &omega;w v22 – ½ rw v12 – h1 – h2 ) / (½ rw v12) (5)<br />
<br />
k3,1 = (&omega;P3,1 + ½ &omega;w v32 – ½ rw v12 – h1 – h3 ) / (½ rw v12) (6)<br />
<br />
<br />
<br />
<br />
<br />
For divergent tests:<br />
<br />
<br />
<br />
k1,2 = (&omega;P1,2 + ½ &omega;w v12 – ½ rw v22 – h1 – h2 ) / (½ rw v12) (7)<br />
<br />
k1,3 = (vP1,3 + ½ &omega;w v12 – ½ rw v32 – h1 – h3 ) / (½ rw v12) (8)<br />
<br />
=='''Test Cases'''==<br />
<br />
All the results are given in Tables 1 to 8, as listed below:<br />
<br />
<br />
<br />
Table 1 Convergent flow, nominal ReD = 5 x 105<br />
<br />
Table 2 Convergent flow, nominal ReD = 7 x 105<br />
<br />
Table 3 Convergent flow, nominal ReD = 9 x 105<br />
<br />
Table 4 Convergent flow, nominal ReD = 1.2 x 106<br />
<br />
Table 5 Divergent flow, nominal ReD = 5 x 105<br />
<br />
Table 6 Divergent flow, nominal ReD = 7 x 105<br />
<br />
Table 7 Divergent flow, nominal ReD = 9 x 105<br />
<br />
Table 8 Divergent flow, nominal ReD = 1.2 x 106<br />
<br />
<br />
<br />
At certain flow ratios, it was apparent that pressures within the ‘Y’ junction were giving rise to ‘negative’ differential pressures, as indicated by the minus signs in the Tables.<br />
<br />
<br />
=='''References'''==<br />
<br />
1. Blake, K. A. The design of piezometer rings. J. Fluid Mech., 1976, 78(2), pp 415-428<br />
<br />
2. Miller, D. S. Internal Flow Systems. Published by BHRA Fluid Engineering, 1978, Ch. 13.<br />
<br />
<br />
=='''Nomenclature'''==<br />
<br />
D1, D2, D3 Internal diameters of pipe branches 1, 2 and 3 m<br />
<br />
h1, h2, h3 Pressure losses for lengths of pipe between the tapping<br />
<br />
planes and ‘eye’ of junction for branches 1, 2 and 3 mbar<br />
<br />
k1,2 Head loss coefficient between branches 1 and 2 for divergent test -<br />
<br />
k1,3 Head loss coefficient between branches 1 and 3 for divergent test -<br />
<br />
k2,1 Head loss coefficient between branches 2 and 1 for convergent test -<br />
<br />
k3,1 Head loss coefficient between branches 3 and 1 for convergent test -<br />
<br />
P Absolute pressure Pa<br />
<br />
Dp1,2 Pressure difference between branches 1 and 2 for divergent test mbar<br />
<br />
Dp1,3 Pressure difference between branches 1 and 3 for divergent test mbar<br />
<br />
Dp2,1 Pressure difference between branches 2 and 1 for convergent test mbar<br />
<br />
Dp3,1 Pressure difference between branches 3 and 1 for convergent test mbar<br />
<br />
Q1, Q2, Q3 Flow rates through branches 1, 2 and 3 litre/s<br />
<br />
ReD Reynolds number, based on diameter of branch 1 -<br />
<br />
t Temperature of water °C<br />
<br />
v1, v2, v3 Mean velocities in branches 1, 2 and 3 m/s<br />
<br />
ωw Dynamic viscosity of water Pa s<br />
<br />
ω w Density of water kg/m3<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC3-10&diff=6049
Test Data AC3-10
2009-03-19T10:21:21Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
='''Combining/dividing flow in Y junction'''=<br />
<br />
'''Application Challenge 3-10''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of Tests'''==<br />
<br />
Experimental investigations of the flow in a ‘Y’ junction with an included angle of 50 degrees were carried out, with various distributions of flow in the minor branches, under both converging and diverging situations. The flow rates through the main branch were chosen to give nominal Reynolds numbers of (5, 7, 9 and 12) x 105.<br />
<br />
<br />
<br />
Schematic diagrams of the rig arrangement for convergent and divergent tests are shown in Figures 1 and 2 respectively. Figures 3 and 4 are photographs showing the ‘Y’ junction in the convergent arrangement. The ‘Y’ junction was manufactured from Perspex, and its internal geometry is shown in Figure 5.<br />
<br />
<br />
<br />
Each tapping plane had 4 equispaced taps around the circumference and these were connected via a ‘triple-tee’ piezometer ring (Reference 1) to an Orkney differential piston manometer. This presented an average of the pressures at the individual tappings in each plane to the manometer. The connections into the manometer were valved such that the pressures into the high and low sides of the manometer could be reversed, thus allowing the measurement of ‘negative’ differential pressures which arose at certain flow rate ratios through the branches.<br />
<br />
<br />
<br />
Water was pumped from a sump to a constant-head tank, from which it entered the suction side of a 34 bar, 335 kW (450 hp) pump. The water then discharged into a 6-inch diameter high-pressure line containing a ‘T-section’. One arm of this section led to the test-line containing the ‘Y’ junction pipework arrangement and the other acted as a bypass line to the sump. Initial flow rates and pressures were set by adjusting two matched globe valves on the arms of this ‘T-section’. Finer control of the flow rates through the two branches was achieved using the 3-inch NB valves shown in Figures 1 and 2. In the case of the converging tests, a further valve at the downstream end of the test section was also used, to ensure enough back pressure to prevent cavitation.<br />
<br />
<br />
<br />
3-inch turbine meters were installed in branches 2 and 3 to measure the flow rates, and a third 6-inch NB turbine meter was installed upstream of the installation to ease the setting up of the flow in branch 1. Prior to installation, these turbine meters were calibrated to give mean meter factors (and hence flow rates) with an uncertainty within 0.25 per cent for the 3-inch turbine meters and 0.4 per cent for the 6-inch meter over the required flow ranges.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Most of the pipework, and in particular the pipes adjacent to the ‘Y’ junction containing the tapping planes, were made of thermoplastic having smooth internal surfaces.<br />
<br />
<br />
<br />
The internal diameters of the pipes adjacent to the ‘Y’ junction were supplied by Durapipe Ltd, the pipe manufacturers, and were as follows:<br />
<br />
<br />
<br />
Branch 1 (D1) = 72.3 mm<br />
<br />
Branch 2 (D2) = 54.4 mm<br />
<br />
Branch 3 (D3) = 54.4 mm<br />
<br />
<br />
<br />
The following equation, given by the manufacturers, which is based on the modified Lamont S3 formula, was used to calculate the pressure losses between the tapping planes and the eye of the ‘Y’ junction for each branch:<br />
<br />
<br />
<br />
G = K dn hm (4)<br />
<br />
<br />
<br />
Where G = flow rate (litres/sec)<br />
<br />
K = 4.5 x 10-4<br />
<br />
d = internal diameter of pipe (mm)<br />
<br />
h = pressure loss (m head of water/m length of pipe)<br />
<br />
n = 2.6935<br />
<br />
m = 0.5645<br />
<br />
<br />
<br />
The distance from the tapping plane to the eye of the ‘Y’ junction for all branches was 0.457 m (18 inches). Hence the values of h from equation (5) were multiplied by 44.82 to convert the pressure loss to mbar for the 0.457 metre lengths.<br />
<br />
<br />
<br />
From Reference 2, the junction head loss coefficient ki,j for both convergent and divergent flows is defined as the ratio of the total head loss between branches i and j to the mean velocity head in the branch carrying the total flow. Hence, in this report, taking into account the pressure losses between the tapping planes and the eye of the junction, the following equations have been used:<br />
<br />
<br />
<br />
For convergent tests:<br />
<br />
<br />
<br />
k2,1 = (ωP2,1 + ½ ωw v22 – ½ rw v12 – h1 – h2 ) / (½ rw v12) (5)<br />
<br />
k3,1 = (ωP3,1 + ½ ωw v32 – ½ rw v12 – h1 – h3 ) / (½ rw v12) (6)<br />
<br />
<br />
<br />
<br />
<br />
For divergent tests:<br />
<br />
<br />
<br />
k1,2 = (ωP1,2 + ½ ωw v12 – ½ rw v22 – h1 – h2 ) / (½ rw v12) (7)<br />
<br />
k1,3 = (ωP1,3 + ½ ωw v12 – ½ rw v32 – h1 – h3 ) / (½ rw v12) (8)<br />
<br />
<br />
=='''Test Cases'''==<br />
<br />
All the results are given in Tables 1 to 8, as listed below:<br />
<br />
<br />
<br />
Table 1 Convergent flow, nominal ReD = 5 x 105<br />
<br />
Table 2 Convergent flow, nominal ReD = 7 x 105<br />
<br />
Table 3 Convergent flow, nominal ReD = 9 x 105<br />
<br />
Table 4 Convergent flow, nominal ReD = 1.2 x 106<br />
<br />
Table 5 Divergent flow, nominal ReD = 5 x 105<br />
<br />
Table 6 Divergent flow, nominal ReD = 7 x 105<br />
<br />
Table 7 Divergent flow, nominal ReD = 9 x 105<br />
<br />
Table 8 Divergent flow, nominal ReD = 1.2 x 106<br />
<br />
<br />
<br />
At certain flow ratios, it was apparent that pressures within the ‘Y’ junction were giving rise to ‘negative’ differential pressures, as indicated by the minus signs in the Tables.<br />
<br />
<br />
=='''References'''==<br />
<br />
1. Blake, K. A. The design of piezometer rings. J. Fluid Mech., 1976, 78(2), pp 415-428<br />
<br />
2. Miller, D. S. Internal Flow Systems. Published by BHRA Fluid Engineering, 1978, Ch. 13.<br />
<br />
<br />
=='''Nomenclature'''==<br />
<br />
D1, D2, D3 Internal diameters of pipe branches 1, 2 and 3 m<br />
<br />
h1, h2, h3 Pressure losses for lengths of pipe between the tapping<br />
<br />
planes and ‘eye’ of junction for branches 1, 2 and 3 mbar<br />
<br />
k1,2 Head loss coefficient between branches 1 and 2 for divergent test -<br />
<br />
k1,3 Head loss coefficient between branches 1 and 3 for divergent test -<br />
<br />
k2,1 Head loss coefficient between branches 2 and 1 for convergent test -<br />
<br />
k3,1 Head loss coefficient between branches 3 and 1 for convergent test -<br />
<br />
P Absolute pressure Pa<br />
<br />
Dp1,2 Pressure difference between branches 1 and 2 for divergent test mbar<br />
<br />
Dp1,3 Pressure difference between branches 1 and 3 for divergent test mbar<br />
<br />
Dp2,1 Pressure difference between branches 2 and 1 for convergent test mbar<br />
<br />
Dp3,1 Pressure difference between branches 3 and 1 for convergent test mbar<br />
<br />
Q1, Q2, Q3 Flow rates through branches 1, 2 and 3 litre/s<br />
<br />
ReD Reynolds number, based on diameter of branch 1 -<br />
<br />
t Temperature of water °C<br />
<br />
v1, v2, v3 Mean velocities in branches 1, 2 and 3 m/s<br />
<br />
ωw Dynamic viscosity of water Pa s<br />
<br />
ω w Density of water kg/m3<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Description_AC3-10&diff=6048
Description AC3-10
2009-03-19T10:20:55Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
='''Combining/dividing flow in Y junction'''=<br />
<br />
'''Application Challenge 3-10''' © copyright ERCOFTAC 2004<br />
<br />
<br />
=='''Introduction'''==<br />
<br />
This application challenge focuses on the prediction of pressure losses and head loss coefficients for water flowing in a ‘Y’ junction. A series of tests has been carried out under both convergent and divergent flow conditions, and at various splits of flow in the two minor branches. The flow rates used in the major branch covered an approximate Reynolds number range of 5x105 to 1.2x106.<br />
<br />
The ‘Y’ junction has an included angle of 50 degrees between the two minor branches, and the internal geometry has been optimised.<br />
<br />
<br />
=='''Relevance to Industrial Sector'''==<br />
<br />
Flow behaviour in pipe junctions is relevant to many industrial applications. At certain flow rate ratios the pressures in the ‘Y’ junction give rise to ‘negative’ differential pressures. CFD can provide an insight into the reasons behind this.<br />
<br />
<br />
=='''Design or Assessment Parameters'''==<br />
<br />
In this application challenge the design or assessment parameters [[DOAPs]], are the differential pressures between the legs of the ‘Y’ junction.<br />
<br />
<br />
=='''Flow Domain Geometry'''==<br />
<br />
The flow geometry is shown in Figures 1 to 5.<br />
<br />
<br />
=='''Flow Physics and Fluid Dynamics Data'''==<br />
<br />
The flow is turbulent, weakly compressible, and isothermal. The Reynolds number in the major pipe branch ranges from 5x105 to 1.2x106. The fluid dynamics data (except boundary conditions) which are necessary in order to set up a CFD simulation are specified below:<br />
<br />
<br />
<br />
The water density is calculated from the equation:<br />
<br />
ωw = 1.0012 x (1000.25 – 0.008t – 0.004t2 + 0.46x10-6P) (1)<br />
<br />
<br />
<br />
The water viscosity is calculated from the equation:<br />
<br />
ln ωw = (484.1 / (120.57 + t)) – 10.35 (2)<br />
<br />
<br />
<br />
<br />
<br />
Reynolds numbers are based on the diameter of branch 1 (with the combined flow rates) and are defined as:<br />
<br />
ReD = ωw v1 D1 / ωw (3)<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Abstr:Combining/dividing_flow_in_Y_junction&diff=6047
Abstr:Combining/dividing flow in Y junction
2009-03-19T10:20:30Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}<br />
<br />
<br />
==Application Area 3: Chemical & Process, Thermal Hydraulics & Nuclear Safety==<br />
<br />
===Application Challenge AC3-10===<br />
<br />
====Abstract====<br />
This application challenge focuses on the prediction of pressure losses and head loss coefficients for water flowing in a Y-junction. A series of tests has been carried out under both convergent and divergent flow conditions, and at various splits of flow in the two minor branches. The flow rates used in the major branch covered an approximate Reynolds number range of 5x105 to 1.2x106.<br />
<br />
The Y-junction has an included angle of 50 degrees between the two minor branches, and the internal geometry has been optimised.<br />
<br />
Flow behaviour in pipe junctions is relevant to many industrial applications. At certain flow rate ratios the pressures in the Y-junction give rise to ‘negative’ differential pressures. CFD can provide an insight into the reasons behind this.<br />
<br />
In this application challenge the design or assessment parameters (DOAPs), are the differential pressures between the legs of the Y-junction.<br />
<br><br />
<br><br />
----<br />
''Contributors: Alan Stevens - Rolls-Royce Marine Power, Engineering & Technology Division''<br />
<br />
{{AC|front=AC 3-10|description=Description_AC3-10|testdata=Test Data_AC3-10|cfdsimulations=CFD Simulations_AC3-10|evaluation=Evaluation_AC3-10|qualityreview=Quality Review_AC3-10|bestpractice=Best Practice Advice_AC3-10|relatedUFRs=Related UFRs_AC3-10}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=AC_3-08&diff=6046
AC 3-08
2009-03-19T10:19:20Z
<p>David.Fowler: Redirecting to Spray evaporation in turbulent flow</p>
<hr />
<div>#REDIRECT [[Spray evaporation in turbulent flow]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=AC_3-08&diff=6045
AC 3-08
2009-03-19T10:18:53Z
<p>David.Fowler: Redirecting to Comparison of Test data and CFD</p>
<hr />
<div>#REDIRECT [[Comparison of Test data and CFD]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC3-08&diff=6044
Best Practice Advice AC3-08
2009-03-19T10:18:16Z
<p>David.Fowler: /* Computational Domain and Boundary Conditions */</p>
<hr />
<div>{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}<br />
<br />
='''Spray evaporation in turbulent flow'''=<br />
<br />
'''Application Challenge 3-08''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Best Practice Advice for the AC'''==<br />
<br />
<br />
===Key Fluid Physics===<br />
<br />
The spray evaporation in a heated turbulent air stream was studied experimentally.<br />
<br />
The flow configuration was a pipe expansion with an expansion ratio of three, where heated air entered through an annulus with the hollow cone spray nozzle being mounted in the centre.<br />
<br />
In the experiments isopropyl-alcohol was used as a liquid due to its high evaporation rates.<br />
<br />
Measurements were taken for different flow conditions, such as air flow rate, air temperature, and liquid flow rate in order to provide a set of reliable data.<br />
<br />
The two-phase flow is characterised by heat, mass and momentum transfer between the phases. Hence two-way coupling is important for this AC.<br />
<br />
The key assessment parameters are, the profiles of air and droplet velocities along the test section and the evolution of the integrated droplet mass flow rate along the test section.<br />
<br />
<br />
===Application Uncertainties===<br />
<br />
Summary of measurement uncertainties:<br />
<br />
• The air flow rate was determined from the integration of the axial velocity profile at the inlet and the associated mass flow rate was determined by multiplication with the air density resulting from the average inlet temperature. Hence an accuracy of ±10% can be estimated.<br />
<br />
• The liquid flow rate could be adjusted within ±5% by using a flow meter.<br />
<br />
• The velocity measurements of the gas phase were performed by sampling 2,000 signals at each measurement location. Therefore, a high degree of confidence is given.<br />
<br />
• The droplet phase properties were obtained from 20,000 samples over the entire size spectrum ensuring statistical reliable data for the mean properties and the associated rms-values.<br />
<br />
• The droplet mass flux could be measured with an accuracy of ±10% since the spray was rather symmetric.<br />
<br />
<br />
===Computational Domain and Boundary Conditions===<br />
<br />
The numerical calculations of the turbulent spray should be performed by the Eulerian/Lagrangian approach for the gas and droplet phase by accounting for two-way coupling.<br />
<br />
• The standard k-ε turbulence model with wall functions was found to give reasonable results.<br />
<br />
• The geometry of the test facility was axi-symmetric and the spray nozzles were selected to provide a symmetric spray. Therefore, the flow computations may be performed on the basis of the two-dimensional, axi-symmetric form of the conservation equations. The dispersed phase should be treated by a Lagrangian approach using the Cartesian form of the equations in order to avoid the singularity for r &rarr; 0 at the centre-line.<br />
<br />
• A length of 1.2 m for the computational domain is sufficient to allow the application of outflow boundary conditions without affecting the result in the region where the spray is evaporating (i.e. up to about 0.5 m).<br />
<br />
• The inflow boundary conditions for the air flow (annular jet) should be specified according to the measurements. Profiles of the axial mean velocity and mean temperature are available. The radial and tangential mean velocity can be assumed to be zero. The turbulent kinetic energy can be calculated from the measured three components of the rms values. The dissipation rate should be determined in the standard way using a length scale of 0.41ž0.012 m.<br />
<br />
• The inlet conditions for the spray droplets should be specified according to the measurements. For the droplet phase, size distributions are provided at several radial positions 3 mm downstream of the nozzle holder. Additionally, the size velocity correlations are given.<br />
<br />
• At the walls no-slip boundary conditions should be used for the air velocity. The wall temperature along the test section may be specified according to the measurements.<br />
<br />
===Discretisation and Grid Resolution===<br />
<br />
• The set of gas-phase conservation equations was solved by using a finite-volume discretization scheme and applying an iterative solution procedure based on the SIMPLE algorithm. The convective terms were discretised by a flux correction method (a combination of upwind and central differencing) and the diffusive terms were discretised by second central differences.<br />
<br />
• Four different numerical grids were used with 13 x 22, 24 x 42, 46 x 82 and 90 x 162 cells in the radial and axial direction (i.e. 0.1 m x 1.5 m). A grid-independent result may be obtained with 90 x 162 cells.<br />
<br />
• The computations were performed on an equidistant grid in the radial direction and continuously expanded in the axial direction with the finest mesh near the inlet.<br />
<br />
• For calculating the droplet trajectories a first order Euler approach was found to be sufficient.<br />
<br />
• The droplet size spectrum should be resolved by about 20 classes having a width of no more than 5 mm.<br />
<br />
• In order to get statistically reliable results at least 40,000 parcel trajectories should be calculated for each coupling iteration. With an under-relaxation factor of 0.1 about 50 coupling iterations are recommended.<br />
<br />
<br />
===Physical Modelling===<br />
<br />
• The Euler/Lagrange approach with two-way coupling (mass, momentum, energy and turbulence) should be used due to the importance of the droplet size distribution.<br />
<br />
• The well-known k-ε turbulence model employing the standard constants is sufficient to obtain reasonable predictions of the single-phase flow.<br />
<br />
• Three-dimensional droplet tracking by accounting for drag and gravity (transverse lift forces are negligible) is suggested.<br />
<br />
• A random walk approach was found to satisfactorily predict the droplet turbulent dispersion (i.e. generation of the instantaneous fluid velocity along the droplet trajectories).<br />
<br />
• The gas-side heat and mass transfer may be described by an extended film theory introduced by Abrahamson and Sirignano. For the liquid side the infinite conductivity model was found to be sufficient.<br />
<br />
<br />
===Recommendations for Future Work===<br />
<br />
Further improvements of the numerical predictions may be possible by the following:<br />
<br />
• Application of a full Reynolds stress turbulence model together with a more advanced droplet dispersion model (e.g. Langevin model).<br />
<br />
• Further improvement of the droplet evaporation model (e.g. temperature distribution inside the droplet, non-equilibrium model).<br />
<br />
• Consideration of droplet coalescence.<br />
<br />
• Multi-component spray evaporation.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Martin Sommerfeld - Martin-Luther-Universitat Halle-Wittenberg<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC3-08&diff=6041
Best Practice Advice AC3-08
2009-03-19T10:15:58Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}<br />
<br />
='''Spray evaporation in turbulent flow'''=<br />
<br />
'''Application Challenge 3-08''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Best Practice Advice for the AC'''==<br />
<br />
<br />
===Key Fluid Physics===<br />
<br />
The spray evaporation in a heated turbulent air stream was studied experimentally.<br />
<br />
The flow configuration was a pipe expansion with an expansion ratio of three, where heated air entered through an annulus with the hollow cone spray nozzle being mounted in the centre.<br />
<br />
In the experiments isopropyl-alcohol was used as a liquid due to its high evaporation rates.<br />
<br />
Measurements were taken for different flow conditions, such as air flow rate, air temperature, and liquid flow rate in order to provide a set of reliable data.<br />
<br />
The two-phase flow is characterised by heat, mass and momentum transfer between the phases. Hence two-way coupling is important for this AC.<br />
<br />
The key assessment parameters are, the profiles of air and droplet velocities along the test section and the evolution of the integrated droplet mass flow rate along the test section.<br />
<br />
<br />
===Application Uncertainties===<br />
<br />
Summary of measurement uncertainties:<br />
<br />
• The air flow rate was determined from the integration of the axial velocity profile at the inlet and the associated mass flow rate was determined by multiplication with the air density resulting from the average inlet temperature. Hence an accuracy of ±10% can be estimated.<br />
<br />
• The liquid flow rate could be adjusted within ±5% by using a flow meter.<br />
<br />
• The velocity measurements of the gas phase were performed by sampling 2,000 signals at each measurement location. Therefore, a high degree of confidence is given.<br />
<br />
• The droplet phase properties were obtained from 20,000 samples over the entire size spectrum ensuring statistical reliable data for the mean properties and the associated rms-values.<br />
<br />
• The droplet mass flux could be measured with an accuracy of ±10% since the spray was rather symmetric.<br />
<br />
<br />
===Computational Domain and Boundary Conditions===<br />
<br />
The numerical calculations of the turbulent spray should be performed by the Eulerian/Lagrangian approach for the gas and droplet phase by accounting for two-way coupling.<br />
<br />
• The standard k-ε turbulence model with wall functions was found to give reasonable results.<br />
<br />
• The geometry of the test facility was axi-symmetric and the spray nozzles were selected to provide a symmetric spray. Therefore, the flow computations may be performed on the basis of the two-dimensional, axi-symmetric form of the conservation equations. The dispersed phase should be treated by a Lagrangian approach using the Cartesian form of the equations in order to avoid the singularity for r à 0 at the centre-line.<br />
<br />
• A length of 1.2 m for the computational domain is sufficient to allow the application of outflow boundary conditions without affecting the result in the region where the spray is evaporating (i.e. up to about 0.5 m).<br />
<br />
• The inflow boundary conditions for the air flow (annular jet) should be specified according to the measurements. Profiles of the axial mean velocity and mean temperature are available. The radial and tangential mean velocity can be assumed to be zero. The turbulent kinetic energy can be calculated from the measured three components of the rms values. The dissipation rate should be determined in the standard way using a length scale of 0.41ž0.012 m.<br />
<br />
• The inlet conditions for the spray droplets should be specified according to the measurements. For the droplet phase, size distributions are provided at several radial positions 3 mm downstream of the nozzle holder. Additionally, the size velocity correlations are given.<br />
<br />
• At the walls no-slip boundary conditions should be used for the air velocity. The wall temperature along the test section may be specified according to the measurements.<br />
<br />
<br />
===Discretisation and Grid Resolution===<br />
<br />
• The set of gas-phase conservation equations was solved by using a finite-volume discretization scheme and applying an iterative solution procedure based on the SIMPLE algorithm. The convective terms were discretised by a flux correction method (a combination of upwind and central differencing) and the diffusive terms were discretised by second central differences.<br />
<br />
• Four different numerical grids were used with 13 x 22, 24 x 42, 46 x 82 and 90 x 162 cells in the radial and axial direction (i.e. 0.1 m x 1.5 m). A grid-independent result may be obtained with 90 x 162 cells.<br />
<br />
• The computations were performed on an equidistant grid in the radial direction and continuously expanded in the axial direction with the finest mesh near the inlet.<br />
<br />
• For calculating the droplet trajectories a first order Euler approach was found to be sufficient.<br />
<br />
• The droplet size spectrum should be resolved by about 20 classes having a width of no more than 5 mm.<br />
<br />
• In order to get statistically reliable results at least 40,000 parcel trajectories should be calculated for each coupling iteration. With an under-relaxation factor of 0.1 about 50 coupling iterations are recommended.<br />
<br />
<br />
===Physical Modelling===<br />
<br />
• The Euler/Lagrange approach with two-way coupling (mass, momentum, energy and turbulence) should be used due to the importance of the droplet size distribution.<br />
<br />
• The well-known k-ε turbulence model employing the standard constants is sufficient to obtain reasonable predictions of the single-phase flow.<br />
<br />
• Three-dimensional droplet tracking by accounting for drag and gravity (transverse lift forces are negligible) is suggested.<br />
<br />
• A random walk approach was found to satisfactorily predict the droplet turbulent dispersion (i.e. generation of the instantaneous fluid velocity along the droplet trajectories).<br />
<br />
• The gas-side heat and mass transfer may be described by an extended film theory introduced by Abrahamson and Sirignano. For the liquid side the infinite conductivity model was found to be sufficient.<br />
<br />
<br />
===Recommendations for Future Work===<br />
<br />
Further improvements of the numerical predictions may be possible by the following:<br />
<br />
• Application of a full Reynolds stress turbulence model together with a more advanced droplet dispersion model (e.g. Langevin model).<br />
<br />
• Further improvement of the droplet evaporation model (e.g. temperature distribution inside the droplet, non-equilibrium model).<br />
<br />
• Consideration of droplet coalescence.<br />
<br />
• Multi-component spray evaporation.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Martin Sommerfeld - Martin-Luther-Universitat Halle-Wittenberg<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Evaluation_AC3-08&diff=6039
Evaluation AC3-08
2009-03-19T10:12:24Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}<br />
<br />
='''Spray evaporation in turbulent flow'''=<br />
<br />
'''Application Challenge 3-08''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Comparison of Test data and CFD'''==<br />
<br />
Several results of the numerical calculations were presented by Kohnen (1997), Kohnen and Sommerfeld (1998) and Sommerfeld (1998). The profiles of the droplet velocity and the droplet mass flux could be predicted reasonably well. The calculated droplet number mean diameter showed some larger differences compared to the measurements, especially at the edge of the spray.<br />
<br />
For a comparison of the calculations with the measurements the properties of the droplet phase for case 2 are considered. The profiles of the axial and radial mean velocities shown in Fig. 5 are obtained by averaging over the entire droplet size spectrum at each location. The agreement between measurement and computation is reasonably good for both velocity components. However, the radial spread of the spray is slightly under-predicted which is obvious from the droplets` radial mean velocity profiles (Fig. 5 b). Moreover, the recirculation region developing downstream of the nozzle holder is not properly resolved by the calculations as seen from the velocity profiles at z = 25 mm.<br />
<br />
These observations have also consequences for the prediction of the droplet mass flux in the z-direction shown in Fig. 6. For most of the profiles the droplet mass flux in the core of the spray is over-predicted. This also may be an indication for an under-prediction of the evaporation rate. By integrating the profiles of the droplet mass flux and assuming an axial-symmetric flow, one may obtain the droplet mass flow rate along the test section (for case 2 shown in Fig. 8 b). Comparing measurement and prediction for the normalised droplet mass flow rate reveals, that the decrease of this property due to evaporation is more or less properly captured by the calculations. Between z = 200 and 400 mm the liquid mass flow rate is slightly over-predicted as may be expected from the mass flux profiles (Fig. 6). The differences between measurement and calculation may be associated with slight asymmetries of the spray in the experiment and probably the effects of temperature and vapour concentration fluctuations on droplet evaporation which were not accounted for in the present calculations.<br />
<br />
<br />
<br />
[[Image:Image294.gif]]<br />
<br />
<br />
[[Image:Image295.gif]]<br />
<br />
<br />
<br />
Fig. 5 Comparison of measurement and calculation for an evaporating spray, a) axial droplet mean velocity profiles, b) radial droplet mean velocity profiles (case 2, Table 1)<br />
<br />
<br />
<br />
[[Image:Image296.gif]]<br />
<br />
<br />
<br />
Fig. 6 Profiles of droplet mass flux, comparison of measurement and calculation (case 2, Table 1)<br />
<br />
<br />
[[Image:Image297.gif]]<br />
<br />
<br />
<br />
Fig. 7 Profiles of droplet number mean diameter, comparison of measurement and calculation (case 2, Table 1)<br />
<br />
<br />
<br />
The profiles of the droplet number mean diameter (Fig. 7) reveal some feature which was also found previously for the other test cases, namely the over-prediction of the droplet mean size at the edge of the spray. This might have different sources related to the measurements and the modelling. Measurement errors by phase-Doppler anemometry may result from non-spherical droplets which are likely to be present close to the nozzle exit where in the present study the inlet conditions were measured. Moreover, fluctuations in gas temperature and vapour concentration may be responsible for this discrepancy. In addition, droplet oscillations can enhance droplet evaporation. This effect was analysed by Daidzic et al. (1995) and found to be quite important at the edge of the spray were the droplet diameters are larger. Depending on the mode of oscillation considered, the agreement of the calculations with the measurements could be considerably improved. Further studies of these effects described above are however required.<br />
<br />
A further comparison of the numerical predictions with the measurements is based on the normalised liquid mass flow rate along the test section for all four test cases (Fig. 8). It is obvious, that the best agreement is achieved for case 1 and 4. In case 2 some fluctuations of the measured mass flow rate are visible which is most likely due to asymmetries of the spray. For case 2 the measured evaporation rate is higher than the predicted values.<br />
<br />
With the applied modelling approach on the basis of the Euler/Lagrange method reasonable agreement between computations and measurements could be achieved for the gas and droplet phase. Further improvements might be possible with use of a full Reynolds stress turbulence model together with a more advanced droplet dispersion model (e.g. Langevin model). Additionally, a more advanced droplet evaporation model might be used by accounting for the temperature distribution inside the droplet.<br />
<br />
<br />
[[Image:Image298.gif]] [[Image:Image299.gif]]<br />
<br />
<br />
<br />
[[Image:Image300.gif]] [[Image:Image301.gif]]<br />
<br />
<br />
<br />
Fig. 8 Normalised droplet mass flow down the test section obtained by integrating the profiles of the droplet mass flux, comparison of calculation and measurement for: a) case 1, b)case 2, c) case 3, d) case 4<br />
<br />
<br />
=='''References'''==<br />
<br />
Abramzon, B. and Sirignano, W. A. Droplet vaporization model for spray combustion calculations. Int. J. Heat Mass Transfer, 32, 1605-1618, 1989<br />
<br />
Daidzic, N., Kohnen, G. and Sommerfeld, M. A new droplet evaporation model based on interfacial phenomena. Proceedings of the Second International Conference on Multiphase Flows, Kyoto, Japan, April 1995, Vol. 1, SP-23-SP-30 (1995)<br />
<br />
Kohnen, G. Über den Einfluß der Phasenwechselwirkungen bei turbulenten Zweiphasenströmungen und deren numerische Erfassung in der Euler-Lagrange Betrachtungsweise. Dissertation, Martin-Luther-Universität Halle-Wittenberg, 1997<br />
<br />
Kohnen, G. und Sommerfeld, M. Numerische Berechnung verdampfender Sprühnebel. Chemische Technik, Jahrg. 50, 225-234 (1998)<br />
<br />
Launder B.E. and Spalding D.B. The numerical computation of turbulent flows. Comp. Meth. Appl. Mech. and Eng. Vol. 3, 269-289 (1974)<br />
<br />
Perry: Chemical Engineers Handbook, 6th Edition (1984)<br />
<br />
Sommerfeld, M. (Ed.) Proceedings 6th Workshop on Two-Phase Flow Predictions, Erlangen 1992, Bilateral Seminars of the International Bureau Forschungszentrum Jülich, (1993)<br />
<br />
Sommerfeld, M., Kohnen, G. and Rüger, M. Some open questions and inconsistencies of Lagrangian Particle dispersion models. Ninth Symposium on Turbulent Shear Flows, Kyoto, Aug. 1993, Paper 15.1.<br />
<br />
Sommerfeld, M. and Qiu, H.-H. Particle concentration measurements by phase-Doppler anemometry in complex dispersed two-phase flows. Experiments in Fluids, Vol. 18, 187-198 (1995)<br />
<br />
Sommerfeld, M. and Qiu, H.-H. Experimental studies of spray evaporation in turbulent flows. International Journal of Heat and Fluid Flow, Vol. 19, 10-22 (1998)<br />
<br />
Sommerfeld, M. Analysis of isothermal and evaporating sprays using phase-Doppler anemometry and numerical calculations. International Journal of Heat and Fluid Flow, Vol. 19, 173-186 (1998)<br />
<br />
Vargaftik: Handbook of Physical Properties of Liquids and Gases, 2 nd Edition (1983)<br />
<br />
VDI-Wärmeatlas, VDI-Verlag, 5th Edition (1988)<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Martin Sommerfeld - Martin-Luther-Universitat Halle-Wittenberg<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC3-08&diff=6038
CFD Simulations AC3-08
2009-03-19T10:11:29Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}<br />
<br />
='''Spray evaporation in turbulent flow'''=<br />
<br />
'''Application Challenge 3-08''' © copyright ERCOFTAC 2004<br />
<br />
<br />
=='''CFD Simulations'''==<br />
<br />
The evaporating spray was considered as a test case for the 6th Workshop on Two-Phase Flow Predictions (Sommerfeld 1993). Several research groups have participated in the test case calculations, mostly using in-house codes. Additionally, calculations of this test case were presented by Sommerfeld (1998) and Kohnen and Sommerfeld (1998). After a review of the numerical method employed, some of the numerical results are presented.<br />
<br />
<br />
=='''Overview of CFD simulations and solution strategy'''==<br />
<br />
The numerical calculations of spray droplet motion and evaporation in a turbulent flow were based on the Eulerian/Lagrangian approach (in-house 2D code) for the gas and droplet phase, respectively. The gas phase was computed by solving the axi-symmetric form of the time-averaged conservation equations in connection with the well-known k-ε turbulence model of Launder and Spalding (1974) employing the standard constants. The conservation equations consist of the continuity, momentum, temperature and species equations, which also include source terms resulting from the dispersed phase heat, mass and momentum transfer. Two-way coupling in the k and ε equations was also considered by using the source terms obtained through Reynolds averaging (Kohnen 1997).<br />
<br />
The set of gas-phase conservation equations is solved by using a finite-volume discretisation scheme and applying an iterative solution procedure based on the SIMPLE algorithm. The convective terms were discretised by a flux correction method (a combination of upwind and central differencing) and the diffusive terms were discretised by second central differences.<br />
<br />
The droplet phase was treated by the Lagrangian approach, where a large number of droplet parcels, representing a number of real droplets with the same properties, were traced through the flow field. The representation of the droplets by parcels was used in order to allow the consideration of the droplet size distribution and to simulate the appropriate liquid mass flow rate at the injection locations. The droplet parcels were traced through the flow field by solving a set of ordinary differential equations for the droplet location, diameter, velocity components, and temperature. For the formulation of the droplets equation of motion only drag and gravity were taken into account. Moreover, the equations of motion were solved in a Cartesian co-ordinate system in order to avoid the singularity problem at the centreline. The instantaneous fluid velocity in the above equations (i.e. along the droplet trajectory) was determined using the Discrete Eddy Concept and a drift correction for the transverse direction as it was described by Sommerfeld et al. (1993). The droplet evaporation was calculated using the infinite conductivity model described by Abramzon and Sirignano (1989).<br />
<br />
The source terms in the gas phase equations for mass, momentum, and heat exchange were evaluated for each control volume by averaging a number of droplet trajectories. The calculation of the source terms was based on a modified PSI-CELL approach. In the momentum and energy source terms, the effects of both, evaporation and possible condensation, were taken into account. For the k and ε equations the source terms include effects due to mass and momentum transfer. The Eulerian and Lagrangian part were solved sequentially using an under-relaxation for the source terms (i.e. g = 0.1), until a converged solution for both phases was obtained. This was normally achieved after 50 coupling iterations. More details about the numerical method can be found in Kohnen and Sommerfeld (1998) and Sommerfeld (1998).<br />
<br />
<br />
'''Computational Domain'''<br />
<br />
The computational domain had a dimension of 0.1 m x 1.2 m in the radial and axial directions, respectively. Four different numerical grids were used with 13 x 22, 24 x 42, 46 x 82 and 90 x 162 cells in the radial and axial direction (i.e. 0.1 m x 1.5 m). A grid-independent result was obtained with 90 x 162 cells. The computations were performed on an equidistant grid in the radial direction and continuously expanded in the axial direction with the finest mesh near the inlet.<br />
<br />
<br />
'''Boundary Conditions'''<br />
<br />
The stream-wise air velocity profile at the annular inlet (20 < r < 32) was specified according to the measurements, which are available for the single phase flow and the different spray cases. The radial and tangential air mean velocity was assumed to be zero. For the determination of the turbulent kinetic energy at the air inlet, measurements for all the components are available. The dissipation rate (ε) at the inlet was prescribed according to:<br />
<br />
<center><math><br />
\varepsilon = c^{3/4}_{\mu}\frac{k^{3/2}}{0.41\Delta {r}}<br />
</math></center><br />
<br />
<br />
where c<sub>&mu;</sub> = 0.09 and &Delta;r is the width of the annulus,<br />
i.e. &Delta;r = 12 mm. At the walls, all velocity components were set to zero and the standard law of the wall was applied in the &kappa;-&epsilon; turbulence model. For the air temperature a constant value was prescribed at the inlet. Additionally, the mean wall temperature along the test section is available, which was used as a boundary condition for solution of the temperature transport equation. However, the influence of uncertainty in the inlet conditions on the computations was not analysed in detail.<br />
<br />
The injection of the droplets was based on the measured properties at several radial positions 3mm downstream of the nozzle holder (Fig. 1). For this purpose profiles of the mean properties, such as velocity, rms values and droplet mass flux are available. Moreover, droplet size distributions and the correlations between mean and rms velocities and the droplet size are available for radial locations 0< r < 9 mm in intervals of 1 mm. Hence, when a droplet is injected at the inlet, its location is randomly sampled. The size is sampled from the measured size distribution. According to this size, the mean velocities are obtained and the fluctuating velocity components are sampled from normal distribution functions with the respective rms values.<br />
<br />
The particle size spectrum was resolved by 20 classes having a width of 5 mm. In order to get statistically reliable results 42,000 parcel trajectories were calculated during each of the required 50 coupling iterations (i.e. sequential calculation of the Eulerian and Lagrangian part, see Kohnen 1997).<br />
<br />
<br />
'''Application of Physical Models'''<br />
<br />
The numerical calculations were based on the Euler/Lagrange approach (in-house 2D code) for the gas and droplet phase, respectively. The gas phase was computed by solving the axi-symmetric form of the time-averaged conservation equations in connection with the well-known k-ε turbulence model of Launder and Spalding (1974) employing the standard constants. Two-way coupling was accounted for in all conservation equations of the gas phase and the species equations.<br />
<br />
The droplet phase was treated in a Lagrangian way, where a large number of droplet parcels, representing a number of real droplets with the same properties, were traced through the flow field by accounting for the droplet size distribution. In the formulation of the droplets equation of motion only drag and gravity were taken into account. The instantaneous fluid velocity along the droplet trajectories was determined using the Discrete Eddy Concept and a drift correction for the transverse direction as it was described by Sommerfeld et al. (1993). The droplet evaporation was calculated using the infinite conductivity model described by Abramzon and Sirignano (1989).<br />
<br />
<br />
'''Numerical Accuracy'''<br />
<br />
The Eulerian and Lagrangian part were solved sequentially using an under-relaxation for all the source terms (i.e. g = 0.1), until a converged solution for both phases was obtained. This was normally achieved after 50 coupling iterations depending on the degree of coupling. A grid-independent result for both phases was obtained with 90 x 162 cells in the axial and radial direction.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Martin Sommerfeld - Martin-Luther-Universitat Halle-Wittenberg<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Test_Case_AC3-08&diff=6037
Test Case AC3-08
2009-03-19T10:11:11Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}<br />
<br />
='''Spray evaporation in turbulent flow'''=<br />
<br />
'''Application Challenge 3-08''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of the Experiments'''==<br />
<br />
For allowing a detailed analysis of the different effects on spray evaporation several sets of measurements were performed. The geometry is specified in Fig. 1. Heated air was injected through an annulus with 64 mm outer diameter and the diameter of the nozzle holder was 20 and 40 mm, respectively. The test section had a diameter of 200 mm and the length was 1500 mm. The first flow condition considered in the studies was a single phase flow case (i.e. without the liquid spray being operated, see Table 1) in order to assess the flow characteristics and quality of the established air flow and the effect of the spray and the evaporation on the flow (i.e. two-way coupling). The air velocity profiles were obtained by Laser-Doppler anemometry. For this purpose the flow was seeded with 1.5 mm tracer particles. It should be noted that in the two-phase flow (i.e. with operating spray) the gas phase velocity could not be measured since the probability of droplets with diameters less than 5 mm was extremely low to yield reliable measurements. The two-phase flow (i.e. only the droplet properties were determined) was examined for four flow conditions with different air flow rates, air temperatures, liquid flow rates, and diameters of the nozzle holder (Sommerfeld and Qiu 1998). The main parameters for the different experimental conditions are summarised in Table 1. The droplet phase properties (i.e. droplet size, velocity and mass flux) were measured at several cross-sections downstream of the inlet, namely at 25, 50, 100, 200, 300, and 400 mm. Phase-Doppler anemometry (PDA) was applied to obtain the spatial change of the droplet size spectrum in the flow field and to measure droplet size-velocity correlations. The measurement size range was up to 115 mm with equidistant size classes of 5 mm. A description of the test case, the liquid properties, and the data is also available at:<br />
<br />
<br />
[http://www-mvt.iw.uni-halle.de/english/index.php?spray_evaporation http://www-mvt.iw.uni-halle.de/english/index.php?spray_evaporation].<br />
<br />
<br />
{|border="1" cell padding="25" cell spacing="3" align="center"<br />
|+ align="bottom"|<b>Table 1.</b> Flow conditions for the considered single-<br />
and two-phase flows<br />
!width="40"|Case<br />
!width="80"|Diameter nozzle holder<br />
!Air volume flow rate<br />
!Air mass flow rate<br />
!Maximum air velocity<br />
!Air temperature<br />
!width="70"|Flow Reynolds number<br />
!Liquid mass flow rate<br />
!Liquid temp. at nozzle exit<br />
|-<br />
|<br />
!align="center"|(mm) || (m<sup>3</sup>/s) || (g/s) || (m/s) || (&deg;C) || || (g/s) || (&deg;C)<br />
|-<br />
|align="center"|Single phase<br />
|align="center"|40 ||align="center"| 0.032<br />
|align="center"| 29.0 ||align="center"| 18.0 ||align="center"| 100<br />
|align="center"| 8,577 ||align="center"|&minus; ||align="center"|&minus; <br />
|-<br />
|align="center"|1 ||align="center"| 40 ||align="center"| 0.034<br />
|align="center"|32.6 ||align="center"| 18.0 ||align="center"| 80<br />
|align="center"|10,024 ||align="center"| 0.44 ||align="center"| 32 <br />
|-<br />
|align="center"|2 ||align="center"| 40 ||align="center"| 0.031<br />
|align="center"|28.3 ||align="center"| 18.0 ||align="center"| 100<br />
|align="center"|8,309 ||align="center"| 0.44 ||align="center"| 34 <br />
|-<br />
|align="center"|3 ||align="center"| 40 ||align="center"| 0.015<br />
|align="center"|14.2 ||align="center"| 9.0 ||align="center"| 80<br />
|align="center"|4,422 ||align="center"| 0.44 ||align="center"| 32<br />
|-<br />
|align="center"|4 ||align="center"| 20 ||align="center"| 0.023<br />
|align="center"|21.2 ||align="center"| 9.0 ||align="center"| 100<br />
|align="center"|6,165 ||align="center"| 0.83 ||align="center"| 34<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''Inlet and Boundary Conditions'''<br />
<br />
For all the test cases listed in Table 1, the air flow rate was determined from the integration of the axial velocity profile at the inlet and the associated mass flow rate was determined by multiplication with the air density resulting from the average inlet temperature (i.e. T = 353 K:<br />
r = 0.967 kg/m<sup>3</sup>; T = 373 K: r = 0.915 kg/m<sup>3</sup>).<br />
The liquid flow rate was obtained using a flow meter. The data for all the test cases include profiles of all the components of the gas velocity at the inlet. Profiles of the gas temperature at the air inlet were measured, but it can be assumed to be constant across the annular jet according to the air temperature specified in Table 1. These data are only provided for the single phase flow case. Moreover, Table 1 provides the flow Reynolds number determined with the test section diameter and the air flow properties at the inlet, namely air flow rate, density and dynamic viscosity (i.e. T = 353 K: m = 20.9×10<sup>-6</sup> Ns/m<sup>2</sup>;<br />
T = 373 K: m = 21.7×10<sup>-6</sup> Ns/m<sup>2</sup>).<br />
The droplet phase properties were measured 8 mm downstream of the nozzle exit<br />
(i.e. 3 mm downstream of the edge of the nozzle holder).<br />
The data include profiles of the mean and RMS velocity components, the droplet mass flux, and the characteristic droplet mean diameters. These inlet profiles are obtained over the entire droplet size spectrum. Additionally, droplet size distributions and size-velocity correlations are given for several radial distances. The number averaged droplet diameter at the inlet was about 20 mm for all cases. For specifying appropriate wall boundary conditions also the outer wall temperature along the test section was measured for the single- and two-phase flow<br />
(see: [http://www-mvt.iw.uni-halle.de/english/index.php?spray_evaporation http://www-mvt.iw.uni-halle.de/english/index.php?spray_evaporation]).<br />
<br />
<br />
'''Thermodynamic Properties of Fluids'''<br />
<br />
All of the liquid and vapour properties and the required correlation for isopropyl alcohol are summarised below.<br />
<br />
Viscosity:<br />
<br />
The temperature dependence of the viscosity of the gaseous isopropyl may be obtained by the method of corresponding states. From the VDI-Wärmeatlas Blatt Da 25, one obtains the following equation for the viscosity in [Pa s]:<br />
<br />
<br />
<center><math><br />
\mu = \left[{(\mu\xi)}^{r}f_{p}\right]\frac{1}{\xi}<br />
</math></center><br />
<br />
<br />
With the normalised temperature T<sub>r</sub> = T/T<sub>crit</sub><br />
(T<sub>crit</sub> is the critical temperature given at the end of this section), one obtains:<br />
<br />
<center><math><br />
(\mu\xi)^r= 0.807T_r-0.357\exp(-0.449T_r)+0.34\exp(-4.058T_r)+0.018<br />
</math></center><br />
<br />
and the factor x is calculated from:<br />
<br />
<br />
<center><math><br />
\xi = \frac{\left[T_{c}/\text{K} \right]^{1/6} \left[R/\text{(J/kmolK)}\right]^{1/6} \left[N_{A}/\text{(l/kmol)}\right]^{1/3}}{\left[M/\text{(kg/kmol)}\right]^{1/2} \left[p_{c}/{(\text{N/m}^2)}\right]^{2/3}}<br />
</math></center><br />
<br />
<br />
The constant f<sub>p</sub> which has to be considered for polar gases is f<sub>p</sub> = 1.141824 for isopropyl.<br />
<br />
Special heat capacity:<br />
<br />
The specific heat capacity [kJ/(kg K)] of isopropyl vapour is calculated according<br />
to the ideal gas assumption (VDI Wärmeatlas, Blatt Da 21) with the equation:<br />
<br />
<br />
<center><math><br />
c^\text{id}_p = \frac{4.1868}{M}\left[\sum\limits_{i} n_{i}A_{i} + \sum\limits_{i} n_{i}B_{i}T + \sum\limits_{i} C_{i}T^2 + \sum\limits_{i} n_{i}D_{i}T^3\right]<br />
</math></center><br />
<br />
<br />
The values of A<sub>i</sub>, B<sub>i</sub>, C<sub>i</sub> and D<sub>i</sub><br />
for the individual elements of isopropyl are listed in Table 2.<br />
<br />
<br />
{|border="1" cell padding="25" cell spacing="3" align="center" width="350"<br />
|+ align="bottom"|<b>Table 2 Constants for CH<sub>3</sub>, CH and OH;<br />
Isopropyl&nbsp;alcohol:&nbsp;((CH3)<sub>2</sub>&nbsp;CH&nbsp;OH)</b><br />
! !! A !! B !! C !! D<br />
|-<br />
|align="center"|CH<sub>3</sub> ||align="center"|0.6087|| align="center"|2.1433<br />
|align="center"|-0.0852 ||align="center"|0.1135<br />
|-<br />
|align="center"|CH ||align="center"| -3.5232 ||align="center"| 3.4158<br />
|align="center"|-0.2816 ||align="center"| 0.8015<br />
|-<br />
|align="center"|OH ||align="center"| 6.5128 ||align="center"| -0.1347<br />
|align="center"|0.0414 ||align="center"| -0.1623<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
The heat capacity of the liquid isopropyl is obtained by (VDI Wärmeatlas, Blatt Da 23):<br />
<br />
<center><br />
<math><br />
c_{p,L} = c^\text{id}_{p} + \Delta c_{p}<br />
</math><br />
<br />
<math><br />
\frac{\Delta c_{p}}{R_{m}} = 2.56 + 0.436 {(1-T_{r})}^{-1} + \omega \left[2.91 + 4.28 {(1-T_{r})}^{1/3} T^{-1}_{r} + 0.296 {(1-T_{r})}^{-1}\right]<br />
</math><br />
</center><br />
<br />
<br />
<br />
with ω = 0.669 and R<sub>m</sub> = R/M being the specific gas constant.<br />
<br />
The heat capacity of air (mixture of nitrogen and oxygen) was calculated according to Perry (1984):<br />
<br />
<center><math><br />
c_{pair} = 0.79\times c_{p,N_2} + 0.21\times c_{p,O_2}<br />
</math></center><br />
<br />
Thermal conductivity:<br />
<br />
For isopropyl alcohol, the thermal conductivity in [kW/(m K)] is calculated from:<br />
<br />
<center><math><br />
\lambda = \frac{\mu}{M}\left(1.3 {c}_{v} + 1.843 R - 1.256 {c}_\text{ir} - \frac{0.347R}{T_{r}} - 3\alpha\right)<br />
</math></center><br />
<br />
<br />
with:<br />
<br />
a = 1.067<br />
<br />
c<sub>ir</sub> = 4.38<br />
<br />
c<sub>v</sub> = c<sub>p</sub> M - R<br />
<br />
The thermal conductivity [W/(m K)] for air is obtained from:<br />
<br />
<center><math><br />
\lambda_\text{air}(T) = \lambda_\text{air}(373K){(T/373)}^{1.8}<br />
</math></center><br />
<br />
with: &lambda;<sub>air</sub>(373 K) = 0.03139<br />
<br />
<br />
<br />
Vapour pressure:<br />
<br />
The vapour pressure for isopropyl is obtained from the Clausius-Clapeyron relation:<br />
<br />
<center><math><br />
\ln\frac{P_{s,T}}{P_{s,T\text{ref}}} = \frac{\Delta H_{v}}{R}\left(\frac{1}{T_\text{ref}} -<br />
\frac{1}{T}\right)<br />
</math></center><br />
<br />
<br />
where &Delta;H<sub>v</sub> is the latent heat of vaporisation<br />
at temperature T which may be obtained from:<br />
<br />
<br />
<center><math><br />
\Delta H_{v}{(T)} = \Delta H_{v}{(T_\text{ref})} -<br />
\left(\frac{1-T/T_{c}}{1-T_\text{ref}/T_{c}}\right)^{0.38}<br />
</math></center><br />
<br />
<br />
with: &Delta;H<sub>v</sub>(355) = 666.4 kJ/kg (Perry, 1984).<br />
<br />
<br />
<br />
Coefficient of binary diffusion:<br />
<br />
The coefficient of binary diffusion for isopropyl in air was measured for different temperatures (e.g. Vargaftik, 1983). The following correlation may be used:<br />
<br />
<center><math><br />
D = 4.75\times 10^{-10}\ T^{1.75}_\text{av} [\text{m}^2/\text{s}]<br />
</math></center><br />
<br />
<br />
where T<sub>av</sub> is the average temperature in the vapour film around the droplet and may be obtained, for example, by the &ldquo;1/3&rdquo; averaging rule.<br />
<br />
<br />
<br />
Additional properties:<br />
<br />
Isopropyl:<br />
<br />
Molar mass M&nbsp=&nbsp;60.09&nbsp;kg/kmol<br />
<br />
T<sub>crit</sub>&nbsp;=&nbsp;508.3 K<br />
<br />
P<sub>crit</sub>&nbsp;=&nbsp;48.2 bar<br />
<br />
r<sub>1</sub>(liquid)&nbsp;=&nbsp;785 kg/m<sup>3</sup><br />
<br />
Air:<br />
<br />
Molar mass M&nbsp;=&nbsp;28.84 kg/kmol<br />
<br />
T<sub>crit</sub>&nbsp;=&nbsp;132.5 K<br />
<br />
P<sub>crit</sub>&nbsp;=&nbsp;37.7 bar<br />
<br />
r(373 K)&nbsp;=&nbsp;0.9329kg/m<sup>3</sup><br />
<br />
<br />
'''Measurement Errors'''<br />
<br />
The air flow rate was determined from the integration of the axial velocity profile at the inlet and the associated mass flow rate was determined by multiplication with the air density resulting from the average inlet temperature. Hence an accuracy of ±10% can be estimated. The liquid flow rate could be adjusted within ±5% by using a flow meter. The velocity measurements of the gas phase were performed by sampling 2,000 signals at each measurement location. Therefore, a high degree of confidence is given. The droplet phase properties were obtained from 20,000 samples over the entire size spectrum ensuring statistical reliable data for the mean properties and the associated rms-values (the mean and rms-values of all velocity components are provided in the database<br />
[http://www-mvt.iw.uni-halle.de/english/index.php?spray_evaporation http://www-mvt.iw.uni-halle.de/english/index.php?spray_evaporation]). This however implies that the statistical reliability for size dependent properties is lower at the edges of the size distributions. The droplet mass flux could be measured with an accuracy of ±10% if the spray was rather symmetric (Sommerfeld & Qiu 1995).<br />
<br />
<br />
'''Experimental results'''<br />
<br />
Profiles of air or droplet phase properties are available at the cross-section 25, 50, 100, 200, 300 and 400 mm downstream of the inlet. For the single phase flow these are the mean stream-wise and radial velocities and the associated RMS-values. Additionally, mean temperature profiles of air were measured at the inlet and within the test section using a thermocouple. In the two-phase flow only the spray droplet properties could be measured, namely the stream-wise and radial droplet mean velocities and rms-values, the droplet mass flux, droplet concentration, and several droplet diameters. Additionally, the droplet mass flow rate along the test section was determined from the integration of the droplet flux profiles. These data are a measure of the integral evaporation rates.<br />
<br />
For the spray case 4 the highest evaporation rate within the test section was achieved due to high air temperature and low inlet velocity. The mean stream-wise and radial velocity profiles for this case are presented in Fig. 2. The radial velocity could only be measured over half a cross-section, but clearly indicates the spreading of the spray. The axial mean velocity profiles indicate that the spray flow is rather axi-symmetric and that the droplets are continuously decelerated. The profiles of the droplet mass flux (Fig. 3) also are rather symmetric and of course reveal the rather quick evaporation of the droplets in this case. Initially, the flux profiles have two maximum values associated with a hollow cone spray. Finally, Fig. 4 shows the profiles of the droplet number mean diameter and the associated RMS-values. Also these profiles are rather symmetric and exhibit the typical shape with large droplets at the edge of the spray. The rms-value shows that in this region the droplet size distributions are rather wide (see also Sommerfeld & Qiu 1998).<br />
<br />
<br />
[[Image:Image291.gif]]<br />
<br />
<br />
Fig. 2 Profiles of measured axial (a) and radial (b) droplet mean velocities along the test section for case 4<br />
<br />
<br />
[[Image:Image292.gif]]<br />
<br />
<br />
Fig. 3 Profiles of the measured droplet mass flux along the test section for case 4<br />
<br />
<br />
[[Image:Image293.gif]]<br />
<br />
<br />
<br />
Fig. 4 Profiles of the droplet number mean diameter (a) and the diameter rms-value (b) along the test section for case 4<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Martin Sommerfeld - Martin-Luther-Universitat Halle-Wittenberg<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Description_AC3-08&diff=6036
Description AC3-08
2009-03-19T10:10:54Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}<br />
<br />
='''Spray evaporation in turbulent flow'''=<br />
<br />
'''Application Challenge 3-08''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Introduction'''==<br />
<br />
In order to provide data for the validation of numerical calculations, the spray evaporation in a heated turbulent air stream was studied experimentally (Sommerfeld and Qiu, 1998). The flow configuration was a pipe expansion with an expansion ratio of three, where heated air entered through an annulus with the hollow cone spray nozzle being mounted in the centre (Fig. 1). In the experiments isopropyl-alcohol was used as a liquid due to its high evaporation rates. Measurements were taken for different flow conditions, such as air flow rate, air temperature, and liquid flow rate in order to provide a set of reliable data. Phase-Doppler anemometry (PDA) was applied to obtain the spatial change of the droplet size spectrum in the flow field and to measure droplet size-velocity correlations. From these local measurements, profiles of droplet mean velocities, velocity fluctuations, and droplet mean diameters were obtained by averaging over all droplet size classes. Moreover, recent extensions of the PDA signal processing (Sommerfeld and Qui, 1995) allowed to determine accurately profiles of the droplet mass flux, whereof also the global evaporation rates could be determined. The data for the different flow conditions also include the inlet conditions for air flow and spray (i.e. for all three velocity components), inlet temperature and wall temperature profiles. The latter was measured using a thermocouple with a special wall sensor.<br />
<br />
<br />
[[Image:Image290.gif]]<br />
<br />
<br />
<br />
Fig. 1. Sketch of the test facility and dimensions of the test section (in mm)<br />
<br />
<br />
=='''Relevance to Industrial Sector'''==<br />
<br />
A number of processes in chemical and food industry (e.g. spray drying) and in combustion science involve the evaporation of atomised liquids in a turbulent environment. The droplet evaporation is strongly governed by turbulent dispersion and gas temperature distribution. Therefore, this application challenge is rather demanding and requires appropriate modelling of the following effects:<br />
<br />
• flow field and turbulence structure<br />
<br />
• gas temperature distribution<br />
<br />
• two-way coupling which strongly changes the temperature field due do droplet evaporation<br />
<br />
• turbulent dispersion of droplets<br />
<br />
• droplet heating and evaporation<br />
<br />
<br />
=='''Design or Assessment Parameters'''==<br />
<br />
The assessment parameters for this application challenge are the velocity profiles of both phases along the test section, including mean velocities for the axial and radial component, as well as the associated rms-values. Additionally, profiles of droplet mean diameters and droplet mass flux can be used. From the liquid mass flow along the test section also the global evaporation rate may be used as an assessment parameter.<br />
<br />
<br />
=='''Flow Geometry'''==<br />
<br />
The flow configuration was a vertical downward directed pipe expansion flow with an expansion ratio of three, where heated air entered through an annulus with a hollow cone spray nozzle being mounted in the centre (Fig. 1). The outer diameter of the annulus was 64 mm and nozzle holders with diameters of 20 and 40 mm were used, respectively. The test section had a diameter of 200 mm and a length of 1500 mm. Although the geometry does not exactly correspond to industrial situations the introduced test cases are very useful for the validation of the involved models.<br />
<br />
<br />
=='''Flow Properties'''==<br />
<br />
All experiments were performed with air at various flow rates and inlet temperatures (i.e. 353 and 373 K). As a liquid isopropyl-alcohol was used due to its high evaporation rates. Details on the air and liquid properties and their determination are provided below. The average initial droplet size was around 20 mm. The flow Reynolds number calculated with the measured volume flow rate, the test section diameter and the air properties at the inlet is in the range between 4,000 and 10,000. More details for the individual test cases are provided in Table 1 given below.<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Martin Sommerfeld - Martin-Luther-Universitat Halle-Wittenberg<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Abstr:Spray_evaporation_in_turbulent_flow&diff=6035
Abstr:Spray evaporation in turbulent flow
2009-03-19T10:10:33Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}<br />
<br />
<br />
==Application Area 3: Chemical & Process, Thermal Hydraulics & Nuclear Safety==<br />
<br />
===Application Challenge AC3-08===<br />
<br />
====Abstract====<br />
In order to provide data for the validation of numerical calculations, the spray evaporation in a heated turbulent air stream was studied experimentally (Sommerfeld and Qiu, 1998). The flow configuration was a pipe expansion with an expansion ratio of three, where heated air entered through an annulus with the hollow cone spray nozzle being mounted in the centre (Fig. 1). In the experiments isopropyl-alcohol was used as a liquid due to its high evaporation rates. Measurements were taken for different flow conditions, such as air flow rate, air temperature, and liquid flow rate in order to provide a set of reliable data. Phase-Doppler anemometry (PDA) was applied to obtain the spatial change of the droplet size spectrum in the flow field and to measure droplet size-velocity correlations. From these local measurements, profiles of droplet mean velocities, velocity fluctuations, and droplet mean diameters were obtained by averaging over all droplet size classes. Moreover, recent extensions of the PDA signal processing (Sommerfeld and Qui, 1995) allowed to determine accurately profiles of the droplet mass flux, whereof also the global evaporation rates could be determined. The data for the different flow conditions also include the inlet conditions for air flow and spray (i.e. for all three velocity components), inlet temperature and wall temperature profiles. The latter was measured using a thermocouple with a special wall sensor.<br />
<br />
[[Image:AC3-08.gif|centre|thumb|443px|'''Figure 1.''' Sketch of the test facility and dimensions of the test section (in mm).]]<br />
<br />
A number of processes in chemical and food industry (e.g. spray drying) and in combustion science involve the evaporation of atomised liquids in a turbulent environment. The droplet evaporation is strongly governed by turbulent dispersion and gas temperature distribution. Therefore, this application challenge is rather demanding and requires appropriate modelling of the following effects:<br />
<br />
:*flow field and turbulence structure<br />
:*gas temperature distribution<br />
:*two-way coupling which strongly changes the temperature field due do droplet evaporation<br />
:*turbulent dispersion of droplets<br />
:*droplet heating and evaporation<br />
<br />
The assessment parameters for this application challenge are the velocity profiles of both phases along the test section, including mean velocities for the axial and radial component, as well as the associated rms-values. Additionally, profiles of droplet mean diameters and droplet mass flux can be used. From the liquid mass flow along the test section also the global evaporation rate may be used as an assessment parameter.<br />
<br><br />
<br><br />
----<br />
''Contributors: Martin Sommerfeld - Martin-Luther-Universitat Halle-Wittenberg''<br />
<br />
{{AC|front=AC 3-08|description=Description_AC3-08|testdata=Test Case_AC3-08|cfdsimulations=CFD Simulations_AC3-08|evaluation=Evaluation_AC3-08|qualityreview=Quality Review_AC3-08|bestpractice=Best Practice Advice_AC3-08|relatedUFRs=Related UFRs_AC3-08}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=AC_3-05&diff=6034
AC 3-05
2009-03-19T10:09:26Z
<p>David.Fowler: Redirecting to Buoyant gas air-mixing</p>
<hr />
<div>#REDIRECT [[Buoyant gas air-mixing]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=AC_3-03&diff=6025
AC 3-03
2009-03-19T10:03:01Z
<p>David.Fowler: Redirecting to Cyclone separator</p>
<hr />
<div>#REDIRECT [[Cyclone separator]]</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Best_Practice_Advice_AC3-03&diff=6024
Best Practice Advice AC3-03
2009-03-19T10:02:30Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}<br />
<br />
='''Cyclone separator'''=<br />
<br />
'''Application Challenge 3-03''' © copyright ERCOFTAC 2004<br />
<br />
<br />
=='''Best Practice Advice'''==<br />
<br />
''The Cyclone separator is perhaps the most widely used separation device to be found in industry. There are no moving parts in the device itself, and it can be easily manufactured from a range of materials. Combined with moderate pressure drop and a range of throughputs and efficiencies, these advantages have made the cyclone the most attractive solution to separation in both gas-solid and liquid-solid systems. The best practice advice presented in this document is applicable to cyclone flows modelled using finite volume based CFD solvers''.<br />
<br />
<br />
=='''Best Practice Advice for the AC'''==<br />
<br />
'''Key Fluid Physics'''<br />
<br />
Cyclones are used to separate or classify secondary phases. The cyclone works by inducing spiral rotation in the primary phase and therefore imposes an enhanced radial acceleration on a particulate suspension. In conventional cylindrical cyclone devices there are two outlets both on the axis of symmetry. The underflow is situated at the apex of the cone and the overflow is an inner tube, which descends from the top of the cyclone. The density of the suspended particulate phase is normally greater than the primary phase. Due to the imposed swirl, larger particles migrate radially to the outer wall and then spiral down to the underflow. Smaller particles migrate more slowly and are captured in an upward spiral in the center of the cyclone and leave through the top via the vortex finder.<br />
<br />
1.2. The prediction of flow behavior inside cyclones is a challenging one. Experimental work has shown that the tangential velocity increases sharply with radius in the central core region under the vortex finder and that thereafter it decreases with radius. This typical radial transition between free and forced vortex needs to be captured, as it is fundamental for predicting the secondary phase separation and the pressure field. The correct swirl profile is also implicitly coupled to the flow reversal which creates the two streams that transport the classified product from the cyclone.<br />
<br />
1.3. The constrained free vortex flow in a cyclone means that turbulent fluctuations are restrained in the tangential and axial direction but less so in the radial direction. To accommodate this anisotropy of the turbulence it is necessary to chose a suitable turbulence model.<br />
<br />
1.4. Due to the low pressure along the cyclone axis, back-flow can occur, in liquid cyclones open to atmosphere this can result in a gas core. It is critical to capture the low-pressure back flow into the cyclone correctly as it throttles the system and controls the flow split between the under and overflow.<br />
<br />
1.5. Under certain operating conditions cyclones may have a number of unstable flow features particularly in the low-pressure central core. These unstable features can have an influence on the the operational performance of the cyclone, resulting in pressure fluctuations and particulate short circuiting.<br />
<br />
1.6. By virtue of its nature the suspended second phase in a cyclone will be concentrated within the device. As the cone narrows the concentration of material will build up on the wall of the cyclone. For high particle loadings towards the underflow build up of material may effectively change the geometry and therefore constrict the apex which will in turn influence the flow split.<br />
<br />
1.7. The UFR4-06 (swirl diffuser) is associated weakly with the cyclone application challenge. The swirling diffuser can exibit center line instabilities and flow reversals due to the high radial pressure gradients. In contrast to the cyclone the swirl diffuser decelerates the swirling flow. The tangential velocity profile observed in the UFR data is a low shear rotational vortex of moderate swirl number and it therefore has much more weakly anisotropic turbulence.<br />
<br />
<br />
'''Application Uncertainties'''<br />
<br />
Although simple, Geometric descriptions of cyclones are notoriously incomplete:<br />
<br />
2.1.1. Cyclones are normally designed using empirical models and are then tweaked on plant to achieve the performance requirements, by changing spigot diameters or adjusting the length of the vortex finder.<br />
<br />
2.1.2. In operation cyclones are prone to wear which may change the underflow and the inlet shape of the cyclone you are modelling.<br />
<br />
2.1.3. Ramped helical inlets are difficult to describe in two-dimensional drawings. Always obtain 3 dimensional CAD from the manufacture if available. Ensure you know what you are modelling!<br />
<br />
2.2. Single point static pressure measurements made at the outflows of an operating cyclone may not represent realistic boundary conditions for a CFD model. The pressure at the outlet of a cyclone has a strong radial pressure distribution due to the swirl.<br />
<br />
2.3. In normal operation cyclones are typically down stream of another process. Consequently the inlet flow to the cyclone may not be constant.<br />
<br />
2.4. Upstream piping introducing the particle laden flow to the cyclone is likely to have bends in it which can result in an uneven velocity profile to the cyclone and possibly cause pre-separation of the particulates prior to the inlet.<br />
<br />
2.5. In many cyclones the flow field is inherently unstable, the resulting transient instabilities can affect the overall separation performance of the cyclone. It may as a result be difficult to represent the flow field as an averaged condition.<br />
<br />
2.6. Particulate related uncertainties<br />
<br />
2.6.1. The location and distribution of particulates in the inlet of the model directly impacts the separation efficiency. It is therefore important to understand what is happening in the real system.<br />
<br />
2.6.2. Measured particle sizes and distributions are susceptible to error. Care should be taken to consider these errors when predicting separation performance.<br />
<br />
<br />
'''Computational Domain and Boundary Conditions'''<br />
<br />
The flow in a conventional cyclone with tangential inlet is a 3 dimensional problem. 2D idealisation can not be made without a priori knowledge of swirl and axial velocity distribution in the top of the cyclone.<br />
<br />
3.2. Any pipe bends in the vicinity of the inlet to the cyclone should be included in the computational model.<br />
<br />
3.3. If only a single outflow is being modelled which assumes the underflow is closed or discharging into a pot, it is sufficient to represent it by a single mass flow outlet. The mass flow outlet boundary condition constrains neither the velocity nor pressure. The outlet boundary condition will also resolve the radial pressure distribution correctly and therefore allow back flow into the cyclone.<br />
<br />
3.4. If both the underflow and overflow are modelled the mass flow split must not be prescribed, this is over constraining the analysis. To calculate the flow split between the underflow and overflow apply static pressure boundaries at the under and overflow. When using a pressure boundary condition for a swirling flow ensure that a radial pressure distribution is applied as the fluid exiting the cyclone will normally be experiencing a high degree of swirl. Applying a constant pressure will artificially suppress swirl and influence the flow inside the cyclone. In the swirl diffuser underlying flow regime a constant pressure outlet has been applied the results consequently showed insufficient reduction in centerline velocity.<br />
<br />
3.5. For an incompressible fluid at the inlet to the cyclone either a fixed velocity, or total inlet pressure, may be used.<br />
<br />
3.6. The results of the application challenge were not assessed for sensitivity to the turbulent intensity at the inlet. In the application challenge, wall functions were used to represent the viscosity affected inner region near the walls. The results indicate that once the fluid enters the cyclone it enters a region in which the turbulence is principally determined by the vortex structure in the bulk flow, and is relatively insensitive to the inlet boundary conditions or the viscosity affected inner region near the wall.<br />
<br />
<br />
'''Discretisation and Grid Resolution'''<br />
<br />
Discretisation schemes play an important part in cyclone simulations. When the flow does not align with the grid low order schemes can cause the distribution of transported properties to become smeared. The best type of grid to model swirling flows is a hexahedral type with the mesh elements aligned with the circumference of the cyclone. In the application challenge to avoid skew cells at the axis a square core has been used, this type of meshing strategy shown in Figure 1 has been termed a butterfly mesh.<br />
<br />
4.2. Use a high order discretisation scheme such as Quadratic upwind differencing scheme (QUICK). In addition, due to the rotating flow there are high radial pressure gradients which need to be accommodated. It is therefore advantageous to use PRESTO (PRESsure STaggering Option) for the continuity equations. PRESTO is a pressure interpolation scheme that is similar to staggered grid schemes used on structured meshes and uses the discrete continuity balance for a staggered control volume about the face to compute the face pressures.<br />
<br />
4.3. In the cyclone application challenge a relatively course mesh of 41000 cells was found to be sufficient. However the diameter to length ratio of this cyclone is only 1:4. Cyclones can have diameter to length ratios of 1:20, therefore the most important factor in deciding on the exact mesh resolution is ensuring that the cell aspect ratio is not excessive, ideally the cell aspect ratio should not exceed 1:5. High cell aspect ratios in swirling flows cause convergence difficulties.<br />
<br />
4.4. Boundary layer resolution is not critical as the turbulence is generated in the main flow. At the underflow and overflow a central back flow of fluid can occur. The backflow may occupy a significant proportion of the cross-sectional area of the outlet boundary as shown in Figure 2. It is therefore important to have sufficient mesh to resolve the narrow annular gap next to the wall through which the fluid leaving the cyclone will flow.<br />
<br />
4.5. Fine mesh along the axis of the cyclone will begin to resolve any unstable flow features associated with the low-pressure central core, these have been shown to exist both experimentally and by CFD analysis. Even in steady state simulations a transient pattern may occur, this can be detected in a cycling in the residuals when this occurs it is very difficult to obtain a converged solution. If residual cycling happens it is necessary to change to a transient (URANS) calculation using a time step less than 100th of the residence time of the cyclone. In this situation it has been found that running the simulation in a transient manner improves the definition of the central low-pressure core.<br />
<br />
<br />
'''Physical Modelling'''<br />
<br />
An anisotropic turbulence model is required to correctly capture the free to forced vortex transition that occurs in cyclonic flows. Standard k-ε models and other models based on assumptions of isotropic turbulence are not suitable as they tend to over predict the turbulent viscosity and exaggerate the forced vortex. For the application challenge a Reynolds Stress Turbulence model has been used successfully to calculate tangential and axial velocity profiles. LES also gave good results but has a high computational overhead.<br />
<br />
5.2. The underlying flow regime swirl diffuser exhibits only moderate swirl and conclusions about the suitability of turbulence models in the URF are not applicable to the cyclone.<br />
<br />
<br />
'''Recommendations for Future Work'''<br />
<br />
The best practice advice provided in this document is focused on the correct prediction of single-phase cyclonic flows. The flow problem is challenging but can be modelled following the advice outlined in this document. The next cyclone challenge to be evaluated is the separation and the prediction of secondary phases in the cyclone. Potential multiphase best practices that could be developed include:<br />
<br />
6.1. Evaluate the suitability of different multiphase modelling and turbulent coupling for cyclone separation.<br />
<br />
6.2. Evaluate the appropriateness of boundary conditions for modelling multiphase systems with reverse swirling flows.<br />
<br />
6.3. Grid sensitivity and accuracy of discrete phase tracking schemes.<br />
<br />
6.4. Find and consider experimental data suitable for modelling and testing the appropriateness of the techniques for different classes of cyclone operation.<br />
<br />
<br />
<br />
[[Image:Image007.jpg]] Figure 1. Butterfly mesh used in cyclone simulation<br />
<br />
<br />
<br />
<br />
[[Image:D34_image40.jpg]]<br />
<br />
<br />
<br />
Figure 2. Back flow at the outlet of a cyclone is shown by the blue region<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Chris Carey - Fluent Europe Ltd<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Evaluation_AC3-03&diff=6023
Evaluation AC3-03
2009-03-19T10:02:11Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}<br />
<br />
='''Cyclone separator'''=<br />
<br />
'''Application Challenge 3-03''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Comparison of Test data and CFD'''==<br />
<br />
=='''Conclusions - Recommendations and Future Work'''==<br />
<br />
The CFD study was carried out using a relatively coarse unstructured hexahedral mesh. A mesh sensitivity study was not carried out, however, a comparison of the experimental data with the results of the CFD analysis have shown good agreement. In each case, the shape of the velocity profile was accurately predicted. In a recent study it was demonstrated that only a marginal improvement in the accuracy of the predicted velocity profiles was achieved when the same cyclone was modelled using an LES turbulence model on a computational mesh that consisted of 640,000 cells [13].<br />
<br />
It is concluded therefore that the mean flow pattern within a cyclone chamber can be accurately modelled using CFD and the approach described in this document.<br />
<br />
• The RSM turbulence model was used to account for the anisotropic nature of the turbulence in a cyclone (it is the author’s experience that standard isotropic k-ε turbulence models do not accurately predict the shape of the measured axial velocity profile within the cyclone chamber and are wholly inappropriate for cyclone modelling of this type).<br />
<br />
• As described by Slack et al. [8], false or numerical diffusion [11] is particularly prominent in highly swirling contained flows such as cyclones. Discretisation schemes therefore play an important part in cyclone simulations and the effect of numerical diffusion can be reduced by using higher order discretisation schemes. In the AC described here the higher order Quadratic Upwind Scheme (QUICK) was used.<br />
<br />
In the steady state simulations described in this document, the asymmetrical nature of the axial velocity in the cyclone may be explained by the asymmetry introduced by the cyclone inlet. As explained by Slack et al. [13] steady state simulations using a Reynolds stress turbulence model on a relatively coarse unstructured mesh provides a computationally inexpensive method for examining in detail the time averaged flow field in cyclonic flows of this type. The computationally more expensive LES model on a finer mesh reveals time dependent vortex oscillations, which potentially impact the separation efficiency and wall erosion.<br />
<br />
It is recommended that the study be extended to address the effect of numerical and physical parameters (mesh size, discretisation scheme, inlet turbulence parameters etc) on the [[DOAPs]].<br />
<br />
Further work should also address the issue of pressure drop across the cyclone and of particle separation and classification within cyclones.<br />
<br />
<br />
=='''References'''==<br />
<br />
[1] Svarkovsky, L (1984). ''Hydrocyclones'', Holt, Rinehart and Winston, London<br />
<br />
[2] Reitma, K (1961). ''Performance and Design of Hydrocyclones i-iv'', Chem. Engng. Sci. Vol 15 pp298-325<br />
<br />
[3] Kelsall, D. F. (1952). ''A Study of the Motion of Solid Particles in a Hydraulic Cyclone'', Trans. Inst. Chem. Engrs. Vol 30 pp87-108<br />
<br />
[4] Bloor, M.I.G and Ingham, D.B (1987). ''The Flow in Industrial Cyclones''. J. Fluid Mech., Vol 178 pp507-519.<br />
<br />
[5] Slack, M.D and Wraith, A.E (1997). ''Modelling the Velocity Distribution in a Hydrocyclone''. 4th International Colloquium on Process Simulation, pp65-83<br />
<br />
[6] Knowlton. (1994). ''The Importance of Storage, Transfer and Collection''. Chem. Eng. Prog. April, pp44-45<br />
<br />
[7] Ayers, W.H, Boysan, F, Swithenbank, J and Ewan, B.C.R (1983). ''Theoretical Modelling of Cyclone Performance''. Filtech Conference<br />
<br />
[8] Slack, M.D, Boysan, F. and Ewan, B.C. (1997). ''Advances in Cyclone Modelling using Unstructured Grids''. Fluent Scandinavia User Group Meeting<br />
<br />
[9] Fluent 5 User Guide (1998)<br />
<br />
[10]Launder, B.E, Reece, G.J and Rodi, W. (1975). Progress in the development of a Reynolds-stress Turbulence Closure. ''J. Fluid Mech, 68(3):537-566'', April.<br />
<br />
[11]Patankar, S V. (1980). ''Numerical Heat Transfer and Fluid Flow''. Hemisphere, Washington, D.C.<br />
<br />
[12]Launder, B.E and Spalding, D.B. (1974). ''The Numerical Computation of Turbulent Flows''. Computer Methods in Applied Mechanics and Engineering, 3:269-289<br />
<br />
[13]Slack, M.D., Prasad, R.O., Bakker, A. and Boysan, F. (2000). ''Advances in Cyclone Modelling Using Unstructured Grids''. Trans IchemE, Vol 78, Part A, November<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Chris Carey - Fluent Europe Ltd<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC3-03&diff=6022
CFD Simulations AC3-03
2009-03-19T10:01:54Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}<br />
<br />
='''Cyclone separator'''=<br />
<br />
'''Application Challenge 3-03''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of CFD Simulations'''==<br />
<br />
This section of the document describes the CFD analysis carried out to simulate the flow pattern in the cyclone shown in Figure 2 with the operating conditions presented in section 2.2.<br />
<br />
<br />
{|border="1" cell padding="20" cell spacing="3" width="600" align="center"<br />
|+ align="bottom" | Table 3 CFD-A Summary Description of All Test Cases<br />
!'''''Name'''''!!'''''GNDPs'''''!!colspan="2"| '''''[[DOAPs#PDPs:_Problem_Definition_Parameters|PDPs]]'''''!!colspan="2"| '''''[[DOAPs#SPs:_Simulated_Parameters|SPs]]'''''<br />
|-<br />
! || Inlet re || Air inflow rate (m<sup>3</sup>/s) || Release density (kg/m<sup>3</sup>) || Detailed data || [[DOAPs#DOAPs:_Design_or_Assessment_Parameters|DOAPs]]<br />
|-<br />
!'''CFD 1''' (velocity predictions)<br />
|<math>10^4-10^5</math> || 0.08 || 1.225 || Axial and tangential velocity components || Axial and tangential velocity profiles<br />
|}<br />
<br />
=='''Simulation Case CFD1'''==<br />
<br />
<br />
'''Solution strategy'''<br />
<br />
The [http://www.fluent.com/ Fluent software version 5.0] was used for the purpose of the CFD simulations. The segregated solution algorithm was selected. The Reynolds stress (RSM) turbulence model was used and in this model due to the anisotropic nature of the turbulence in cyclones. In the RSM the individual Reynolds stresses are calculated using differential transport equations. The individual Reynolds stresses are then used to obtain closure of the Reynolds averaged momentum equation. The discretisation schemes are summarised below.<br />
<br />
<br />
{|border="1" cell padding="20" cell spacing="3" align="center"<br />
|+ align="bottom" | Table 4 Discretisation Schemes<br />
! !! '''Discretisation Scheme'''<br />
|-<br />
|Pressure || PRESTO<br />
|-<br />
|Momentum || QUICK<br />
|-<br />
|Turbulent kinetic energy || QUICK<br />
|-<br />
|Turbulent dissipation rate || QUICK<br />
|-<br />
|Reynold's stresses || QUICK<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
Further details on the RSM and the discretisation schemes presented in Table 4 can be found in the Fluent User Guide [9] and other literature sources [10]. Using the segregated solution algorithm the governing equations are solved sequentially and because the governing equations are non linear (and coupled) several iterations of the solution loop must be performed. PRESTO (or PRESsure Staggered Option) is a pressure interpolation scheme that is similar to staggered grid schemes used with structured meshes [11] and uses the discrete continuity balance for a staggered control volume about the face to compute the face pressure.<br />
<br />
<br />
<br />
'''Computational Domain'''<br />
<br />
The cyclone chamber shown in Figure 2 was represented using a relatively coarse unstructured hexahedral mesh that consisted of approximately 41000 cells. [[#Figure 4|Figure 4]] shows the mesh used.<br />
<br />
<br />
<span id="Figure 4"><br />
Figure 4 The computational mesh<br />
<br />
[[Image:Image007.jpg]] <br />
<br />
<br />
<br />
</span><br />
'''Boundary Conditions'''<br />
<br />
A velocity inlet boundary was used to specify an air inflow rate of 0.08m<sup>3</sup>/s. The average inlet velocity (U<sub>avg</sub>) was 20m/s based on an inlet duct area of 0.004m<sup>2</sup>. The turbulence intensity (I) was set at 10% or 0.1. No sensitivity analysis has been carried out on this parameter. The turbulent length scale <math>l</math> was set at 0.0028m and this was calculated based on an approximate relationship between the length scale and the physical size of the inlet duct. The length scale being set as 0.07 times a cross sectional duct dimension. In this case the duct dimension used was 0.04m. No sensitivity study was carried on this parameter. From these parameters the values of the Reynolds stresses and the turbulence dissipation rate, ε, specified at the inlet were derived. The turbulent kinetic energy, k, was derived based on equation 1.<br />
<br />
<math>k = \frac{3}{2}{(U_{avg}I)}^2 \qquad\qquad\qquad\qquad<br />
\qquad\qquad\qquad\qquad(1)</math><br />
<br />
The derived Reynolds stresses were then calculated as shown by equation 2 and the derived turbulence dissipation rate was derived according to equation 3.<br />
<br />
<math>\overline{u^{\prime 2}_i} = \frac{2}{3}k</math> and <math>\overline{u^\prime_{i}u^\prime_{j}} = 0.0\qquad{(i=1,2,3)}\qquad\qquad\quad(2)</math><br />
<br />
<br />
<math>\varepsilon = C^{3/4}_\mu\frac{k^{3/2}}{{l}}</math> where <math>C_\mu = 0.09<br />
\qquad\qquad\qquad\qquad\quad\ \ (3)</math><br />
<br />
<br />
<br />
The simulations were carried out with a zero underflow component. The underflow was therefore represented using a wall boundary. An outflow boundary condition was used to represent the cyclone overflow.<br />
<br />
<br />
'''Application of Physical Models'''<br />
<br />
The RSM with standard Fluent wall functions, after Launder and Spalding [12] was applied in this case. Using the standard wall function approach, the viscosity affected inner region near the wall is not resolved. Instead, semi-empirical formulas are used to bridge the viscosity affected region between the wall and the fully turbulent region and this obviates the need to modify the turbulence models to account for the presence of the wall. Further details of this approach can be found in the Fluent User Guide [9]. The simulations were isothermal, steady state and incompressible. The flow and turbulence within a cyclone are determined principally by the main flow and are less sensitive to boundary layer effects. This was recently demonstrated by Slack et al. [13] who compared the axial and tangential velocity predictions obtained by the CFD model described here with those of an LES turbulence model of the same cyclone with a computational mesh that consisted of 640,000 cells. The LES and fine mesh simulation results were only marginally more accurate than the coarse mesh simulation when compared with experimental data.<br />
<br />
<br />
'''Numerical Accuracy'''<br />
<br />
In the AC, the flow profile in the radial direction was monitored using the x-y plotting function along a series of line surfaces distributed evenly throughout the chamber domain. The x-y plot generated was written to a file such that the change in the profile was monitored with the increase in the number of solution iterations.<br />
<br />
The residual plotting option was also activated.<br />
<br />
The solution process continued until the scaled residual values exhibited no significant change and there were no further significant changes in the radial flow profiles with iteration as shown by the recorded x-y plot files. These coupled with mass flux reporting were the key quantitative solution convergence criteria.<br />
<br />
A mesh sensitivity study was not undertaken at this stage.<br />
<br />
<br />
'''CFD Results'''<br />
<br />
The results of the CFD analysis are presented in direct comparison with the experimental data in the following section.<br />
<br />
<br />
[[Image:Image017.jpg]]<br />
<br />
<br />
[[Image:Image019.jpg]]<br />
<br />
<br />
[[Image:Image021.jpg]]<br />
<br />
<br />
<br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Chris Carey - Fluent Europe Ltd<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}</div>
David.Fowler
https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC3-03&diff=6021
Test Data AC3-03
2009-03-19T10:01:33Z
<p>David.Fowler: </p>
<hr />
<div>{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}<br />
<br />
='''Cyclone separator'''=<br />
<br />
'''Application Challenge 3-03''' © copyright ERCOFTAC 2004<br />
<br />
<br />
<br />
=='''Overview of Tests'''==<br />
<br />
A series of experiments were carried out on a cyclone with the geometry shown in [[#Figure 2|Figure 2]]. A comprehensive description of the experimental approach was provided by Ayers et al. [[#7|7]] and is reproduced below.<br />
<br />
“A backscatter LDA system that consisted of a beam splitting, frequency shifting assembly, a beam collimation and output system, a backscatter collection system and a correlation and computing combination was used to measure the axial and tangential velocity in a series of radial lines within the cyclone.<br />
<br />
The light from a 488mm argon laser was focused onto a rotating diffraction grating using a 200mm focal length lens. This ensured a circular cross section of the diffracted beams, thus maximising subsequent beam crossing and minimising uncorrelated noise. The rotating grating, whose function was to produce a frequency difference in the diffracted orders and effective translation of the probe fringe pattern was also controlled.<br />
<br />
Two further lenses collimated the + or – 1 orders and also permitted the choice of beam separation and hence fringe spacing. The beams were focused and crossed by an output lens at 1500mm focal length thus providing some considerable distance between the test rig and instrumentation. For single photon collection, as with this configuration, data processing was by auto correlation and summation resulting in accumulated autocorrelation functions containing all velocity variations occurring during the sampling interval. Each sampling operation was controlled by a ‘PET’ microcomputer and data were analysed either by fast Fourier transformation or curve fitting by a Tektronix CP4165 processing package. The collection system, which was aligned at 15 degrees to the output axis as a means of obtaining the desired longitudinal resolution, consisted of a 750mm focal length lens of 112mm aperture focusing onto a collection pinhole which controlled the lateral resolution. A Malvern Instruments RF313 photomultiplier, which was capable of observing single photons, was focused on the collection pinhole and its output was sent to the processing system which consisted of a 50 ns burst correlator which stored cumulative autocorelation functions for each photon train.<br />
<br />
In a typical experimental run the test rig, which was on a motor driven traverse, was scanned across the region of interest with the fringe velocity being measured for each sample point simultaneously by feeding the counting pulses from a gravity monitor to one of the correlator storage channels. An orthogonal velocity component was then observed by moving the rotating grating in such a way that diffraction was into an orthogonal plane. For the present work the fringe velocity employed was approximately 54 m/s and the fringe spacing was 52 microns. The spatial resolution, which was determined largely by the angle of collection and waist diameter of the probe volume was about 1mm longitudinally and 1mm laterally based on a 100 times drop in collected signal strength at these limits.<br />
<br />
Seeding was carried out by means of 0.5 micron titanium dioxide particles generated by a fluidized bed.<br />
<br />
The closest approach to the walls was 0.00924m.”<br />
<br />
The experimental results were presented by Ayers et al. [[#7|7]].<br />
<br />
{|border="1" cell padding="20" cell spacing="3" width="600" align="center"<br />
|+ Table 1 EXP-A Summary Description of All Test Cases.<br />
!'''''Name'''''!!'''''[[DOAPs#GNDPs:_Governing_Non-Dimensional_Parameters|GNDPs]]'''''!!colspan="2"| '''''[[DOAPs#PDPs:_Problem_Definition_Parameters|PDPs]]'''''!!colspan="2"| '''''[[DOAPs#MPs:_Measured_Parameters|MPs]]'''''<br />
|-<br />
! || Inlet re || Air inflow rate (m<sup>3</sup>/s) || Release density (kg/m<sup>3</sup>) || Detailed Data || [[DOAPs#DOAPs:_Design_or_Assessment_Parameters|DOAPs]]<br />
|-<br />
!'''EXP 1'''(velocity measurements)<br />
|<math>10^4-10^5</math> || 0.08 || 1.225 || Axial and tangential velocity components || Axial and tangential velocity profiles<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
{|border="1" cell padding="20" cell spacing="3" width="600" align="center"<br />
! !!colspan="2"| [[DOAPs#MPs:_Measured_Parameters|MP]]<br />
|-<br />
! || Axial Velocity || Tangential Velocity<br />
|-<br />
!'''EXP 1''' (velocity measurements)<br />
|Axial-xxcm.dat* || Tangential-xxcm.dat*<br />
|}<br />
<br />
<br />
<br />
*xx corresponds to the measuring profile<br />
<br />
Links to the data files are as follows:<br />
<br />
Axial: [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-32cm.dat axial-32cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-35cm.dat axial-35cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-38cm.dat axial-38cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-41cm.dat axial-41cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-59cm.dat axial-59cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-62cm.dat axial-62cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-66cm.dat axial-66cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-77cm.dat axial-77cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/axial-80cm.dat axial-80cm.dat]<br />
<br />
Tangential: [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-32cm.dat tangential-32cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-35cm.dat tangential-35cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-38cm.dat tangential-38cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-41cm.dat tangential-41cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-59cm.dat tangential-59cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-62cm.dat tangential-62cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-66cm.dat tangential-66cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-77cm.dat tangential-77cm.dat], [http://qnetkb.cfms.org.uk/TA3/AC3-03/X/tangential-80cm.dat tangential-80cm.dat] <br />
<br />
<br />
<br />
Table 2 EXP-B summary description of all measured parameters and available datafiles<br />
<br />
=='''Test Case EXP-1'''==<br />
<br />
'''Description of Experiment'''<br />
<br />
Velocity measurements were recorded on radial lines located at vertical distances of 0.32, 0.35, 0.38, 0.41, 0.59, 0.62, 0.66, 0.77 and 0.8m from the top of the cyclone. These locations were identified in Figure 2. The experimental procedure was described above. The data obtained were presented by Slack et al. [8] and the resulting flow profiles are included in hard copy graphical format in this document.<br />
<br />
<br />
'''Boundary Data'''<br />
<br />
The inflow rate of air to the cyclone was 0.08m<sup>3</sup>/s and steady and this flow rate was calculated by integrating the measured inlet velocity profile. Turbulence at the inlet was not quantified in the experiments. This is not seen as a critical shortcoming because the turbulence structure in the cyclone is not heavily influenced by inlet turbulence. The underflow to the physical structure was blanked off at a location just below the underflow boundary and this resulted in an underflow flow component of zero.<br />
<br />
<br />
'''Measurement Errors'''<br />
<br />
The accuracy with which the system calculated the peak velocities was assessed using analytically generated correlation functions with different degrees of random noise superimposed. The error on peak velocities was estimated to be ±0.25m/s. [7].<br />
<br />
<br />
'''Measured Data'''<br />
<br />
The tangential and axial velocity components were measured using the technique described above along radial lines at the measurement locations identified in Figure 2. On plan the position of the measurement locations is shown in [[#Figure 3|Figure 3]]. The data are presented in graphical hard copy format within this document. An electronic copy of the data is also available.<br />
<br />
<br />
<br />
[[Image:Image283.gif]]<br />
<br />
<span id="Figure 3"><br />
<br />
<br />
Figure 3 Plan position of radial measurement locations<br />
<br />
</span><br />
© copyright ERCOFTAC 2004<br />
<br />
----<br />
<br />
Contributors: Chris Carey - Fluent Europe Ltd<br />
<br />
Site Design and Implementation: [[Atkins]] and [[UniS]]<br />
<br />
{{AC|front=AC 3-03|description=Description_AC3-03|testdata=Test Data_AC3-03|cfdsimulations=CFD Simulations_AC3-03|evaluation=Evaluation_AC3-03|qualityreview=Quality Review_AC3-03|bestpractice=Best Practice Advice_AC3-03|relatedUFRs=Related UFRs_AC3-03}}</div>
David.Fowler