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{{UFR|front=UFR 3-06|description=UFR 3-06 Description|references=UFR 3-06 References|testcase=UFR 3-06 Test Case|evaluation=UFR 3-06 Evaluation|qualityreview=UFR 3-06 Quality Review|bestpractice=UFR 3-06 Best Practice Advice|relatedACs=UFR 3-06 Related ACs}}
{{UFR|front=UFR 3-07|description=UFR 3-07 Description|references=UFR 3-07 References|testcase=UFR 3-07 Test Case|evaluation=UFR 3-07 Evaluation|qualityreview=UFR 3-07 Quality Review|bestpractice=UFR 3-07 Best Practice Advice|relatedACs=UFR 3-07 Related ACs}}




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= Natural and mixed convection boundary layers on<br />vertical heated walls (B) =
= Natural and mixed convection boundary layers on vertical heated walls (A) =


Underlying Flow Regime 3-07 <font size="-2" color="#888888">               © copyright ERCOFTAC 2004</font>
Underlying Flow Regime 3-06 <font size="-2" color="#888888">               © copyright ERCOFTAC 2004</font>


= Description =




= Description =


== Introduction ==
== Introduction ==


The effects of buoyancy on heat transfer can be predicted readily for laminar flows. When the flow is in the upward direction past a heated surface (or downwards past a cooled surface) heat transfer is enhanced, whereas in the opposite cases heat transfer is impaired. These influences are the consequence of the distortion of the velocity field.
The flow under consideration is a low mach number flow of a strongly heated gas inside a vertical circular tube. The experimental work of A.M.Shehata and D.M.McEligot (3) which is used to define this UFR supplements and extends earlier data for internal flows in small tubes (D&lt;13mm) with temperature dependent transport properties that could only provide integralparameters.


However, the situation is different with turbulent flows, as heat transfer is dictated by changes in turbulent diffusion. In configurations with forced and free convection aligned, local heat transfer coefficients significantly lower than those for forced flow alone can result. In contrast, for downward flow in heated tubes buoyancy forces cause a general enhancement of the turbulent diffusion properties of the flow, with the result that wall temperature distributions are well behaved and heat transfer coefficients are higher than those for forced flow alone. Eventually as the free convection component becomes more and more dominant, heat transfer for upward flow also becomes enhanced and in the limit the heat transfer coefficients for the two cases are the same.
These recent data are used to assess turbulence models by comparing measures and computed distributions of the mean streamwise velocity and temperature in this well defined experiment involving strong influence on the initial turbulent field, of the variation of the gas transport properties and the thickening of the viscous layer (the so called laminarization effect) which are caused by intense heating at the wall. Intense heating is defined here by a ratio wall to bulk absolute temperatures greater than 2.5.


This UFR is of particular relevance to British Energy’s and Magnox Electric’s Application Challenges.
This UFR is of particular relevance for the design of gas cooled nuclear reactors and the use of a gas as a coolant in power generation systems.


== Review of UFR studies and choice of test case ==
== Review of UFR studies and choice of test case ==


Studies of Petukhov and Nolde (1959), Petukhov and Strigin (1968), Herbert and Sterns (1968,1972), Jackson and Fewster (1977), Rouai (1987), Buyukalaca (1993) performed experiments with descending water flow in heated tubes. Jackson et al (2000) considered downward water flow in a heated annulus.
A variety of basic studies has been conducted examining turbulence structure in simple boundary layers with constant properties and uniform wall temperatures. A strong heating atthe wall induced by a nearly constant high heat flux boundary condition involves significant transport property variation and buoyancy effects and makes necessary to further assess the predictive capabilities of turbulence models in that situation. Experiments for air flowing upwards in small heated vertical tubes with temperature dependent transport properties were made by Humble, Lowdermilk and Desmon (4), Jackson (5), McEligot, Magee and Leppert (6), Perkins and Worsoe-Schmidt (7) and others. These studies were lacking of internal profile measurements for temperature and velocities but they provided some average data to make preliminary tests of turbulence models accounting for temperature-dependent transport properties and the influence of intense heating on turbulent flows in tubes.  
 
Studies of mixed convection heat transfer to air in a vertical tube with opposing forced and free components were made by Eckert and Diaguila (1954), Khosla, Hoffman and Pollock (1974), Brown and Gauvin (1965,1966) and Axcell (1975). Easby (1978) studied nitrogen at pressures up to 4 bar. Fewster (1976) conducted a programme of experiments on buoyancy-opposed mixed convection using supercritical pressure CO<sub>2</sub>. In general, an enhancement of heat transfer relative to that for forced convection under corresponding conditions was reported.
 
Buyukalaca (1993) has produced a review of buoyancy-opposed flow for liquids such as water, oil, etc. He analysed the earlier data and his own experimental data using the semi-empirical ideas of Jackson and Hall (1979), and achieved an accurate correlation for buoyancy-opposed turbulent mixed convection flow in a vertical pipe.
 
Data for air under buoyancy-opposed flow conditions have been obtained by Eckert and Diaguila (1954), Khosla, Hoffman and Pollock (1974) and Axcell (1975). However, they all used tubes of short length to diameter ratio in their studies, and their data may be significantly complicated by entrance effects. Li (1994) has considered this flow, and his experiment does not suffer from the same complications as those of the earlier work.
 
Experiments for air flowing upwards in a heated vertical tube were made by Steiner (1971), Byrne and Ejiogu (1971), Carr, Connor and Buhr (1973), Perkins and McEligot (1975), Polyakov and Shindin (1986), Vilemas, Poskas and Kaupas (1992), Li (1994).
 
'''''2.1  ''''''''''Buoyancy Parameters'''''
 
This section discusses parameters that can be used to characterise the phenomena associated with vertical flows and heated tubes.
 
In a given mixed convection system, the Nusselt number is a function of Gr, Re, Pr, x/D and Tw/Tb. Although the general trend of heat transfer may be described by such a parameter, none of the available buoyancy parameters correlate the heat transfer data perfectly because of the complicated behaviour of developing turbulent mixed convection in the buoyancy aided condition. Jackson et al (1989) obtained the following equation


{| align="left"
In (3) Shehata and McEligot have provided new data on mean velocity profiles along with mean temperature profiles, wall temperature and axial pressure distributions in a carefully controlled experiment. These data have been compared in (1) to the computational results of a number of two equations turbulence models for turbulence kinetic energy and its dissipation rate <ε or the related quantity ω. The definition of this UFR makes an extensive use and summarizes these two recent publications.
| width="183" |
|-
|
|
[[Image:U3-07d32_files_image002.gif]]
|}


<br clear="ALL" />  <br clear="ALL" />
'''Non dimensional Parameters'''


The negative sign refers to the buoyancy-aided case and the positive to the buoyancy-opposed one. Gr<sup><nowiki>*</nowiki></sup> is the Grashof number based on wall heat flux, i.e.
The Reynolds number Re = G*D/μ and the non dimensional heating rate q<sup>+</sup><sub>in</sub> = q&prime;&prime;w/G*Cp<sub>in</sub>*T<sub>in</sub> evolve naturally from non-dimensionalizing the governing equations and boundary conditions in pipe flow with an imposed wall heat flux distribution (8).G is the mean mass flux (mass flow-rate divided by the cross sectional area) D is the tube diameter, μ the absolute viscosity q&prime;&prime; is the prescribed heat flux at the wall, , Cp the specific heat at constant temperature, T the absolute temperature.  


{| align="left"
The &ldquo;in&rdquo; index means that the value is related to the inlet.
| width="270" |
The &ldquo;w&rdquo; index means that the value is related to the wall. The experimental data reported in (3) are available for the following set of parameters: Low Reynolds numbers (4260 and 6080), moderate, high and intense heating rates (q<sup>+</sup><sub>in</sub> = 0.0018, 0.0035, 0.0045) yielding flows ranging from turbulent to laminarized
|-
|
|
[[Image:U3-07d32_files_image004.gif]]
|}


<br clear="ALL" />  <br clear="ALL" />
'''Computational Studies of Mixed Convection in circular tubes with intense heating'''


In Yu (1991) and Li (1994), the buoyancy parameter B<sub>0</sub> is introduced:
The various two equations models used in the study reported in (1) are of the Low Reynolds number (k, ε) type, they differ in respect of the coefficients of the diffusive terms and also in respect of additional source terms which are introduced in some of them to account for pressure diffusion of k and production of ε.


{| align="left"
These models are detailed in the references cited hereunder:JL: Low Reynolds number (k, ε) turbulence model proposed by Jones and Launder(10)LS: Low Reynolds number (k, ε) turbulence model proposed by Launder and Sharma (11)CH: Low Reynolds number (k, v) turbulence model proposed by Chien (12)LB: Low Reynolds number (k, ε) turbulence model proposed by Lam and Bremhorst (13)MRS: Low Reynolds number (k, ε) turbulence model proposed by Michelassi et al. (14)SH: Low Reynolds number (k, ε) turbulence model proposed by Shi and Hsu (15)TAS: Low Reynolds number (k, τ) turbulence model proposed by Thangan et al (16)
| width="231" |
|-
|
|
[[Image:U3-07d32_files_image006.gif]]
|}


<br clear="ALL" />  <br clear="ALL" />
'''Choice of UFR'''


'''''2.2  ''''''''''Computational Studies of Turbulent Mixed Convection in a Vertical Tube'''''
Three experiments described Shin-ichi Satake, Tomoaki Kunugi, Mohsen Shehata and D.M.McEligot in (3) are chosen as a test case. They are called runs 445, 635 and 618. Run 445 is for Re= 4260 ,
q<sup>+</sup><sub>in</sub> = 0.0045Run 635 is for Re= 6080 , q<sup>+</sup><sub>in</sub> = 0.0035 Run 618 is for Re= 6080 , q<sup>+</sup><sub>in</sub> = 0.0018


Various types of turbulence closures have been used, including (a) prescribed eddy viscosity models, (b) algebraic turbulent viscosity models, (c) one and (d) two equation transport models and (e) stress transport models. Both high and low Reynolds number forms of the k-ε model have been tried. When the high Reynolds number model has been used wall functions have been employed. The simpler models (a)-(c) do not provide satisfactory predictions. The standard k-ε model with traditional wall functions offer an improvement but there are significant discrepancies. Generally, the enhancement or reduction in heat transfer is under-estimated.
These runs are used because they cover a wide range of heating rates and the Reynolds number is representative of the Reynolds number used in real power generation units. The flow conditions at the entrance of the heated section are fully established as it comes after a long enough adiabatic section. The wall heat flux distribution is given with a claimed accuracy of 3%.
 
Cotton and Jackson (1987) carried out a study of turbulent mixed convection in vertical tubes using the low Reynolds number k-ε model of Launder and Sharma (1974). This model reproduced to good accuracy both the experimental heat transfer and field profiles for the air data of Carr, Connor and Buhr (1983). Li (1994) found a similar result for his experiments of upward and downward air flow in a heated tube.
 
'''''2.3  ''''''''''Choice of UFR'''''
 
The experiments described by Li (1994) are chosen as a test case. He undertook experiments of upward and downward air flow in a heated tube for various values of the Reynolds number and buoyancy parameter. This case has been chosen because (a) the tests were constructed to learn the lessons of previous experiments; for example, the test section is long enough to remove flow development effects, and (b) because it was a well constructed test.


<font size="-2" color="#888888">© copyright ERCOFTAC 2004</font><br />
<font size="-2" color="#888888">© copyright ERCOFTAC 2004</font><br />
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Contributors: Mike Rabbitt - British Energy
Contributors: André Latrobe - CEA / DRN / Department de Thermohydraulique
 


{{UFR|front=UFR 3-07|description=UFR 3-07 Description|references=UFR 3-07 References|testcase=UFR 3-07 Test Case|evaluation=UFR 3-07 Evaluation|qualityreview=UFR 3-07 Quality Review|bestpractice=UFR 3-07 Best Practice Advice|relatedACs=UFR 3-07 Related ACs}}


[[Category:Underlying Flow Regime]]
{{UFR|front=UFR 3-06|description=UFR 3-06 Description|references=UFR 3-06 References|testcase=UFR 3-06 Test Case|evaluation=UFR 3-06 Evaluation|qualityreview=UFR 3-06 Quality Review|bestpractice=UFR 3-06 Best Practice Advice|relatedACs=UFR 3-06 Related ACs}}

Latest revision as of 12:51, 12 February 2017

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References




Natural and mixed convection boundary layers on vertical heated walls (A)

Underlying Flow Regime 3-06               © copyright ERCOFTAC 2004

Description

Introduction

The flow under consideration is a low mach number flow of a strongly heated gas inside a vertical circular tube. The experimental work of A.M.Shehata and D.M.McEligot (3) which is used to define this UFR supplements and extends earlier data for internal flows in small tubes (D<13mm) with temperature dependent transport properties that could only provide integralparameters.

These recent data are used to assess turbulence models by comparing measures and computed distributions of the mean streamwise velocity and temperature in this well defined experiment involving strong influence on the initial turbulent field, of the variation of the gas transport properties and the thickening of the viscous layer (the so called laminarization effect) which are caused by intense heating at the wall. Intense heating is defined here by a ratio wall to bulk absolute temperatures greater than 2.5.

This UFR is of particular relevance for the design of gas cooled nuclear reactors and the use of a gas as a coolant in power generation systems.

Review of UFR studies and choice of test case

A variety of basic studies has been conducted examining turbulence structure in simple boundary layers with constant properties and uniform wall temperatures. A strong heating atthe wall induced by a nearly constant high heat flux boundary condition involves significant transport property variation and buoyancy effects and makes necessary to further assess the predictive capabilities of turbulence models in that situation. Experiments for air flowing upwards in small heated vertical tubes with temperature dependent transport properties were made by Humble, Lowdermilk and Desmon (4), Jackson (5), McEligot, Magee and Leppert (6), Perkins and Worsoe-Schmidt (7) and others. These studies were lacking of internal profile measurements for temperature and velocities but they provided some average data to make preliminary tests of turbulence models accounting for temperature-dependent transport properties and the influence of intense heating on turbulent flows in tubes.

In (3) Shehata and McEligot have provided new data on mean velocity profiles along with mean temperature profiles, wall temperature and axial pressure distributions in a carefully controlled experiment. These data have been compared in (1) to the computational results of a number of two equations turbulence models for turbulence kinetic energy and its dissipation rate <ε or the related quantity ω. The definition of this UFR makes an extensive use and summarizes these two recent publications.

Non dimensional Parameters

The Reynolds number Re = G*D/μ and the non dimensional heating rate q+in = q′′w/G*Cpin*Tin evolve naturally from non-dimensionalizing the governing equations and boundary conditions in pipe flow with an imposed wall heat flux distribution (8).G is the mean mass flux (mass flow-rate divided by the cross sectional area) D is the tube diameter, μ the absolute viscosity q′′ is the prescribed heat flux at the wall, , Cp the specific heat at constant temperature, T the absolute temperature.

The “in” index means that the value is related to the inlet. The “w” index means that the value is related to the wall. The experimental data reported in (3) are available for the following set of parameters: Low Reynolds numbers (4260 and 6080), moderate, high and intense heating rates (q+in = 0.0018, 0.0035, 0.0045) yielding flows ranging from turbulent to laminarized

Computational Studies of Mixed Convection in circular tubes with intense heating

The various two equations models used in the study reported in (1) are of the Low Reynolds number (k, ε) type, they differ in respect of the coefficients of the diffusive terms and also in respect of additional source terms which are introduced in some of them to account for pressure diffusion of k and production of ε.

These models are detailed in the references cited hereunder:JL: Low Reynolds number (k, ε) turbulence model proposed by Jones and Launder(10)LS: Low Reynolds number (k, ε) turbulence model proposed by Launder and Sharma (11)CH: Low Reynolds number (k, v) turbulence model proposed by Chien (12)LB: Low Reynolds number (k, ε) turbulence model proposed by Lam and Bremhorst (13)MRS: Low Reynolds number (k, ε) turbulence model proposed by Michelassi et al. (14)SH: Low Reynolds number (k, ε) turbulence model proposed by Shi and Hsu (15)TAS: Low Reynolds number (k, τ) turbulence model proposed by Thangan et al (16)

Choice of UFR

Three experiments described Shin-ichi Satake, Tomoaki Kunugi, Mohsen Shehata and D.M.McEligot in (3) are chosen as a test case. They are called runs 445, 635 and 618. Run 445 is for Re= 4260 , q+in = 0.0045Run 635 is for Re= 6080 , q+in = 0.0035 Run 618 is for Re= 6080 , q+in = 0.0018

These runs are used because they cover a wide range of heating rates and the Reynolds number is representative of the Reynolds number used in real power generation units. The flow conditions at the entrance of the heated section are fully established as it comes after a long enough adiabatic section. The wall heat flux distribution is given with a claimed accuracy of 3%.

© copyright ERCOFTAC 2004


Contributors: André Latrobe - CEA / DRN / Department de Thermohydraulique


Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

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