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= Best Practice Advice =
= Best Practice Advice =
{{Demo_UFR_BPA}}
== Key Physics ==
== Key Physics ==
{{Demo_UFR_BPA1}}
The  flow  in  the  present  three-dimensional  diffuser  configurations  is
== Numerical Modelling ==
extremely complex, despite a simple geometry: namely a "through flow"  in  a
{{Demo_UFR_BPA2}}
duct — with the cross-section of its "central  part"  exhibiting  a  certain
== Physical Modelling ==
expansion and having one clearly  defined  inlet  and  one  clearly  defined
{{Demo_UFR_BPA3}}
outlet. The basic  feature  of  the  flow  is  a  complex  three-dimensional
separation pattern being the consequence of  an  adverse  pressure  gradient
imposed on the flow through a duct expansion.  Two  diffuser  configurations
characterized by  slightly  different  expansion  geometry  but  leading  to
completely different recirculation zone  topology  have  been  investigated.
The differences are with respect to the separation  onset  and  reattachment
(form and position  of  the  3D  separation/reattachment  line)  —  multiple
corner separation and corner reattachment — as well as with  the  shape  and
size (length, thickness, fraction of the cross-sectional  area  occupied  by
separation) of the recirculation pattern. An important  prerequisite  for  a
successful reproduction of the separating flow  structure  in  the  diffuser
section  is  the  correct  capturing  of  the  flow  in  the  inlet  duct
characterized by intensive secondary currents — being  normal  to  the  main
flow direction — induced by the Reynolds stress anisotropy.
 
==Numerical Issues==
===Discretization===
It is well-known  that  the  accuracy  of  the  spatial  and
temporal discretization in the LES-framework  should  be  at  least  of  the
second-order. DNS results, which  we  regarded  here  more  as  a  reference
database, were obtained by applying a code with much higher accuracy  level.
All LES and LES-related  simulations  were  carried  out  with  second-order
accurate  discretization  schemes.  The  latter  simulations  imply  the
application of Hybrid LES/RANS models. These model  schemes  employ  a  RANS
model, consisting mostly of two additional (for k and  ε)  equations  (e.g.,
the TUD-HLR model). For the equations governing  such  turbulent  quantities
some upwinding can be  used  by  applying  the  so  called  "flux  blending"
technique without noticeable influence on the quality of the results.
 
===Grid resolution and grid quality===
It is interesting to note  that  virtually
the best agreement with the reference experimental database was obtained  by
applying a relatively coarse grid (1.6 and 2.0 Mio. grid cells in total  for
diffuser 1 and 2 respectively) whose cells were distributed  uniformly  over
the entire  solution  domain.  In  this  LES  simulation  performed  by  the
Karlsruhe group (ITS-LES-SM) the standard Smagorinsky model was  applied  in
conjunction with wall functions for wall treatment. There  was  no  specific
refinement in the region of separation and reattachment. This example  shows
that results of high quality (with respect to the time-averaged  quantities)
can be obtained on a moderate grid size  —  for  diffuser  2  there  was  no
significant difference to the wall-resolving LES with 42.0 Mio.  cells.  The
much finer resolutions applied by HSU-LES-DSM (up to 18 Mio. cells;  Dynamic
Smagorinsky model was used — DSM) and TUD-LES-DSM (the  geometry  was  meshed
with the grid consisting of up to 4 Mio. cells in total) resulted in a  very
similar outcome with no  noticeable  improvement  compared  to  the  ITS-LES
results. The reasons for that lie in the nature of the flow in  the  present
3D diffuser (see the discussion in
[[UFR_4-16_Best_Practice_Advice#Computational_domain_and_boundary_conditions|2.3]] and
[[UFR_4-16_Best_Practice_Advice#Physical_modelling|2.4]]).
 
==Computational domain and boundary conditions==
===Computational  domain===
The  computational  domain  follows  exactly  the
experimentally  investigated  configuration.  The  computational  domain
comprises a part of the inlet duct  (with  length  up  to  ''5h''),  the  entire
diffuser section (''15h'') and the straight outflow duct (''12.5h'';  the  outflow
boundary conditions are applied at the plane coinciding with the  transition
to the converging duct).  Some  computational  groups  located  the  outflow
plane "somewhere" in the converging duct, e.g. TUD-LES  adopted  a  solution
domain with the outlet positioned well within the converging duct at  length
''9h'' (let us recall that its length is ''10h'' before  transitioning  to  a  pipe;
see
[[UFR_4-16#figure1|Fig. 1]] in the [[UFR_4-16#Abstract|Abstract]] and [[UFR_4-16_Description#figure2|Fig. 2]]
in the [[UFR_4-16_Description#Description|Description]] section).
 
===Inlet===
All  computations  presented,  irrespective  of  the  model  applied,
started with the velocity and turbulence-quantity profiles corresponding  to
a fully-developed duct  flow.  The  latter  profiles  were  the  results  of
separate/precursor computations of the inflow duct of  a  certain  length  —
mostly ''5h'' in the  case  of  the  eddy-resolving  methods  —  using  periodic
inlet/outlet boundary conditions  and  the  same  model,  the  diffuser  was
consequently computed. It should be noted that  the  3D  streamwise-periodic
channel of length ''5h'' used for the inflow  generation  might  be  too  short,
keeping in mind the spatial extent of the  characteristic  eddy  structures,
which is in general larger  (due  to  the  secondary  currents)  than  in  a
(nominally 2D) channel flow  with  the  spanwise  homogeneity.  Furthermore,
Nikitin (2008)  argued  that  an  auxiliary  streamwise-periodic  simulation
might not be suitable since it causes a spatial periodicity,  which  is  not
physical for turbulent flows. Let us recall that the solution domain in  the
DNS of
[[UFR_4-16_References#24|Ohlsson ''et al.'' (2010)]]
comprises an inflow  development  duct  of  ''63h''
length, accounting even for the transition of the initially laminar  inflow.
The present simplification of the numerical setup is certainly adequate  for
the RANS computations but is also pertinent to the hybrid  LES/RANS  method,
since its overall aim is to  improve  the  efficiency  (lower  computational
costs) and applicability to complex geometries.  In  order  to  achieve  the
same basis for mutual comparison of the  presently  employed  LES  and  HLR,
both methods used the same inflow conditions,  i.e.  the  same  inflow  duct
length. In conclusion, the inflow originating from  a  separate  computation
of  fully-developed  duct  flow  by  using  periodic  inlet/outlet  boundary
conditions is regarded as satisfactory; this is especially valid keeping  in
mind that the focus of the present study  was  found  to  be  on  the
time-averaged flow field which was in reasonable  agreement  with  the  reference
databases.
 
===Wall===
No-slip  conditions  along  the  diffuser  walls  are  to  be  applied
"irrespective" of whether the governing equations are to  be  integrated  to
the  wall  itself  —  application  of  the  exact  boundary  conditions
corresponding to the viscous sublayer region — or some  "bridging"  by  wall
functions for "modelling" the near-wall region is used. The results  suggest
that the  near-wall  treatment  is  not  of  decisive  importance.  In  this
configuration the flow unsteadiness is introduced  into  the  wall  boundary
layers from the core flow in accordance with the  so-called  "top-to-bottom"
process. This fact justifies the use of the wall  functions  in  conjunction
with some models  allowing  a  coarser  grid  resolution  in  the  near-wall
regions. This was confirmed in conjunction with  the  high  Reynolds  number
Reynolds stress model (TUD-RSM) but also in the LES framework (ITS-LES-SM).
 
===Outlet===
Different groups positioned the outlet plane  differently;  however,
the outlet plane location was in all cases sufficiently far  away  from  the
"zone of interest",  i.e.  from  the  diffuser  section.  According  to  the
experimental and DNS reference database  the  separation  bubble  ends  well
within the first half of the straight outlet duct at about  ''6h''  (the  length
of this duct segment  is  ''12.5h'').  Some  groups  located  the  outlet  plane
approximately at the end of the outlet  duct  (applying  both  zero-gradient
and  convective-outflow  conditions)  and  some  of  them  well  within  the
converging duct. The ANSYS group extended the straight  outlet  part  up  to
''45h'' and  applied  zero-gradient  conditions  (RANS  computations  have  been
performed). Keeping in mind that in the focus of  the  evaluation  were  the
time-averaged mean flow and turbulence quantities one can conclude that  the
outlet plane location and  associated  outlet  boundary  conditions  do  not
represent a critical issue.
 
== Physical modelling ==
The advice given here follows mainly from the ERCOFTAC workshops, but it is
largely supported also by the results obtained in the ATAAC project.
 
The comparison with the experimental data demonstrated that '''DNS and LES'''  can
reproduce  the  separated  flow  in  the  3D-diffusers  and  the  geometric
sensitivity of the flow within experimental uncertainties. From an  analysis
of the data the following setup recommendations  for  LES  can  be  deduced:
There is no need to compute the long inlet channel, instead an  inflow  data
generator suffices. There is also no need to compute the  rear  contraction,
since an outflow with buffer zone worked  well.  Averaging  statistics  over
approximately 100 flow-through times (formed with U<sub>b</sub>  and  diffuser  length)
is recommended, although smaller flow-through times can also  lead  to  correct
results (see TUD contribution). For LES, the type of  SGS  model  and  near-
wall modeling / resolution seems less  important  than  resolving  the  free
shear layers and the largest  coherent  structures  in  the  center  of  the
diffuser. An economical Smagorinsky-type SGS-model in conjunction with wall-
functions and a simple equidistant grid can suffice to predict  the  complex
separated  flow  in  the  two  asymmetric  diffusers  (see  ITS  Karlsruhe
contribution).
 
A conclusion on the '''hybrid LES/RANS simulations''' is that the high  degree  of
geometric sensitivity found in the experiments can be well reproduced  on  a
rather coarse grid.  The  separation  regions  in  both  slightly  different
diffusers spread as expected which is not natural for RANS. An exception  is
the DES method which delivers poor results and thus  cannot  be  recommended
for such internal flows, but note that in the ATAAC project IDDES produced
fairly good results for diffuser 1.
Furthermore, the hybrid methods  generally  deliver
better agreement of the mean and r.m.s.  velocities  with  the  measurements
than several LES predictions even when the latter  were  carried  out  on  a
much finer grid. Consequently, Hybrid LES/RANS approaches in general  are  a
promising tool but still need further evaluation.
 
The linear '''eddy-viscosity RANS''' models show no sensitivity to changes in  the
geometry of the diffuser section, and generally poor performance.
The results obtained  for  both  diffusers
indicate almost identical  flow  topology.  The  reason  for  that  must  be
primarily sought in the models' incapability to  account  for  the  Reynolds
stress anisotropy governing the secondary currents in the inflow  duct.  The
results obtained  by  the  models  based  on  the  anisotropy-resolving
'''RSM concept''' (both differential and algebraic) offer a much  more  differentiated
picture of the flow field in  reasonable  agreement  with  the  experimental
data, but less so than LES and Hybrid methods as
deviations  still  exist.  This  is  a  consequence  of  the
incapability of RANS models in general (an unsteady  computation  brings  no
improvement) to account for any spectral dynamics associated with the  large
energetic eddies dominating the separated shear layers.
 
== Application Uncertainties ==
== Application Uncertainties ==
{{Demo_UFR_BPA4}}
The configuration considered is confined by rigid walls and  has  one  inlet
(with prescribed inflow) and one outlet  positioned  sufficiently  far  away
from the diffuser section (see discussion associated to the outlet  boundary
conditions,
[[UFR_4-16_Best_Practice_Advice#Outlet|Section 2.3.4]]);
at both  planes  there  is  an  entirely  positive
through flow characterized by a fairly uniform  velocity  profile  over  the
most of the cross-section. One can say that the present geometry  represents
a non-ambiguously defined flow  configuration.  Accordingly,  there  is  not
much room for any uncertainty with respect to the flow  geometry,  operating
and boundary conditions.
 
== Recommendations for Future Work ==
== Recommendations for Future Work ==
{{Demo_UFR_BPA5}}
The corner separation is a flow phenomenon of great  industrial  importance:
it is relevant to all junction-shaped geometries  in  general;  a  prominent
example is the junction between an aircraft wing and its fuselage.  However,
in such cases of practical relevance the Reynolds number  is  usually  large
while in the diffuser flows considered here the Reynolds  number  (Re=10000)
is fairly low, i.e. not really industrially relevant. The  case  originators
extended  their  investigation  up  to  a  Reynolds  number  of  30000;
unfortunately only the surface pressure development along  the  flat  bottom
wall was measured (
[[UFR_4-16_References#8|Cherry ''et&nbsp;al.'', 2009]]).
Hence, investigations at  a  higher,
more industrially-relevant Reynolds number (even up to a Million)  would  be
desirable.
<br/>
<br/>
----
----

Latest revision as of 14:40, 12 February 2017

Flow in a 3D diffuser

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

Confined flows

Underlying Flow Regime 4-16

Best Practice Advice

Key Physics

The flow in the present three-dimensional diffuser configurations is extremely complex, despite a simple geometry: namely a "through flow" in a duct — with the cross-section of its "central part" exhibiting a certain expansion and having one clearly defined inlet and one clearly defined outlet. The basic feature of the flow is a complex three-dimensional separation pattern being the consequence of an adverse pressure gradient imposed on the flow through a duct expansion. Two diffuser configurations characterized by slightly different expansion geometry but leading to completely different recirculation zone topology have been investigated. The differences are with respect to the separation onset and reattachment (form and position of the 3D separation/reattachment line) — multiple corner separation and corner reattachment — as well as with the shape and size (length, thickness, fraction of the cross-sectional area occupied by separation) of the recirculation pattern. An important prerequisite for a successful reproduction of the separating flow structure in the diffuser section is the correct capturing of the flow in the inlet duct characterized by intensive secondary currents — being normal to the main flow direction — induced by the Reynolds stress anisotropy.

Numerical Issues

Discretization

It is well-known that the accuracy of the spatial and temporal discretization in the LES-framework should be at least of the second-order. DNS results, which we regarded here more as a reference database, were obtained by applying a code with much higher accuracy level. All LES and LES-related simulations were carried out with second-order accurate discretization schemes. The latter simulations imply the application of Hybrid LES/RANS models. These model schemes employ a RANS model, consisting mostly of two additional (for k and ε) equations (e.g., the TUD-HLR model). For the equations governing such turbulent quantities some upwinding can be used by applying the so called "flux blending" technique without noticeable influence on the quality of the results.

Grid resolution and grid quality

It is interesting to note that virtually the best agreement with the reference experimental database was obtained by applying a relatively coarse grid (1.6 and 2.0 Mio. grid cells in total for diffuser 1 and 2 respectively) whose cells were distributed uniformly over the entire solution domain. In this LES simulation performed by the Karlsruhe group (ITS-LES-SM) the standard Smagorinsky model was applied in conjunction with wall functions for wall treatment. There was no specific refinement in the region of separation and reattachment. This example shows that results of high quality (with respect to the time-averaged quantities) can be obtained on a moderate grid size — for diffuser 2 there was no significant difference to the wall-resolving LES with 42.0 Mio. cells. The much finer resolutions applied by HSU-LES-DSM (up to 18 Mio. cells; Dynamic Smagorinsky model was used — DSM) and TUD-LES-DSM (the geometry was meshed with the grid consisting of up to 4 Mio. cells in total) resulted in a very similar outcome with no noticeable improvement compared to the ITS-LES results. The reasons for that lie in the nature of the flow in the present 3D diffuser (see the discussion in 2.3 and 2.4).

Computational domain and boundary conditions

Computational domain

The computational domain follows exactly the experimentally investigated configuration. The computational domain comprises a part of the inlet duct (with length up to 5h), the entire diffuser section (15h) and the straight outflow duct (12.5h; the outflow boundary conditions are applied at the plane coinciding with the transition to the converging duct). Some computational groups located the outflow plane "somewhere" in the converging duct, e.g. TUD-LES adopted a solution domain with the outlet positioned well within the converging duct at length 9h (let us recall that its length is 10h before transitioning to a pipe; see Fig. 1 in the Abstract and Fig. 2 in the Description section).

Inlet

All computations presented, irrespective of the model applied, started with the velocity and turbulence-quantity profiles corresponding to a fully-developed duct flow. The latter profiles were the results of separate/precursor computations of the inflow duct of a certain length — mostly 5h in the case of the eddy-resolving methods — using periodic inlet/outlet boundary conditions and the same model, the diffuser was consequently computed. It should be noted that the 3D streamwise-periodic channel of length 5h used for the inflow generation might be too short, keeping in mind the spatial extent of the characteristic eddy structures, which is in general larger (due to the secondary currents) than in a (nominally 2D) channel flow with the spanwise homogeneity. Furthermore, Nikitin (2008) argued that an auxiliary streamwise-periodic simulation might not be suitable since it causes a spatial periodicity, which is not physical for turbulent flows. Let us recall that the solution domain in the DNS of Ohlsson et al. (2010) comprises an inflow development duct of 63h length, accounting even for the transition of the initially laminar inflow. The present simplification of the numerical setup is certainly adequate for the RANS computations but is also pertinent to the hybrid LES/RANS method, since its overall aim is to improve the efficiency (lower computational costs) and applicability to complex geometries. In order to achieve the same basis for mutual comparison of the presently employed LES and HLR, both methods used the same inflow conditions, i.e. the same inflow duct length. In conclusion, the inflow originating from a separate computation of fully-developed duct flow by using periodic inlet/outlet boundary conditions is regarded as satisfactory; this is especially valid keeping in mind that the focus of the present study was found to be on the time-averaged flow field which was in reasonable agreement with the reference databases.

Wall

No-slip conditions along the diffuser walls are to be applied "irrespective" of whether the governing equations are to be integrated to the wall itself — application of the exact boundary conditions corresponding to the viscous sublayer region — or some "bridging" by wall functions for "modelling" the near-wall region is used. The results suggest that the near-wall treatment is not of decisive importance. In this configuration the flow unsteadiness is introduced into the wall boundary layers from the core flow in accordance with the so-called "top-to-bottom" process. This fact justifies the use of the wall functions in conjunction with some models allowing a coarser grid resolution in the near-wall regions. This was confirmed in conjunction with the high Reynolds number Reynolds stress model (TUD-RSM) but also in the LES framework (ITS-LES-SM).

Outlet

Different groups positioned the outlet plane differently; however, the outlet plane location was in all cases sufficiently far away from the "zone of interest", i.e. from the diffuser section. According to the experimental and DNS reference database the separation bubble ends well within the first half of the straight outlet duct at about 6h (the length of this duct segment is 12.5h). Some groups located the outlet plane approximately at the end of the outlet duct (applying both zero-gradient and convective-outflow conditions) and some of them well within the converging duct. The ANSYS group extended the straight outlet part up to 45h and applied zero-gradient conditions (RANS computations have been performed). Keeping in mind that in the focus of the evaluation were the time-averaged mean flow and turbulence quantities one can conclude that the outlet plane location and associated outlet boundary conditions do not represent a critical issue.

Physical modelling

The advice given here follows mainly from the ERCOFTAC workshops, but it is largely supported also by the results obtained in the ATAAC project.

The comparison with the experimental data demonstrated that DNS and LES can reproduce the separated flow in the 3D-diffusers and the geometric sensitivity of the flow within experimental uncertainties. From an analysis of the data the following setup recommendations for LES can be deduced: There is no need to compute the long inlet channel, instead an inflow data generator suffices. There is also no need to compute the rear contraction, since an outflow with buffer zone worked well. Averaging statistics over approximately 100 flow-through times (formed with Ub and diffuser length) is recommended, although smaller flow-through times can also lead to correct results (see TUD contribution). For LES, the type of SGS model and near- wall modeling / resolution seems less important than resolving the free shear layers and the largest coherent structures in the center of the diffuser. An economical Smagorinsky-type SGS-model in conjunction with wall- functions and a simple equidistant grid can suffice to predict the complex separated flow in the two asymmetric diffusers (see ITS Karlsruhe contribution).

A conclusion on the hybrid LES/RANS simulations is that the high degree of geometric sensitivity found in the experiments can be well reproduced on a rather coarse grid. The separation regions in both slightly different diffusers spread as expected which is not natural for RANS. An exception is the DES method which delivers poor results and thus cannot be recommended for such internal flows, but note that in the ATAAC project IDDES produced fairly good results for diffuser 1. Furthermore, the hybrid methods generally deliver better agreement of the mean and r.m.s. velocities with the measurements than several LES predictions even when the latter were carried out on a much finer grid. Consequently, Hybrid LES/RANS approaches in general are a promising tool but still need further evaluation.

The linear eddy-viscosity RANS models show no sensitivity to changes in the geometry of the diffuser section, and generally poor performance. The results obtained for both diffusers indicate almost identical flow topology. The reason for that must be primarily sought in the models' incapability to account for the Reynolds stress anisotropy governing the secondary currents in the inflow duct. The results obtained by the models based on the anisotropy-resolving RSM concept (both differential and algebraic) offer a much more differentiated picture of the flow field in reasonable agreement with the experimental data, but less so than LES and Hybrid methods as deviations still exist. This is a consequence of the incapability of RANS models in general (an unsteady computation brings no improvement) to account for any spectral dynamics associated with the large energetic eddies dominating the separated shear layers.

Application Uncertainties

The configuration considered is confined by rigid walls and has one inlet (with prescribed inflow) and one outlet positioned sufficiently far away from the diffuser section (see discussion associated to the outlet boundary conditions, Section 2.3.4); at both planes there is an entirely positive through flow characterized by a fairly uniform velocity profile over the most of the cross-section. One can say that the present geometry represents a non-ambiguously defined flow configuration. Accordingly, there is not much room for any uncertainty with respect to the flow geometry, operating and boundary conditions.

Recommendations for Future Work

The corner separation is a flow phenomenon of great industrial importance: it is relevant to all junction-shaped geometries in general; a prominent example is the junction between an aircraft wing and its fuselage. However, in such cases of practical relevance the Reynolds number is usually large while in the diffuser flows considered here the Reynolds number (Re=10000) is fairly low, i.e. not really industrially relevant. The case originators extended their investigation up to a Reynolds number of 30000; unfortunately only the surface pressure development along the flat bottom wall was measured ( Cherry et al., 2009). Hence, investigations at a higher, more industrially-relevant Reynolds number (even up to a Million) would be desirable.



Contributed by: Suad Jakirlić, Gisa John-Puthenveettil — Technische Universität Darmstadt

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References


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