UFR 4-16 Evaluation: Difference between revisions

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=Evaluation of the results=
=Evaluation of the results=
Both 3D diffuser configurations have served as test cases of  the  13th  and
Both 3D diffuser configurations have served as test cases of  the  13th  and
14th ERCOFTAC SIG15 Workshops on refined turbulence  modelling, Steiner  et
14th ERCOFTAC SIG15 Workshops on refined turbulence  modelling,
al. (2009) and Jakirlic et al.  (2010b). In  addition  to  different  RANS
[[UFR_4-16_References#30|Steiner  ''et al.'' (2009)]]
and [[UFR_4-16_References#15|Jakirlić ''et al.'' (2010b)]].
In  addition  to  different  RANS
models, the LES  and  LES-related  methods  (different  seamless  and  zonal
models, the LES  and  LES-related  methods  (different  seamless  and  zonal
hybrid LES/RANS - HLR models;  DES Detached  Eddy  Simulation)  were
hybrid LES/RANS – HLR – models;  DES – Detached  Eddy  Simulation)  were
comparatively  assessed  (visit  www.ercoftac.org;  under  SIG15);  the
comparatively  assessed  (visit  [http://www.ercoftac.org www.ercoftac.org];  under  SIG15);  the
comparative analysis of selected results is presented in the section "Cross-
comparative analysis of selected results is presented in the section
Comparison of CFD calculations with experimental  results"  of  the  present
[[UFR_4-16_Evaluation#Cross-comparison_of_CFD_calculations_with_experimental_results|"Cross-Comparison of CFD calculations with experimental  results"]] of  the  present
contribution.  Before  starting  with  the  latter,  some  key  physical
contribution.  Before  starting  with  the  latter,  some  key  physical
characteristics illustrated appropriately are discussed as follows.
characteristics illustrated appropriately are discussed as follows.
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===Developed ("equilibrium") flow in the inflow duct / secondary currents===
===Developed ("equilibrium") flow in the inflow duct / secondary currents===
Fig. 20 depicts the linear plot of the axial velocity component  across  the
[[UFR_4-16_Evaluation#figure20|Fig. 20]]
central  plane  (z/B=0.5)  of  the  inflow  duct  at  x/h=-2  obtained
depicts the linear plot of the axial velocity component  across  the
central  plane  (''z/B=0.5'')  of  the  inflow  duct  at  ''x/h= -2''   obtained
experimentally  indicating  a  symmetric  profile.  The  inflow  conditions
experimentally  indicating  a  symmetric  profile.  The  inflow  conditions
correspond clearly to  those  typical  for  a  fully-developed,  equilibrium
correspond clearly to  those  typical  for  a  fully-developed,  equilibrium
flow. This is provided by a long inflow duct  whose  length  corresponds  to
flow. This is provided by a long inflow duct  whose  length  corresponds  to
62.9 channel heights. Fig. 21 shows the semi-log plot of the axial  velocity
62.9 channel heights.
component across the central plane (z/B=0.5) of the inflow duct  at  x/h=-2.
[[UFR_4-16_Evaluation#figure21|Fig. 21]] shows the semi-log plot of the axial  velocity
component across the central plane (''z/B=0.5'') of the inflow duct  at  ''x/h= -2''.
The velocity profile shape obtained by DNS follows closely  the  logarithmic
The velocity profile shape obtained by DNS follows closely  the  logarithmic
law, despite a certain departure  from  it.  This  departure,  expressed  in
law, despite a certain departure  from  it.  This  departure,  expressed  in
terms of a slight underprediction  of  the  coefficient  B  in  the  log-law
terms of a slight underprediction  of  the  coefficient  B  in  the  log-law
([pic] with B=5.2), can also be regarded  as  a  consequence  of  the  back-
(''U<sup>+</sup>''=&nbsp;ln(''y<sup>+</sup>'')&nbsp;/&nbsp;''&kappa;''&nbsp;+&nbsp;''B'' with ''B=5.2''&nbsp;),
influence of the adverse pressure gradient evoked  by  the  flow  expansion.
can also be regarded  as  a  consequence  of  the  back-influence of the
The pressure coefficient evolution, displayed in Fig. 24, reveals a  related
adverse pressure gradient evoked  by  the  flow  expansion.
pressure increase already in the  inflow  duct  ([pic]).  The  LES  and  HLR
The pressure coefficient evolution, displayed in [[UFR_4-16_Evaluation#figure24|Fig. 24]], reveals a  related
results (Jakirlic et al., 2010a) exhibit a  certain  overprediction  of  the
pressure increase already in the  inflow  duct  (''x/h&nbsp;&le;&nbsp;0''&nbsp;).  The  LES  and  HLR
results ([[UFR_4-16_References#14|Jakirli&#x107; ''et&nbsp;al.'', 2010a]])
exhibit a  certain  overprediction  of  the
velocity in the logarithmic region. This seems to  indicate  that  the  grid
velocity in the logarithmic region. This seems to  indicate  that  the  grid
may not have  been  fine  enough.  On  the  other  hand,  the  corresponding
may not have  been  fine  enough.  On  the  other  hand,  the  corresponding
underprediction  of  the  friction  velocity  U?,  serving  here  for  the
underprediction  of  the  friction  velocity  ''U<sub>&tau;</sub>''&nbsp;,  serving  here  for  the
normalization -  [pic], contributed  also  to  such  an  outcome  (the
normalization&nbsp;&nbsp;''U<sup>+</sup>''&nbsp;=&nbsp;''U''&nbsp;/&nbsp;''U<sub>&tau;</sub>''&nbsp;,
quantitative information about the U? velocity can  be  extracted  from  the
contributed  also  to  such  an  outcome  (the
friction factor evolution, Fig. 14 in the chapter "Test case studied").
quantitative information about the ''U<sub>&tau;</sub>''&nbsp; velocity can  be  extracted  from  the
friction factor evolution, [[UFR_4-16_Test_Case#figure14|Fig. 14]] in the chapter "Test Case Study").




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rectangular cross-section is no longer unidirectional. It  is  characterized
rectangular cross-section is no longer unidirectional. It  is  characterized
by a secondary motion with velocity components perpendicular  to  the  axial
by a secondary motion with velocity components perpendicular  to  the  axial
direction, Fig. 22. This secondary flow transporting momentum into the  duct
direction, [[UFR_4-16_Evaluation#figure22|Fig. 22]].
This secondary flow transporting momentum into the  duct
corners is characterized by jets directed towards the duct  walls  bisecting
corners is characterized by jets directed towards the duct  walls  bisecting
each corner with associated  vortices  at  both  sides  of  each  jet.  This
each corner with associated  vortices  at  both  sides  of  each  jet.  This
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generally known, beyond the  reach  of  the  (linear)  eddy-viscosity  model
generally known, beyond the  reach  of  the  (linear)  eddy-viscosity  model
group in contrast  to  the  Reynolds  stress  model  schemes;  corresponding
group in contrast  to  the  Reynolds  stress  model  schemes;  corresponding
result of the latter model is depicted in Fig. 22c). Indeed,  the  Reynolds
result of the latter model is depicted in [[UFR_4-16_Evaluation#figure22|Fig.&nbsp;22c]]).
Indeed,  the  Reynolds
stress gradients cause the generation of forces which induce the  normal-to-
stress gradients cause the generation of forces which induce the  normal-to-
the-wall velocity components  in  the  secondary  flow  plane.  Accordingly,
the-wall velocity components  in  the  secondary  flow  plane.  Accordingly,
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important prerequisite for a successful computation  of  the  diffuser  flow
important prerequisite for a successful computation  of  the  diffuser  flow
(see the Section "Cross-Comparison of  CFD  calculations  with  experimental
(see the Section "Cross-Comparison of  CFD  calculations  with  experimental
results"). Fig. 22 displays the time-averaged velocity vectors in the cross-
results"). [[UFR_4-16_Evaluation#figure22|Fig.&nbsp;22]]
plane y-z located at x/h=-2 obtained experimentally and  computationally  by
displays the time-averaged velocity vectors in the cross-plane ''y&ndash;z''
located at ''x/h=&nbsp;-2'' obtained experimentally and  computationally  by
a zonal Hybrid LES/RANS (HLR) model and by the GL  RSM  model.  Despite  the
a zonal Hybrid LES/RANS (HLR) model and by the GL  RSM  model.  Despite  the
relatively low intensity of the secondary motion - the largest velocity  has
relatively low intensity of the secondary motion &mdash; the largest velocity  has
the magnitude of approximately <(1-2)% of the axial bulk velocity ([pic]-
the magnitude of approximately <(1-2)% of the axial bulk velocity
(&nbsp;''U<sub>bulk</sub>&nbsp;=&nbsp;1&nbsp;''m/s''&nbsp;&mdash;
its influence on the flow in the diffuser is significant.  Unlike  with  the
its influence on the flow in the diffuser is significant.  Unlike  with  the
"anisotropy-blind" k-? model (not shown here), the qualitative agreement  of
"anisotropy-blind" k-&epsilon; model (not shown here), the qualitative agreement  of
the HLR and RSM models achieved with respect to the secondary flow  topology
the HLR and RSM models achieved with respect to the secondary flow  topology
discussed above is obvious.
discussed above is obvious.
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area. The following figures should give the potential practitioners  insight
area. The following figures should give the potential practitioners  insight
into the  topology  and  magnitude  of  the  pressure  recovery  within  the
into the  topology  and  magnitude  of  the  pressure  recovery  within  the
diffuser  section. Fig. 24-upper  displays  the  non-dimensional  pressure
diffuser  section.
gradient p+=dp/dx / (?U3?) used  traditionally  to  characterize  the
[[UFR_4-16_Evaluation#figure24|Fig.&nbsp;24-upper]] displays  the  non-dimensional  pressure
gradient
''p<sup>+</sup>''&nbsp;=&nbsp;''v&nbsp;dp/dx''&nbsp;/&nbsp;(''&rho;U<sub>&tau;</sub><sup>3</sup>''&nbsp;)
used  traditionally  to  characterize  the
intensity of the pressure increase in a boundary layers  subjected  to  APG.
intensity of the pressure increase in a boundary layers  subjected  to  APG.
Accordingly, the displayed results enable a direct comparison with some  APG
Accordingly, the displayed results enable a direct comparison with some  APG
boundary layer experiments. E.g., the range of  p+  between  0.01-0.025  was
boundary layer experiments. E.g., the range of  ''p<sup>+</sup>'' between  0.01-0.025  was
documented in the Nagano et al. (1993) experiments, indicating a much  lower
documented in the [[UFR_4-16_References#21|Nagano ''et&nbsp;al.'' (1993)]] experiments, indicating a much  lower
level than in the present diffuser.  Although  the  results  presented  were
level than in the present diffuser.  Although  the  results  presented  were
extracted from the LES and Hybrid LES/RANS simulations their quality  is  of
extracted from the LES and Hybrid LES/RANS simulations their quality  is  of
a fairly high level,  keeping  in  mind  good  agreement  of  the  near-wall
a fairly high level,  keeping  in  mind  good  agreement  of  the  near-wall
velocity field (see the section "Cross-Comparison of CFD  calculations  with
velocity field (see the section "Cross-Comparison of CFD  calculations  with
experimental results"), skin-friction (Fig. 14 in  the  chapter "Test  case
experimental results"), skin-friction
studied")  and  surface  pressure (Fig. 24-lower)  development  with  the
([[UFR_4-16_Test_Case#figure14|Fig.&nbsp;14]] in  the  chapter
[[UFR_4-16_Test_Case#Test_Case_Study|"Test  Case Study"]])  and  surface  pressure
([[UFR_4-16_Evaluation#figure24|Fig.&nbsp;24-lower]])  development  with  the
reference experimental and DNS results.
reference experimental and DNS results.


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|[[Image:UFR4-16_figure24a.jpg|740px]]
|[[Image:UFR4-16_figure24a.jpg|740px]]
|-
|-
|[[Image:UFR4-16_figure24a.jpg|740px]]
|[[Image:UFR4-16_figure24b.jpg|740px]]
|-
|-
|'''Figure 24:'''  Development  of  the  dimensionless  pressure  gradient  p+  and surface pressure coefficient along the bottom flat wall of the  diffuser  1. The data are extracted from the HLR-simulation, [[UFR_4-16_References#14|Jakirli&#x107; ''et&nbsp;al.'' (2010a)]]
|'''Figure 24:'''  Development  of  the  dimensionless  pressure  gradient  p+  and surface pressure coefficient along the bottom flat wall of the  diffuser  1. The data are extracted from the HLR-simulation, [[UFR_4-16_References#14|Jakirli&#x107; ''et&nbsp;al.'' (2010a)]]
Line 150: Line 166:




Fig. 25 displays the semi-log profile  of  the  axial  velocity  across  the
[[UFR_4-16_Evaluation#figure25|Fig.&nbsp;25]] displays the semi-log profile  of  the  axial  velocity  across  the
recirculation zone (at x/h=10) indicating a behaviour,  typical  of  a  flow
recirculation zone (at ''x/h=10'') indicating a behaviour,  typical  of  a  flow
affected  by  an  adverse  pressure  gradient  - underprediction  of  the
affected  by  an  adverse  pressure  gradient  &mdash; underprediction  of  the
logarithmic law and strong enhancement of  the  turbulence  intensity  (note
logarithmic law and strong enhancement of  the  turbulence  intensity  (note
the modulation of Reynolds stress field towards weakening  of  the  Reynolds
the modulation of Reynolds stress field towards weakening  of  the  Reynolds
stress  anisotropy,  Fig. 17  in  the  Chapter   "Test   Case   Studied",
stress  anisotropy,  [[UFR_4-16_Test_Case#figure17|Fig.&nbsp;17]] in  the  Chapter
[[UFR_4-16_Test_Case#Test_Case_Study|"Test Case Study"]],
corresponding to a substantial  mean  flow  deformation  in  the  streamwise
corresponding to a substantial  mean  flow  deformation  in  the  streamwise
direction, Fig. 15).
direction, [[UFR_4-16_Test_Case#figure15|Fig.&nbsp;15]]).




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See Fig. 18 and associated discussions in Section "Test  Case Studied" for
See [[UFR_4-16_Test_Case#figure18|Fig.&nbsp;18]] and associated discussions in Section
[[UFR_4-16_Test_Case#Test_Case_Study|"Test  Case Study"]] for
the topology of the separated flow in both diffuser configurations.
the topology of the separated flow in both diffuser configurations.


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LES/RANS (including DES) frameworks is  based  to  a  large  extent  on  the
LES/RANS (including DES) frameworks is  based  to  a  large  extent  on  the
activity  conducted  within  the  two  previously-mentioned  ERCOFTAC-SIG15
activity  conducted  within  the  two  previously-mentioned  ERCOFTAC-SIG15
Workshops on  Refined  Turbulence  Modelling, Steiner  et al.  (2009)  and
Workshops on  Refined  Turbulence  Modelling,
Jakirlic et al. (2010b), see  "List  of  References".  A  large  amount  of
[[UFR_4-16_References#30|Steiner  ''et&nbsp;al.'' (2009)]] and
[[UFR_4-16_References#15|Jakirli&#x107; ''et&nbsp;al.'' (2010b)]],
see  [[UFR_4-16_References#References|"List  of  References"]].  A  large  amount  of
simulation results along with detailed comparison  with  the  experimentally
simulation results along with detailed comparison  with  the  experimentally
obtained  reference  data  has  been  assembled.  The  diversity  of  the
obtained  reference  data  has  been  assembled.  The  diversity  of  the
models/methods applied can be seen from Tables 1 and 2 (Section:  Test  Case
models/methods applied can be seen from
Studied). The  specification  of  the  models  used  as  well  as  further
[[UFR_4-16_Test_Case#table1|Table 1]] and [[UFR_4-16_Test_Case#table2|Table 2]]
(Section:  [[UFR_4-16_Test_Case#Test_Case_Study|Test  Case Study]]).
The  specification  of  the  models  used  as  well  as  further
computational  details  -  details  about  the  numerical  code  used,
computational  details  -  details  about  the  numerical  code  used,
discretization schemes/code accuracy, grid arrangement/resolution,  temporal
discretization schemes/code accuracy, grid arrangement/resolution,  temporal
resolution,  details  about  the  inflow  (also  about  fluctuating  inflow
resolution,  details  about  the  inflow  (also  about  fluctuating  inflow
generation where applicable) and outflow conditions, etc.  - are  given  in
generation where applicable) and outflow conditions, etc.  &mdash; are  given  in
the short summaries provided by  each  computational  group,  which  can  be
the short summaries provided by  each  computational  group,  which  can  be
downloaded (see the appropriate link to the "workshop proceedings" at the
downloaded (see the appropriate link to the
end of this file).
[[UFR_4-16_Evaluation#Available CFD results:_ERCOFTAC_SIG15_Workshop_Proceedings|"workshop proceedings" at the end of this section]]).


In this section, a short summary of some  specific  outcomes  and  the  most
In this section, a short summary of some  specific  outcomes  and  the  most
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Here, just a selection of the results obtained will be shown and  discussed.
Here, just a selection of the results obtained will be shown and  discussed.
At the end of the section links  are  given  to  the  files (the "workshop
At the end of the section links  are  given  to  the  files
proceedings") comprising among  others  the  detailed  descriptions  of  the
(the [[UFR_4-16_Evaluation#Available CFD results:_ERCOFTAC_SIG15_Workshop_Proceedings|"workshop proceedings"]])
comprising among  others  the  detailed  descriptions  of  the
numerical methods and turbulence models used by all participating groups  as
numerical methods and turbulence models used by all participating groups  as
well as the complete cross-comparisons of all  reference  and  computational
well as the complete cross-comparisons of all  reference  and  computational
results concerning the mean  velocity  and  turbulence  fields  at  vertical
results concerning the mean  velocity  and  turbulence  fields  at  vertical
planes  at  two  spanwise  positions  (z/B=1/2  and  z/B=7/8)  and  fifteen
planes  at  two  spanwise  positions  (''z/B=1/2'' and  ''z/B=7/8''&nbsp;)  and  fifteen
streamwise positions.
streamwise positions.


In the meantime a number of additional computational  studies  dealing  with
In the meantime a number of additional computational  studies  dealing  with
the flow in the present 3D  diffuser  configurations  have  been  published.
the flow in the present 3D  diffuser  configurations  have  been  published.
Brief information on these hs been given in the "Relevant Studies" Section.
Brief information on these has been given in the
"[[UFR_4-16_Description#Relevant_studies|Relevant Studies]]" Section.


===DNS and LES===
===DNS and LES===
Typical LES results for the two diffusers are shown in Fig. 26. The  iso-
Typical LES results for the two diffusers are shown in
contours of the zero mean streamwise velocity component are plotted and  the
[[UFR_4-16_Evaluation#figure26|Fig.&nbsp;26]].
The  iso-contours of the zero mean streamwise velocity component are plotted and  the
mean separation lines are highlighted by white dashed  lines.  Three  highly
mean separation lines are highlighted by white dashed  lines.  Three  highly
complex shaped regions of mean reverse flow can be discerned: SB1,  SB2  and
complex shaped regions of mean reverse flow can be discerned: SB1,  SB2  and
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SB1 is an artefact of the specific setup shown here, where the  rounded
SB1 is an artefact of the specific setup shown here, where the  rounded
corners at the inlet of the diffuser were replaced by sharp edges.  SB2  and
corners at the inlet of the diffuser were replaced by sharp edges.  SB2  and
SB3 match, within experimental uncertainties, the reference data  of Cherry
SB3 match, within experimental uncertainties, the reference data  of
et al. (2008) and, according to Ohlsson et al. (2010), are  even  closer  to
[[UFR_4-16_References#7|Cherry ''et&nbsp;al.'' (2008)]] and, according to
[[UFR_4-16_References#24|Ohlsson ''et&nbsp;al.'' (2010)]], are  even  closer  to
the DNS data than the experiments.
the DNS data than the experiments.


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For diffusers 1 and 2, there are nine and  four  LES  results,  respectively
For diffusers 1 and 2, there are nine and  four  LES  results,  respectively
(see Tables 1 and 2). These were obtained on various grids ranging from  1.1
(see [[UFR_4-16_Test_Case#table1|Table 1]] and
[[UFR_4-16_Test_Case#table2|Table 2]]).
These were obtained on various grids ranging from  1.1
to 42.9 million cells, by employing different SGS models,  wall  models  and
to 42.9 million cells, by employing different SGS models,  wall  models  and
numerical methods, and by varying the size of the computational  domain.  As
numerical methods, and by varying the size of the computational  domain.  As
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and SGS model, and resolution requirements.
and SGS model, and resolution requirements.


In Fig. 27, the  pressure  recovery  predictions  of  the  various  LES  for
In [[UFR_4-16_Evaluation#figure27|Fig.&nbsp;27]],
the  pressure  recovery  predictions  of  the  various  LES  for
diffuser 1 are compared with the experimental and DNS data. All but one  LES
diffuser 1 are compared with the experimental and DNS data. All but one  LES
performed well. A similar outcome  can  be  seen  in  the  mean  and  r.m.s.
performed well. A similar outcome  can  be  seen  in  the  mean  and  r.m.s.
velocity profiles, Figs. 30 and 31. The inadequate LES was performed on  the
velocity profiles, [[UFR_4-16_Evaluation#figure30|Figs.&nbsp;30]]
and [[UFR_4-16_Evaluation#figure31|31]]. The inadequate LES was performed on  the
coarsest grid that was designed for RANS calculations, i.e. most cells  were
coarsest grid that was designed for RANS calculations, i.e. most cells  were
placed near the walls. A more detailed analysis showed that, for LES, it  is
placed near the walls. A more detailed analysis showed that, for LES, it  is
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and, therefore, promote reattachment. Other factors, like  numerical  method
and, therefore, promote reattachment. Other factors, like  numerical  method
and SGS models, played a minor role. Even  the  near-wall  region  could  be
and SGS models, played a minor role. Even  the  near-wall  region  could  be
bridged by wall-function models  (see  also Schneider  et al.,  2010).  In
bridged by wall-function models  (see  also
[[UFR_4-16_References#25|Schneider  ''et&nbsp;al.'',  2010]]).  In
addition, it was verified that the precursor simulation of a  periodic  duct
addition, it was verified that the precursor simulation of a  periodic  duct
flow can produce accurate unsteady inlet data, hence leading to  substantial
flow can produce accurate unsteady inlet data, hence leading to  substantial
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for the DNS). Also an outflow boundary with a buffer  layer  placed  in  the
for the DNS). Also an outflow boundary with a buffer  layer  placed  in  the
straight part of the outlet duct turned out to  be  sufficient  compared  to
straight part of the outlet duct turned out to  be  sufficient  compared  to
computing also the outlet contraction far downstream (see Figs. 3 and 4  in
computing also the outlet contraction far downstream (see
the section "Test case studied").
[[UFR_4-16_Test_Case#figure3|Fig.&nbsp;3]] and
[[UFR_4-16_Test_Case#figure4|Fig.&nbsp;4]] in
the section [[UFR_4-16_Test_Case#Test_Case_Study|"Test Case Study"]]).




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In Fig. 28,  mean  streamwise  velocity  contours  at  five  cross-sections
<div id="172million"></div>
(x/h=2, 5, 8, 12 and 15) of diffuser 1 are  shown  using  the  same  contour
In [[UFR_4-16_Evaluation#figure28|Fig.&nbsp;28]],  mean  streamwise  velocity  contours  at  five  cross-sections
(''x/h=2, 5, 8, 12'' and ''15''&nbsp;) of diffuser 1 are  shown  using  the  same  contour
levels for the experimental reference data and three selected LES.  Overall,
levels for the experimental reference data and three selected LES.  Overall,
the agreement is fairly good and all three LES deliver  results  of  similar
the agreement is fairly good and all three LES deliver  results  of  similar
quality if  compared  to  the  DNS  (see Fig. 13  in  Section "Test case
quality if  compared  to  the  DNS  (see
studied"). While the DNS uses 172 million cells and  a  high-order  accurate
[[UFR_4-16_Test_Case#figure13|Fig.&nbsp;13]] in  Section
[[UFR_4-16_Test_Case#Test_Case_Study|"Test Case Study"]]).
While the DNS uses 172 million cells and  a  high-order  accurate
flow solver, HSU LES DSM and TUD LES DSM use both sophisticated  SGS  models
flow solver, HSU LES DSM and TUD LES DSM use both sophisticated  SGS  models
(dynamic version of the Smagorinsky model)  and  wall-resolving  grids  with
(dynamic version of the Smagorinsky model)  and  wall-resolving  grids  with
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grid in conjunction with an adaptive wall-function. To  discern  differences
grid in conjunction with an adaptive wall-function. To  discern  differences
more clearly, the zero  velocity  line  is  marked  by  a  thicker  line  to
more clearly, the zero  velocity  line  is  marked  by  a  thicker  line  to
highlight the reverse flow region. In the LES results for x/h=12, a bump  in
highlight the reverse flow region. In the LES results for ''x/h=12'', a bump  in
this line can be seen, whereas the experimental data suggests  a  horizontal
this line can be seen, whereas the experimental data suggests  a  horizontal
line. Therefore, at  first  glance,  this  bump  appears  to  be  unnatural.
line. Therefore, at  first  glance,  this  bump  appears  to  be  unnatural.
However, the DNS data reveal the same feature. Considering  the  uncertainty
However, the DNS data reveal the same feature. Considering  the  uncertainty
in determining the zero-velocity line, the  bump  may  possibly  be  present
in determining the zero-velocity line, the  bump  may  possibly  be  present
even in the experiments. Moreover, a recent study (Schneider et al.,  2011)
even in the experiments. Moreover, a recent study
([[UFR_4-16_References#26|Schneider ''et&nbsp;al.,'' 2011]])
demonstrates that the strength of secondary flow patterns in the inlet  duct
demonstrates that the strength of secondary flow patterns in the inlet  duct
has a strong impact on the existence of this  bump  and  how  pronounced  it
has a strong impact on the existence of this  bump  and  how  pronounced  it
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<div id="figure28"></div>
<div id="figure28"></div>
{|align="center" width="750"
{|align="center" width="750"
|[[Image:UFR4-16_figure28_scale.png|180px]]
|
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure28_scale.png|174px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure28_scale.png|174px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure28_scale.png|174px]]
|[[Image:UFR4-16_figure28_scale.png|174px]]
|-
|-
|[[Image:UFR4-16_figure28_1.jpg|180px]]
|[[Image:UFR4-16_figure33_xh2.png|25px]]
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|[[Image:UFR4-16_figure28_1.jpg|174px]]
|[[Image:UFR4-16_figure28_3.png|180px]]
|[[Image:UFR4-16_figure28_2.png|174px]]
|[[Image:UFR4-16_figure28_4.png|180px]]
|[[Image:UFR4-16_figure28_3.png|174px]]
|[[Image:UFR4-16_figure28_4.png|174px]]
|-
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|[[Image:UFR4-16_figure28_5.png|180px]]
|[[Image:UFR4-16_figure33_xh5.png|25px]]
|[[Image:UFR4-16_figure28_6.png|180px]]
|[[Image:UFR4-16_figure28_5.png|174px]]
|[[Image:UFR4-16_figure28_7.png|180px]]
|[[Image:UFR4-16_figure28_6.png|174px]]
|[[Image:UFR4-16_figure28_8.png|180px]]
|[[Image:UFR4-16_figure28_7.png|174px]]
|[[Image:UFR4-16_figure28_8.png|174px]]
|-
|-
|[[Image:UFR4-16_figure28_9.jpg|180px]]
|[[Image:UFR4-16_figure33_xh8.png|25px]]
|[[Image:UFR4-16_figure28_10.png|180px]]
|[[Image:UFR4-16_figure28_9.jpg|174px]]
|[[Image:UFR4-16_figure28_11.png|180px]]
|[[Image:UFR4-16_figure28_10.png|174px]]
|[[Image:UFR4-16_figure28_12.png|180px]]
|[[Image:UFR4-16_figure28_11.png|174px]]
|[[Image:UFR4-16_figure28_12.png|174px]]
|-
|-
|[[Image:UFR4-16_figure28_13.jpg|180px]]
|[[Image:UFR4-16_figure33_xh12.png|25px]]
|[[Image:UFR4-16_figure28_14.png|180px]]
|[[Image:UFR4-16_figure28_13.jpg|174px]]
|[[Image:UFR4-16_figure28_15.png|180px]]
|[[Image:UFR4-16_figure28_14.png|174px]]
|[[Image:UFR4-16_figure28_16.png|180px]]
|[[Image:UFR4-16_figure28_15.png|174px]]
|[[Image:UFR4-16_figure28_16.png|174px]]
|-
|-
|[[Image:UFR4-16_figure28_17.png|180px]]
|[[Image:UFR4-16_figure33_xh15.png|25px]]
|[[Image:UFR4-16_figure28_18.png|180px]]
|[[Image:UFR4-16_figure28_17.png|174px]]
|[[Image:UFR4-16_figure28_19.png|180px]]
|[[Image:UFR4-16_figure28_18.png|174px]]
|[[Image:UFR4-16_figure28_20.png|180px]]
|[[Image:UFR4-16_figure28_19.png|174px]]
|[[Image:UFR4-16_figure28_20.png|174px]]
|-
|-
!
!Experiment!!LES-TUD!!LES-HSU!!LES-UKA-ITS
!Experiment!!LES-TUD!!LES-HSU!!LES-UKA-ITS
|-
|-
|colspan="4"|'''Figure 28:''' Diffuser 1 &mdash; Mean streamwise velocity contours at  five  selected streamwise positions within diffuser section obtained by LES  (see  Fig. 13 in Section "Test case studied" for the DNS results)
|colspan="5"|'''Figure 28:''' Diffuser 1 &mdash; Mean streamwise velocity contours at  five  selected streamwise positions within diffuser section obtained by LES  (see  [[UFR_4-16_Test_Case#figure13|Fig.&nbsp;13]] in Section [[UFR_4-16_Test_Case#Test_Case_Study|"Test Case Study"]] for the DNS results)
|}
|}




Fig. 29 displays mean streamwise velocity  contours  at  five  cross-sections
[[UFR_4-16_Evaluation#figure29|Fig.&nbsp;29]]
(x/h=2, 5, 8, 12 and 15) of diffuser 2 illustrating the  LES  capability  to
displays mean streamwise velocity  contours  at  five  cross-sections
capture  the  influence  of  the  geometry  modifications  on  the  three-
(''x/h=2, 5, 8, 12'' and ''15''&nbsp;) of diffuser 2 illustrating the  LES  capability  to
dimensional separation pattern. The similarity between the  two  latter  LES
capture  the  influence  of  the  geometry  modifications  on  the  three-dimensional separation pattern.
The similarity between the  two  latter  LES
result  sets  obtained  by  UKA-ITS,  LES-NWM  (wall-modelled  using  wall
result  sets  obtained  by  UKA-ITS,  LES-NWM  (wall-modelled  using  wall
functions) and  LES-NWR  (wall-resolved),  is  obvious  despite  significant
functions) and  LES-NWR  (wall-resolved),  is  obvious  despite  significant
Line 389: Line 434:


An open issue is the asymmetry in the streamwise  velocity  profile  of  the
An open issue is the asymmetry in the streamwise  velocity  profile  of  the
diffuser inlet as found by the experiments (Fig. 20). This could neither  be
diffuser inlet as found by the experiments ([[UFR_4-16_Evaluation#figure20|Fig.&nbsp;20]]).
This could neither  be
reproduced by DNS with the complete inlet channel nor  by  LES  with  inflow
reproduced by DNS with the complete inlet channel nor  by  LES  with  inflow
data generators. The origin of this asymmetry remains unclear. In  addition,
data generators. The origin of this asymmetry remains unclear. In  addition,
Line 400: Line 446:




For diffuser 1, Figs. 30 and  31  compare  calculated  and  measured  mean
For diffuser 1, [[UFR_4-16_Evaluation#figure30|Figs.&nbsp;30]]
and  [[UFR_4-16_Evaluation#figure31|31]] compare  calculated  and  measured  mean
velocity and streamwise turbulence intensity profiles at  fourteen  selected
velocity and streamwise turbulence intensity profiles at  fourteen  selected
locations within the inflow duct, diffuser section and straight outlet  duct
locations within the inflow duct, diffuser section and straight outlet  duct
in two vertical  planes,  the  one  coinciding  with  the  central  spanwise
in two vertical  planes,  the  one  coinciding  with  the  central  spanwise
position z/B=1/2 and the second positioned  closer  to  the  deflected  side
position ''z/B=1/2'' and the second positioned  closer  to  the  deflected  side
wall at z/B=7/8. The overall agreement of the results  obtained  by  LES  by
wall at ''z/B=7/8''. The overall agreement of the results  obtained  by  LES  by
three groups (HSU, UKA-IST and TUD) with the experimental database  is  very
three groups (HSU, UKA-IST and TUD) with the experimental database  is  very
good. The most important differences are found in the  early  stage  of  the
good. The most important differences are found in the  early  stage  of  the
separation process at the upper  deflected  wall (Figs. 30-upper and 31-
separation process at the upper  deflected  wall  
upper) as well as in the core region  of  the  diffuser  section.  The  most
([[UFR_4-16_Evaluation#figure30|Figs.&nbsp;30-upper]]
and [[UFR_4-16_Evaluation#figure31|31-upper]])
as well as in the core region  of  the  diffuser  section.  The  most
consistent agreement was obtained by the  UKA-ITS  group  despite  a  fairly
consistent agreement was obtained by the  UKA-ITS  group  despite  a  fairly
moderate number of grid cells (only 1.6 Mio. in  total);  the  (significant)
moderate number of grid cells (only 1.6 Mio. in  total);  the  (significant)
differences in the grid resolution are given in Table 1 (Section "Test Case
differences in the grid resolution are given in
Studied"). The UKA-ITS group applied uniform grid cells distribution in  the
[[UFR_4-16_Test_Case#table1|Table&nbsp;1]] (Section "[[UFR_4-16_Test_Case#Test_Case_Study|Test Case Study]]").
y-direction using a wall function method for the wall treatment.  The  other
The UKA-ITS group applied uniform grid cells distribution in  the
''y''-direction using a wall function method for the wall treatment.  The  other
two LES-simulations  were  performed  using  a  much  finer  near-wall  grid
two LES-simulations  were  performed  using  a  much  finer  near-wall  grid
resolution (integration up to the wall has been  applied),  but  a  somewhat
resolution (integration up to the wall has been  applied),  but  a  somewhat
Line 431: Line 481:




mean separation lines are highlighted by white dashed linesThree highly
<div id="figure31"></div>
complex shaped regions of mean reverse flow can be discerned: SB1SB2 and
{|align="center" width="750" cellspacing="0"
SB3.
|[[Image:UFR4-16_figure31a.jpg|740px]]
SB1 is an artefact of the specific setup shown here, where the  rounded
|-
corners at the inlet of the diffuser were replaced by sharp edges. SB2 and
|[[Image:UFR4-16_figure31b.jpg|740px]]
SB3 match, within experimental uncertainties, the reference data of Cherry
|-
et al. (2008) and, according to Ohlsson et al. (2010), are  even closer to
|'''Figure 31:''' Diffuser 1 - Evolution of the  profiles  of  the  axial  velocity components and streamwise turbulence intensity in the vertical plane ''x-y''  at the spanwise locations ''z/B=7/8'' obtained by means of LES
the DNS data than the experiments.
|}
 
===Hybrid LES/RANS (HLR)===
These schemes, hybridizing the RANS and LES methods aimed at a reduction  of
spatial  and  temporal  resolution, have  recently  experienced  growing
popularity in the CFD community. Their goal is to combine the advantages of
both methods in order to provide a computational procedure that is  capable
of capturing the large-scale eddy structures with  a  broader  spectrum  and
the  bulk  flow unsteadiness  &mdash;  as  encountered  in  the  flows  involving
separation, but at affordable costs. Interested readers are referred  to  a
relevant review about hybrid LES/RANS methods  by
[[UFR_4-16_References#9|Fröhlich and von  Terzi (2008)]].
We mention here only their  general  classification  into  two  main
groups: the zonal, two-layer schemes &mdash; a RANS model resolving the  near-wall
region is linked at a distinct interface with the conventional LES  covering
the outer layer (flow core) &mdash; and the seamless  models,  where a RANS-like
model formulation, mimicking a sub-scale model, is  applied  in  the  entire
flow domain.
 
====Diffuser 1====
As can be seen from [[UFR_4-16_Test_Case#table1|Table&nbsp;1]],
four HLR results are available for diffuser 1.
Besides the classical DES method
([[UFR_4-16_References#28|Spalart ''et&nbsp;al.'', 1997]]) based  on  the  one-
equation turbulence model by Spalart-Allmaras (1994), TUD has carried out  a
simulation based on their hybrid method. It relies on the low-Re  k-&epsilon;  model
due to Launder and Sharma (1974) applied in the  near-wall  region  and  the
Smagorinsky model in the core flow. HSU applied  their  own  hybrid  concept
applying an anisotropy-resolving explicit algebraic  Reynolds  stress  model
in the near-wall region and a consistent one-equation SGS model in  the  LES
zone (Jaffrezic and Breuer, 2008;
[[UFR_4-16_References#3|Breuer, 2010]]). In both HLR, the  interface
between  LES  and (U)RANS  is  dynamically  determined  using  different
conditions. Finally, KU adopted a non-linear  eddy-viscosity  model  in  the
RANS region and the SGS model by Inagaki et al. (2005) in  the  LES  part.
Since HSU covered a computational domain of -5&nbsp;&le;&nbsp;''x/h''&nbsp;&le;&nbsp;37.5
the total number  of  grid
cells is a little bit higher than in the other cases.  Otherwise  the  grids
are comparable to each other.
 
[[UFR_4-16_Evaluation#figure32|Fig.&nbsp;32]]
gives a  first  impression  about  the predictive quality of  the
results  obtained  showing  the  distribution  of  the  surface  pressure
coefficient along the lower wall at the central plane.




<div id="figure26"></div>
<div id="figure32"></div>
{|align="center" width="750" cellspacing="10"
{|align="center" width="750"
|style="border: 1px solid black;"|[[Image:UFR4-16_figure26.png|740px]]
|[[Image:UFR4-16_figure32.png|740px]]
|-
|-
|'''Figure 26:''' Mean streamwise velocity  iso-contours  illustrating  the  three-dimensional mean separation  patterns  in  both  considered configurations, diffuser 1 (left) and diffuser  2  (right),  obtained  by  LES  (ITS).  From [[UFR_4-16_References#25|Schneider ''et&nbsp;al.'' (2010)]]
|'''Figure 32:''' HLR-results, pressure coefficient along the bottom flat wall of Diffuser 1
|}
|}




For diffusers 1 and 2, there are nine and four LES resultsrespectively
The results of TUD HLR and HSU HLR are found to be in  good  agreement  with
(see Tables 1 and 2). These were obtained on various grids ranging from 1.1
the experimental data as well as the DNS data, where the best coincidence
to 42.9 million cells, by employing different SGS modelswall models and
is observed for TUD HLR. Obviously, the pressure recovery  for  DES  is  too
numerical methods, and by varying the size of the computational domainAs
low. It should be  emphasized  that both  latter  hybrid  simulations  were
opposed to the DNS, for all LES, unsteady inlet data were generated using a
performed using the same grid resolution (see [[UFR_4-16_Test_Case#table1|Table&nbsp;1]]).
periodic duct setup as a precursor simulation. The various contributions
Bearing  in  mind
varied always in some aspects, but also had sufficient commonalities, such
that DES was developed for external aerodynamic flows, it is not  unexpected
that careful analysis allowed drawing conclusions on the  following
that it fails under the circumstances of an internal  separated  flow  at  a
aspects: inflow data generationplacement   of   inflow  and   outflow
fairly low bulk Reynolds number (improved  versions  of  the  DES  method  &mdash;
boundaries, relevance of the near-wall region, role of the numerical method
Delayed DES  and  Improved  Delayed  DES  &mdash;  were  not  applied  presently).
and SGS model, and resolution requirements.
Furthermore, the performance of KU HLR is similar to DES. Since  this  HLR
approach is overall similar to TUD HLR and HSU  HLRthis  non-satisfactory
outcome is difficult to explain.
 
[[UFR_4-16_Evaluation#figure33|Fig.&nbsp;33]]
depicts the  time-averaged  streamwise  velocity  contours  at  five
cross-sections. The bold line indicates zero-streamwise-velocity and thus
encloses the recirculation region. As visible  from  the  experimental  data
the recirculation starts at the upper-right corner, i.e. the corner between
the two diverging walls. At ''x/h=5'', the separation bubble remains in the
corner, both in the experiments and in the simulations by TUD  HLR  and  HSU
HLR. However, both predictions show  an  inaccurate pressure  distribution,
i.e. TUD DES and KU HLR deliver a completely separated flow region along
the entire upper wall. For DES the flow is even separated along the  side
wall.  At  the next cross-section (''x/h=8''&nbsp;)it  can  be  seen  that   the
recirculation region has started to spread across the top of the  diffuser.
Again, TUD DES and KU HLR predict enlarged separation  regions  compared  to
the experiment, whereas the  other  two  approaches  perform  well.  Further
downstream, at ''x/h=12'' and ''15'', a massive separation region  can  be  observed
covering  the entire  top  wall of the  diffuser.  Overall  an  excellent
agreement between the hybrid predictions  and the  measurements  is  found,
except for DES which yields a too small separation  region  (note  that  the
same grid was used for TUD-DES as for the TUD-HLR computations).


In Fig. 27, the  pressure  recovery  predictions  of  the  various  LES  for
diffuser 1 are compared with the experimental and DNS data. All but one  LES
performed well. A similar outcome  can  be  seen  in  the  mean  and  r.m.s.
velocity profiles, Figs. 30 and 31. The inadequate LES was performed on  the
coarsest grid that was designed for RANS calculations, i.e. most cells  were
placed near the walls. A more detailed analysis showed that, for LES, it  is
important to have sufficient resolution in the core area of  the  diffusers.
This resolution is needed to accurately  compute  the  production  of  large
coherent structures that exchange momentum and kinetic energy  in  the  flow
and, therefore, promote reattachment. Other factors, like  numerical  method
and SGS models, played a minor role. Even  the  near-wall  region  could  be
bridged by wall-function models  (see  also  Schneider  et  al.,  2010).  In
addition, it was verified that the precursor simulation of a  periodic  duct
flow can produce accurate unsteady inlet data, hence leading to  substantial
savings in grid points compared to computing the  complete  inlet  duct  (as
for the DNS). Also an outflow boundary with a buffer  layer  placed  in  the
straight part of the outlet duct turned out to  be  sufficient  compared  to
computing also the outlet contraction far downstream (see Figs. 3 and  4  in
the section "Test case studied").




<div id="figure27"></div>
<div id="figure33"></div>
{|align="center" width="750"
{|align="center" width="750"
|[[Image:UFR4-16_figure27.png|740px]]
|
|[[Image:UFR4-16_figure33_scale.png|135px]]
|[[Image:UFR4-16_figure33_scale.png|135px]]
|[[Image:UFR4-16_figure33_scale.png|135px]]
|[[Image:UFR4-16_figure33_scale.png|135px]]
|[[Image:UFR4-16_figure33_scale.png|135px]]
|-
|[[Image:UFR4-16_figure33_xh2.png|25px]]
|[[Image:UFR4-16_figure33_1.jpg|135px]]
|[[Image:UFR4-16_figure33_2.png|135px]]
|[[Image:UFR4-16_figure33_3.jpg|135px]]
|[[Image:UFR4-16_figure33_4.png|135px]]
|[[Image:UFR4-16_figure33_5.png|135px]]
|-
|[[Image:UFR4-16_figure33_xh5.png|25px]]
|[[Image:UFR4-16_figure33_6.jpg|135px]]
|[[Image:UFR4-16_figure33_7.png|135px]]
|[[Image:UFR4-16_figure33_8.jpg|135px]]
|[[Image:UFR4-16_figure33_9.png|135px]]
|[[Image:UFR4-16_figure33_10.png|135px]]
|-
|[[Image:UFR4-16_figure33_xh8.png|25px]]
|[[Image:UFR4-16_figure33_11.jpg|135px]]
|[[Image:UFR4-16_figure33_12.png|135px]]
|[[Image:UFR4-16_figure33_13.jpg|135px]]
|[[Image:UFR4-16_figure33_14.png|135px]]
|[[Image:UFR4-16_figure33_15.png|135px]]
|-
|[[Image:UFR4-16_figure33_xh12.png|25px]]
|[[Image:UFR4-16_figure33_16.jpg|135px]]
|[[Image:UFR4-16_figure33_17.png|135px]]
|[[Image:UFR4-16_figure33_18.jpg|135px]]
|[[Image:UFR4-16_figure33_19.png|135px]]
|[[Image:UFR4-16_figure33_20.png|135px]]
|-
|[[Image:UFR4-16_figure33_xh15.png|25px]]
|[[Image:UFR4-16_figure33_21.jpg|135px]]
|[[Image:UFR4-16_figure33_22.png|135px]]
|[[Image:UFR4-16_figure33_23.jpg|135px]]
|[[Image:UFR4-16_figure33_24.png|135px]]
|[[Image:UFR4-16_figure33_25.png|135px]]
|-
!
!Experiment!!HSU-HLR!!TUD-HLR!!KU-HLR!!TUD-DES
|-
|-
|'''Figure 27:''' Pressure coefficient along the bottom flat wall of Diffuser 1 obtained by experiment, DNS and various LES (streamwise distance  normalized by diffuser length)
|colspan="6"|'''Figure 33:''' HLR-results, contours of streamwise  velocity at cross-sections ''x/h = 2, 5, 8, 12'' and ''15'' of Diffuser 1
|}
|}




In Fig.  28,  mean  streamwise velocity  contours at  five cross-sections
Contours of the streamwise velocity fluctuations are depicted in [[UFR_4-16_Evaluation#figure34|Fig.&nbsp;34]]
(x/h=2, 5, 8, 12 and 15) of diffuser 1 are shown using  the  same  contour
for three cross-sections. As can be seen, both TUD HLR and HSU HLR deliver
levels for the experimental reference data and three selected LES. Overall,
a reasonable agreement with the measurements. The level and location of the
the agreement is fairly good and all three LES deliver results of similar
maxima are well captured. That is not the case for TUD DES and KU HLR which
quality if compared to the  DNS (see Fig13 in Section "Test case
strongly overpredict the level of the  r.m.s.  values.  Again,  both
studied"). While the DNS uses 172 million cells and a high-order  accurate
simulations show a large coincidenceFor a more detailed comparison,
flow solver, HSU LES DSM and TUD LES DSM use both sophisticated SGS models
profiles of the  mean and  r.m.s. velocities were extracted at various
(dynamic version of the Smagorinsky model) and wall-resolving grids with
locations in the flow field
17.6 million cells (HSU) and 4 million cells (TUD) and ITS LES  SM  employs
(see [[UFR_4-16_Evaluation#Available_CFD_results:_ERCOFTAC_SIG15_Workshop_Proceedings|workshop proceedings]]
even only 1.6 million cells, the Smagorinsky model and a simple  equidistant
at [http://www.ercoftac.org www.ercoftac.org], under SIG15).
grid in conjunction with an adaptive wall-function. To  discern  differences
They support the trends found in the  contour plots and are
more clearly, the zero velocity line is  marked by a  thicker  line  to
thus not reproduced here.
highlight the reverse flow region. In the LES results for x/h=12, a bump in
 
this line can be seen, whereas the experimental data suggests horizontal
The DES method used by TUD is the one of [[UFR_4-16_References#28|Spalart ''et&nbsp;al.''1997]]
line. Therefore, at first glance, this bump appears to be unnatural.
(denoted by DES97 in some references). The reasons for such a poor result could be an
However, the DNS data reveal the same feature. Considering the  uncertainty
inappropriate position of interface between the near-wall RANS region
in determining the zero-velocity line, the bump may possibly  be present
(covered by the Spalart-Allmaras one-equation model) and the  flow core
even in the experiments. Moreover, a recent study (Schneider et al., 2011)
simulated by LES depending solely on the numerical grid applied. In the DES-upgrades
demonstrates that the strength of secondary flow patterns in the inlet  duct
&mdash; Delayed DES and Improved Delayed DES &mdash; this issue is further
has a strong impact on the existence of this bump and how pronounced it
elaborated, [[UFR_4-16_References#29|Spalart (2009)]].
will be. Even a complete change in the location of the reverse flow region
As already emphasized, the grid used presently
can be attained, for cases where the sense of rotation of the secondary
is the same used also in TUD-HLR. No attempt to modify the grid for DES
flow was altered.
appropriately was undertaken.




<div id="figure28"></div>
<div id="figure34"></div>
{|align="center" width="750"
{|align="center" width="750"
|[[Image:UFR4-16_figure28_scale.png|180px]]
|colspan="6" align="center"|[[Image:UFR4-16_figure34_bar.png|500px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|-
|-
|[[Image:UFR4-16_figure28_1.jpg|180px]]
|
|[[Image:UFR4-16_figure28_2.png|180px]]
|[[Image:UFR4-16_figure34_scale.png|135px]]
|[[Image:UFR4-16_figure28_3.png|180px]]
|[[Image:UFR4-16_figure34_scale.png|135px]]
|[[Image:UFR4-16_figure28_4.png|180px]]
|[[Image:UFR4-16_figure34_scale.png|135px]]
|[[Image:UFR4-16_figure34_scale.png|135px]]
|[[Image:UFR4-16_figure34_scale.png|135px]]
|-
|-
|[[Image:UFR4-16_figure28_5.png|180px]]
|[[Image:UFR4-16_figure33_xh5.png|25px]]
|[[Image:UFR4-16_figure28_6.png|180px]]
|[[Image:UFR4-16_figure34_1.png|135px]]
|[[Image:UFR4-16_figure28_7.png|180px]]
|[[Image:UFR4-16_figure34_2.png|135px]]
|[[Image:UFR4-16_figure28_8.png|180px]]
|[[Image:UFR4-16_figure34_3.png|135px]]
|[[Image:UFR4-16_figure34_4.png|135px]]
|[[Image:UFR4-16_figure34_5.png|135px]]
|-
|-
|[[Image:UFR4-16_figure28_9.jpg|180px]]
|[[Image:UFR4-16_figure33_xh8.png|25px]]
|[[Image:UFR4-16_figure28_10.png|180px]]
|[[Image:UFR4-16_figure34_6.png|135px]]
|[[Image:UFR4-16_figure28_11.png|180px]]
|[[Image:UFR4-16_figure34_7.png|135px]]
|[[Image:UFR4-16_figure28_12.png|180px]]
|[[Image:UFR4-16_figure34_8.png|135px]]
|[[Image:UFR4-16_figure34_9.png|135px]]
|[[Image:UFR4-16_figure34_10.png|135px]]
|-
|-
|[[Image:UFR4-16_figure28_13.jpg|180px]]
|[[Image:UFR4-16_figure33_xh12.png|25px]]
|[[Image:UFR4-16_figure28_14.png|180px]]
|[[Image:UFR4-16_figure34_11.png|135px]]
|[[Image:UFR4-16_figure28_15.png|180px]]
|[[Image:UFR4-16_figure34_12.png|135px]]
|[[Image:UFR4-16_figure28_16.png|180px]]
|[[Image:UFR4-16_figure34_13.png|135px]]
|[[Image:UFR4-16_figure34_14.png|135px]]
|[[Image:UFR4-16_figure34_15.png|135px]]
|-
|-
|[[Image:UFR4-16_figure28_17.png|180px]]
!
|[[Image:UFR4-16_figure28_18.png|180px]]
!Experiment!!HSU-HLR!!TUD-HLR!!KU-HLR!!TUD-DES
|[[Image:UFR4-16_figure28_19.png|180px]]
|[[Image:UFR4-16_figure28_20.png|180px]]
|-
!Experiment!!LES-TUD!!LES-HSU!!LES-UKA-ITS
|-
|-
|colspan="4"|'''Figure 28:''' Diffuser 1 &mdash; Mean streamwise velocity contours at  five  selected streamwise positions within diffuser section obtained by LES  (see  Fig. 13 in Section "Test case studied" for the DNS results)
|colspan="6"|'''Figure 34:''' HLR-results, contours of streamwise rms velocity (''u<sub>rms</sub>/U<sub>b</sub>&nbsp;&times;&nbsp;100'') at cross-sections ''x/h = 5, 8'' and ''12'' of Diffuser 1
|}
|}




Fig. 29 displays mean streamwise velocity contours at five cross-sections
In conclusion, hybrid methods perform generally well for the separated  flow
(x/h=2, 5, 8, 12 and 15) of diffuser 2 illustrating the  LES capability to
in diffuser 1. DES was not expected to work well for such an  internal  flow
capture the influence  of the  geometry modifications on  the  three-
and thus fulfills the expectations. Nevertheless,  it remains unclear why
dimensional separation pattern. The similarity between the  two latter LES
the results of KU HLR strongly deviate from the other two hybrid approaches
result sets obtained by UKA-ITSLES-NWM (wall-modelled  using  wall
although, on first sight, the methods seem to be similar.
functions) and  LES-NWR (wall-resolved), is obvious despite significant
 
difference in grid size: 2 Mio. cells in total for wall-modelled LES and
 
42.9 Mio. cells in total for wall-resolved LES.
HLR calculations for diffuser 1 were also carried out in the ATAAC
project using two-layer, IDDES and SAS methods and are reported in
the documents for which links are given in
[[UFR_4-16_Test_Case#CFD_Methods|Test Case Studies&nbsp;&ndash;&nbsp;CFD Methods]].
 
====Diffuser 2====
For the diffuser 2 the same hybrid methods were applied as for diffuser 1,
except for DES (see [[UFR_4-16_Test_Case#table2|Table&nbsp;2]]).
Furthermore, the grids applied are comparable
to those used for diffuser 1. Since neither experimental  nor  DNS  data
are available for the pressure distribution, the discussion starts with the
contours of the time-averaged streamwise velocity at five  cross-sections
depicted in [[UFR_4-16_Evaluation#figure35|Fig.&nbsp;35]].
As expected based  on  the  experimental results, the
shape of the separation bubble in diffuser 2 differs fundamentally from the
recirculation zone found in diffuser 1. In contrast to diffuser 1where
the reverse-flow region spreads across the  top wall,  in  diffuser  2,  it
remains localized near the sharp corner and the side wall. This feature  is
correctly reproduced by all three hybrid simulations. Nevertheless, the
extensions of the recirculation regions differ. TUD HLR yields slightly  too
small zones compared to the measurements, whereas the zones predicted by
HSU HLR are slightly too large and KU HLR shows no unique trend.




<div id="figure29"></div>
<div id="figure35"></div>
{|align="center" width="750" border="0"
{|align="center" width="750" border="0"
|colspan="5" align="left"|'''Experiment'''
|colspan="5" align="left"|'''Experiment'''
|-
|-
|[[Image:UFR4-16_figure29_1.png|148px]]
|[[Image:UFR4-16_figure35_1.png|148px]]
|[[Image:UFR4-16_figure29_2.png|148px]]
|[[Image:UFR4-16_figure35_2.png|148px]]
|[[Image:UFR4-16_figure29_3.png|148px]]
|[[Image:UFR4-16_figure35_3.png|148px]]
|[[Image:UFR4-16_figure29_4.png|148px]]
|[[Image:UFR4-16_figure35_4.png|148px]]
|[[Image:UFR4-16_figure29_5.png|148px]]
|[[Image:UFR4-16_figure35_5.png|148px]]
|-
|-
|colspan="5" align="left"|'''LES-TUD'''
|colspan="5" align="left"|'''HSU-HLR'''
|-
|-
|[[Image:UFR4-16_figure29_6.png|148px]]
|[[Image:UFR4-16_figure35_6.png|148px]]
|[[Image:UFR4-16_figure29_7.png|148px]]
|[[Image:UFR4-16_figure35_7.png|148px]]
|[[Image:UFR4-16_figure29_8.png|148px]]
|[[Image:UFR4-16_figure35_8.png|148px]]
|[[Image:UFR4-16_figure29_9.png|148px]]
|[[Image:UFR4-16_figure35_9.png|148px]]
|[[Image:UFR4-16_figure29_10.png|148px]]
|[[Image:UFR4-16_figure35_10.png|148px]]
|-
|-
|colspan="5" align="left"|'''LES-NWM  UKA-IST'''
|colspan="5" align="left"|'''TUD-HLR'''
|-
|-
|[[Image:UFR4-16_figure29_11.png|148px]]
|[[Image:UFR4-16_figure35_11.png|148px]]
|[[Image:UFR4-16_figure29_12.png|148px]]
|[[Image:UFR4-16_figure35_12.png|148px]]
|[[Image:UFR4-16_figure29_13.png|148px]]
|[[Image:UFR4-16_figure35_13.png|148px]]
|[[Image:UFR4-16_figure29_14.png|148px]]
|[[Image:UFR4-16_figure35_14.png|148px]]
|[[Image:UFR4-16_figure29_15.png|148px]]
|[[Image:UFR4-16_figure35_15.png|148px]]
|-
|-
|colspan="5" align="left"|'''LES-NWR  UKA-IST'''
|colspan="5" align="left"|'''KU-HLR'''
|-
|-
|[[Image:UFR4-16_figure29_16.png|148px]]
|[[Image:UFR4-16_figure35_16.png|148px]]
|[[Image:UFR4-16_figure29_17.png|148px]]
|[[Image:UFR4-16_figure35_17.png|148px]]
|[[Image:UFR4-16_figure29_18.png|148px]]
|[[Image:UFR4-16_figure35_18.png|148px]]
|[[Image:UFR4-16_figure29_19.png|148px]]
|[[Image:UFR4-16_figure35_19.png|148px]]
|[[Image:UFR4-16_figure29_20.png|148px]]
|[[Image:UFR4-16_figure35_20.png|148px]]
|-
|-
!x/h=2!!x/h=5!!x/h=8!!x/h=12!!x/h=15  
!x/h=2!!x/h=5!!x/h=8!!x/h=12!!x/h=15  
|-
|-
|colspan="5"|'''Figure 29:''' Diffuser 2 &mdash; Mean streamwise velocity contours at  five  selected streamwise positions within diffuser section obtained by LES  (LES-NWM  &mdash; Wall-Modelled (wall functions) LES; LES-NWR &mdash; Wall-Resolving LES)
|colspan="5"|'''Figure 35:''' Figure 35: HLR-results, contours of streamwise  velocity at cross-sections ''x/h = 2, 5, 8, 12'' and ''15'' of diffuser 2
|}
|}




An open issue is the asymmetry in the streamwise velocity profile of  the
In comparison to diffuser 1, similar distributions of the rms values of  the
diffuser inlet as found by the experiments (Fig. 20). This could neither be
streamwise stress component (see cross-comparison in the
reproduced by DNS with the complete inlet channel nor by LES with inflow
[[UFR_4-16_Evaluation#Available_CFD_results:_ERCOFTAC_SIG15_Workshop_Proceedings|workshop proceedings]] at the end of this section)
data generators. The origin of this asymmetry remains unclear. In addition,
are found for  HSU  HLR and KU HLR.  In
DNS and LES data exhibit a higher velocity at the lower wall than
contrast, for TUD HLR a strong reduction of  the velocity  fluctuations  is
experiments. Otherwise, eddy-resolving strategies, like DNS and  LEScould
observed in the  streamwise  direction  which  is clearly visible in the
capture the separated flow in the 3d-diffusers  and   the   geometric
backmost cross-sections. The reason for this behavior is unclear, since  the
sensitivity of the flow sufficiently well, as long as the  secondary  motion
same method shows a different trend for diffuser 1Unfortunately,
in the inlet duct and the generation of the  large  coherent  structures  in
higher-order statistics were not measured  for this case and thus a final
the free shear layers inside the diffuser were resolved sufficiently.
evaluation is difficult.
 
===RANS===
Numerous RANS models were applied ranging from some standard eddy-viscosity
and full Reynolds stress models (e.g., standard  k-&epsilon;  model,  k-&omega;  SST, the
basic differential Reynolds stress model due to Gibson  and  Launder1978,
and a relevant quadratic version due to  Speziale  et  al., 1991) to some
explicit algebraic Reynolds stress model versions (EARSM) and linear/non-
linear, EVM and RSM models based on the Durbin's elliptic relaxation  method
(ERM, 1991), see [[UFR_4-16_Test_Case#table1|Table&nbsp;1]] and
[[UFR_4-16_Test_Case#table2|Table&nbsp;2]] for detailed specification.
RANS calculations were carried out in the ATAAC project with the
linear (isotropic) SST eddy-viscosity model and with
stress-anisotropy-resolving algebraic (EARMS) and differential
(EBRSM) models and are reported in the documents for which links are
given in [[UFR_4-16_Test_Case#CFD_Methods|Test Case Studies&nbsp;&ndash;&nbsp;CFD Methods]].


An important prerequisite for the  successful  computation  is  the  correct
capturing of the flow in the inflow duct  which  features  secondary  motion
characterized by jets directed towards  the  channel  walls  bisecting  each
corner and associated vortices at both sides  of  each  jet,  see
[[UFR_4-16_Evaluation#figure22|Fig.&nbsp;22]].
These secondary currents are induced  by  the  Reynolds  stress  anisotropy,
which is, as generally  known,  beyond  the  reach  of  the  (linear)
eddy-viscosity model group, in contrast to the  Reynolds  stress  model  schemes.
That the latter model groups yields a  qualitatively  correct  behaviour  is
shown in [[UFR_4-16_Evaluation#figure22|Fig.&nbsp;22c]].


For diffuser 1, Figs30 and 31 compare calculated and  measured  mean
[[UFR_4-16_Evaluation#figure36|Fig.&nbsp;36]]
velocity and streamwise turbulence intensity profiles at fourteen selected
shows the contour plots of the axial velocity component in two
locations within the inflow duct, diffuser section and straight outlet duct
characteristic streamwise cross-sectional areas of diffuser 1 obtained by a
in two vertical planes, the  one coinciding with the  central spanwise
selection of different RANS model versionsbeing  representative of all
position z/B=1/2 and the second positioned closer to the  deflected side
applied model formulations. Whereas the initial separation zone development
wall at z/B=7/8. The overall agreement of the results obtained by  LES by
(''x/h=5''&nbsp;) follows qualitatively the  reference results,  its  subsequent
three groups (HSU, UKA-IST and TUD) with the experimental database is very
evolution  exhibits  different  patterns depending on the  model concept
good. The most important differences are found in the early stage of the
applied. The k-&omega; SST model and the &zeta;-f model (a numerically robust version
separation process at the upper  deflected  wall (Figs30-upper and  31-
of Durbin's v2-f model proposed by Hanjalic ''et&nbsp;al.'',  2004; the separation
upper) as well as in the core region of the  diffuser section. The most
pattern obtained by both UoM versions of the v2-f model &mdash; Laurence  ''et&nbsp;al.'',
consistent agreement was obtained by the UKA-ITS group  despite a fairly
2004 &mdash; follows closely the  &zeta;-f  resultsresulted in  a flow separating
moderate number of grid cells (only 1.6 Mio. in  total); the  (significant)
completely at the deflected side wall contrary to the experimental findings
differences in the grid resolution are given in Table 1 (Section "Test Case
indicating the separation zone  along  the upper  deflected  wall.  Similar
Studied"). The UKA-ITS group applied uniform grid cells distribution in  the
results were obtained with all eddy-viscosity-based models listed in
y-direction using a wall function method for the wall treatment. The  other
[[UFR_4-16_Test_Case#table1|Table&nbsp;1]].
two LES-simulations were performed using a much finer near-wall  grid
Keeping in  mind the  inherent incapability of this model group  to
resolution (integration up to the wall has been applied), but somewhat
correctly represent the afore-mentioned secondary motion across the inflow
coarser grid in the core flow. The grid and  wall modelling issues  are
duct, this outcome represents no surprise. The RSM model group returned  the
discussed in the introductory part of this section.
flow topology in  much  better  agreement  with the  experimental  results.
Whereas the basic RSM model (denoted by GLRSM) resulted  in  a  separation
pattern occupying both upper corners (similar behaviour was documented in
the case of the ANSYS BSL-RSM model) the application of both EARSM model
versions (applied by ANSYS) and  the  Elliptic  Blending RSM (near-wall
differential model based on the ERM method; Manceau and  Hanjalic, 2002)
returned the 3D separation pattern occupying entirely the upper sloped wall
in good agreement with experiment.




<div id="figure30"></div>
<div id="figure36"></div>
{|align="center" width="750" cellspacing="0"
{|align="center" width="750"
|[[Image:UFR4-16_figure30a.jpg|740px]]
|
|
|colspan="2" align="center"|'''Experiment, x/h=5'''
|colspan="1" align="left"|'''Experiment, x/h=15'''
|-
|
|
|colspan="2" align="center"|[[Image:UFR4-16_figure36_1.jpg|135px]]
|colspan="1" align="left"|[[Image:UFR4-16_figure36_2.jpg|135px]]
|
|-
|[[Image:UFR4-16_figure33_xh5.png|25px]]
|[[Image:UFR4-16_figure36_3.png|135px]]
|[[Image:UFR4-16_figure36_4.png|135px]]
|[[Image:UFR4-16_figure36_5.png|135px]]
|[[Image:UFR4-16_figure36_6.png|135px]]
|[[Image:UFR4-16_figure36_7.png|135px]]
|-
|-
|[[Image:UFR4-16_figure30b.jpg|740px]]
|[[Image:UFR4-16_figure33_xh15.png|25px]]
|[[Image:UFR4-16_figure36_8.png|135px]]
|[[Image:UFR4-16_figure36_9.png|135px]]
|[[Image:UFR4-16_figure36_10.png|135px]]
|[[Image:UFR4-16_figure36_11.png|135px]]
|[[Image:UFR4-16_figure36_12.png|135px]]
|-
|-
|'''Figure 30:''' Diffuser 1 - Evolution of the  profiles  of  the  axial  velocity components and streamwise turbulence intensity in the vertical plane ''x-y''  at the central spanwise locations ''z/B=1/2'' obtained by means of LES
!
|}
!ANSYS SST!!IUS ZETA-F!!TUD-GLRSM!!UoM RIJEBM!!ANSYS-EARSM
 
 
mean separation lines are highlighted by white dashed  lines.  Three  highly
complex shaped regions of mean reverse flow can be discerned: SB1,  SB2  and
SB3.
SB1 is an artefact of the specific setup shown here, where the  rounded
corners at the inlet of the diffuser were replaced by sharp edges.  SB2  and
SB3 match, within experimental uncertainties, the reference data  of  Cherry
et al. (2008) and, according to Ohlsson et al. (2010), are  even  closer  to
the DNS data than the experiments.
 
 
<div id="figure26"></div>
{|align="center" width="750" cellspacing="10"
|style="border: 1px solid black;"|[[Image:UFR4-16_figure26.png|740px]]
|-
|-
|'''Figure 26:''' Mean streamwise velocity  iso-contours illustrating  the  three-dimensional mean separation  patterns  in  both  considered  configurations, diffuser 1 (left) and diffuser  2 (right), obtained by LES (ITS). From [[UFR_4-16_References#25|Schneider ''et&nbsp;al.'' (2010)]]
|colspan="6"|'''Figure 36:''' Iso-contours of the axial velocity field in the cross planes ''y-z'' at two selected streamwise locations within the Diffuser 1 section obtained by different RANS models (thick line denotes the zero-velocity linein comparison with experiments
|}
|}




For diffusers 1 and 2, there are nine and  four LES results, respectively
[[UFR_4-16_Evaluation#figure37a|Figs.&nbsp;37&nbsp;a)]] and [[UFR_4-16_Evaluation#figure37b|b)]]
(see Tables 1 and 2). These were obtained on various grids ranging from 1.1
illustrate the pressure coefficient development along
to 42.9 million cells, by employing different SGS models, wall models and
the lower  flat  wall.  The  poor  agreement  (underprediction  of  the
numerical methods, and by varying the size of the computational domain. As
''Cp''&nbsp;- magnitude in the diffuser section) obtained  by  the eddy-viscosity model
opposed to the DNS, for all LES, unsteady inlet data were generated using a
group in [[UFR_4-16_Evaluation#figure37a|Fig.&nbsp;37&nbsp;a)]]
periodic duct setup as a precursor simulationThe various contributions
(here only the predictions of application  of  the  ERM-based EVM models are depicted)
varied always in some aspects, but also had sufficient commonalitiessuch
is consistent with the  incorrect prediction
that a careful analysis allowed drawing conclusions on the  following
of the  velocity fieldApart  from  some  unexpectedly large departures
aspects: inflow data generation, placement   of   inflow   and  outflow
(pertinent especially to ANSYS-WJ model, which returned correctly the shape
boundaries, relevance of the near-wall region, role of the numerical method
of the separation region, and to the UoM-RIJSSG model, application of which
and SGS model, and resolution requirements.
led to similar results as  the TUD-GLRSM model; the absence of a wall
 
reflection term in the latter can be blamed for the  latter  deviation)  all
In Fig. 27, the pressure recovery predictions of  the various LES for
other  results  agree reasonably well with the   reference   data.   The
diffuser 1 are compared with the experimental and DNS data. All but one  LES
differences  between  the  results  pertain  partially  to  different  grid
performed well. A similar outcome can be seen in the mean and r.m.s.
resolutions. According to
velocity profiles, Figs. 30 and 31. The inadequate LES was performed on the
[[UFR_4-16_Test_Case#table1|Table&nbsp;1]]
coarsest grid that was designed for RANS calculations, i.e. most cells were
most RANS computations were performed
placed near the walls. A more detailed analysis showed that, for LES, it is
with grids comprising a comparable number of  grid cells (between 1.6-1.9
important to have sufficient resolution in the core area of  the  diffusers.
Miocells; exceptions are UoM and OPU contributions). However,  the
This resolution is needed to accurately compute the production  of large
solution  domains  adopted  were  of  different  lengths:  e.gthe  ANSYS
coherent structures that exchange momentum and kinetic energy in the  flow
colleagues adopted the straight outlet duct being almost ''30h'' long &mdash;  in all
and, therefore, promote reattachment. Other factors, like numerical method
other cases this length amounted up to ''10h''; accordingly  the  resolution in
and SGS models, played a minor role. Even the near-wall region could be
the diffuser section &mdash; despite the total number  of  the  grid cells being
bridged by wall-function models (see also Schneider et  al.,  2010). In
about 1.6 Mio. &mdash; was somewhat lower). The large departures obtained by two
addition, it was verified that the precursor simulation of a periodic duct
advanced models &mdash; Non-linear k-&epsilon; model and Two-Component Limit RSM model in
flow can produce accurate unsteady inlet data, hence leading to  substantial
conjunction with analytical wall functions,
savings in grid points compared to computing the complete inlet duct (as
[[UFR_4-16_Test_Case#table1|Table&nbsp;1]]
for the DNS). Also an outflow boundary with a buffer  layer  placed  in the
&mdash; applied by OPU/UniOs
straight part of the outlet duct turned out to be sufficient compared to
cannot be plausibly discussed here due to the extremely coarse grid
computing also the outlet contraction far downstream (see Figs. 3 and 4 in
containing only 0.2 Mio. cells. Unfortunately the contributors didn't make
the section "Test case studied").
an attempt to refine the grid  appropriately. The streamwise fluctuation
intensity field predicted by the RANS models will not be discussed hereIt
can only be said that the results obtained by the three RSM models (see iso-contours
of the  axial  velocity field displayed in
[[UFR_4-16_Evaluation#figure36|Fig.&nbsp;36]]) are in
qualitatively good agreement  with  the  experiment  indicating  intensified
turbulence  production  in  the regions  bordering  the  separation  zone
characterized by large velocity gradients.




<div id="figure27"></div>
<div id="figure37a"></div>
{|align="center" width="750"
{|align="center" width="750"
|[[Image:UFR4-16_figure27.png|740px]]
|[[Image:UFR4-16_figure37a.png|740px]]
|-
|-
|'''Figure 27:''' Pressure coefficient along the bottom flat  wall of Diffuser 1 obtained by experiment, DNS and various LES (streamwise distance  normalized by diffuser length)
|'''Figure 37a:''' Pressure coefficient evolution in diffuser 1  along the bottom flat wall obtained  by advanced eddy-viscosity model schemes:  elliptic-relaxation-method-based models and a non-linear model
|}
|}


In Fig.  28,  mean  streamwise  velocity  contours  at  five  cross-sections
(x/h=2, 5, 8, 12 and 15) of diffuser 1 are  shown  using  the  same  contour
levels for the experimental reference data and three selected LES.  Overall,
the agreement is fairly good and all three LES deliver  results  of  similar
quality if  compared  to  the  DNS  (see  Fig.  13  in  Section  "Test  case
studied"). While the DNS uses 172 million cells and  a  high-order  accurate
flow solver, HSU LES DSM and TUD LES DSM use both sophisticated  SGS  models
(dynamic version of the Smagorinsky model)  and  wall-resolving  grids  with
17.6 million cells (HSU) and 4 million cells (TUD) and ITS  LES  SM  employs
even only 1.6 million cells, the Smagorinsky model and a simple  equidistant
grid in conjunction with an adaptive wall-function. To  discern  differences
more clearly, the zero  velocity  line  is  marked  by  a  thicker  line  to
highlight the reverse flow region. In the LES results for x/h=12, a bump  in
this line can be seen, whereas the experimental data suggests  a  horizontal
line. Therefore, at  first  glance,  this  bump  appears  to  be  unnatural.
However, the DNS data reveal the same feature. Considering  the  uncertainty
in determining the zero-velocity line, the  bump  may  possibly  be  present
even in the experiments. Moreover, a recent study (Schneider et  al.,  2011)
demonstrates that the strength of secondary flow patterns in the inlet  duct
has a strong impact on the existence of this  bump  and  how  pronounced  it
will be. Even a complete change in the location of the reverse  flow  region
can be attained, for cases where the sense  of  rotation  of  the  secondary
flow was altered.




<div id="figure28"></div>
<div id="figure37b"></div>
{|align="center" width="750"
{|align="center" width="750"
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure37b.png|740px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|[[Image:UFR4-16_figure28_scale.png|180px]]
|-
|[[Image:UFR4-16_figure28_1.jpg|180px]]
|[[Image:UFR4-16_figure28_2.png|180px]]
|[[Image:UFR4-16_figure28_3.png|180px]]
|[[Image:UFR4-16_figure28_4.png|180px]]
|-
|[[Image:UFR4-16_figure28_5.png|180px]]
|[[Image:UFR4-16_figure28_6.png|180px]]
|[[Image:UFR4-16_figure28_7.png|180px]]
|[[Image:UFR4-16_figure28_8.png|180px]]
|-
|[[Image:UFR4-16_figure28_9.jpg|180px]]
|[[Image:UFR4-16_figure28_10.png|180px]]
|[[Image:UFR4-16_figure28_11.png|180px]]
|[[Image:UFR4-16_figure28_12.png|180px]]
|-
|[[Image:UFR4-16_figure28_13.jpg|180px]]
|[[Image:UFR4-16_figure28_14.png|180px]]
|[[Image:UFR4-16_figure28_15.png|180px]]
|[[Image:UFR4-16_figure28_16.png|180px]]
|-
|[[Image:UFR4-16_figure28_17.png|180px]]
|[[Image:UFR4-16_figure28_18.png|180px]]
|[[Image:UFR4-16_figure28_19.png|180px]]
|[[Image:UFR4-16_figure28_20.png|180px]]
|-
!Experiment!!LES-TUD!!LES-HSU!!LES-UKA-ITS
|-
|-
|colspan="4"|'''Figure 28:''' Diffuser 1 &mdash; Mean streamwise velocity contours at five selected streamwise positions within diffuser section obtained by LES  (see  Fig. 13 in Section "Test case studied" for the DNS results)
|'''Figure 37b:''' Pressure coefficient evolution in diffuser along  the bottom flat wall obtained by the Reynolds-stress model concept
|}
|}




Fig. 29 displays mean streamwise velocity  contours at five cross-sections
The velocity field characterizing the flow structure in the  diffuser  2  is
(x/h=2, 5, 8, 12 and 15) of diffuser 2 illustrating the  LES capability to
illustrated in [[UFR_4-16_Evaluation#figure38|Fig.&nbsp;38]]
capture the  influence of the  geometry modifications on   the   three-
by displaying the iso-contours of the axial  velocity
dimensional separation pattern. The similarity between the  two latter LES
field in the cross planes ''y-z'' at three selected streamwise locations. As
result  sets obtained  by  UKA-ITSLES-NWM (wall-modelled  using  wall
discussed previously (sections devoted  to  DNS/LES  and HLR  results) the
functions) and LES-NWR (wall-resolved), is obvious despite significant
separation zone here is completely situated at the deflected side wall.  The
difference in grid size: 2 Mio. cells in total for wall-modelled LES  and
application of most RANS models to  the  diffuser 1  configuration  has
42.9 Mio. cells in total for wall-resolved LES.
incorrectly resulted in a separation pattern pertinent to  diffuser  2 (see
[[UFR_4-16_Evaluation#figure36|Fig.&nbsp;36]]).
The  results  depicted  in  [[UFR_4-16_Evaluation#figure38|Fig.&nbsp;38]]
exhibiting,  at  least
qualitatively, the experimentally determined flow structure are therefore
"expected".  However, the  differences in the  shape  and size of   the
recirculation zone are obvious. The linear &zeta;-f model  (UniRo  contributions)
resulted in a by far too large recirculation zone leading to intensive  flow
acceleration in the through-flow portion,  i.e. positive-velocity region.
This result can be regarded as  representative  for all other  linear  EVM
models used. Important improvement was obtained  by  applying  a  non-linear
formulation of the &zeta;-f model.  The  recirculation  region  is  substantially
reduced to yield a much better quantitative agreement with the  experimental
findings. The separation bubble obtained by  selected  RSM  models  shows  a
shape that is closest to the experimental results, but there  are  important
differences concerning some details. All three RSM models resulted  in  the
separation region to be situated in the corners between two deflected walls
and between the sloped side wall and the lower flat wall,  contrary  to  the
experimental finding. However, these  tiny  separated  regions  are  of  low
backflow intensity, so that the quantitative agreement can  be  regarded  as
reasonable (this statement is valid also for the diffuser  1).  For  a  more
quantitative  comparison  the  readers  are referred  to  the
[[UFR_4-16_Evaluation#Available_CFD_results:_ERCOFTAC_SIG15_Workshop_Proceedings|"workshop proceedings"]].
 
It should also be  emphasized that  the  near-wall  treatment was not of
decisive  importance. In  this  configuration  the  flow  unsteadiness  was
introduced into the wall boundary layer from the  core  flow  in  accordance
with  the  so-called "top-to-bottom"  process  (communication  with  M.
Leschziner). This fact justified the use of wall  functions  in  conjunction
with some RANS models (it is also valid for some LES simulations, see  e.g.
ITS contribution) enabling  a  coarser  grid  resolution  in the  near-wall
regions.




<div id="figure29"></div>
<div id="figure38"></div>
{|align="center" width="750" border="0"
{|align="center" width="750"
|colspan="5" align="left"|'''Experiment'''
|
|colspan="2" align="center"|'''Experiment, x/h=5'''
|align="center"|'''Experiment, x/h=8'''
|colspan="2" align="center"|'''Experiment, x/h=15'''
|-
|-
|[[Image:UFR4-16_figure29_1.png|148px]]
|
|[[Image:UFR4-16_figure29_2.png|148px]]
|colspan="2" align="center"|[[Image:UFR4-16_figure38_1.png|135px]]
|[[Image:UFR4-16_figure29_3.png|148px]]
|[[Image:UFR4-16_figure38_2.png|140px]]
|[[Image:UFR4-16_figure29_4.png|148px]]
|colspan="2" align="center"|[[Image:UFR4-16_figure38_3.png|135px]]
|[[Image:UFR4-16_figure29_5.png|148px]]
|-
|-
|colspan="5" align="left"|'''LES-TUD'''
|[[Image:UFR4-16_figure33_xh5.png|25px]]
|[[Image:UFR4-16_figure38_4.png|135px]]
|[[Image:UFR4-16_figure38_5.png|135px]]
|[[Image:UFR4-16_figure38_6.png|135px]]
|[[Image:UFR4-16_figure38_7.png|135px]]
|[[Image:UFR4-16_figure38_8.png|135px]]
|-
|-
|[[Image:UFR4-16_figure29_6.png|148px]]
|[[Image:UFR4-16_figure33_xh8.png|25px]]
|[[Image:UFR4-16_figure29_7.png|148px]]
|[[Image:UFR4-16_figure38_9.png|135px]]
|[[Image:UFR4-16_figure29_8.png|148px]]
|[[Image:UFR4-16_figure38_10.png|135px]]
|[[Image:UFR4-16_figure29_9.png|148px]]
|[[Image:UFR4-16_figure38_11.png|135px]]
|[[Image:UFR4-16_figure29_10.png|148px]]
|[[Image:UFR4-16_figure38_12.png|135px]]
|[[Image:UFR4-16_figure38_13.png|135px]]
|-
|-
|colspan="5" align="left"|'''LES-NWM  UKA-IST'''
|[[Image:UFR4-16_figure33_xh15.png|25px]]
|[[Image:UFR4-16_figure38_14.png|135px]]
|[[Image:UFR4-16_figure38_15.png|135px]]
|[[Image:UFR4-16_figure38_16.png|135px]]
|[[Image:UFR4-16_figure38_17.png|135px]]
|[[Image:UFR4-16_figure38_18.png|135px]]
|-
|-
|[[Image:UFR4-16_figure29_11.png|148px]]
!
|[[Image:UFR4-16_figure29_12.png|148px]]
!UniRo-ZF!!UniRo ZF-NL!!TUD-GLRSM!!UoM RIJEBM!!ANSYS-EARSM
|[[Image:UFR4-16_figure29_13.png|148px]]
|[[Image:UFR4-16_figure29_14.png|148px]]
|[[Image:UFR4-16_figure29_15.png|148px]]
|-
|-
|colspan="5" align="left"|'''LES-NWR UKA-IST'''
|colspan="6"|'''Figure 38:''' Selection of RANS-results, contours  of  streamwise  velocity at cross-sections ''x/h = 5, 8'' and ''15'' of Diffuser 2 (the dark blue area in the ANSYS-EARSM computation represents the reverse flow region)
|-
|[[Image:UFR4-16_figure29_16.png|148px]]
|[[Image:UFR4-16_figure29_17.png|148px]]
|[[Image:UFR4-16_figure29_18.png|148px]]
|[[Image:UFR4-16_figure29_19.png|148px]]
|[[Image:UFR4-16_figure29_20.png|148px]]
|-
!x/h=2!!x/h=5!!x/h=8!!x/h=12!!x/h=15
|-
|colspan="5"|'''Figure 29:''' Diffuser 2 &mdash; Mean streamwise velocity contours at five selected streamwise positions within diffuser section  obtained  by  LES  (LES-NWM &mdash; Wall-Modelled (wall functions) LES; LES-NWR &mdash; Wall-Resolving LES)
|}
|}


===Available CFD results: ERCOFTAC SIG15 Workshop Proceedings===
The following documents are  freely  available  (see  also  www.ercoftac.org
under SIG15):


An open issue is the asymmetry in the streamwise velocity profile of  the
*Short summaries comprising the computational method descriptions used by participating computational groups from  the  13th Workshop (Technical University Graz, Austria, September, 2008) - [[Media:UFR4-16_13th-Workshop_summaries.pdf|13th-Workshop_summaries.pdf]]
diffuser inlet as found by the experiments (Fig. 20). This could neither  be
*Short summaries comprising the computational method descriptions used by participating computational groups from the 14th Workshop ("La Sapienza" University    of   Rome,    Italy,   September,   2009)    -    [[Media:UFR4-16_14th-Workshop_summaries.pdf|14th-Workshop_summaries.pdf]]
reproduced by DNS with the complete inlet channel nor  by  LES  with  inflow
*Diffuser 1: List of the participants and computational models applied - [[Media:UFR4-16_Diffuser1_contributers.pdf|Diffuser1_contributers.pdf]]
data generators. The origin of this asymmetry remains unclear. In  addition,
*Diffuser 1: cross-comparison of the results obtained by LES and  Hybrid LES/RANS methods - [[Media:UFR4-16_Diffuser1_LES-and-HLR.pdf|Diffuser1_LES-and-HLR.pdf]]
DNS and  LES  data  exhibit  a  higher  velocity  at  the  lower  wall  than
*Diffuser 1: cross-comparison of the results obtained by RANS method: Eddy-viscosity models (only linear model formulations) - [[Media:UFR4-16_Diffuser1_RANS-EVM.pdf|Diffuser1_RANS-EVM.pdf]]
experiments. Otherwise, eddy-resolving strategies, like DNS and  LES,  could
*Diffuser 1: cross-comparison of the results  obtained  by  RANS method: Eddy-viscosity models (formulations based on the  Elliptic-relaxation method) - [[Media:UFR4-16_Diffuser1_RANS-EVM-ERM.pdf|Diffuser1_RANS-EVM-ERM.pdf]]
capture  the  separated  flow  in  the  3d-diffusers  and  the  geometric
*Diffuser 1: cross-comparison of the results obtained by RANS method: Reynolds stress models - [[Media:UFR4-16_Diffuser1_RANS-RSM.pdf|Diffuser1_RANS-RSM.pdf]]
sensitivity of the flow sufficiently well, as long as the  secondary  motion
*Diffuser 2: List of the participants and computational models applied - [[Media:UFR4-16_Diffuser2_contributers.pdf|Diffuser2_contributers.pdf]]
in the inlet duct and the generation of the large  coherent  structures  in
*Diffuser 2: cross-comparison of the results obtained by LES and Hybrid LES/RANS methods - [[Media:UFR4-16_Diffuser2_LES-and-HLR.pdf|Diffuser2_LES-and-HLR.pdf]]
the free shear layers inside the diffuser were resolved sufficiently.
*Diffuser 2: cross-comparison of the results obtained by RANS method: Eddy-viscosity models - [[Media:UFR4-16_Diffuser2_RANS-EVM.pdf|Diffuser2_RANS-EVM.pdf]]
 
*Diffuser 2: cross-comparison of the results obtained by RANS method: Reynolds stress models - [[Media:UFR4-16_Diffuser2_RANS-RSM.pdf|Diffuser2_RANS-RSM.pdf]]
 
For diffuser 1, Figs.  30 and  31  compare  calculated  and measured  mean
velocity and streamwise turbulence intensity profiles at  fourteen  selected
locations within the inflow duct, diffuser section and straight outlet duct
in two vertical planes, the one  coinciding  with  the  central  spanwise
position z/B=1/2 and the second positioned  closer  to  the  deflected  side
wall at z/B=7/8. The overall agreement of the results  obtained  by  LES by
three groups (HSU, UKA-IST and TUD) with the experimental database is very
good. The most important differences are found in the  early  stage  of the
separation process at the upper deflected  wall  (Figs. 30-upper  and  31-
upper) as well as in the core region of the diffuser section. The  most
consistent agreement was obtained by the  UKA-ITS  group  despite  a  fairly
moderate number of grid cells (only 1.6 Mio. in  total);  the  (significant)
differences in the grid resolution are given in Table 1 (Section "Test Case
Studied"). The UKA-ITS group applied uniform grid cells distribution in  the
y-direction using a wall function method for the wall treatment. The  other
two LES-simulations were performed using a  much  finer  near-wall  grid
resolution (integration up to the wall has been applied), but a somewhat
coarser grid in the core flow. The  grid  and  wall  modelling  issues  are
discussed in the introductory part of this section.


<div id="figure30"></div>
{|align="center" width="750" cellspacing="0"
|[[Image:UFR4-16_figure30a.jpg|740px]]
|-
|[[Image:UFR4-16_figure30b.jpg|740px]]
|-
|'''Figure 30:''' Diffuser 1 - Evolution of the  profiles  of  the  axial  velocity components and streamwise turbulence intensity in the vertical plane ''x-y''  at the central spanwise locations ''z/B=1/2'' obtained by means of LES
|}
<div id="figure31"></div>
{|align="center" width="750" cellspacing="0"
|[[Image:UFR4-16_figure31a.jpg|740px]]
|-
|[[Image:UFR4-16_figure31b.jpg|740px]]
|-
|'''Figure 31:''' Diffuser 1 - Evolution of the  profiles  of  the  axial  velocity components and streamwise turbulence intensity in the vertical plane ''x-y''  at the spanwise locations ''z/B=7/8'' obtained by means of LES
|}
===Hybrid LES/RANS (HLR)===
These schemes, hybridizing the RANS and LES methods aimed at a reduction  of
spatial  and  temporal  resolution,  have  recently  experienced  growing
popularity in the CFD community. Their goal is to combine the advantages  of
both methods in order to provide a computational procedure that  is  capable
of capturing the large-scale eddy structures with  a  broader  spectrum  and
the  bulk  flow  unsteadiness  -  as  encountered  in  the  flows  involving
separation, but at affordable costs. Interested readers are  referred  to  a
relevant review about hybrid LES/RANS methods  by  Fröhlich  and  von  Terzi
(2008). We mention here only their  general  classification  into  two  main
groups: the zonal, two-layer schemes - a RANS model resolving the  near-wall
region is linked at a distinct interface with the conventional LES  covering
the outer layer (flow core) - and the seamless  models,  where  a  RANS-like
model formulation, mimicking a sub-scale model, is  applied  in  the  entire
flow domain.
Diffuser 1
As can be seen from Table 1, four HLR results are available for diffuser  1.
Besides the classical DES method (Spalart et al., 1997) based  on  the  one-
equation turbulence model by Spalart-Allmaras (1994), TUD has carried out  a
simulation based on their hybrid method. It relies on the low-Re  k-?  model
due to Launder and Sharma (1974) applied in the  near-wall  region  and  the
Smagorinsky model in the core flow. HSU applied  their  own  hybrid  concept
applying an anisotropy-resolving explicit algebraic  Reynolds  stress  model
in the near-wall region and a consistent one-equation SGS model in  the  LES
zone (Jaffrezic and Breuer, 2008; Breuer, 2010). In both HLR, the  interface
between  LES  and  (U)RANS  is  dynamically  determined  using  different
conditions. Finally, KU adopted a non-linear  eddy-viscosity  model  in  the
RANS region and the SGS model by Inagaki et al.  (2005)  in  the  LES  part.
Since HSU covered a computational domain of [pic] the total number  of  grid
cells is a little bit higher than in the other cases.  Otherwise  the  grids
are comparable to each other.
Fig. 32 gives a  first  impression  about  the  predictive  quality  of  the
results  obtained  showing  the  distribution  of  the  surface  pressure
coefficient along the lower wall at the central plane.





Latest revision as of 14:39, 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

Evaluation of the results

Both 3D diffuser configurations have served as test cases of the 13th and 14th ERCOFTAC SIG15 Workshops on refined turbulence modelling, Steiner et al. (2009) and Jakirlić et al. (2010b). In addition to different RANS models, the LES and LES-related methods (different seamless and zonal hybrid LES/RANS – HLR – models; DES – Detached Eddy Simulation) were comparatively assessed (visit www.ercoftac.org; under SIG15); the comparative analysis of selected results is presented in the section "Cross-Comparison of CFD calculations with experimental results" of the present contribution. Before starting with the latter, some key physical characteristics illustrated appropriately are discussed as follows.

Physical issues/characteristics of the flow in a 3D diffuser

Here an overview of the most important flow features posing a special challenge to the turbulence modeling is given. Their correct capturing is of decisive importance with respect to the quality of the final results. In order to illustrate these phenomena the experimental and DNS results are used along with some results obtained by LES, hybrid LES/RANS and RANS methods by the groups participating at the SIG15 workshop.

Developed ("equilibrium") flow in the inflow duct / secondary currents

Fig. 20 depicts the linear plot of the axial velocity component across the central plane (z/B=0.5) of the inflow duct at x/h= -2 obtained experimentally indicating a symmetric profile. The inflow conditions correspond clearly to those typical for a fully-developed, equilibrium flow. This is provided by a long inflow duct whose length corresponds to 62.9 channel heights. Fig. 21 shows the semi-log plot of the axial velocity component across the central plane (z/B=0.5) of the inflow duct at x/h= -2. The velocity profile shape obtained by DNS follows closely the logarithmic law, despite a certain departure from it. This departure, expressed in terms of a slight underprediction of the coefficient B in the log-law (U+= ln(y+) / κ + B with B=5.2 ), can also be regarded as a consequence of the back-influence of the adverse pressure gradient evoked by the flow expansion. The pressure coefficient evolution, displayed in Fig. 24, reveals a related pressure increase already in the inflow duct (x/h ≤ 0 ). The LES and HLR results (Jakirlić et al., 2010a) exhibit a certain overprediction of the velocity in the logarithmic region. This seems to indicate that the grid may not have been fine enough. On the other hand, the corresponding underprediction of the friction velocity Uτ , serving here for the normalization  U+ = U / Uτ , contributed also to such an outcome (the quantitative information about the Uτ  velocity can be extracted from the friction factor evolution, Fig. 14 in the chapter "Test Case Study").


UFR4-16 figure20.png
Figure 20: Axial velocity profile corresponding to the "fully-developed" flow in the inflow duct (x/h = -2). Courtesy of J. Eaton (Stanford University)


UFR4-16 figure21.jpg
Figure 21: Axial velocity profile in semi-log coordinates corresponding to the "fully-developed" flow in the inflow duct (x/h = -2). From Jakirlić et al. (2010a)


Unlike the flow through a circular pipe, the flow in a duct with rectangular cross-section is no longer unidirectional. It is characterized by a secondary motion with velocity components perpendicular to the axial direction, Fig. 22. This secondary flow transporting momentum into the duct corners is characterized by jets directed towards the duct walls bisecting each corner with associated vortices at both sides of each jet. This secondary current is Prandtl's flow of the second kind (possible only for turbulent flows) induced by the Reynolds stress anisotropy (which is, as generally known, beyond the reach of the (linear) eddy-viscosity model group in contrast to the Reynolds stress model schemes; corresponding result of the latter model is depicted in Fig. 22c). Indeed, the Reynolds stress gradients cause the generation of forces which induce the normal-to- the-wall velocity components in the secondary flow plane. Accordingly, correct capturing of the anisotropy of turbulence in the inflow duct is an important prerequisite for a successful computation of the diffuser flow (see the Section "Cross-Comparison of CFD calculations with experimental results"). Fig. 22 displays the time-averaged velocity vectors in the cross-plane y–z located at x/h= -2 obtained experimentally and computationally by a zonal Hybrid LES/RANS (HLR) model and by the GL RSM model. Despite the relatively low intensity of the secondary motion — the largest velocity has the magnitude of approximately <(1-2)% of the axial bulk velocity ( Ubulk = 1 m/s ) — its influence on the flow in the diffuser is significant. Unlike with the "anisotropy-blind" k-ε model (not shown here), the qualitative agreement of the HLR and RSM models achieved with respect to the secondary flow topology discussed above is obvious.


a) Experiment ———————> 0.1 m/s
UFR4-16 figure22a.png
b) HLR (TU Darmstadt)
UFR4-16 figure22b.png
c) GL RSM (TU Darmstadt)
UFR4-16 figure22c.png
Figure 22: Velocity vectors in the y-z plane in the inflow duct (GL RSM – RSM model due to Gibson and Launder, 1978)

Adverse Pressure Gradient (APG) effects

The boundary layer separation is the direct consequence of the Adverse Pressure Gradient imposed on the duct flow by expanding the cross-section area. The following figures should give the potential practitioners insight into the topology and magnitude of the pressure recovery within the diffuser section. Fig. 24-upper displays the non-dimensional pressure gradient p+ = v dp/dx / (ρUτ3 ) used traditionally to characterize the intensity of the pressure increase in a boundary layers subjected to APG. Accordingly, the displayed results enable a direct comparison with some APG boundary layer experiments. E.g., the range of p+ between 0.01-0.025 was documented in the Nagano et al. (1993) experiments, indicating a much lower level than in the present diffuser. Although the results presented were extracted from the LES and Hybrid LES/RANS simulations their quality is of a fairly high level, keeping in mind good agreement of the near-wall velocity field (see the section "Cross-Comparison of CFD calculations with experimental results"), skin-friction (Fig. 14 in the chapter "Test Case Study") and surface pressure (Fig. 24-lower) development with the reference experimental and DNS results.


UFR4-16 figure23.png
Figure 23: Development of the pressure field in the diffuser 1. The data are extracted from the HLR-simulation, Jakirlić et al. (2010a) and John-Puthenveettil (2012)


UFR4-16 figure24a.jpg
UFR4-16 figure24b.jpg
Figure 24: Development of the dimensionless pressure gradient p+ and surface pressure coefficient along the bottom flat wall of the diffuser 1. The data are extracted from the HLR-simulation, Jakirlić et al. (2010a)


Fig. 25 displays the semi-log profile of the axial velocity across the recirculation zone (at x/h=10) indicating a behaviour, typical of a flow affected by an adverse pressure gradient — underprediction of the logarithmic law and strong enhancement of the turbulence intensity (note the modulation of Reynolds stress field towards weakening of the Reynolds stress anisotropy, Fig. 17 in the Chapter "Test Case Study", corresponding to a substantial mean flow deformation in the streamwise direction, Fig. 15).


UFR4-16 figure25.jpg
Figure 25: Semi-log plots of axial velocity component at a cross-section in the interior of the diffuser 1 (x/h=10) being affected by APG. From Jakirlić et al. (2010a)


See Fig. 18 and associated discussions in Section "Test Case Study" for the topology of the separated flow in both diffuser configurations.

Cross-comparison of CFD calculations with experimental results

The present cross-comparison of the results obtained by different calculation methods in the DNS, LES, RANS, zonal and seamless Hybrid LES/RANS (including DES) frameworks is based to a large extent on the activity conducted within the two previously-mentioned ERCOFTAC-SIG15 Workshops on Refined Turbulence Modelling, Steiner et al. (2009) and Jakirlić et al. (2010b), see "List of References". A large amount of simulation results along with detailed comparison with the experimentally obtained reference data has been assembled. The diversity of the models/methods applied can be seen from Table 1 and Table 2 (Section: Test Case Study). The specification of the models used as well as further computational details - details about the numerical code used, discretization schemes/code accuracy, grid arrangement/resolution, temporal resolution, details about the inflow (also about fluctuating inflow generation where applicable) and outflow conditions, etc. — are given in the short summaries provided by each computational group, which can be downloaded (see the appropriate link to the "workshop proceedings" at the end of this section).

In this section, a short summary of some specific outcomes and the most important conclusions are given. The presentation of results and corresponding discussion is given separately for DNS/LES, hybrid LES/RANS (HLR) and RANS methods. The analysis of the results obtained was conducted with respect to the size and shape of the flow separation pattern and associated mean flow and turbulence features: pressure redistribution along the lower non-deflected wall, axial velocity contours, axial velocity and Reynolds stress component profiles at selected streamwise and spanwise positions.

Here, just a selection of the results obtained will be shown and discussed. At the end of the section links are given to the files (the "workshop proceedings") comprising among others the detailed descriptions of the numerical methods and turbulence models used by all participating groups as well as the complete cross-comparisons of all reference and computational results concerning the mean velocity and turbulence fields at vertical planes at two spanwise positions (z/B=1/2 and z/B=7/8 ) and fifteen streamwise positions.

In the meantime a number of additional computational studies dealing with the flow in the present 3D diffuser configurations have been published. Brief information on these has been given in the "Relevant Studies" Section.

DNS and LES

Typical LES results for the two diffusers are shown in Fig. 26. The iso-contours of the zero mean streamwise velocity component are plotted and the mean separation lines are highlighted by white dashed lines. Three highly complex shaped regions of mean reverse flow can be discerned: SB1, SB2 and SB3. SB1 is an artefact of the specific setup shown here, where the rounded corners at the inlet of the diffuser were replaced by sharp edges. SB2 and SB3 match, within experimental uncertainties, the reference data of Cherry et al. (2008) and, according to Ohlsson et al. (2010), are even closer to the DNS data than the experiments.


UFR4-16 figure26.png
Figure 26: Mean streamwise velocity iso-contours illustrating the three-dimensional mean separation patterns in both considered configurations, diffuser 1 (left) and diffuser 2 (right), obtained by LES (ITS). From Schneider et al. (2010)


For diffusers 1 and 2, there are nine and four LES results, respectively (see Table 1 and Table 2). These were obtained on various grids ranging from 1.1 to 42.9 million cells, by employing different SGS models, wall models and numerical methods, and by varying the size of the computational domain. As opposed to the DNS, for all LES, unsteady inlet data were generated using a periodic duct setup as a precursor simulation. The various contributions varied always in some aspects, but also had sufficient commonalities, such that a careful analysis allowed drawing conclusions on the following aspects: inflow data generation, placement of inflow and outflow boundaries, relevance of the near-wall region, role of the numerical method and SGS model, and resolution requirements.

In Fig. 27, the pressure recovery predictions of the various LES for diffuser 1 are compared with the experimental and DNS data. All but one LES performed well. A similar outcome can be seen in the mean and r.m.s. velocity profiles, Figs. 30 and 31. The inadequate LES was performed on the coarsest grid that was designed for RANS calculations, i.e. most cells were placed near the walls. A more detailed analysis showed that, for LES, it is important to have sufficient resolution in the core area of the diffusers. This resolution is needed to accurately compute the production of large coherent structures that exchange momentum and kinetic energy in the flow and, therefore, promote reattachment. Other factors, like numerical method and SGS models, played a minor role. Even the near-wall region could be bridged by wall-function models (see also Schneider et al., 2010). In addition, it was verified that the precursor simulation of a periodic duct flow can produce accurate unsteady inlet data, hence leading to substantial savings in grid points compared to computing the complete inlet duct (as for the DNS). Also an outflow boundary with a buffer layer placed in the straight part of the outlet duct turned out to be sufficient compared to computing also the outlet contraction far downstream (see Fig. 3 and Fig. 4 in the section "Test Case Study").


UFR4-16 figure27.png
Figure 27: Pressure coefficient along the bottom flat wall of Diffuser 1 obtained by experiment, DNS and various LES (streamwise distance normalized by diffuser length)


In Fig. 28, mean streamwise velocity contours at five cross-sections (x/h=2, 5, 8, 12 and 15 ) of diffuser 1 are shown using the same contour levels for the experimental reference data and three selected LES. Overall, the agreement is fairly good and all three LES deliver results of similar quality if compared to the DNS (see Fig. 13 in Section "Test Case Study"). While the DNS uses 172 million cells and a high-order accurate flow solver, HSU LES DSM and TUD LES DSM use both sophisticated SGS models (dynamic version of the Smagorinsky model) and wall-resolving grids with 17.6 million cells (HSU) and 4 million cells (TUD) and ITS LES SM employs even only 1.6 million cells, the Smagorinsky model and a simple equidistant grid in conjunction with an adaptive wall-function. To discern differences more clearly, the zero velocity line is marked by a thicker line to highlight the reverse flow region. In the LES results for x/h=12, a bump in this line can be seen, whereas the experimental data suggests a horizontal line. Therefore, at first glance, this bump appears to be unnatural. However, the DNS data reveal the same feature. Considering the uncertainty in determining the zero-velocity line, the bump may possibly be present even in the experiments. Moreover, a recent study (Schneider et al., 2011) demonstrates that the strength of secondary flow patterns in the inlet duct has a strong impact on the existence of this bump and how pronounced it will be. Even a complete change in the location of the reverse flow region can be attained, for cases where the sense of rotation of the secondary flow was altered.


UFR4-16 figure28 scale.png UFR4-16 figure28 scale.png UFR4-16 figure28 scale.png UFR4-16 figure28 scale.png
UFR4-16 figure33 xh2.png UFR4-16 figure28 1.jpg UFR4-16 figure28 2.png UFR4-16 figure28 3.png UFR4-16 figure28 4.png
UFR4-16 figure33 xh5.png UFR4-16 figure28 5.png UFR4-16 figure28 6.png UFR4-16 figure28 7.png UFR4-16 figure28 8.png
UFR4-16 figure33 xh8.png UFR4-16 figure28 9.jpg UFR4-16 figure28 10.png UFR4-16 figure28 11.png UFR4-16 figure28 12.png
UFR4-16 figure33 xh12.png UFR4-16 figure28 13.jpg UFR4-16 figure28 14.png UFR4-16 figure28 15.png UFR4-16 figure28 16.png
UFR4-16 figure33 xh15.png UFR4-16 figure28 17.png UFR4-16 figure28 18.png UFR4-16 figure28 19.png UFR4-16 figure28 20.png
Experiment LES-TUD LES-HSU LES-UKA-ITS
Figure 28: Diffuser 1 — Mean streamwise velocity contours at five selected streamwise positions within diffuser section obtained by LES (see Fig. 13 in Section "Test Case Study" for the DNS results)


Fig. 29 displays mean streamwise velocity contours at five cross-sections (x/h=2, 5, 8, 12 and 15 ) of diffuser 2 illustrating the LES capability to capture the influence of the geometry modifications on the three-dimensional separation pattern. The similarity between the two latter LES result sets obtained by UKA-ITS, LES-NWM (wall-modelled using wall functions) and LES-NWR (wall-resolved), is obvious despite significant difference in grid size: 2 Mio. cells in total for wall-modelled LES and 42.9 Mio. cells in total for wall-resolved LES.


Experiment
UFR4-16 figure29 1.png UFR4-16 figure29 2.png UFR4-16 figure29 3.png UFR4-16 figure29 4.png UFR4-16 figure29 5.png
LES-TUD
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LES-NWM UKA-IST
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LES-NWR UKA-IST
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x/h=2 x/h=5 x/h=8 x/h=12 x/h=15
Figure 29: Diffuser 2 — Mean streamwise velocity contours at five selected streamwise positions within diffuser section obtained by LES (LES-NWM — Wall-Modelled (wall functions) LES; LES-NWR — Wall-Resolving LES)


An open issue is the asymmetry in the streamwise velocity profile of the diffuser inlet as found by the experiments (Fig. 20). This could neither be reproduced by DNS with the complete inlet channel nor by LES with inflow data generators. The origin of this asymmetry remains unclear. In addition, DNS and LES data exhibit a higher velocity at the lower wall than experiments. Otherwise, eddy-resolving strategies, like DNS and LES, could capture the separated flow in the 3d-diffusers and the geometric sensitivity of the flow sufficiently well, as long as the secondary motion in the inlet duct and the generation of the large coherent structures in the free shear layers inside the diffuser were resolved sufficiently.


For diffuser 1, Figs. 30 and 31 compare calculated and measured mean velocity and streamwise turbulence intensity profiles at fourteen selected locations within the inflow duct, diffuser section and straight outlet duct in two vertical planes, the one coinciding with the central spanwise position z/B=1/2 and the second positioned closer to the deflected side wall at z/B=7/8. The overall agreement of the results obtained by LES by three groups (HSU, UKA-IST and TUD) with the experimental database is very good. The most important differences are found in the early stage of the separation process at the upper deflected wall (Figs. 30-upper and 31-upper) as well as in the core region of the diffuser section. The most consistent agreement was obtained by the UKA-ITS group despite a fairly moderate number of grid cells (only 1.6 Mio. in total); the (significant) differences in the grid resolution are given in Table 1 (Section "Test Case Study"). The UKA-ITS group applied uniform grid cells distribution in the y-direction using a wall function method for the wall treatment. The other two LES-simulations were performed using a much finer near-wall grid resolution (integration up to the wall has been applied), but a somewhat coarser grid in the core flow. The grid and wall modelling issues are discussed in the introductory part of this section.


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Figure 30: Diffuser 1 - Evolution of the profiles of the axial velocity components and streamwise turbulence intensity in the vertical plane x-y at the central spanwise locations z/B=1/2 obtained by means of LES


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UFR4-16 figure31b.jpg
Figure 31: Diffuser 1 - Evolution of the profiles of the axial velocity components and streamwise turbulence intensity in the vertical plane x-y at the spanwise locations z/B=7/8 obtained by means of LES

Hybrid LES/RANS (HLR)

These schemes, hybridizing the RANS and LES methods aimed at a reduction of spatial and temporal resolution, have recently experienced growing popularity in the CFD community. Their goal is to combine the advantages of both methods in order to provide a computational procedure that is capable of capturing the large-scale eddy structures with a broader spectrum and the bulk flow unsteadiness — as encountered in the flows involving separation, but at affordable costs. Interested readers are referred to a relevant review about hybrid LES/RANS methods by Fröhlich and von Terzi (2008). We mention here only their general classification into two main groups: the zonal, two-layer schemes — a RANS model resolving the near-wall region is linked at a distinct interface with the conventional LES covering the outer layer (flow core) — and the seamless models, where a RANS-like model formulation, mimicking a sub-scale model, is applied in the entire flow domain.

Diffuser 1

As can be seen from Table 1, four HLR results are available for diffuser 1. Besides the classical DES method (Spalart et al., 1997) based on the one- equation turbulence model by Spalart-Allmaras (1994), TUD has carried out a simulation based on their hybrid method. It relies on the low-Re k-ε model due to Launder and Sharma (1974) applied in the near-wall region and the Smagorinsky model in the core flow. HSU applied their own hybrid concept applying an anisotropy-resolving explicit algebraic Reynolds stress model in the near-wall region and a consistent one-equation SGS model in the LES zone (Jaffrezic and Breuer, 2008; Breuer, 2010). In both HLR, the interface between LES and (U)RANS is dynamically determined using different conditions. Finally, KU adopted a non-linear eddy-viscosity model in the RANS region and the SGS model by Inagaki et al. (2005) in the LES part. Since HSU covered a computational domain of -5 ≤ x/h ≤ 37.5 the total number of grid cells is a little bit higher than in the other cases. Otherwise the grids are comparable to each other.

Fig. 32 gives a first impression about the predictive quality of the results obtained showing the distribution of the surface pressure coefficient along the lower wall at the central plane.


UFR4-16 figure32.png
Figure 32: HLR-results, pressure coefficient along the bottom flat wall of Diffuser 1


The results of TUD HLR and HSU HLR are found to be in good agreement with the experimental data as well as the DNS data, where the best coincidence is observed for TUD HLR. Obviously, the pressure recovery for DES is too low. It should be emphasized that both latter hybrid simulations were performed using the same grid resolution (see Table 1). Bearing in mind that DES was developed for external aerodynamic flows, it is not unexpected that it fails under the circumstances of an internal separated flow at a fairly low bulk Reynolds number (improved versions of the DES method — Delayed DES and Improved Delayed DES — were not applied presently). Furthermore, the performance of KU HLR is similar to DES. Since this HLR approach is overall similar to TUD HLR and HSU HLR, this non-satisfactory outcome is difficult to explain.

Fig. 33 depicts the time-averaged streamwise velocity contours at five cross-sections. The bold line indicates zero-streamwise-velocity and thus encloses the recirculation region. As visible from the experimental data the recirculation starts at the upper-right corner, i.e. the corner between the two diverging walls. At x/h=5, the separation bubble remains in the corner, both in the experiments and in the simulations by TUD HLR and HSU HLR. However, both predictions show an inaccurate pressure distribution, i.e. TUD DES and KU HLR deliver a completely separated flow region along the entire upper wall. For DES the flow is even separated along the side wall. At the next cross-section (x/h=8 ), it can be seen that the recirculation region has started to spread across the top of the diffuser. Again, TUD DES and KU HLR predict enlarged separation regions compared to the experiment, whereas the other two approaches perform well. Further downstream, at x/h=12 and 15, a massive separation region can be observed covering the entire top wall of the diffuser. Overall an excellent agreement between the hybrid predictions and the measurements is found, except for DES which yields a too small separation region (note that the same grid was used for TUD-DES as for the TUD-HLR computations).


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Experiment HSU-HLR TUD-HLR KU-HLR TUD-DES
Figure 33: HLR-results, contours of streamwise velocity at cross-sections x/h = 2, 5, 8, 12 and 15 of Diffuser 1


Contours of the streamwise velocity fluctuations are depicted in Fig. 34 for three cross-sections. As can be seen, both TUD HLR and HSU HLR deliver a reasonable agreement with the measurements. The level and location of the maxima are well captured. That is not the case for TUD DES and KU HLR which strongly overpredict the level of the r.m.s. values. Again, both simulations show a large coincidence. For a more detailed comparison, profiles of the mean and r.m.s. velocities were extracted at various locations in the flow field (see workshop proceedings at www.ercoftac.org, under SIG15). They support the trends found in the contour plots and are thus not reproduced here.

The DES method used by TUD is the one of Spalart et al., 1997 (denoted by DES97 in some references). The reasons for such a poor result could be an inappropriate position of interface between the near-wall RANS region (covered by the Spalart-Allmaras one-equation model) and the flow core simulated by LES depending solely on the numerical grid applied. In the DES-upgrades — Delayed DES and Improved Delayed DES — this issue is further elaborated, Spalart (2009). As already emphasized, the grid used presently is the same used also in TUD-HLR. No attempt to modify the grid for DES appropriately was undertaken.


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Experiment HSU-HLR TUD-HLR KU-HLR TUD-DES
Figure 34: HLR-results, contours of streamwise rms velocity (urms/Ub × 100) at cross-sections x/h = 5, 8 and 12 of Diffuser 1


In conclusion, hybrid methods perform generally well for the separated flow in diffuser 1. DES was not expected to work well for such an internal flow and thus fulfills the expectations. Nevertheless, it remains unclear why the results of KU HLR strongly deviate from the other two hybrid approaches although, on first sight, the methods seem to be similar.


HLR calculations for diffuser 1 were also carried out in the ATAAC project using two-layer, IDDES and SAS methods and are reported in the documents for which links are given in Test Case Studies – CFD Methods.

Diffuser 2

For the diffuser 2 the same hybrid methods were applied as for diffuser 1, except for DES (see Table 2). Furthermore, the grids applied are comparable to those used for diffuser 1. Since neither experimental nor DNS data are available for the pressure distribution, the discussion starts with the contours of the time-averaged streamwise velocity at five cross-sections depicted in Fig. 35. As expected based on the experimental results, the shape of the separation bubble in diffuser 2 differs fundamentally from the recirculation zone found in diffuser 1. In contrast to diffuser 1, where the reverse-flow region spreads across the top wall, in diffuser 2, it remains localized near the sharp corner and the side wall. This feature is correctly reproduced by all three hybrid simulations. Nevertheless, the extensions of the recirculation regions differ. TUD HLR yields slightly too small zones compared to the measurements, whereas the zones predicted by HSU HLR are slightly too large and KU HLR shows no unique trend.


Experiment
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HSU-HLR
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TUD-HLR
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KU-HLR
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x/h=2 x/h=5 x/h=8 x/h=12 x/h=15
Figure 35: Figure 35: HLR-results, contours of streamwise velocity at cross-sections x/h = 2, 5, 8, 12 and 15 of diffuser 2


In comparison to diffuser 1, similar distributions of the rms values of the streamwise stress component (see cross-comparison in the workshop proceedings at the end of this section) are found for HSU HLR and KU HLR. In contrast, for TUD HLR a strong reduction of the velocity fluctuations is observed in the streamwise direction which is clearly visible in the backmost cross-sections. The reason for this behavior is unclear, since the same method shows a different trend for diffuser 1. Unfortunately, higher-order statistics were not measured for this case and thus a final evaluation is difficult.

RANS

Numerous RANS models were applied ranging from some standard eddy-viscosity and full Reynolds stress models (e.g., standard k-ε model, k-ω SST, the basic differential Reynolds stress model due to Gibson and Launder, 1978, and a relevant quadratic version due to Speziale et al., 1991) to some explicit algebraic Reynolds stress model versions (EARSM) and linear/non- linear, EVM and RSM models based on the Durbin's elliptic relaxation method (ERM, 1991), see Table 1 and Table 2 for detailed specification. RANS calculations were carried out in the ATAAC project with the linear (isotropic) SST eddy-viscosity model and with stress-anisotropy-resolving algebraic (EARMS) and differential (EBRSM) models and are reported in the documents for which links are given in Test Case Studies – CFD Methods.

An important prerequisite for the successful computation is the correct capturing of the flow in the inflow duct which features secondary motion characterized by jets directed towards the channel walls bisecting each corner and associated vortices at both sides of each jet, see Fig. 22. These secondary currents are induced by the Reynolds stress anisotropy, which is, as generally known, beyond the reach of the (linear) eddy-viscosity model group, in contrast to the Reynolds stress model schemes. That the latter model groups yields a qualitatively correct behaviour is shown in Fig. 22c.

Fig. 36 shows the contour plots of the axial velocity component in two characteristic streamwise cross-sectional areas of diffuser 1 obtained by a selection of different RANS model versions, being representative of all applied model formulations. Whereas the initial separation zone development (x/h=5 ) follows qualitatively the reference results, its subsequent evolution exhibits different patterns depending on the model concept applied. The k-ω SST model and the ζ-f model (a numerically robust version of Durbin's v2-f model proposed by Hanjalic et al., 2004; the separation pattern obtained by both UoM versions of the v2-f model — Laurence et al., 2004 — follows closely the ζ-f results) resulted in a flow separating completely at the deflected side wall contrary to the experimental findings indicating the separation zone along the upper deflected wall. Similar results were obtained with all eddy-viscosity-based models listed in Table 1. Keeping in mind the inherent incapability of this model group to correctly represent the afore-mentioned secondary motion across the inflow duct, this outcome represents no surprise. The RSM model group returned the flow topology in much better agreement with the experimental results. Whereas the basic RSM model (denoted by GLRSM) resulted in a separation pattern occupying both upper corners (similar behaviour was documented in the case of the ANSYS BSL-RSM model) the application of both EARSM model versions (applied by ANSYS) and the Elliptic Blending RSM (a near-wall differential model based on the ERM method; Manceau and Hanjalic, 2002) returned the 3D separation pattern occupying entirely the upper sloped wall in good agreement with experiment.


Experiment, x/h=5 Experiment, x/h=15
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ANSYS SST IUS ZETA-F TUD-GLRSM UoM RIJEBM ANSYS-EARSM
Figure 36: Iso-contours of the axial velocity field in the cross planes y-z at two selected streamwise locations within the Diffuser 1 section obtained by different RANS models (thick line denotes the zero-velocity line) in comparison with experiments


Figs. 37 a) and b) illustrate the pressure coefficient development along the lower flat wall. The poor agreement (underprediction of the Cp - magnitude in the diffuser section) obtained by the eddy-viscosity model group in Fig. 37 a) (here only the predictions of application of the ERM-based EVM models are depicted) is consistent with the incorrect prediction of the velocity field. Apart from some unexpectedly large departures (pertinent especially to ANSYS-WJ model, which returned correctly the shape of the separation region, and to the UoM-RIJSSG model, application of which led to similar results as the TUD-GLRSM model; the absence of a wall reflection term in the latter can be blamed for the latter deviation) all other results agree reasonably well with the reference data. The differences between the results pertain partially to different grid resolutions. According to Table 1 most RANS computations were performed with grids comprising a comparable number of grid cells (between 1.6-1.9 Mio. cells; exceptions are UoM and OPU contributions). However, the solution domains adopted were of different lengths: e.g. the ANSYS colleagues adopted the straight outlet duct being almost 30h long — in all other cases this length amounted up to 10h; accordingly the resolution in the diffuser section — despite the total number of the grid cells being about 1.6 Mio. — was somewhat lower). The large departures obtained by two advanced models — Non-linear k-ε model and Two-Component Limit RSM model in conjunction with analytical wall functions, Table 1 — applied by OPU/UniOs cannot be plausibly discussed here due to the extremely coarse grid containing only 0.2 Mio. cells. Unfortunately the contributors didn't make an attempt to refine the grid appropriately. The streamwise fluctuation intensity field predicted by the RANS models will not be discussed here. It can only be said that the results obtained by the three RSM models (see iso-contours of the axial velocity field displayed in Fig. 36) are in qualitatively good agreement with the experiment indicating intensified turbulence production in the regions bordering the separation zone characterized by large velocity gradients.


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Figure 37a: Pressure coefficient evolution in diffuser 1 along the bottom flat wall obtained by advanced eddy-viscosity model schemes: elliptic-relaxation-method-based models and a non-linear model


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Figure 37b: Pressure coefficient evolution in diffuser 1 along the bottom flat wall obtained by the Reynolds-stress model concept


The velocity field characterizing the flow structure in the diffuser 2 is illustrated in Fig. 38 by displaying the iso-contours of the axial velocity field in the cross planes y-z at three selected streamwise locations. As discussed previously (sections devoted to DNS/LES and HLR results) the separation zone here is completely situated at the deflected side wall. The application of most RANS models to the diffuser 1 configuration has incorrectly resulted in a separation pattern pertinent to diffuser 2 (see Fig. 36). The results depicted in Fig. 38 exhibiting, at least qualitatively, the experimentally determined flow structure are therefore "expected". However, the differences in the shape and size of the recirculation zone are obvious. The linear ζ-f model (UniRo contributions) resulted in a by far too large recirculation zone leading to intensive flow acceleration in the through-flow portion, i.e. positive-velocity region. This result can be regarded as representative for all other linear EVM models used. Important improvement was obtained by applying a non-linear formulation of the ζ-f model. The recirculation region is substantially reduced to yield a much better quantitative agreement with the experimental findings. The separation bubble obtained by selected RSM models shows a shape that is closest to the experimental results, but there are important differences concerning some details. All three RSM models resulted in the separation region to be situated in the corners between two deflected walls and between the sloped side wall and the lower flat wall, contrary to the experimental finding. However, these tiny separated regions are of low backflow intensity, so that the quantitative agreement can be regarded as reasonable (this statement is valid also for the diffuser 1). For a more quantitative comparison the readers are referred to the "workshop proceedings".

It should also be emphasized that the near-wall treatment was not of decisive importance. In this configuration the flow unsteadiness was introduced into the wall boundary layer from the core flow in accordance with the so-called "top-to-bottom" process (communication with M. Leschziner). This fact justified the use of wall functions in conjunction with some RANS models (it is also valid for some LES simulations, see e.g. ITS contribution) enabling a coarser grid resolution in the near-wall regions.


Experiment, x/h=5 Experiment, x/h=8 Experiment, x/h=15
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UniRo-ZF UniRo ZF-NL TUD-GLRSM UoM RIJEBM ANSYS-EARSM
Figure 38: Selection of RANS-results, contours of streamwise velocity at cross-sections x/h = 5, 8 and 15 of Diffuser 2 (the dark blue area in the ANSYS-EARSM computation represents the reverse flow region)

Available CFD results: ERCOFTAC SIG15 Workshop Proceedings

The following documents are freely available (see also www.ercoftac.org under SIG15):

  • Short summaries comprising the computational method descriptions used by participating computational groups from the 13th Workshop (Technical University Graz, Austria, September, 2008) - 13th-Workshop_summaries.pdf
  • Short summaries comprising the computational method descriptions used by participating computational groups from the 14th Workshop ("La Sapienza" University of Rome, Italy, September, 2009) - 14th-Workshop_summaries.pdf
  • Diffuser 1: List of the participants and computational models applied - Diffuser1_contributers.pdf
  • Diffuser 1: cross-comparison of the results obtained by LES and Hybrid LES/RANS methods - Diffuser1_LES-and-HLR.pdf
  • Diffuser 1: cross-comparison of the results obtained by RANS method: Eddy-viscosity models (only linear model formulations) - Diffuser1_RANS-EVM.pdf
  • Diffuser 1: cross-comparison of the results obtained by RANS method: Eddy-viscosity models (formulations based on the Elliptic-relaxation method) - Diffuser1_RANS-EVM-ERM.pdf
  • Diffuser 1: cross-comparison of the results obtained by RANS method: Reynolds stress models - Diffuser1_RANS-RSM.pdf
  • Diffuser 2: List of the participants and computational models applied - Diffuser2_contributers.pdf
  • Diffuser 2: cross-comparison of the results obtained by LES and Hybrid LES/RANS methods - Diffuser2_LES-and-HLR.pdf
  • Diffuser 2: cross-comparison of the results obtained by RANS method: Eddy-viscosity models - Diffuser2_RANS-EVM.pdf
  • Diffuser 2: cross-comparison of the results obtained by RANS method: Reynolds stress models - Diffuser2_RANS-RSM.pdf





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

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