UFR 3-32 Test Case: Difference between revisions

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plate where a turbulent boundary layer is formed (see [[UFR_3-32_Test_Case#figure2|Figure 2]]).
plate where a turbulent boundary layer is formed (see [[UFR_3-32_Test_Case#figure2|Figure 2]]).
In  this case, the flat plate is the floor of the test section. The shock wave  is
In  this case, the flat plate is the floor of the test section. The shock wave  is
produced by a shock generator. The angle <math>{\theta}</math> of the  shock  generator  with
produced by a shock generator. The angle <math>{\left.\theta\right.}</math> of the  shock  generator  with
respect to the external flow is supposed to  be  the  same  as  the  flow
respect to the external flow is supposed to  be  the  same  as  the  flow
deflection; this is  a  very  good  approximation  in  the  present  flow
deflection; this is  a  very  good  approximation  in  the  present  flow
conditions. Two cases are studied, corresponding to flow deflections <math>{\theta}</math> of
conditions. Two cases are studied, corresponding to flow deflections <math>{\left.\theta\right.}</math> of
8° and of 9.5° at the nominal Mach number 2.25. They are both  separated.
8° and of 9.5° at the nominal Mach number 2.25. They are both  separated.
This experiment is designed to provide the  characteristics  of  the  low
This experiment is designed to provide the  characteristics  of  the  low
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The external Mach number, i.e. in  the  external  flow  upstream  of  the
The external Mach number, i.e. in  the  external  flow  upstream  of  the
interaction  is  /M//(/=2.25,  stagnation  pressure  in  the  potential  flow
interaction  is  <math>{\left.M_e=2.25\right.}</math>,  stagnation  pressure  in  the  potential  flow
upstream  of  the  interaction  is  /p//tref/=50 663 N/m2;  the  stagnation
upstream  of  the  interaction  is  <math>{p_\mathit{tref}=50663\ \mathrm{N/m^2}}</math>;  the  stagnation
temperature in the outer flow /T//tref/ is typically atmospheric, and remains
temperature in the outer flow <math>{\left.T_\mathit{tref}\right.}</math> is typically atmospheric, and remains
close to 300K.
close to 300K.
The incoming boundary layer is fully turbulent. It  develops  on  a  flat
The incoming boundary layer is fully turbulent. It  develops  on  a  flat
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The first campaign of measurements called "case-2006" was performed  with
The first campaign of measurements called "case-2006" was performed  with
the following parameters:
the following parameters:
{|align="center" border="1" cellpadding="5"
|<math>{x\ (\mathrm{mm})}</math>||<math>{\left.M_e\right.}</math>||<math>{p_\mathit{tref}\ (\mathrm{N/m^2})}</math>
|<math>{T_\mathit{tref}\ (\mathrm{K})}</math>||<math>{\left.\delta\ (99%,\ \mathrm{mm})\right.}</math>
|<math>{\left.R_\delta\right.}</math>||<math>{\left.\theta\ (\mathrm{mm})\right.}</math>||<math>{\left.R_\theta\right.}</math>
|-
|align="center"|<math>{\left.260\right.}</math>||align="center"|<math>{\left.2.25\right.}</math>
|align="center"|<math>{\left.50663\right.}</math>||align="center"|<math>{\left.300\right.}</math>
|align="center"|<math>{\left.11.0\right.}</math>||align="center"|<math>{\left.58760\right.}</math>
|align="center"|<math>{\left.0.95\right.}</math>||align="center"|<math>{\left.5070\right.}</math>
|}




The origin of the abscissa is taken at the end of the contoured  part  of
The origin of the abscissa is taken at the end of the contoured  part  of
the nozzle block. /R//?/ and /R//?/ are respectively the Reynolds  numbers  based
the nozzle block. <math>{\left.R_\delta\right.}</math> and <math>{\left.R_\theta\right.}</math>
are respectively the Reynolds  numbers  based
on layer thickness and on momentum thickness. A  second  campaign  called
on layer thickness and on momentum thickness. A  second  campaign  called
"case-2007"  corresponds  to  the  following  conditions,  in  which  the
"case-2007"  corresponds  to  the  following  conditions,  in  which  the
thickness of the incoming boundary layer is smaller than in the  previous
thickness of the incoming boundary layer is smaller than in the  previous
case.
case.
{|align="center" border="1" cellpadding="5"
|<math>{x\ (\mathrm{mm})}</math>||<math>{\left.M_e\right.}</math>||<math>{p_\mathit{tref}\ (\mathrm{N/m^2})}</math>
|<math>{T_\mathit{tref}\ (\mathrm{K})}</math>||<math>{\left.\delta\ (99%,\ \mathrm{mm})\right.}</math>
|<math>{\left.R_\delta\right.}</math>||<math>{\left.\theta\ (\mathrm{mm})\right.}</math>||<math>{\left.R_\theta\right.}</math>
|-
|align="center"|<math>{\left.260\right.}</math>||align="center"|<math>{\left.2.25\right.}</math>
|align="center"|<math>{\left.50663\right.}</math>||align="center"|<math>{\left.300\right.}</math>
|align="center"|<math>{\left.10.0\right.}</math>||align="center"|<math>{\left.53420\right.}</math>
|align="center"|<math>{\left.0.87\right.}</math>||align="center"|<math>{\left.4640\right.}</math>
|}




The details of the geometry and of the flow conditions can  be  accessed
The details of the geometry and of the flow conditions can  be  accessed
in the UFAST data base in Doerffer (2009).
in the UFAST data base in [[UFR_3-32_References#1|Doerffer&nbsp;(2009)]].
A description of the geometry and the CAD files are given here:
{|align = "center" border="1" cellpadding="5"
|align="center"|[[Media:UFR3-32_geometry_experiment.pdf|geometry_experiment.pdf]]
|-
|align="center"|[[Media:UFR3-32_672_cao_iusti_long1.tin.txt|cao_iusti_long1.tin]]
|-
|align="center"|[[Media:UFR3-32_671_cao_iusti_long1-2.igs|cao_iusti_long1.igs]]
|}
 
 


The measured quantities are the wall pressure (mean, rms value and
The measured quantities are the wall pressure (mean, rms value and
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planes obtained by Particle Image Velocimetry (PIV) and by Laser Doppler
planes obtained by Particle Image Velocimetry (PIV) and by Laser Doppler
Velocimetry (LDV). The two components (longitudinal, normal to the wall)
Velocimetry (LDV). The two components (longitudinal, normal to the wall)
(/U/ , /V)/ of the mean velocity and (/u'/ , /v'/ ) of the fluctuating velocity
<math>{\left.(U,V)\right.}</math> of the mean velocity and <math>{\left.(u',v')\right.}</math>
have been measured. The Reynolds stresses [pic], [pic], [pic] have been
of the fluctuating velocity have been measured.
determined. The spectra of the wall pressure, which are very sensitive
The Reynolds stresses <math>{\overline{u'^2},\ \overline{v'^2},\ \overline{u'v'}}</math> have been determined.
The spectra of the wall pressure, which are very sensitive
to the shock system unsteadiness, have also been determined.
to the shock system unsteadiness, have also been determined.
More precisely, two measurement campaigns are given denoted by 2006 and 2007, at slightly different Reynolds number (see here above).
In the 2006 campaign, wall pressure measurements were performed: fluctuations are characterized by their variance and their power spectral density. PIV measurements were performed in the symmetry plane of the test section (mean velocity and normal shear stresses). In the 2007 data, only PIV data were obtained, with Reynolds stresses including shear stresses. Finally stereo PIV was use to take measurements in horizontal planes to detect 3-d features. Four horizontal planes were considered. Mean velocity was measured, and only in one plane (elevation h2) the normal stresses were obtained. The details are given in the 'readme' files below and the measurement results in the associated data files.


== Test Case Experiments ==
== Test Case Experiments ==
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radiated by the boundary layers.  Its  level  is  less  than  0.1%  for
radiated by the boundary layers.  Its  level  is  less  than  0.1%  for
velocity turbulence intensity. The range of Reynolds  numbers  produced
velocity turbulence intensity. The range of Reynolds  numbers  produced
in this facility encompasses moderate values (typically /R//?/?5000);  this
in this facility encompasses moderate values (typically <math>{R_\theta\approx 5000}</math>);  this
makes the experiments well adapted  to  advanced  modelling  techniques
makes the experiments well adapted  to  advanced  modelling  techniques
like LES, which, in their  present  state  are  feasible  for  moderate
like LES, which, in their  present  state  are  feasible  for  moderate
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are located at a distance larger than 25 cm downstream of the contoured
are located at a distance larger than 25 cm downstream of the contoured
part of the nozzle block (more than 25 boundary layer thicknesses). All
part of the nozzle block (more than 25 boundary layer thicknesses). All
/x/ coordinates in the following correspond to an  origin  taken  at  the
''x'' coordinates in the following correspond to an  origin  taken  at  the
beginning of the flat part of the nozzle wall,  and  located  388.6  mm
beginning of the flat part of the nozzle wall,  and  located  388.6  mm
downstream of the sonic neck. Downstream of the interaction a diverging
downstream of the sonic neck. Downstream of the interaction a diverging
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The incoming boundary layer is turbulent and  fully  developed.  It  is
The incoming boundary layer is turbulent and  fully  developed.  It  is
subjected to a shock wave produced by a shock generator placed  in  the
subjected to a shock wave produced by a shock generator placed  in  the
external flow, as indicated in figures 1 and 2. A shock generator  made
external flow, as indicated in [[UFR_3-32_Test_Case#figure1|figures 1]] and [[UFR_3-32_Test_Case#figure2|2]].
of a sharp-edged plate is fixed on the ceiling of the wind  tunnel.  It
A shock generator  made of a sharp-edged plate is fixed on the ceiling of the wind  tunnel.  It
is placed in the free-stream and its leading edge  is  located  in  the
is placed in the free-stream and its leading edge  is  located  in  the
potential flow. It entirely spans the test  section  and  generates  an
potential flow. It entirely spans the test  section  and  generates  an
oblique shock wave impinging on the floor  boundary  layer.  Its  angle
oblique shock wave impinging on the floor  boundary  layer.  Its  angle
with respect to the potential flow /?/ is set at 8° and 9.5°, for the two
with respect to the potential flow <math>{\left.\theta\right.}</math> is set at 8° and 9.5°, for the two
cases documented here. The global organisation  of  the  oblique  shock
cases documented here. The global organisation  of  the  oblique  shock
wave boundary  layer  interaction  visualised  by  spark  Schlieren  is
wave boundary  layer  interaction  visualised  by  spark  Schlieren  is
presented in Figure 3, for which the external flow deviation is 8°, and
presented in [[UFR_3-32_Test_Case#figure3|Figure 3]], for which the external flow deviation is 8°, and
the pressure gradient is  strong  enough  for  the  boundary  layer  to
the pressure gradient is  strong  enough  for  the  boundary  layer  to
separate. Two interactions are documented, corresponding to  deviations
separate. Two interactions are documented, corresponding to  deviations
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|-
|-
|align="center"|'''Figure 3:''' Schlieren of the interaction,  <math>{\theta=8^\circ}</math>
|align="center"|'''Figure 3:''' Schlieren of the interaction,  <math>{\theta=8^\circ}</math>
|}
The measurement data are given here, with appropriate README files describing the data format.
{|border ="1" cellpadding="10" align="center"
|align="center"|[[Media:UFR3-32_readme_piv_case2006.txt|README_piv_2006.txt]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_95d_case2006_2.csv|IUSTI_95d_case2006_2.csv]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_8d_case2006_2.csv|IUSTI_8d_case2006_2.csv]]
|}
{|border ="1" cellpadding="10" align="center"
|align="center"|[[Media:UFR3-32_readme_piv_2007.txt|README_piv_2007.txt]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_theta95_case2007_2.csv|IUSTI_theta95_2.csv]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_theta8_case2007_2.csv|IUSTI_theta8_2.csv]]
|}
{|border="1" cellpadding="10" align="center"
|align="center" colspan="2"|[[Media:UFR3-32_Readme_IUSTI_UFAST_WP3_PIV3D_Horizontal_20080227.txt|README_IUSTI_UFAST_WP3_PIV3D_Horizontal_20080227.txt]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_upstreamBL_h1_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_upstreamBL_h1_AJVGoff_mean.plt]]
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_interaction_h1_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_interaction_h1_AJVGoff_mean.plt]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_upstreamBL_h2_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_upstreamBL_h2_AJVGoff_mean.plt]]
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_interaction_h2_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_interaction_h2_AJVGoff_mean.plt]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_upstreamBL_h4_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_upstreamBL_h4_AJVGoff_mean.plt]]
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_interaction_h4_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_interaction_h4_AJVGoff_mean.plt]]
|-
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_upstreamBL_h6_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_upstreamBL_h6_AJVGoff_mean.plt]]
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_interaction_h6_AJVGoff_mean.plt|IUSTI_UFAST_WP3_PIV3D_interaction_h6_AJVGoff_mean.plt]]
|-
|
|align="center"|[[Media:UFR3-32_IUSTI_UFAST_WP3_PIV3D_interaction_h2_AJVGoff_std.plt|IUSTI_UFAST_WP3_PIV3D_interaction_h2_AJVGoff_std.plt]]
|}
{|border="1" cellpadding="10" align="center"
|align="center" colspan="2"|[[Media:UFR3-32_readme_Press_Spctr_case2006.txt|README_Pressure_Spectrum_case2006.txt]]
|-
|align="center"|[[Media:UFR3-32_pressure_spectrum_80_kulite.csv|pressure_spectrum_80_kulite.csv]]
|align="center"|[[Media:UFR3-32_pressure_spectrum_95_kulite.csv|pressure_spectrum_95_kulite.csv]]
|-
|align="center"|[[Media:UFR3-32_Pressure_Moments_80_longitudinal_distribution.dat|Pressure_Moments_80_longitudinal_distribution.dat]]
|align="center"|[[Media:UFR3-32_Pressure_Moments_95_longitudinal_distribution.dat|Pressure_Moments_95_longitudinal_distribution.dat]]
|}
|}


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about 1 micron, and provides sufficient resolution.  A  PIV/LDA  cross-
about 1 micron, and provides sufficient resolution.  A  PIV/LDA  cross-
check in the incoming boundary layer showed a good  agreement  of  mean
check in the incoming boundary layer showed a good  agreement  of  mean
velocity, even at distances as small as /y/+=40. This comparison suggests
velocity, even at distances as small as <math>{y^+=40}</math>. This comparison suggests
that the longitudinal velocity is measured with a typical  accuracy  of 1%.
that the longitudinal velocity is measured with a typical  accuracy  of 1%.


Particular problems arise for Reynolds stress  measurements,  sensitive
Particular problems arise for Reynolds stress  measurements,  sensitive
to the phenomenon of peak locking. The field of view of  the  receiving
to the phenomenon of peak locking. The field of view of  the  receiving
optics was set to avoid this effect. Note that the shear  stress  [pic]
optics was set to avoid this effect. Note that the shear  stress  <math>{\overline{u'v'}}</math>
is particularly sensitive to this peak locking, but  not  so  much  the
is particularly sensitive to this peak locking, but  not  so  much  the
normal components *[pic]*and [pic]. The final check is given  in  Figure
normal components <math>{\overline{u'^2}}</math> and <math>{\overline{v'^2}}</math>.
4, for which the wall friction used  for  normalization  of  the  shear
The final check is given  in  [[UFR_3-32_Test_Case#figure4|Figure&nbsp;4]], for which the wall friction
stress was derived from the log-law. In this  figure,  the  solid  line
used  for  normalization  of  the  shear stress was derived from the log-law.
represents the subsonic data of Klebanoff (1954).
In this  figure,  the  solid  line represents the subsonic data of [[UFR_3-32_References#11|Klebanoff&nbsp;(1954)]].


<div id="figure4"></div>
<div id="figure4"></div>
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The LDV measurements are free from peak locking. They follow rather  closely
The LDV measurements are free from peak locking. They follow rather  closely
Klebanoff's results. The  PIV  measurements  are  also  in  the  same  spot,
Klebanoff's results. The  PIV  measurements  are  also  in  the  same  spot,
excepted close to the wall (/y///?/<0.05), where measurements are  not  expected
excepted close to the wall <math>{\left(y/\delta < 0.05\right)}</math>, where measurements are  not  expected
to be accurate. The scatter among the data suggests  that  the  accuracy  of
to be accurate. The scatter among the data suggests  that  the  accuracy  of
the measurements is about 10% for [pic].
the measurements is about 10% for <math>{\overline{u'v'}}</math>.


===Two-dimensionality of the flow===
===Two-dimensionality of the flow===
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velocity in a plane at a distance of 1mm from  the  wall,  in  the  boundary
velocity in a plane at a distance of 1mm from  the  wall,  in  the  boundary
layer upstream  of  the  interaction.  It  is  found  that  a  the  spanwise
layer upstream  of  the  interaction.  It  is  found  that  a  the  spanwise
variations of /U/ are les than  ±  5  m/s,  i.e. less  than  1%  of  /U//e/,  and
variations of <math>{\left.U\right.}</math> are les than  &plusmn;5  m/s,  i.e.
therefore at the limit of  the  accuracy  of  measurements(see  Dussauge,
less  than  1%  of  <math>{\left.U_e\right.}</math>,  and
Piponniau 2008).
therefore at the limit of  the  accuracy  of  measurements
(see  [[UFR_3-32_References#6|Dussauge&nbsp;&&nbsp;Piponniau&nbsp;2008]]).


The effect of side wall has also been investigated numerically and  will  be
The effect of side wall has also been investigated numerically and  will  be
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===LES (SOTON)===
===LES (SOTON)===
The numerical method and the set of simulations  are  thoroughly  documented
The numerical method and the set of simulations  are  thoroughly  documented
in Touber & Sandham (2009, 2011) and Touber (2010)  and  are  not  repeated
in [[UFR_3-32_References#16|Touber&nbsp;&&nbsp;Sandham&nbsp;(2009,&nbsp;2011)]]
and [[UFR_3-32_References#15|Touber&nbsp;(2010)]] and  are  not  repeated
here. The code for LES uses  high-order  explicit  finite  differences  with
here. The code for LES uses  high-order  explicit  finite  differences  with
shock-capturing and a subgrid model is activated. The published  papers  and
shock-capturing and a subgrid model is activated. The published  papers  and
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The inflow boundary layer  was  specified  by  an  approximate  (van  Driest
The inflow boundary layer  was  specified  by  an  approximate  (van  Driest
scaled) mean profile superimposed with fluctuations obtained from a  digital
scaled) mean profile superimposed with fluctuations obtained from a  digital
filter technique (the computer code for this is provided in  Touber, 2010).
filter technique (the computer code for this is provided in  [[UFR_3-32_References#15|Touber,&nbsp;2010]]).
The method was compared with an alternative deterministic model (Sandham et
The method was compared with an alternative deterministic model
al, 2003) which gave similar results in terms of a distance  downstream  for
([[UFR_3-32_mis_References#17|Sandham&nbsp;''et&nbsp;al,''&nbsp;2003]])
which gave similar results in terms of a distance  downstream  for
the  skin  friction  to  settle  down.  The  digital  filter  technique  was
the  skin  friction  to  settle  down.  The  digital  filter  technique  was
ultimately preferred to the deterministic fluctuation  model  since  it  did
ultimately preferred to the deterministic fluctuation  model  since  it  did
not introduce particular spikes into the spectrum of the  inflow  turbulence
not introduce particular spikes into the spectrum of the  inflow  turbulence
that might later be confused with the low-frequency response  that  was  the
that might later be confused with the low-frequency response  that  was  the
ultimate interest (Touber & Sandham 2011). The  distance  allowed  in  the
ultimate interest ([[UFR_3-32_References#17|Touber&nbsp;&&nbsp;Sandham&nbsp;2011]]).
The  distance  allowed  in  the
simulation for the boundary layer to relax to equilibrium before  the  shock
simulation for the boundary layer to relax to equilibrium before  the  shock
impingement was not varied.  To  study  low  frequency  characteristics  the
impingement was not varied.  To  study  low  frequency  characteristics  the
simulation was run for 25.4 low frequency cycles (with  frequency  0.035U/L,
simulation was run for 25.4 low frequency cycles (with  frequency  <math>{0.035U/L}</math>,
where U is the free stream velocity and L is the interaction  length,  equal
where <math>{U}</math> is the free stream velocity and <math>{L}</math> is the interaction  length,  equal
to the distance from the origin of  the  reflected  shock  to  the  inviscid
to the distance from the origin of  the  reflected  shock  to  the  inviscid
impingement location), equivalent to over 100 through-flows of  the  domain.
impingement location), equivalent to over 100 through-flows of  the  domain.
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characteristic conditions were applied at  the  remaining  boundaries,  with
characteristic conditions were applied at  the  remaining  boundaries,  with
the shock triggered by imposing the Rankin-Hugoniot relations.
the shock triggered by imposing the Rankin-Hugoniot relations.
===DES (ONERA/DAAP)===
===DES (ONERA/DAAP)===
Details of the computational approach are provided  in  Garnier (2009)  and
Details of the computational approach are provided  in  [[UFR_3-32_References#10|Garnier&nbsp;(2009)]] and
are not repeated here in full. The code FLU3M is a finite-volume solver  for
are not repeated here in full. The code FLU3M is a finite-volume solver  for
the compressible Navier-Stokes  equations.  The  numerical  scheme  for  the
the compressible Navier-Stokes  equations.  The  numerical  scheme  for  the
temporal integration is the implicit scheme of  Gear  described  in  Péchier
temporal integration is the implicit scheme of  Gear  described  in  [[UFR_3-32_References#12|Péchier&nbsp;(2001)]].
(2001). With the chosen time step, the subiterative  process  which  insures
With the chosen time step, the subiterative  process  which  insures
the second order time accuracy converges by one order  of  magnitude  within
the second order time accuracy converges by one order  of  magnitude  within
five iterations. The maximum CFL number remains lower than  20.  The  choice
five iterations. The maximum CFL number remains lower than  20.  The  choice
Line 269: Line 364:
employed to guarantee the stability of the  solution  in  presence  of  flow
employed to guarantee the stability of the  solution  in  presence  of  flow
discontinuities. These schemes are then necessarily dissipative and  careful
discontinuities. These schemes are then necessarily dissipative and  careful
attention needs to be paid to the design of limiters (Garnier, 2009).
attention needs to be paid to the design of limiters ([[UFR_3-32_References#10|Garnier,&nbsp;2009]]).


Generally in DES methods, the length scale which appears in the  dissipation
Generally in DES methods, the length scale which appears in the  dissipation
Line 287: Line 382:
LES. This technique suffers from the same constraints as LES which  must  be
LES. This technique suffers from the same constraints as LES which  must  be
fed with realistic inflow fluctuations. For this application, the  Synthetic
fed with realistic inflow fluctuations. For this application, the  Synthetic
Eddy Method (SEM) technique (Garnier 2009) has been employed. It  is  based
Eddy Method (SEM) technique ([[UFR_3-32_References#10|Garnier&nbsp;2009]]) has been employed.
upon a superposition of  analytically  defined  eddies  whose  distributions
It  is  based upon a superposition of  analytically  defined  eddies  whose  distributions
follow imposed Reynolds stress profiles. These eddies are  injected  at  the
follow imposed Reynolds stress profiles. These eddies are  injected  at  the
computational domain inflow in a random way to avoid  the  generation  of  a
computational domain inflow in a random way to avoid  the  generation  of  a
Line 300: Line 395:
----
----
{{ACContribs
{{ACContribs
|authors=Jean-Paul Dussauge
|authors=Jean-Paul Dussauge (*), P. Dupont (*) , N. Sandham (**), E. Garnier (***)
|organisation=Orange
|organisation= (*)&nbsp;Aix-Marseille Université, and Centre National de la Recherche Scientifique UM 7343, (**)&nbsp;University of Southampton, (***)&nbsp;ONERA/DAAP, Meudon, France
}}
}}
{{UFRHeader
{{UFRHeader

Latest revision as of 13:45, 12 February 2017

Planar shock-wave boundary-layer interaction

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

Semi-confined Flows

Underlying Flow Regime 3-32

Test Case Study

Brief Description of the Study Test Case

The flow under investigation is an oblique shock reflection on a flat plate where a turbulent boundary layer is formed (see Figure 2). In this case, the flat plate is the floor of the test section. The shock wave is produced by a shock generator. The angle of the shock generator with respect to the external flow is supposed to be the same as the flow deflection; this is a very good approximation in the present flow conditions. Two cases are studied, corresponding to flow deflections of 8° and of 9.5° at the nominal Mach number 2.25. They are both separated. This experiment is designed to provide the characteristics of the low frequency unsteadiness found in such conditions, and affecting the reflected (or separation) shock wave and the separated zone itself. The deflection is produced by a shock generator, i.e. a tilted flat plate, fixed on the ceiling of the wind tunnel, and leaving a sufficient gap to let a passage to the ceiling boundary layer, without affecting the flow around the shock generator leading edge. The implementation of the shock generator is given in Figure 1.

UFR 3-32 fig1.png
Figure 1: Sketch of the test section showing the contoured nozzle block and the shock generator

A sketch of the configuration is given in Figure 2.

UFR 3-32 fig2.png
Figure 2: Sketch of the interaction (not to scale)

The external Mach number, i.e. in the external flow upstream of the interaction is , stagnation pressure in the potential flow upstream of the interaction is ; the stagnation temperature in the outer flow is typically atmospheric, and remains close to 300K. The incoming boundary layer is fully turbulent. It develops on a flat plate with nearly adiabatic constant wall temperature. The conditions in the incoming boundary layer are summed up in the following tables.

The first campaign of measurements called "case-2006" was performed with the following parameters:



The origin of the abscissa is taken at the end of the contoured part of the nozzle block. and are respectively the Reynolds numbers based on layer thickness and on momentum thickness. A second campaign called "case-2007" corresponds to the following conditions, in which the thickness of the incoming boundary layer is smaller than in the previous case.



The details of the geometry and of the flow conditions can be accessed in the UFAST data base in Doerffer (2009). A description of the geometry and the CAD files are given here:

geometry_experiment.pdf
cao_iusti_long1.tin
cao_iusti_long1.igs


The measured quantities are the wall pressure (mean, rms value and spectra) along the interaction, and 2-d velocity fields in vertical planes obtained by Particle Image Velocimetry (PIV) and by Laser Doppler Velocimetry (LDV). The two components (longitudinal, normal to the wall) of the mean velocity and of the fluctuating velocity have been measured. The Reynolds stresses have been determined. The spectra of the wall pressure, which are very sensitive to the shock system unsteadiness, have also been determined. More precisely, two measurement campaigns are given denoted by 2006 and 2007, at slightly different Reynolds number (see here above). In the 2006 campaign, wall pressure measurements were performed: fluctuations are characterized by their variance and their power spectral density. PIV measurements were performed in the symmetry plane of the test section (mean velocity and normal shear stresses). In the 2007 data, only PIV data were obtained, with Reynolds stresses including shear stresses. Finally stereo PIV was use to take measurements in horizontal planes to detect 3-d features. Four horizontal planes were considered. Mean velocity was measured, and only in one plane (elevation h2) the normal stresses were obtained. The details are given in the 'readme' files below and the measurement results in the associated data files.

Test Case Experiments

The experiment was carried out in the hypo-turbulent supersonic wind tunnel at IUSTI. It is a continuous facility with a closed-loop circuit. It can be operated for 4 hours with well controlled operating conditions. It is operated at a nominal Mach number of 2.25. The air is dried and the perturbations produced by the machinery are damped by appropriate devices: a Helmholtz resonator to remove the frequencies related to the compressor rotation, a heat exchanger, a drier acting continuously and a settling chamber. A regulation system stabilizes the stagnation pressure to a prescribed setting. Typically, when the wind tunnel is operated at a stagnation pressure of 0.5 bar, its variations in time are less than ±0.2%. The stagnation temperature is typically atmospheric; with a typical drift of 1K/hour. The level of background turbulence in the outer flow is essentially due to aerodynamic noise radiated by the boundary layers. Its level is less than 0.1% for velocity turbulence intensity. The range of Reynolds numbers produced in this facility encompasses moderate values (typically ); this makes the experiments well adapted to advanced modelling techniques like LES, which, in their present state are feasible for moderate Reynolds numbers.

The two-dimensional supersonic equilibrium turbulent boundary layer under investigation develops on the wind tunnel floor, which is a flat plate. The incoming conditions (inlet conditions for the interaction) are located at a distance larger than 25 cm downstream of the contoured part of the nozzle block (more than 25 boundary layer thicknesses). All x coordinates in the following correspond to an origin taken at the beginning of the flat part of the nozzle wall, and located 388.6 mm downstream of the sonic neck. Downstream of the interaction a diverging diffuser brings the flow from supersonic to subsonic conditions. Various devices are placed in the loop to prevent the propagation of aerodynamic noise.

The incoming boundary layer is turbulent and fully developed. It is subjected to a shock wave produced by a shock generator placed in the external flow, as indicated in figures 1 and 2. A shock generator made of a sharp-edged plate is fixed on the ceiling of the wind tunnel. It is placed in the free-stream and its leading edge is located in the potential flow. It entirely spans the test section and generates an oblique shock wave impinging on the floor boundary layer. Its angle with respect to the potential flow is set at 8° and 9.5°, for the two cases documented here. The global organisation of the oblique shock wave boundary layer interaction visualised by spark Schlieren is presented in Figure 3, for which the external flow deviation is 8°, and the pressure gradient is strong enough for the boundary layer to separate. Two interactions are documented, corresponding to deviations of 8° and 9.5°.

UFR 3-32 fig3.png
Figure 3: Schlieren of the interaction,


The measurement data are given here, with appropriate README files describing the data format.


README_piv_2006.txt
IUSTI_95d_case2006_2.csv
IUSTI_8d_case2006_2.csv


README_piv_2007.txt
IUSTI_theta95_2.csv
IUSTI_theta8_2.csv


README_IUSTI_UFAST_WP3_PIV3D_Horizontal_20080227.txt
IUSTI_UFAST_WP3_PIV3D_upstreamBL_h1_AJVGoff_mean.plt IUSTI_UFAST_WP3_PIV3D_interaction_h1_AJVGoff_mean.plt
IUSTI_UFAST_WP3_PIV3D_upstreamBL_h2_AJVGoff_mean.plt IUSTI_UFAST_WP3_PIV3D_interaction_h2_AJVGoff_mean.plt
IUSTI_UFAST_WP3_PIV3D_upstreamBL_h4_AJVGoff_mean.plt IUSTI_UFAST_WP3_PIV3D_interaction_h4_AJVGoff_mean.plt
IUSTI_UFAST_WP3_PIV3D_upstreamBL_h6_AJVGoff_mean.plt IUSTI_UFAST_WP3_PIV3D_interaction_h6_AJVGoff_mean.plt
IUSTI_UFAST_WP3_PIV3D_interaction_h2_AJVGoff_std.plt


README_Pressure_Spectrum_case2006.txt
pressure_spectrum_80_kulite.csv pressure_spectrum_95_kulite.csv
Pressure_Moments_80_longitudinal_distribution.dat Pressure_Moments_95_longitudinal_distribution.dat

Measurement accuracy

As mentioned in the previous section, wall pressure measurements were performed along the interaction with Kulite transducers (type XCW-062) mounted flush to the wall. Two components of velocity were measured in the incoming boundary layer, in the interaction and downstream of reattachment.

Pressure measurements

The Kulite transducers have a limited bandwidth, typically 40 kHz. They are unable to resolve turbulent fluctuations in the incoming boundary layer. However, they are convenient to measure the fluctuations induced by the shock motion (frequency about 500 Hz) or the large eddies in the separated zone (about 6 kHz).

Velocity measurements

The size of the data samples was rather large, more than 5000, so that problems of statistical convergence for mean velocity and Reynolds stresses are expected to be avoided. The uncertainties therefore arise only from biases. PIV and LDV were used as independent measurement methods. LDV was used mainly for comparisons with PIV, and by cross- check, to validate PIV measurements. The flow was seeded with particles of incense smoke. Test through a shock wave showed that their size is about 1 micron, and provides sufficient resolution. A PIV/LDA cross- check in the incoming boundary layer showed a good agreement of mean velocity, even at distances as small as . This comparison suggests that the longitudinal velocity is measured with a typical accuracy of 1%.

Particular problems arise for Reynolds stress measurements, sensitive to the phenomenon of peak locking. The field of view of the receiving optics was set to avoid this effect. Note that the shear stress is particularly sensitive to this peak locking, but not so much the normal components and . The final check is given in Figure 4, for which the wall friction used for normalization of the shear stress was derived from the log-law. In this figure, the solid line represents the subsonic data of Klebanoff (1954).

UFR 3-32 fig4.png
Figure 4: Comparison of shear stress measurements by PIV and by LDV, closed squares: PIV ; open diamonds: LDV. from Dussauge et al. 2009.

The LDV measurements are free from peak locking. They follow rather closely Klebanoff's results. The PIV measurements are also in the same spot, excepted close to the wall , where measurements are not expected to be accurate. The scatter among the data suggests that the accuracy of the measurements is about 10% for .

Two-dimensionality of the flow

The two-dimensional character of the flow has been tested, in particular, because of the presence of particle injectors at the wall, upstream of the sonic throat, which can produce periodic spanwise perturbations. This was checked by measuring by PIV the spanwise distribution of longitudinal velocity in a plane at a distance of 1mm from the wall, in the boundary layer upstream of the interaction. It is found that a the spanwise variations of are les than ±5 m/s, i.e. less than 1% of , and therefore at the limit of the accuracy of measurements (see Dussauge & Piponniau 2008).

The effect of side wall has also been investigated numerically and will be discussed in section 6. We can anticipate the results of this discussion, by saying that along the centreline, the flow can be considered as approximately two-dimensional. However, although the physics of the flow are unchanged, the presence of the sidewalls changes the length of the interaction. Since the frequency depends on the length of interaction, this changes its value, but not the Strouhal number based on the length and on the frequency.

CFD Methods

Two cases are considered for simulation, with shock generator angles of 8.0 and 9.5 degrees. At the lower angle the flow, whilst not two-dimensional, does not appear to be strongly affected by the presence of side walls and in this case an LES with periodic spanwise boundary conditions was carried out. At the higher angle the flow is strongly three-dimensional in the mean, requiring a calculation to include the full span of the wind tunnel. In this case DES were carried out.

LES (SOTON)

The numerical method and the set of simulations are thoroughly documented in Touber & Sandham (2009, 2011) and Touber (2010) and are not repeated here. The code for LES uses high-order explicit finite differences with shock-capturing and a subgrid model is activated. The published papers and thesis include a study of grid and domain size sensitivity. It was found that for small spanwise domain sizes the results were particularly sensitive to the width of the computational domain. The final domain used in the simulation presented here had a domain size equal to 1.6 times the separation bubble length, five times the domain width of the previous reference simulation. In the wall-normal direction the edge of the domain is 4.1 times the 99% boundary layer thickness at the shock impingement location. This location was not varied, but is far enough away for the reflected shock not to interfere with the redeveloping turbulent boundary layer downstream of the interaction after a possible weak reflection from the upper boundary (which is treated with characteristic boundary conditions which limit any reflections.

In practice the grids (ranging from 13.5 to 132 million grid points) are fine enough that the wall layer is reasonably well resolved, as demonstrated by a grid sensitivity study reported in the cited papers. For the calculations presented here the turbulent boundary layer upstream of the interaction is resolved on a grid with a spacing in wall units (i.e. normalised with the friction velocity and the kinematic viscosity at the wall) of 33 in the streamwise direction, 12 in the spanwise direction and with a smallest grid cell of size 1.3 in the normal direction.

The inflow boundary layer was specified by an approximate (van Driest scaled) mean profile superimposed with fluctuations obtained from a digital filter technique (the computer code for this is provided in Touber, 2010). The method was compared with an alternative deterministic model (Sandham et al, 2003) which gave similar results in terms of a distance downstream for the skin friction to settle down. The digital filter technique was ultimately preferred to the deterministic fluctuation model since it did not introduce particular spikes into the spectrum of the inflow turbulence that might later be confused with the low-frequency response that was the ultimate interest (Touber & Sandham 2011). The distance allowed in the simulation for the boundary layer to relax to equilibrium before the shock impingement was not varied. To study low frequency characteristics the simulation was run for 25.4 low frequency cycles (with frequency , where is the free stream velocity and is the interaction length, equal to the distance from the origin of the reflected shock to the inviscid impingement location), equivalent to over 100 through-flows of the domain. A no-slip fixed temperature condition was applied at the walls and characteristic conditions were applied at the remaining boundaries, with the shock triggered by imposing the Rankin-Hugoniot relations.

DES (ONERA/DAAP)

Details of the computational approach are provided in Garnier (2009) and are not repeated here in full. The code FLU3M is a finite-volume solver for the compressible Navier-Stokes equations. The numerical scheme for the temporal integration is the implicit scheme of Gear described in Péchier (2001). With the chosen time step, the subiterative process which insures the second order time accuracy converges by one order of magnitude within five iterations. The maximum CFL number remains lower than 20. The choice of the numerical scheme dedicated to the computation of the convective fluxes is of particular importance in this type of application where shock waves and turbulence are intimately linked. Shock-capturing schemes must be employed to guarantee the stability of the solution in presence of flow discontinuities. These schemes are then necessarily dissipative and careful attention needs to be paid to the design of limiters (Garnier, 2009).

Generally in DES methods, the length scale which appears in the dissipation term of the Spalart-Allmaras model is the minimum of 0.65 and of the distance to the wall. For the SDES (stimulated detached eddy simulation), the objective is that the turbulence model behaves as a classical subgrid scale model as in LES; the length scale is then estimated as the cubic root of the cell volume instead of the directional maximum of the grid size. Furthermore, the damping functions of the Spalart-Allmaras model are modified to force a LES behaviour. Building a mesh based on cells of 50 wall units in both longitudinal and spanwise directions (instead of 12-18 for LES in the spanwise direction), the interface between RANS and LES in DES mode is located at less than 10 wall units from the wall. Above this limit, SDES behaves as a classical LES with, however, a subgrid scale model formulated in a different way. Below this height, the SDES behaves as a Spalart-Allmaras model which can here be considered as a wall model for LES. This technique suffers from the same constraints as LES which must be fed with realistic inflow fluctuations. For this application, the Synthetic Eddy Method (SEM) technique (Garnier 2009) has been employed. It is based upon a superposition of analytically defined eddies whose distributions follow imposed Reynolds stress profiles. These eddies are injected at the computational domain inflow in a random way to avoid the generation of a streamwise-periodic flow. Nevertheless, some adaptation distance is needed to obtain realistic turbulence. On the side walls, RANS is used everywhere above the boundary layer of the lower wall whereas SDES is used below. 33 points discretize the wall normal gradient in each of the lateral boundary layer.




Contributed by: Jean-Paul Dussauge (*), P. Dupont (*) , N. Sandham (**), E. Garnier (***) — (*) Aix-Marseille Université, and Centre National de la Recherche Scientifique UM 7343, (**) University of Southampton, (***) ONERA/DAAP, Meudon, France

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