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=== Underlying Flow Regime 3-32 ===  
=== Underlying Flow Regime 3-32 ===  
= Description =
= Description =
<!--{{LoremIpsum}}-->
== Introduction ==
== Introduction ==
{{Demo_UFR_Desc_Intro}}
The problem of the unsteadiness in shock wave/boundary layer interactions
(SWBLI) is challenging in many  respects.  A  more  general  question  is
related to the unsteadiness or "breathing" of separated  flows,  whatever
the regime, subsonic or supersonic. This is a problem that  is  important
for  both  applications  and  basic  research.  In  many  aeronautical
applications,  such  as  aircraft  profiles,  air  intakes,  turbines  or
compressors, shock waves are formed and generally lead to separation. The
resulting separation bubbles are unsteady, in the sense that they produce
frequencies much lower (by at least two orders  of  magnitude)  than  the
identified frequencies of the turbulent flow. Another  difficulty  arises
if high-speed flows are considered, in which  case  the  unsteadiness  is
also dependent on Mach number.
 
A  first  point  is  the  understanding  of  the  origin  of  these  low
frequencies:  how  is  it  possible  to  produce,  from  the  turbulent
fluctuations of the  boundary  layer,  very  low  frequencies,  involving
scales differing from the turbulent layer itself generally by two  orders
of magnitude? Several possibilities have been examined in recent years. A
first one assumes that the superstructures of the incoming layer (hairpin
packets of length about 20''&delta;''  or  more)  make  the  shock  wave  and  the
separated zone move
([[UFR_3-32_References#8|Ganapathisubramani&nbsp;''et&nbsp;al,''&nbsp;2007,&nbsp;2009]]).
A second  one
([[UFR_3-32_References#13|Piponniau&nbsp;''et&nbsp;al&nbsp;'' 2009]])
considers that the low frequencies  are  produced
by a process of emptying/filling of the  separation  bubble.  Because  of
fluid entrainment, the air of the separation zone is drained by the large
structures,  Kelvin-Helmholtz-like,  formed  at  the  edge  of  the
recirculating zone, and is progressively  emptied,  until  it  is  filled
again by air incoming in the reverse direction. The second scenario seems
more appropriate, since it is able to reproduce the dominant  frequencies
in shock reflections, while the first one fails for  this  flow  case.  A
point which can  be  underlined  is  that  the  scales  involved  in  the
unsteadiness are not directly related to the incoming boundary layer, and
therefore  cannot  be  reduced  by  some  simple  similarity  to  the
characteristics of the boundary layer. This latter point is reinforced by
a third approach ([[UFR_3-32_References#17|Touber & Sandham, 2011]]),
based on a simplified momentum
integral analysis, which shows how the low  frequency  can  develop  from
uncorrelated broadband stochastic forcing of a separating boundary layer.
 
From the CFD point of view, such flows remain challenging. Many  attempts
have been made to compute SWBLI, to  determine  the  mean  and  turbulent
fields or the unsteadiness. The few attempts of applying  compressibility
flow  corrections  in  turbulence  modelling  have  demonstrated  an
insufficient  predictive  capability  of  unsteady  flows  with  strong
compressibility  effects  and  attempts  to  'extrapolate'  turbulence
modelling from incompressible flows have also  proven  insufficient  for
the accurate prediction of the buffeting phenomenon and of  transonic-dip
flutter (examples: research program ETMA, Vieweg, Vol.  65  and  European
research program  UNSI,  final  report  edited  by  Springer,  Vol.  81),
concerning the simulation of buffeting phenomenon and of  shock  unsteady
motion. A difficulty for RANS methods comes probably from their tuning to
simple, self-similar equilibrium situations, and hence cannot  cope  with
the  new  scales  which  are  typically  out  of  equilibrium,  having  a
particular dynamics. More recently the hybrid approach DES (Detached Eddy
Simulation), that is an inherently 3D approach, has been applied  to  the
transonic  flows  around  airfoils,  indicating  the  crucial  need  for
improvement of flow-physics knowledge concerning the modification of  the
turbulence scales due to the unsteadiness and compressibility.
 
It seems that methods like LES do not suffer from the same limitations as
RANS; a consequence is that hybrid methods like the different versions of
DES may represent an interesting compromise by combining the  flexibility
of LES and the  economy  in  computational  resources  of  RANS.  On  the
numerical side, such flows represent some challenging aspects: there  are
the usual requirements on meshes, since in LES computations the mesh size
acts as a filter and therefore is part of the modelling,  and  there  are
other difficulties since unsteady shocks should be adequately represented
by the computations, without being confused with turbulence.
 
For the present  application  to  shock-wave/boundary-layer  interaction,
experiments provide detailed descriptions of the flow, for the  mean  and
turbulent fields, and for the characterization of the  unsteadiness.  The
data are compared to the results  of  computations,  using  LES,  several
types of DES, and  URANS  and  RANS  methods  based  on  Spalart-Allmaras
modelling. The discussions will  also  lead  to  the  assessment  of  the
importance of taking in account the 3D effects for  predicting  correctly
the separated zone and in turn, the interaction unsteadiness.
 
== Review of UFR studies and choice of test case ==
== Review of UFR studies and choice of test case ==
{{Demo_UFR_Desc_Review}}
Shock-wave/boundary-layer interactions (SWBLI) remain challenging for the
physical understanding and for numerical simulations, in particular  when
they lead to flow separation, which is in general unsteady. In the  past,
in  pioneering  work  performed  at  Princeton  University  and  at  the
University of Austin, some aspects of  the  unsteadiness  of  SWBLI  were
examined (see for example [[UFR_3-32_References#3|Dolling&nbsp;(2001)]]
and  [[UFR_3-32_References#14|Smits&nbsp;&&nbsp;Dussauge&nbsp;(2006)]]  for
reviews). Many cases were investigated, such as corner flows, blunt  body
interactions  and  3D  interactions;  they  provided  in  many  cases
measurements  of  wall  pressure  fluctuations,  and  led  to  first
understanding of shock unsteadiness and  separated  flow  breathing.  The
European  program  UFAST  organised  considerable  effort  to  study  and
document this question. Among all the possible  interactions,  particular
attention was paid to the case of oblique shock reflection, which imposes
severe compression to boundary layers.  Moreover,  this  occurs  in  many
particular situations, such as air intakes, compressors,  turbines  etc.,
and can be very detrimental for the structures. It was  felt  that  there
was a need for experiments at moderate Reynolds numbers to serve as  test
cases for advanced turbulence modelling like LES or  DES.  Several  cases
were studied  experimentally  at  Mach  numbers  of  1.7,  2.0  and  2.25
respectively at  Delft  University  of  Technology  (TU  Delft),  at  the
Institute of Theoretical and Applied Mechanics (ITAM) Novosibirsk  and  at
the Institut Universitaire des Systèmes  Thermiques  Industriels  (IUSTI)
Marseille. All the experiments include statistical  measurements  of  the
flow field (mean and fluctuating) and a characterization of  unsteadiness
by the measurements of spectra. Details of the experiments can  be  found
in [[UFR_3-32_References#1|Doerffer&nbsp;(2009)]].
Numerical simulations within  UFAST  include  a  large
number of turbulence  modelling  approaches,  together  with  2D  and  3D
computations. The simulations were performed by  NUMECA  (Brussels),  IMF
Toulouse,  UAN  (Karkhov),  SOTON  (University  of  Southampton),  and
ONERA/DAAP. [[UFR_3-32_Description#table1|Table 1]],
taken from Garnier (Chapter 10 in  [[UFR_3-32_References#2|Doerffer&nbsp;''et&nbsp;al.''&nbsp;2010]]),
sums up the different attempts by the different groups.
 
As reported in [[UFR_3-32_References#1|Doerffer&nbsp;(2009)]] and in
[[UFR_3-32_References#2|Doerffer&nbsp;''et&nbsp;al.''&nbsp;(2010)]],  it  is
interesting to focus on the IUSTI  experiments,  both  because  they  are
extensively documented, including  some  three-dimensional  aspects,  and
because the associated computations have led to comparisons between RANS,
URANS, hybrid methods like DES,  and  LES.  RANS  methods  by  principle
cannot catch the unsteadiness. They can however  give  some  indications,
provided they can predict the size of the interactions. In some analyses,
this size is related to the characteristic frequency of the shock motion,
so that it can indirectly  provide  indications  on  its  time  dependent
behaviour. However, the conclusions show of course the potential  of  LES
and DES to determine unsteadiness. The results have also  underlined  the
importance of 3D effects in nozzles of finite span, which  contribute  to
the organization of the separated zone. The present document is based  on
the numerical simulations of ONERA/DAAP (DES and LES)  and  SOTON  (LES),
although we make some reference to RANS simulations.
 
 
<div id="table1"></div>
{|align="center" border="1" cellpadding="5"
! !!Temporal Scheme!!Spatial Scheme!!Modelling!!Remark
|-
|align="center"|NUMECA||align="center"|Runge-Kutta + IRS||align="center"|Jameson
|align="center"|''RANS:'' SA, ''k-&epsilon;'', SST, v2-f
''Hybrid:'' DES-SA
|align="center"|Multigrid
|-
|align="center"|IMFT||align="center"|DTA||align="center"|Roe (Van Leer limiter)
|align="center"|''RANS:'' SA
''Hybrid:'' DES, OES
|align="center"|&nbsp;
|-
|align="center"|UAN||align="center"|Implicit ''O''(2)||align="center"|ENO Godunov ''O''(2)
|align="center"|''RANS:'' ''k-&omega;'', SST
|align="center"|Realisabilty cond. in turb. model
|-
|align="center"|SOTON||align="center"|RK3||align="center"|Centred ''O''(4) + TV model
|align="center"|''LES:'' MTS, DYN
|align="center"|Digital filter for inf. cond.
|-
|align="center"|ONERA||align="center"|Implicit ''O''(2)||align="center"|Roe ''O''(2) + TVD filter
|align="center"|''RANS:'' MSM, SA
''Hybrid:'' DDES SA based, SDES SA based
|align="cenetr"|Synthetic Eddy Method (SEM) inflow conditions
|}
 
 
<center>'''Table 1:''' Brief description of the codes from [[UFR_3-32_References#2|Garnier (2010)]]</center>
 
<br/>
<br/>
----
----
{{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

Description

Introduction

The problem of the unsteadiness in shock wave/boundary layer interactions (SWBLI) is challenging in many respects. A more general question is related to the unsteadiness or "breathing" of separated flows, whatever the regime, subsonic or supersonic. This is a problem that is important for both applications and basic research. In many aeronautical applications, such as aircraft profiles, air intakes, turbines or compressors, shock waves are formed and generally lead to separation. The resulting separation bubbles are unsteady, in the sense that they produce frequencies much lower (by at least two orders of magnitude) than the identified frequencies of the turbulent flow. Another difficulty arises if high-speed flows are considered, in which case the unsteadiness is also dependent on Mach number.

A first point is the understanding of the origin of these low frequencies: how is it possible to produce, from the turbulent fluctuations of the boundary layer, very low frequencies, involving scales differing from the turbulent layer itself generally by two orders of magnitude? Several possibilities have been examined in recent years. A first one assumes that the superstructures of the incoming layer (hairpin packets of length about 20δ or more) make the shock wave and the separated zone move (Ganapathisubramani et al, 2007, 2009). A second one (Piponniau et al  2009) considers that the low frequencies are produced by a process of emptying/filling of the separation bubble. Because of fluid entrainment, the air of the separation zone is drained by the large structures, Kelvin-Helmholtz-like, formed at the edge of the recirculating zone, and is progressively emptied, until it is filled again by air incoming in the reverse direction. The second scenario seems more appropriate, since it is able to reproduce the dominant frequencies in shock reflections, while the first one fails for this flow case. A point which can be underlined is that the scales involved in the unsteadiness are not directly related to the incoming boundary layer, and therefore cannot be reduced by some simple similarity to the characteristics of the boundary layer. This latter point is reinforced by a third approach (Touber & Sandham, 2011), based on a simplified momentum integral analysis, which shows how the low frequency can develop from uncorrelated broadband stochastic forcing of a separating boundary layer.

From the CFD point of view, such flows remain challenging. Many attempts have been made to compute SWBLI, to determine the mean and turbulent fields or the unsteadiness. The few attempts of applying compressibility flow corrections in turbulence modelling have demonstrated an insufficient predictive capability of unsteady flows with strong compressibility effects and attempts to 'extrapolate' turbulence modelling from incompressible flows have also proven insufficient for the accurate prediction of the buffeting phenomenon and of transonic-dip flutter (examples: research program ETMA, Vieweg, Vol. 65 and European research program UNSI, final report edited by Springer, Vol. 81), concerning the simulation of buffeting phenomenon and of shock unsteady motion. A difficulty for RANS methods comes probably from their tuning to simple, self-similar equilibrium situations, and hence cannot cope with the new scales which are typically out of equilibrium, having a particular dynamics. More recently the hybrid approach DES (Detached Eddy Simulation), that is an inherently 3D approach, has been applied to the transonic flows around airfoils, indicating the crucial need for improvement of flow-physics knowledge concerning the modification of the turbulence scales due to the unsteadiness and compressibility.

It seems that methods like LES do not suffer from the same limitations as RANS; a consequence is that hybrid methods like the different versions of DES may represent an interesting compromise by combining the flexibility of LES and the economy in computational resources of RANS. On the numerical side, such flows represent some challenging aspects: there are the usual requirements on meshes, since in LES computations the mesh size acts as a filter and therefore is part of the modelling, and there are other difficulties since unsteady shocks should be adequately represented by the computations, without being confused with turbulence.

For the present application to shock-wave/boundary-layer interaction, experiments provide detailed descriptions of the flow, for the mean and turbulent fields, and for the characterization of the unsteadiness. The data are compared to the results of computations, using LES, several types of DES, and URANS and RANS methods based on Spalart-Allmaras modelling. The discussions will also lead to the assessment of the importance of taking in account the 3D effects for predicting correctly the separated zone and in turn, the interaction unsteadiness.

Review of UFR studies and choice of test case

Shock-wave/boundary-layer interactions (SWBLI) remain challenging for the physical understanding and for numerical simulations, in particular when they lead to flow separation, which is in general unsteady. In the past, in pioneering work performed at Princeton University and at the University of Austin, some aspects of the unsteadiness of SWBLI were examined (see for example Dolling (2001) and Smits & Dussauge (2006) for reviews). Many cases were investigated, such as corner flows, blunt body interactions and 3D interactions; they provided in many cases measurements of wall pressure fluctuations, and led to first understanding of shock unsteadiness and separated flow breathing. The European program UFAST organised considerable effort to study and document this question. Among all the possible interactions, particular attention was paid to the case of oblique shock reflection, which imposes severe compression to boundary layers. Moreover, this occurs in many particular situations, such as air intakes, compressors, turbines etc., and can be very detrimental for the structures. It was felt that there was a need for experiments at moderate Reynolds numbers to serve as test cases for advanced turbulence modelling like LES or DES. Several cases were studied experimentally at Mach numbers of 1.7, 2.0 and 2.25 respectively at Delft University of Technology (TU Delft), at the Institute of Theoretical and Applied Mechanics (ITAM) Novosibirsk and at the Institut Universitaire des Systèmes Thermiques Industriels (IUSTI) Marseille. All the experiments include statistical measurements of the flow field (mean and fluctuating) and a characterization of unsteadiness by the measurements of spectra. Details of the experiments can be found in Doerffer (2009). Numerical simulations within UFAST include a large number of turbulence modelling approaches, together with 2D and 3D computations. The simulations were performed by NUMECA (Brussels), IMF Toulouse, UAN (Karkhov), SOTON (University of Southampton), and ONERA/DAAP. Table 1, taken from Garnier (Chapter 10 in Doerffer et al. 2010), sums up the different attempts by the different groups.

As reported in Doerffer (2009) and in Doerffer et al. (2010), it is interesting to focus on the IUSTI experiments, both because they are extensively documented, including some three-dimensional aspects, and because the associated computations have led to comparisons between RANS, URANS, hybrid methods like DES, and LES. RANS methods by principle cannot catch the unsteadiness. They can however give some indications, provided they can predict the size of the interactions. In some analyses, this size is related to the characteristic frequency of the shock motion, so that it can indirectly provide indications on its time dependent behaviour. However, the conclusions show of course the potential of LES and DES to determine unsteadiness. The results have also underlined the importance of 3D effects in nozzles of finite span, which contribute to the organization of the separated zone. The present document is based on the numerical simulations of ONERA/DAAP (DES and LES) and SOTON (LES), although we make some reference to RANS simulations.


Temporal Scheme Spatial Scheme Modelling Remark
NUMECA Runge-Kutta + IRS Jameson RANS: SA, k-ε, SST, v2-f

Hybrid: DES-SA

Multigrid
IMFT DTA Roe (Van Leer limiter) RANS: SA

Hybrid: DES, OES

 
UAN Implicit O(2) ENO Godunov O(2) RANS: k-ω, SST Realisabilty cond. in turb. model
SOTON RK3 Centred O(4) + TV model LES: MTS, DYN Digital filter for inf. cond.
ONERA Implicit O(2) Roe O(2) + TVD filter RANS: MSM, SA

Hybrid: DDES SA based, SDES SA based

Synthetic Eddy Method (SEM) inflow conditions


Table 1: Brief description of the codes from Garnier (2010)




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

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References


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