Transcript Hybrid RANS-LES presentation for TSFP 3

A combined RANS-LES strategy with
arbitrary interface location for near-wall
flows
Michael Leschziner and Lionel Temmerman
Imperial College London
1
Overview
1.
Motivation
2.
Method Description
3.
Observation from Past Work
4.
Modelling practice and Methodology
5.
Results for Channel Flow
6.
Results for Hill Flow
7.
Concluding Remarks
2
Motivation
 Grid requirements for LES of wall-bounded flows:

 x  50


y  2
 z  20
1.8
 Number of nodes rises as R e L (Chapman (1979))
 High Reynolds LES is prohibitively expensive
 Cost reducing strategies:
• Wall functions (Schumann (1975); Werner and Wengle (1993));
• Zonal approach (Balaras et al (1996));
• Hybrid RANS-LES methods (DES - Spalart et al (1997); Hamba
(2001)).
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Alternative Approaches
 Wall functions:
• Mostly based on log-law approximations;
• Tends to be ‘adequate’ in simple shear flows;
• Inadequate for separated flows (no universal behaviour).
 Zonal approach:
• Simplified set of equations resolved near the wall (TBL
equations);
• Saving results from the removal of the Poisson problem;
• Not adequate for all flows.
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Alternative Approaches
 Hybrid RANS-LES strategies:
• Part of the turbulence is modelled in the ‘RANS’ layer;
• Allow to use large aspect ratio cells – we hope!
• Location of the interface:
 either decided by user;
 or controlled by cell dimensions – compare y and  =
f(x,y,z) as in DES;
 Interface shift done via modifications of the grid: shift away from
the wall  higher x and z;
 High streamwise/spanwise resolution required in some flows
(separated) even with RANS methods  interface may be too
close to the wall.
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Method Description
Imposed RANS conditions
Imposed LES conditions
at interface
at interface
LES Domain
RANS Layer
RANS layer prescribed by reference to the wall distance.
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Observations from Previous Work
 In the URANS region, the
resolved and the
modelled contributions to
the motion are of equal
importance.
 Total is too high  need
of an ad hoc modification
to reduce the total
motion.
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Modelling Practice
 RANS model: one-equation transport model for
turbulence energy (Wolfshtein (1969));
 SGS model: One-equation transport model for SGS
energy (Yoshizawa and Horiuti (1985))
 Assumption: RANS and LES grids are identical at the
interface;
 Target:
• Velocity: U
RANS
int
U
LES
int
LES
• Viscosity:  tRANS


, int
t , int
• Modelled energy: k
RANS
mod, int
;
;
LES
 k mod, int
.
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Methodology

RAN S
m od

LES
m od
with
 mod
RANS
 C  l k
0 .5
 m od,int
LES
hence
C  ,int 
0.5
l  k R A N S ,int
< . > : spatial average in the homogeneous directions.
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Methodology
Function 1
C   0.09 
C
 ,int
1  exp   y   
 0.09 
1  exp   y int  int  
Function 2


y
fo r
 C   0 .0 9
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

C
 C  0 .0 9    ,in t



y

 27

 0 .0 9  1  ex p (  ( y  y ( y  3 4 )) /  ) 
1  ex p (  y in t  y ( y


 3 4 ) /  in t ) 
fo r y

 27
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Channel Flow – Case Description
 Periodic channel flow;
 Re b  42200 ;
 RANS-LES and coarse LES:
• Computational domain: 2  h  2 h   h ;

• Grid: 64 x 64 x 32 cells with y c (1)  0 . 4 and  x   z ;
 Dense LES:
• Computational domain: 2 h  2 h  0 . 5 h;

• Grid: 512 x 128 x 128 cells with y c (1)  0 . 75 .
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Channel Flow - Results
512 x 128 x 128 cells
64 x 64 x 32 cells
Time-averaged velocity and shear stress profiles for the LES computations.
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Channel Flow - Results
Time-averaged C profiles across the RANS layer (64 x 64 x 32 cells).
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Channel Flow - Results
Time-averaged velocity profiles for the hybrid RANS-LES computations
(64 x 64 x 32 cells).
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Channel Flow - Results
Time-averaged shear stress and turbulent energy profiles for the hybrid
RANS-LES computations (64 x 64 x 32 cells).
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Channel Flow - Observations
 Encouraging results.
 The response to the parameters change is small.
 Response to the change of location of the
interface:
• Change in the proportion of modelled motion;
• Variation in the width of near-wall total turbulence
energy peak.
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Hill Flow – Case Description
 Periodic channel flow with constrictions at both ends
 Reynolds number based on channel height and bulk
velocity is 21560
 Data from highly resolved LES computations (5 x 106 cells)
by Temmerman et al (2003)
 Domain size: 9h x 3.036 h x 4.5 h (h=hill height)
 Grid details:
• Discretisation: 112 x 64 x 56 cells (4 x 105 cells);
• Near-wall resolution: y+c(1) 1;
• Spanwise and streamwise resolution: x = z.
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Hill Flow - Results
Left: location of the RANS-LES near-wall interface.
Right: Distribution of C along the interface
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Hill Flow - Results
196 x 128 x 186 cells
(x/h)sep. = 0.22
(x/h)reat. = 4.72
(x/h)sep. = 0.21
(x/h)reat. = 5.30
112 x 64 x 56 cells
(x/h)sep. = 0.23
(x/h)reat. = 4.64
(x/h)sep. = 0.23
(x/h)reat. = 5.76
Averaged streamlines for the reference simulation, LES, DES and RANS-LES
cases.
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Hill Flow - Results
Left: Distribution of C across the lower RANS layer (right).
Right: Streamwise velocity profiles in wall units at x/h = 2.0.
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Hill Flow - Results
Streamwise velocity profiles at x/h = 2.0.
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Hill Flow - Results
Turbulent viscosity profiles at two streamwise positions.
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Hill Flow - Observations
 The location of reattachment is overestimated by the
hybrid RANS-LES and DES probably because of the
wrong prediction of the wall shear stress.
 Compared to the channel case, C has a similar
behaviour.
 Overall, good agreement with the reference data.
 Difficult to draw definitive conclusions; too low Reynolds
number.
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Concluding Remarks
 New hybrid RANS-LES method allowing:
• Freedom in locating the interface;
• Dynamic adjustment of the RANS model to ensure continuity
across the interface.
 For identical grids, the results obtained with the
RANS-LES approach were significantly better than
those obtained with LES.
 Application to a recirculating flow:
• Results are non-conclusive due to low Reynolds number 
new test case (separated hydrofoil at Rec = 2.15 x 106);
• The hybrid RANS-LES approach overestimates the
recirculation zone length.
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