Turbulence modelling from the perspective of the commercial CFD

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Turbulence modelling from the perspective of the
commercial CFD



Workshop Advances in Numerical Algorithms


Dr. B. Basara


AVL List GmbH

Graz, Austria, September 10
-
13, 2003

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Content




-

Introduction (motivation, some examples)

-

Computational grids

-

Numerical method (control volume method)

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Turbulence models

-

Conclusions




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Motivation

-

Computational Fluid Dynamics (CFD) is used to solve fluid flow and
associated transport processes.

-

Complex ‚real
-
life‘ flows are predominantly turbulent

-

Turbulence models are considered as an Achilles‘ heel of modern
CFD

-

‚Plugged‘ on numerical algorithms and used in various calculations

of fluid flow, the turbulence models are the largest source of error

-

However, numerical algorithms often define the range of usability of
various complex turbulence model

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Some ‘real
-
life’ examples

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Turbulence models

2
3
j
i i k
ij i j
i j j i k
U
DU U U
P
u u
Dt x x x x x
   
 
 

 
 
     
 
 
 
    
 
 
 
-

robust ?

-

accurate ?

-

where is the optimum?

i j
u u


-
known as Reynolds stresses are modelled

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User Defined


Boundary Layer


Entirely Conform

Meshing Options



Semi
-
Automatic



Entirely Conform



User Defined


Boundary Layer



Entirely Hex



Entirely Conform




Arbitrary Interfaces

Automatic Tet Mesh

Automatic Hex Mesh

Block Structured Mesh

Multi
-
Domain Meshing

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Calculation

grids

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Solution algorithm directly


includes:



Arbitrary Interfaces


local grid refinement


rearrangement of

the cells due to moving/sliding



Finite Volume Method

-

polyhedral control volume

-

co
-
located variable arrangement

-

connectivity is defined for cell
-
face
-
cell


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Control volumes

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Discretization method

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Surface and volume integrals

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Discretization method




All dependent variables are stored at the
geometric center of a control volume (co
-
located or non
-
staggered variable
arrangement); at boundaries they are defined
at the centers of the CV boundary faces.


The surface integrals are approximated by
using the values of integrands that prevail at
the geometric center (known as the midpoint
rule approximation).


For evaluation of dependent variables, their
derivatives and fluid properties at locations
other then cell centers, linear variation in
space is assumed.



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Gauss‘ formula, deferred correction approach ...

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Central and upwind differencing schemes

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Higher order schemes

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Discretization procedure

-
convection

-
diffusion

-
Algebraic equations

solved by the biconjugate gradient method in conjunction with the

incomplete Cholesky preconditioning technique or by the Algebraic

multigrid

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Face Velocity (pressure
-
velocity coupling)

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Momentum equation and the standard k
-
e

m潤敬

2
3
j
i i k
ij i j
i j j i k
U
DU U U
P
u u
Dt x x x x x
   
 
 

 
 
     
 
 
 
    
 
 
 
2
2
3
i j t ij ij
u u S k
  
  
1
2
j
i
ij
j i
U
U
S
x x




 



 


2
t
k
C

 
e

K
-
e

-

robust ?

( )
t
k
j k j
Dk k
P
Dt x x

  e 



 
 
   


 
 

 


1 3 2
k t
k
k j k j
U
D
C P C k C
Dt x k x x
e e e

e e e
  e 



   

 
    


   
  

   


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Reynolds
-
stress model

-

RSM (AVL Swift uses
SSG)

1
2
i i
k u u

1 3 2
k
k i j
k j i
U
D k
C P C k C C u u
Dt x k x x
e e e e
e e e
e
e 
   


   
   
 
   
2'

3
i j i j j i j i j
i
k i k j k s k l
k k k k k l
j
i
ij
j i
u u u u U u u u u
U
k
U u u u u C u u
t x x x x x x
u
u
p
x x
    



      e 


e
  
 
 
     
 
 
 
 
 
 
  
 
 
 
,,?
i i j
U u u p coupling


RSM

-

accurate ?

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A
vortex shedding around a square cylinder
(Re=21400). Predictions with RSM (SSG) model.

Table 1.
Predictions and measurements of integral parameters.

Cd

Cl’

Str
Present RSM
2.28
1.39
0.141
Measurements
2.16-2.28
1.1-1.4
0.130-0.139
-
velocity

-
t.k.e

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Example: VW model

-1,5
-1
-0,5
0
0,5
1
1,5
0
0,2
0,4
0,6
0,8
1
DATA
SWIFT k-eps
SWIFT RSM
Data k
-
e

RSM


-
In the case of RSM model, a description of

the flow pattern over the slant is very close

to the measured one as shown in Figures.


-
Predicted pressure distribution by RSM is
in very good agreement with the
measurements.

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Renault model

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K
-
e

瑵rbul敮琠浯d敬produ捥猠瑯ol敳猠
獥s慲慴aonon瑨攠r敡eindo


Transient RSM approach has been used.Global
coefficients (lift and drag) fit better to the
measurement


RSM is closer to measured Cp curve specially
on the rear end of the car


The CPU time by RSM was 4 times longer, the
same mesh has been used




Ford KA

Experiment

SWIFT RSM

SWIFT k
-
e

External Car Aerodynamics

R

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External Car Aerodynamics

R

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AVL HTM
model


2
3
j
i i k
ij i j
i j j i k
U
DU U U
P
u u
Dt x x x x x
   
 
 

 
 
     
 
 
 
    
 
 
 
2'

3
i j i j j i j i j
i
k i k j k s k l
k k k k k l
j
i
ij
j i
u u u u U u u u u
U
k
U u u u u C u u
t x x x x x x
u
u
p
x x
    



      e 


e
  
 
 
     
 
 
 
 
 
 
  
 
 
 
1 3 2
k
k i j
k j i
U
D k
C P C k C C u u
Dt x k x x
e e e e
e e e
e
e 
   


   
   
 
   
1
2
i i
k u u

2
2
3
i j t ij ij
u u S k
  
  
2
t
k
C

 
e

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AVL HTM
model

-
Therefore, AVL HTM model is more accurate than the k
-
e

model

-
AVL HTM model is more robust than the RSM

-
AVL HTM model introduces following formula instead using the constant value

in Boussinesq’s relation, thus

2
2
/
2
i
i j
j
ij ij
U
k
C u u S
x
S S S

e
 
 

 
 
 
 

 
 

-

Equation above is checked by using DNS data.

C

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Example: a vortex shedding flow

-
transient calculations show a large variations of



C

-
measurements

-
measurements

-
calculations

-
calculations

, Basara et al. 2001

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Example: Backward
-
facing step


K
-
e



HTM

-
the worst convergence rate

achieved with RSM, see

Figure above (the grid is
orthogonal !).

-

Basara & Jakirlic (2003)

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Example: 180 degree turn
-
around duct

K
-
e

RSM

AVL HTM

180 degree

0.02 0.2
C

 
-
separation predicted with HTM and RSM but not

with the k
-
e
model (Basara 2001).

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Prototype
VRAK



Results Comparison





Drag

D

%


䱩晴


D





Exp.


0.359


0.336


Case 1

k
-
e

〮㌶0

㈮㐵

〮㐶0

〮ㄳ


䡔e

〮㌵0

㈮㈲

〮㌶0

〮〲0







Real
-
life application: EADE
Benchmark

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Simplified Bus

-
A separation point is fixed by
the shape of the body and
therefore the flow pattern
predicted by two models is very
similar.

-
Note the difference of the
turbulence kinetic energy at the
front part of the body as well as
behind the body.

-
Therefore, the ‘acoustic
module’ will get different
sources !

K
-
e

HTM

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A linearized Euler Method Based Prediction of
Turbulence Induced Noise using Time
-
averaged
Flow Properties.


The turbulence is regarded as the autonomous source of the noise and therefore it is very important
to get a proper intensity and the distribution of turbulence kinetic energy.The time
-
accurate sources
can be extracted from the results of time
-
averaged RANS. The radiation of the acoustic sources is
determined using a Linearized Euler Solver. Etc.

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Conclusions

-

Alternatives: DNS, LES, DES, PANS ?

-

LES and DNS are too costly for most engineering calculations and require additional modelling for
other flow classes e.g. multiphase flow, combustion, etc., which still have to be resolved.

-

DES and PANS are under investigations

-

However, the RANS framework, in conjunction with turbulence models, can be expected to remain the
main ‘tool’ to solve practical industrial applications for a long time


-
Courtesy of Dr. B.Niceno

(AVL sponsored PhD work at TU Delft)