Advanced Simulation Technologies
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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)

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
2.162.28
1.11.4
0.1300.139

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 keps
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ol敳猠
獥s慲慴aonon瑨攠r敡eindo
•
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)
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