A Synthetic Eddy Method for
generating inflow conditions for LES
N. Jarrin, S. Benhamadouche, D. Laurence, R. Prosser
1
Table of Contents
• Introduction to Synthetic Turbulence
• The Synthetic Eddy Method
• Numerical Test Cases
– Spatially Decaying Isotropic Turbulence
– Inlet/Outlet Plane Channel Flow Re*=395
• Conclusions and Future Work
2
Introduction to Synthetic
Turbulence
• A need specific to LES and DNS
• A wide range of applications
– Initialisation of flow fields
– inlet boundary conditions, embedded LES
– Forcing at the interface of hybrid RANS/LES
• How to generate realistic turbulence?
– Most efficient methods are not industrial (database rescaling, POD)
– Synthetic generation of turbulence from RANS statistics
• random method
• spectral method (Lee et al. Physics of Fluids 1992)
• digital filtering (Klein et al. Journal of Computational Physics, 2003)
3
Synthetic Eddy Method (SEM)
Principle
x
– A turbulent flow is a superposition of coherent eddies
– Each eddy is described by a shape function f (x )
[− rx ; rx ]× [− ry ; ry ]× [− rz ; rz ]
– Each eddy has a random position
( yi , z i )
i
with compact support
on the inlet plane
– Each eddy is convected through the inlet plane
until it is not active anymore ( xi > rx ), then a
new one is regenerated at xi = − rx
4
Synthetic Eddy Method (SEM)
•
Formulation
– The eddy signal
1
v j ( x, t ) =
N
N
∑ε
i =1
i
f j ( x − x i (t ))
N = number of vortices
ε i = ±1
– Rescaling
ui ( x, t ) = U i ( x) + aij ( x) v j ( x, t )
(aij ( x)) Choleski decomposition of ( Rij ( x))
(by construction, not computed)
5
Synthetic Eddy Method (SEM)
•
Signal characteristics
– Mean velocity and Reynolds stresses profiles
– Autocorrelation function and energy spectrum imposed by shape function
R11 (r ) = f1 ( x) f1 ( x + r )
– Low computational cost due to limited number of eddies
– Divergence free inlet condition with divergence free shape functions
•
Free parameters
– Length and time scales (tuning is objective of current work)
– Shape function of eddies (tuning is objective of current work)
6
Spatially Decaying Isotropic
Turbulence
•
Parameters
– Uc = 20, k = 3/2,
•
Mesh
•
Numerical Procedure
υ = 10 −4
– Lx * Ly * Lx = 6π × 2π × 2π
– Nx * Ny * Nz = 192*64*64 cells
– Finite volume unstructured incompressible code: Code_Saturne
– Smagorinsky model with Cs = 0.18
•
Tests
– 1) Compare methods,
2) Size of eddies,
3) Shape of eddies
7
HIT: Methods inlet
f (r )
1) … Random method
2) ___ SEM with 3D isotropic spots (
f (r )
gaussian)
3) - - - DIG (gaussian filter)
2
4) -.-.- SPE ( k 2 exp − k 2  spectrum)
k0 

1)
3D spots approach
2)
E (k )
3)
k
4)
8
HIT: Methods results
k
Sk
nx
nx
k1−5 / 3
E11 ( k1 )
SEM
k1−5 / 3
E11 ( k1 )
RAND
9
HIT: Eddies Size
1) … Random method
E (k )
2) - - - SEM with 3D isotropic spots (small)
3) ___ SEM with 3D isotropic spots (medium)
4) - .- . - SEM with 3D isotropic spots (big)
1)
2)
k
3)
4)
10
nx
HIT: Eddies Shape
1) ... SEM with 3D isotropic spots (gaussian)
2) - - - SEM with 3D vortices (gaussian)
3) ___ SEM with 3D isotropic spots (model function)
3D vortices approach
E (k )
1)
2)
3)
k
11
HIT: Shape results
E11 ( k1 )
k
k1−5 / 3
nx
SEM model shape function
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Channel Flow Re*=395
•
Mesh
– Nx * Ny * Nz = 160*30*30 cells
– ∆x+ ≈ 60, ∆z+ ≈ 40, ∆y+min ≈ 1
– inlet/outlet b.c.
•
Numerical Procedure
– Code_Saturne
– Smagorinsky model CS = 0.065
– Precursor periodic channel flow, statistics are fed into synthetic methods
– All inflow data have same mean and Reynolds stresses profiles
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Channel: Methods results
Q Contours
RAND
PREC
SEML02
SPECL02
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Channel: Methods results
c f c f0
x
u2
x
uv
x
15
Channel: Length-scale results
LINT
SEML01 Small spots
y+
c f c f0
SEML02 Medium spots
v2
SEML04 Large spots
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Channel: Shape results
•
•
•
SEM Medium Spots ( x x x )
SEM with 3D Vortices ( __ )
SEM with Wall Model ( - - - )
In the centre
At the wall
l = max(∆z , k 3 / 2 / ε )
Ruu (z )
Wall model approach
PREC
Ruu (z )
SEM Wall Model
c f c f0
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Conclusions & Future Works
• SEM gives good results compared to other synthetic
methods
• Influence of the length-scale of the inflow
• How to improve the SEM
– Better modelisation of the large scales?
– Better modelisation of the small scales, wavelet analysis
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