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R. Poletto¹, A. Revell, T. Craft, N. Jarrin
Towards a DF-SEM
University of Manchester
5 May 2010
Email: [email protected]
R. Poletto – Towards a DF-SEM
1
RANS
1 – Method description
2 – DFSEM development
3 – Code_Saturne
➢
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LES
A – Introduction
B – Method scheme
C – Fluctuating velocities
Inlet condition for the LES, to
couple RANS and LES, requires
the creation of a synthetic
turbulent velocity field from a
previous RANS solutions
Define the area where it is necessary to use the LES
➢ Obtain a RANS solution at the inlet (velocity profile, k, ε, ω, …)
➢ Use this solution to activate any synthetic turbulence method
and create the LES inlet
- Periodic ChanFlow
- Random numbers
- Vortex method
- Spectral method
- Turb. fluctuations
- SEM
- DFSEM
...
No inlet. We solve LES as long as we get a periodic profile
Applies some random generated fluctuation
Uses the vorticity to define the v-w inlet velocity components
Fluctuations are generated using trigonometric functions
It defines cosinusoidal fluctuations in each directions
An eddies distribution creates the fluctuations
As SEM, but the eddies create divergence free velocities
...
R. Poletto – Towards a DF-SEM
2
1 – Method description
2 – DFSEM development
3 – Code_Saturne
A – Introduction
B – Method scheme
C – Fluctuating velocities
Create a random set of points (eddies
centres) and calculate for each of them
some characteristics (σ, Reynolds stresses)
Calculate the fluctuating velocities
using the generated eddies positions
Convect the eddies positions
R. Poletto – Towards a DF-SEM
3
1 – Method description
2 – DFSEM development
3 – Code_Saturne
A – Introduction
B – Method scheme
C – Fluctuating velocities
SEM
the ck takes into account the Lund coefficients → complete reconstruction of
the Reynolds stresses statistics
fσ is a shape function → defines the velocity distribution around the eddy
centres xk
DFSEM
the cross product makes the method
divergence free
qσ is a shape function and it must have
the following characteristics:
dependent only on rk
R. Poletto – Towards a DF-SEM
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1 – Method description
2 – DFSEM development
3 – Code_Saturne
A – Introduction
B – Method scheme
C – Fluctuating velocities
Vb = Eddy box volume
N = Eddy number
Stream function
We need the stream
function, whose Laplacian
is the vorticity field and
whose rotor is the velocity
field
σ = Eddy lengh scale
α = Eddy intensity
gσ = Eddy shape function
Vorticity rotor
We can eliminate
the second term,
since we want a
divergence
free
velocity
Green Function
R. Poletto – Towards a DF-SEM
In the DF-SEM we basically
apply the SEM fluctuations
to the vorticity field instead
of the velocity field.
Then, from the synthetic
vorticity field we calculate a
Divergence Free velocity
field
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1 – Method description
2 – DFSEM development
3 – Code_Saturne
A – Introduction
B – Method scheme
C – Fluctuating velocities
Vb = Eddy box volume
N = Eddy number
Stream function
We need the stream
function, whose Laplacian
is the vorticity field and
whose rotor is the velocity
field
σ = Eddy lengh scale
α = Eddy intensity
gσ = Eddy shape function
Vorticity rotor
We can eliminate
the second term,
since we want a
divergence
free
velocity
Green Function
R. Poletto – Towards a DF-SEM
Relation
between
eddies
shape function in velocity field
and the one in vorticity field
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1 – Method description
2 – DFSEM development
3 – Code_Saturne
A – Reynolds stresses
B – Future development
WHERE
The output Reynolds stresses in the DFSEM depends on:
distances of the eddies
squared shape function
We may split the inlet into several
parts and introduce in each part a
particular shape function, which
better fits the local Reynolds tensor.
R. Poletto – Towards a DF-SEM
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1 – Method description
2 – DFSEM development
3 – Code_Saturne
R. Poletto – Towards a DF-SEM
A – Reynolds stresses
B – Future development
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1 – Method description
2 – DFSEM development
3 – Code_Saturne
usini1.F
A – Implementation
B – Results
activation of the synthetic
turbulence subroutines
caltri.F
memsyn.F
tridim.F
memory management
(usclim.F)
ussynt.F
user adjustable subroutine which sets the synthetic turbulence
method (random numbers, SEM, DFSEM, …) and the inlet
surfaces and it reads the previous RANS solution
syntur.F
it implements all the synthetic turbulence
methods and applies them to the inlet surfaces
R. Poletto – Towards a DF-SEM
varsem.h
main variables used by
the new subroutines
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1 – Method description
2 – DFSEM development
3 – Code_Saturne
* Results by N. Jarrin
R. Poletto – Towards a DF-SEM
A – Implementation
B – Results
SEM compared with other synthetic
turbulence methods shows a better
fitting. Of course it still needs to be
improved (and the DFSEM may give
us a chance) in order to get a quicker
convergence to the periodic LES
result.
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