Simulation of Compressible CavaSim
Simulation of Cavitating Flows
Using a Novel Stochastic Field Formulation
, FSM
Franco Magagnato
KIT, FSM
Andreas G. Claas
KIT, IKET
8th International Symposium on Cavitation
CAV2012
August 13-16, 2012, Singapore
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KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Outline of the presentation
Motivation for compressible cavitation
The novel Stochastic Field Method
Homogenous equilibrium cavitation model of Okuda/Ikohagi
Numerical method used in SPARC
First results for a cavitating diffusor
Conclusions and outlook
2
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Compressible cavitation
Cavitation is often modeled with incompressible methods, but
inside the bubble very low speed of sounds occurs.
In incompressible simulation the speed of sound is infinite.
Compressible cavitation is more appropriate but also more difficult
to simulate numerically.
Turbulence is usually modeled with RANS, here we use LES.
The turbulence-two-phase flow interaction is often neglected.
We propose a novel method based on
the Eulerian Stochastic Field Theory.
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KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Cavitation model
(Okuda and Ikohagi)
The vapor-liquid mixture is modeled with a equation of state for
water (Tammann) and for ideal gas.
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KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Cavitation model
(Okuda and Ikohagi)



  
 0

 0 
 vv  pi 
 v 
 

 0 
x
x
xi
 







 v v  pj 
 v 
  yi 
 0 
 , G  
W   y ,F    y
,
H





v

0

v
v

p
k
zi
 z
 z






 E 
 v E  pv 
 ij v j  qi 
 0 









 Y 
 0

S Y 
 v Y 

S (Y )  Ce A (1   ) l

 g

S (Y ) 
S (Y )  
S(Y)
5
if p  pv
otherwise
 pv*  p

 2R T
g s

pv*  p
S (Y )  Cc A (1   )
2Rg Ts
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe

Eulerian Stochastic Field method
Valino proposed Stochastic Euler PDF-Transport for combustion processes



dn  U i  xi n  dt  1   xi   xi n  dt  S  n  dt
 2 
  x n  dWi n  1 2 C
n= N scalar stochastic fields
i
n


    dt
 = frequency of the stochastic
Ui = velocity components
‘= effective diffusivity
dWi = Wiener process (random)

S() = Source term of transport equation
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1
 sgs
  sgs
 Cd
2
Eulerian Stochastic Field method
For cavitating flow we solve N samples for the mass vapour
mass fraction Y (N >=8)
n
Y n
  Y n 

Y
 
dt   2 
dY   U i
dt 
dWi n 
 xi
xi
xi  xi 
n
 Y n  Y 
2
Tsgs
 
dt  S Y dt
n
1 N n
Y  Y
N n1
As source term S(Y) any cavitation model can be used
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KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Numerical method used in SPARC
•
3D block-structured Finite-Volume-Scheme
•
Compressible LES and DNS
•
Dynamic Smagorinsky subgrid-scale model
•
Up to 5th order accurate cell centred scheme in space
•
Preconditioning according to Choi and Merkle
•
Full geometric Multigrid-Method
•
2nd order time accurate dual time stepping-scheme
• Appr. Riemann solver (Roe, HLLC) and Artificial Dissipation schemes
• Parallel computation using 512 processors
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KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Numerical setup for the diffuser
Mesh contains 107 cv
Inlet velocity u=10.8 m/s
Inlet void fraction α =0.05%
Reynolds number Re=2.7 *106
Dynamic Smagorinsky model used
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LES results for the diffusor
Void ratio in the symmetry plane
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Stream-wise velocity component in
the symmetry plane
LES results for the diffusor
Velocity at station 1
Velocity at station 4
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Velocity at station 2
Velocity at station 5
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Velocity at station 3
LES results for the diffusor
Void ratio at station 1
Void ratio at station 4
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Void ratio at station 2
Void ratio at station 5
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Void ratio at station 3
Conclusions
A novel Eulerian Stochastic Field formulation has been proposed for
the turbulence-two-phase flow interaction.
Eight additional transport equations are sufficient for reliable
simulation
It can be combined with many cavitation models.
A first 3D validation case for cavitating flow shows encouraging
agreement with the experiment (Concalves et al.)
Additional 3D LES are underway for calibrating the constants in the
Eulerian SFM.
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Compressible cavitation
(Okuda and Ikohagi)
Cavitation is modeled with the local homogeneous equilibrium
model of Okuda and Ikohagi
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LES of a NACA0015
Synthetic Eddy Method
(SEM) at inlet with
tu = 10%
Lt = 0.004m
 = 0.1%
Non-reflecting static
pressure boundary
condition at the outlet
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