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Simulation of Compressible CavaSim
Simulation of Cavitating FlowsUsing a Novel Stochastic Field Formulation
, FSMFranco Magagnato Andreas G. Claas KIT, FSM KIT, IKET
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
8th International Symposium on CavitationCAV2012
August 13-16, 2012, Singapore
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe2
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
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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.
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
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Cavitation model(Okuda and Ikohagi)
The vapor-liquid mixture is modeled with a equation of state for water (Tammann) and for ideal gas.
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
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Cavitation model(Okuda and Ikohagi)
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
YS
H
qv
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Yv
vpEv
kpvv
jpvv
ipvv
F
Y
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v
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v
W
ijij
zi
yi
xi
z
y
x
z
y
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0
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,,
otherwise
ppifYSYS v
S(Y)
)()(
-
sg
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le
TR
ppACYS
2)1()(
*
sg
vc
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ppACYS
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Eulerian Stochastic Field method
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
1i i i
n n n ni x x xd U dt dt S dt
Valino proposed Stochastic Euler PDF-Transport for combustion processes
2 1 2i
n n nx idW C dt
n= N scalar stochastic fields
Ui = velocity components
‘= effective diffusivity
dWi = Wiener process (random) 2
1
sgs
dsgs
C
= frequency of the stochastic
S() = Source term of transport equation
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Eulerian Stochastic Field method
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
For cavitating flow we solve N samples for the mass vapour mass fraction Y (N >=8)
ni
i
n
i
n
ii
n
in dW
x
Ydt
x
Y
xdt
x
YUdY 2
N
n
nYN
Y1
1 dtYSdtT
YY n
sgs
n
2
As source term S(Y) any cavitation model can be used
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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
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
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Numerical setup for the diffuser
Mesh contains 107 cvInlet velocity u=10.8 m/sInlet void fraction α =0.05% Reynolds number Re=2.7 *106 Dynamic Smagorinsky model used
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
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LES results for the diffusor
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Void ratio in the symmetry plane Stream-wise velocity component in the symmetry plane
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LES results for the diffusor
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Velocity at station 1 Velocity at station 2 Velocity at station 3
Velocity at station 4 Velocity at station 5
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LES results for the diffusor
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
Void ratio at station 1 Void ratio at station 2 Void ratio at station 3
Void ratio at station 4 Void ratio at station 5
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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.
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
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Compressible cavitation(Okuda and Ikohagi)
Cavitation is modeled with the local homogeneous equilibrium model of Okuda and Ikohagi
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe
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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
KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe