1 Simulation of Compressible CavaSim Simulation of Cavitating Flows Using a Novel Stochastic Field Formulation, FSM Franco Magagnato Andreas G. Claas KIT,

1

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

3

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.


4

Cavitation model(Okuda and Ikohagi)

The vapor-liquid mixture is modeled with a equation of state for water (Tammann) and for ideal gas.


5

Cavitation model(Okuda and Ikohagi)


YS

H

qv

G

Yv

vpEv

kpvv

jpvv

ipvv

F

Y

E

v

v

v

W

ijij

zi

yi

xi

z

y

x

z

y

x

0

0

0

0

0

,

0

0

,,

otherwise

ppifYSYS v

S(Y)

)()(

-

sg

v

g

le

TR

ppACYS

2)1()(

*

sg

vc

TR

ppACYS

2)1()(

*

6

Eulerian Stochastic Field method


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

7

Eulerian Stochastic Field method


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

8

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


9

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


10

LES results for the diffusor


Void ratio in the symmetry plane Stream-wise velocity component in the symmetry plane

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Velocity at station 1 Velocity at station 2 Velocity at station 3

Velocity at station 4 Velocity at station 5

12



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.


14

Compressible cavitation(Okuda and Ikohagi)

Cavitation is modeled with the local homogeneous equilibrium model of Okuda and Ikohagi


15

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


1 Simulation of Compressible CavaSim Simulation of Cavitating Flows Using a Novel Stochastic Field Formulation, FSM Franco Magagnato Andreas G. Claas KIT,

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