1. 1 Simulation of Compressible CavaSim Simulation of Cavitating Flows Using a Novel Stochastic Field Formulation, FSM Franco Magagnato Andreas G. Claas KIT, FSM KIT, IKET KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe 8 th International Symposium on Cavitation CAV2012 August 13-16, 2012, Singapore

2. KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe 2 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. 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. KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe

4. 4 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

5. 5 Cavitation model (Okuda and Ikohagi) KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe

6. 6 Eulerian Stochastic Field method KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe Valino proposed Stochastic Euler PDF-Transport for combustion processes  n  = N scalar stochastic fields U i = velocity components  ‘  = effective diffusivity dW i = Wiener process (random)  = frequency of the stochastic S(  ) = Source term of transport equation

7. 7 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) As source term S(Y) any cavitation model can be used

8. 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 KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe

9. 9 Numerical setup for the diffuser Mesh contains 10 7 cv Inlet velocity u=10.8 m/s Inlet void fraction α =0.05% Reynolds number Re=2.7 *10 6 Dynamic Smagorinsky model used KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe

10. 10 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

11. 11 LES results for the diffusor KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe Velocity at station 1Velocity at station 2 Velocity at station 3 Velocity at station 4 Velocity at station 5

12. 12 LES results for the diffusor KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe Void ratio at station 1Void ratio at station 2 Void ratio at station 3 Void ratio at station 4 Void ratio at station 5

13. 13 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

14. 14 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

15. 15 LES of a NACA0015 Synthetic Eddy Method (SEM) at inlet with tu = 10% L t = 0.004m  = 0.1% Non-reflecting static pressure boundary condition at the outlet KIT. The cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe