1. 1 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3D-1D coupling of compressible density-based CFD solvers for cavitating flows Martina Friedrich, Uwe Iben, Henning Kreschel (Robert Bosch GmbH), Romuald Skoda (Ruhr University Bochum), Claus-Dieter Munz (University of Stuttgart) August 13 th -16 th 2012: 8 th International Symposium on Cavitation Abstract No. 28

2. 2 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3D-1D coupling of CFD solvers for cavitating flows Content  Introduction  3D-1D coupling interface models  Numerical results  Summary and Outlook

3. 3 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 1. Introduction: 3D-1D coupling (compressible code) 3D-1D coupling of CFD solvers Example: cavitating hydraulic system cut for 3D simulation: Which boundary condition? cavitation 3D simulation computing time : 3D-Simulation only of interesting part of the system with suitable boundary conditions.

4. 4 p=const. or p(t) DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 1. Introduction: 3D-1D coupling (compressible code) 3D-1D coupling of CFD solvers Simulation of cavitating hydraulic system BC 1BC 2 =const. or collapsed cavitation bubble cavitation bubble omitted pressure wave reflection at outlet reflection at wall compressible, explicit 3D CFD solver: Euler equations with barotropic equation of state reflections also at inlet (not focused here) artificial influence on cavitation bubbles possible incompressible 3D CFD solver

5. 5 compressible, explicit 3D CFD solver: Euler equations with barotropic equation of state compressible, explicit 3D and 1D CFD solver: Euler equations with barotropic equation of state p=const. or p(t) BC 2 p=const. or p(t) DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 1. Introduction: 3D-1D coupling (compressible code) 3D-1D coupling of CFD solvers Simulation: cavitating hydraulic system BC 1BC 2 =const. or 3D solver 1D solver no reflection at coupling interface Aim: 3D-1D coupling interface models for compressible CFD solvers 3D-1D coupling interface

6. 6 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 2. Interface models 3D-1D coupling of CFD solvers Simulation: cavitating hydraulic system 3D-1D coupling interface models (exchange at each timestep): PVar: primitive variables (commonly used for incompressible codes) Flux: numerical fluxes calculated using cross-section averaged primitive variables p=const. or p(t) BC 1BC 2 =const. or 1D solver 3D-1D coupling interface 3D solver 2D Aim: mass and streamwise momentum conserving coupling algorithm!

7. 7 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 2. Interface models 3D-1D coupling of CFD solvers Aim: Simulation of complete cavitating hydraulic systems 3D simulation cavitation 1D simulation 3D-1D simulation Improve: 1) prediction of system behaviour, 2) boundary condition for CFD simulations

8. 8 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers a) Reference solution: 1D pressure wave (Riemann Problem) 1D solver p1= const., u=0 m/sp2<< p1, u=0 m/s 1D solver u x 0 t1 t2 t3 t4 time travelling 1D pressure waves

9. 9 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers a) PVar: 1D pressure wave (Riemann Problem) 1D solver 2D solver 2D-1D coupling interface: apply interface model PVar p1= const., u=0 m/sp2<< p1, u=0 m/s 1D solver u x 0 t1 t2 t3 t4 time u x 1D solver 2D solver 2D-1D coupling interface: PVar

10. 10 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers b) 2D reference solution: 2D pressure wave ( ) t1t2 t3 t4 pressure velocity x-directionvelocity y-direction x t5 2D simulation y 1D solver

11. 11 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers b) PVar: 2D pressure wave ( ) 2D-1D interface pressure velocity x-directionvelocity y-direction 2D-1D coupling: interface model “PVar” t5 y x 1D solver

12. 12 p=const. or p(t) DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers PVar: cavitating hydraulic system (2D) BC 1 =const. or BC 2 reflection at outlet 2D-1D coupling: PVar 1D solver 2D-1D coupling: interface model “PVar”

13. 13 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers a) Flux: 1D pressure wave (Riemann Problem) 1D solver 2D solver 2D-1D coupling interface: apply interface model p1= const., u=0 m/sp2<< p1, u=0 m/s 1D solver u x 0 t1 t2 t3 t4 time travelling 1D pressure waves u x 1D solver 2D solver 2D-1D coupling interface: Flux

14. 14 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers b) 2D reference solution: 2D pressure wave ( ) t5 pressure velocity x-directionvelocity y-direction y x 2D simulation 1D solver

15. 15 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers b) Flux: 2D pressure wave ( ) 2D-1D interface pressure velocity x-directionvelocity y-direction 2D-1D coupling: interface model “Flux” t5 y x 1D solver

16. 16 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers b) Flux: 2D pressure wave ( ) <6% <1.5% mass error 2D – 2D-1D Flux: < 3.5e-6 % * %-error: cross-section area average related to max. value * 2D-1D coupling: interface model “Flux”

17. 17 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3D-1D coupling of CFD solvers for cavitating flows 3D-1D coupling of CFD solvers b) 2D reference solution: 2D pressure wave ( ) velocity y-direction area average

18. 18 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers c) 2D reference solution: 2D pressure waves ( ) t1 pressure velocity x-directionvelocity y-direction 2D simulation t2 t3t4 x y 1D solver

19. 19 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers c) Flux: 2D pressure waves ( ) t4>0 mass error 2D – 2D-1D Flux: <1.0e-4 % %-error: cross-section area average related to max. value <4.5% <2.5%

20. 20 p=const. or p(t) DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3. Numerical results 3D-1D coupling of CFD solvers Flux: cavitating hydraulic system (2D) BC 1 =const. or BC 2 no reflection at coupling interface 2D-1D coupling: Flux 2D simulation (longer channel) 1D solver 2D solver

21. 21 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 4. Summary and Outlook 3D-1D coupling of CFD solvers Aim: 3D-1D coupling interface models for compressible CFD solvers Result: Interface models to couple compressible 2D and 1D CFD solvers: PVar Flux Summary 2D-1D interface y x 1D solver pressure y x 1D solver 2D-1D interface

22. 22 computing time DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 4. Summary and Outlook 3D-1D coupling of CFD solvers Summary: 3D-1D simulation for hydraulic systems 3D simulation cavitation 1D simulation 3D-1D simulation BC 1 BC 2

23. 23 computing time DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 4. Summary and Outlook 3D-1D coupling of CFD solvers Outlook: 3D-1D simulation for complete hydraulic systems 3D simulation cavitation 1D simulation 3D-1D simulation

24. 24 DS-PC/EIP5, Friedrich | 13-16/08/2012 | © Robert Bosch GmbH 2012. All rights reserved, also regarding any disposal, exploitation, reproduction, editing, distribution, as well as in the event of applications for industrial property rights. 3D-1D coupling of compressible density-based CFD solvers for cavitating flows Martina Friedrich, Uwe Iben, Henning Kreschel (Robert Bosch GmbH), Romuald Skoda (Ruhr University Bochum), Claus-Dieter Munz (University of Stuttgart) August 13 th -16 th 2012: 8 th International Symposium on Cavitation Abstract No. 28