1. Multiphase 05, Porquerolles, April 20, 2005 Simulation of hydrodynamic wave loading by a 3D 2-phase numerical model Multiphase05 Rik Wemmenhove University of Groningen, dept. of Mathematics

2. Multiphase 05, Porquerolles, April 20, 2005 Introduction: applications Green water loading Tank sloshing LNG tanker, © DNV

3. Multiphase 05, Porquerolles, April 20, 2005 Offshore applications Green water loading Bow slamming Sloshing in tanks Ship launching Floating objects etc.

4. Multiphase 05, Porquerolles, April 20, 2005 Offshore flow phenomena

5. Multiphase 05, Porquerolles, April 20, 2005 Two-phase flow at wave impact (1)

6. Multiphase 05, Porquerolles, April 20, 2005 Two-phase flow at wave impact (2) Pressure level during wave impact Sources: Wood et al, JWPCOE, 2000, 126, 2000. Bullock et al, Coast. Eng., 46, 2002.

7. Multiphase 05, Porquerolles, April 20, 2005 Two-phase flow at wave impact (3) Source: Deane & Stokes, Nature (418), 839-844, 2002

8. Multiphase 05, Porquerolles, April 20, 2005 Modeling two phases  = const  = 0 p = 0  = const p = p(  ) 1-phase2-phase incompressible 2-phase compressible  = const

9. Multiphase 05, Porquerolles, April 20, 2005 ComFLOW: Incompressible model (1) Mass conservation: Momentum equation:

10. Multiphase 05, Porquerolles, April 20, 2005 Incompressible discretisation (1) Mass conservation Momentum equation  velocity Poisson equation  pressure n = previous timestep n+1 = next timestep

11. Multiphase 05, Porquerolles, April 20, 2005 Incompressible discretisation (2) F s = 0.5 F b = 1.0 F s = 0.5 F b = 1.0 F s = liquid cell fraction F b = open cell fraction air water solid

12. Multiphase 05, Porquerolles, April 20, 2005 Validation: rising bubble

13. Multiphase 05, Porquerolles, April 20, 2005 Validation: dambreak experiment Dambreak experiment MARIN (Maritime Research Institute Netherlands) & ComFLOW simulation

14. Multiphase 05, Porquerolles, April 20, 2005 Dambreak experiment (1): water height Grid size: 180 x 60 x 60

15. Multiphase 05, Porquerolles, April 20, 2005 Dambreak experiment (2): pressure level Grid size: 180 x 60 x 60

16. Multiphase 05, Porquerolles, April 20, 2005 Evaluation incompressible model Smoother pressure signal for dambreak experiment Simulation of air physics may be improved by taking compressibility into account

17. Multiphase 05, Porquerolles, April 20, 2005 Future developments: compressible model Incompressible water phase Adiabatic p-  relation in air

18. Multiphase 05, Porquerolles, April 20, 2005 http://www.math.rug.nl/~veldman/comflo/comflo.html More literature about ComFLOW? Source: An Album of Fluid Motion, Van Dyke, 1982