Development of an immersed boundary method for multiphase flow
Final Report Abstract
Multiphase flows involve moving and deforming embedded interfaces. Their numerical simulation is a great challenge of computational fluid dynamics. Typically, a single set of equations is used to describe the evolution of the flow field in both phases. The fluid in these phases is often assumed to be incompressible and the governing equations are commonly solved using a fractional-step method. In such a projection approach the pressure variable is determined from the divergencefree constraint of the incompressible flow field. Applied to single-phase incompressible flows with constant density and viscosity, this results in a constant-coefficient Poisson equation to be solved, for which efficient numerical methods are available. In the case of a multiphase flow, however, the resulting Poisson equation possesses variable coefficients, making its solution more difficult especially when the material properties significantly vary. In the present work a projection approach for a one-equation multiphase model is developed in which the flow equations with constant fluid properties, i.e., density and viscosity, can be solved. More specifically, the Navier-Stokes equations are solved with the constant properties of the lighter phase, which allows to use efficient standard numerical methods. The effect of the variable density and viscosity is accounted for by a forcing term, which couples the flow field to an artificial velocity field that carries the additional mass. The forcing term is a function of a free parameter, by which the strength of the coupling can be adjusted. In the limit of an infinitely strong coupling the original Navier-Stokes equations for multiphase flows are recovered. The phase interface is in this purely Eulerian approach described using the level-set method. The method was further extended to include surface tension effects and to allow for complex flows with embedded solid boundaries. The latter was achieved by incorporating an immersedboundary method into the newly developed model. In this method, the presence of embedded solids is accounted for by additional forcing terms. The new method was tested for several multiphase flow problems such as the canonical Rayleigh-Taylor instability test case and the simulation of surface waves. The results show that the solutions converge when the strength of the coupling between the flow field and the artificial velocity field is increased. These converged solutions agree convincingly with established results from the literature. More complex test cases involving mutual interactions of multiphase interfaces and embedded solid boundaries were successfully simulated and demonstrate the capabilities of the formulation for flow problems of realistic complexity.
Publications
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A Cartesian cut-cell method for sharp moving boundaries. AIAA Paper 2011-3387, 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI
C. Günther, M. Meinke, W. Schröder, D. Hartmann
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A projection approach for multiphase flows. AIAA Paper 2011- 3831, 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI
D. Hartmann, T. Colonius
