AuthorSunitha Nagrath
TitleAdaptive Stabilized Finite Element Analysis of Multi-Phase Flows using Level Set Approach
SchoolRensselaer Polytechnic Institute
AbstractMultiphase flows containing mixtures of liquids, gases, and solids abound in both nature and many technological processes. Better understanding of multiphase flows could improve processes ranging from heat transfer and atomization to suspensions, cavitation, and condensation processes. The present work is focused on developing a stabilized finite element method to solve the multi-phase compressible/incompressible flow problems in three dimensions using a level set approach. The Streamline-Upwind/Petrov-Galerkin method was used to discretize the governing flow and level set equations. The method developed enables accurate simulation of flows with large density and viscosity differences, as well as surface tension, and allows the fronts to self-intersect, merge, break, and change topology. A novel ghost fluid approach was implemented to remove the spurious non-physical oscillations across the material interface because of smeared density profile. An adaptive mesh strategy was designed to study various problems with optimum computational cost.

Various numerical studies were performed, namely, effect of viscosity and surface tension on single and multiple bubble dynamics, non-linear dynamics of free surface flows, single and two-phase shock tube, converging spherical shock and Rayleigh-Taylor interfacial instabilities. Using the developed framework, an effort is made to develop a three-dimensional algorithm for the hydrodynamic simulation of single bubble sonoluminescence. As a preliminary step towards the simulation of single bubble sonoluminescence, the hydrodynamics of the collapse and rebound of a 10 micron air bubble in water is studied with direct numerical simulations. With numerical simulations, it was shown that due to the inertial effect of the liquid compressing the gas, a bubble implosion takes place. The air bubble reaches a minimum radius during the implosion and then bounces back due to the high internal gas pressure. It is observed that, during the final stages of collapse, the bubble experiences an instability causing the bubble to form a non-spherical shape. The simulation results obtained were qualitatively similar to those observed/predicted in the previous experimental/numerical studies. The motion of the air/water interface during the initial stages of the collapse was found to be consistent with the Rayleigh-Plesset model. However, the three dimensional simulations show that during the final stage of energetic implosions, the bubble may become asymmetric, which is contrary to the spherical symmetry assumed in previous studies. Indeed, the shape instabilities observed during bubble implosions indicated an ellipsoidal shaped bubble. A linear stability analysis based on spherical harmonics also indicated that an elliptic bubble shape would be expected.

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