Towards Numerical Methods for Two Phase Flow Simulations Undergoing Phase-Change Phenomena

Anumolu, C. R. L. Towards Numerical Methods for Two Phase Flow Simulations Undergoing Phase-Change Phenomena. University of Wisconsin-Madison, 2017.

Numerical method to simulate phase-change phenomena is developed using gradient augmented level set strategy (GALS) for advection and reinitialization. Sharp capturing of jump in velocity and pressure is achieved using Ghost Fluid Method. A single phase approach is followed to obtain solution for the energy equation where the governing equation is solved in each fluid phase by explicitly identifying the interface. Explicit identification of the interface is used to properly chose stencil locations in approximating convection and diffusion terms of the energy equation so that a single phase treatment is enforced in the solution procedure.

Two approaches to locate the interface are studied in this work; (i) a cubic Hermite interpolating polynomial which is inherent to GALS approach and yields spatially fourth order accurate interface location, (ii) a level set weighted approach which has been used in the level set literature that locates the interface using adjacent level set values as weights along a given axis on a cell edge. The added advantage of cubic Hermite interpolating polynomial over traditional level set weighted approach in approximating the differential terms near the interface is demonstrated.

Numerical simulation of phase-change phenomena using level set approach has been the topic of research in the past, however comparison of different numerical strategies with in the category of level set methods have not been presented. Using the level set transport step as the key difference we present a comparative study in this work. Test cases include 1D Stefan problem, 1D absorption problem, 2D bubble growth under a prescribed mass transfer rate, 2D Frank sphere type problem, and a 3D growing bubble subjected to buoyant forces. Both GALS and SLS approaches yielded similar results for 1D test cases due to the choice of the function which is linear and is continuously reinitialized maintaining the signed distance property, resulting in the interface location upto same level of accuracy. Gradient augmented level set based numerical approach resulted in slightly better results for test cases in higher dimensions and with high fluid density ratios.