A Novel Diffuse-Interface Method for Compressible Multiphase Flows

Multiphase flows have a wide range of applications in natural and engineering processes. In this talk, I’ll present a novel diffuse-interface model and robust numerical methods for simulations of compressible multiphase flows.

I’ll first present the accurate conservative diffuse-interface/phase-field (ACDI) model for the simulation of multiphase flows. This method conserves the mass of each of the phases, and results in bounded transport of the volume fraction while maintaining the interface thickness on the order of only one to two grid points. I’ll present results from the canonical test cases, showing the improvement in the accuracy of interface shape and surface tension forces over the commonly used second-order conservative phase-field method. The capability of the ACDI model to maintain such sharp interfaces without the need for any special geometric treatment, unlike the sharp-interface methods, makes it a highly attractive interface-capturing method for accurate simulation of multiphase flows at an affordable cost.

Next, for the simulation of compressible multiphase flows, a five-equation model that consists of transport equations for the volume fraction, the mass of each phase, momentum, and total energy is used. Starting from this baseline five-equation model, I’ll present modifications to the model in such a way that the resulting system of equations can be discretized using a non-dissipative central scheme that is suitable for the simulation of turbulent flows. The resulting model is conservative, accurate, scalable, and maintains a constant interface thickness throughout the simulation. I will present simulations of canonical and complex turbulent compressible multiphase flows.

For stable and accurate numerical simulations of compressible flows, particularly at higher Reynolds numbers (Re), it is known that a discrete entropy condition needs to be satisfied in addition to the discrete conservation of kinetic energy. I’ll present a numerical flux formulation for the five-equation model that satisfies this condition (a KEEP scheme) and show that this formulation results in stable numerical simulations of compressible turbulent multiphase flows at high Re.

Finally, I’ll briefly highlight some of the related research efforts on the use of these methods for the simulation of shock-interface interaction problems, phase change, and multi-material systems.