A Diffuse Interface Framework for Shock-Driven Vaporization in Compressible Multiphase Systems

This work introduces an extended diffuse-interface formulation to capture shock-induced vaporization and interface evolution in compressible multiphase systems relevant to rotating detonation engines (RDEs). Building on a full Navier-Stokes framework with curvature-based surface tension modeling, we propose an updated evolution equation for the phase field eta that includes interfacial mass transfer effects. By deriving a source term based on the classical Spalding number, the new model represents vaporization across the interface as a function of local thermodynamic and transport properties. The method is implemented in the ALAMO multiphysics code using a Roe-type Godunov solver with AMReX-enabled adaptive mesh refinement. A shock droplet configuration demonstrates the ability of the diffuse interface solver to capture strong deformation, ligament shedding, and topological change in a compressible liquid–gas system. A spherical bubble test with an exaggerated surface tension and the new Spalding based source term confirms that the phase field responds with physically consistent shrinkage, stable interface motion, and a compressible pressure response. Together these results establish a conservative, interface resolving foundation for future simulations of liquid fueled rotating detonation engines in which droplet breakup, surface area growth, and vaporization must be treated in a coupled manner.