Hydrodynamic cavitation with non-condensable gases: A thickened interface method with differentiable non-equilibrium thermodynamics based on van der Waals theory

The van der Waals theory of phase transformations offers a fundamental framework for non-equilibrium thermodynamics of phase transforming fluids that can be coupled with flow using the Coleman-Noll procedure. Until recently, computations based on this modeling framework had been limited to very small length scales and low speed flows, but recent advances enable simulations at large Reynolds numbers and length scales. Here, we extend the van der Waals modeling framework and the enabling computational methods that were proposed for single-component fluids to a mixture of a phase-transforming fluid and a non-condensable gas. A key element of innovation in our approach is the development of an interface enlargement algorithm coupled with a stabilized numerical scheme that can robustly handle large density variations and remain stable in the non-hyperbolic region of the phase diagram. The accuracy, stability and robustness of the numerical method were verified through extensive numerical testing, including the use of theoretical and manufactured solutions as well as simulations of cavitating flow past a cylinder. Our simulations also show that the overall approach reproduces some of the experimental observations in cavitating flows with non-condensable gas in dissolution and in the form of nuclei, which underscores its potential to better predict and understand cavitating flows of mixtures.