Development of A Novel Turbulence Model for Multiphase and Hypersonic Flow Problems

Accurate prediction of turbulence across sharp density gradients is critical for modeling interfacial transport, phase change, and thermal instabilities in cryogenic multiphase and hypersonic flows. Conventional turbulence models based on mass-specific turbulent kinetic energy (k) often exhibit nonphysical behavior near density discontinuities, necessitating empirical damping or ad hoc corrections. This work presents a turbulence modeling framework based on transport of the turbulent kinetic energy density, ρk. By reformulating the turbulent kinetic energy equation in conservative form, the proposed approach enforces physically consistent behavior across density interfaces and shock waves while improving numerical robustness in variable-density flows. The formulation is derived from the incompressible k equation and extended to variable-density flows using Favre averaging without modification of standard dissipation-rate closures. The ρk-based model is implemented within a volume-of-fluid (VOF) framework and evaluated using stratified air–liquid channel flow benchmarks relevant to cryogenic fluid management. Results show smooth turbulence behavior across interfaces, reduced mesh sensitivity, and elimination of empirical interface damping, with improved agreement against experimental data. The formulation is also applicable to hypersonic flows, where shocks introduce abrupt density changes and strong coupling between turbulence and energy dissipation. Overall, the ρk formulation provides a unified and physically consistent turbulence modeling framework for multiphase and hypersonic aerospace applications.