Consistent, energy-conserving momentum transport for simulations of two-phase flows using the phase field equations

•Introduced consistent, energy-conserving momentum transport for phase field methods.•Analytically proved conservation properties of the consistent momentum transport.•Simulated realistic high Re jet in crossflow to show improved robustness and accuracy. Realistic two-phase flow problems of interest often involve high Re flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, kinetic energy conserving momentum transport scheme in the context of a second order conservative phase field method. This is achieved by (1) accounting for the mass flux associated with the right-hand-side of the phase field equation in the convective flux of the conservative form of the momentum transport equation—a correction absent in previous phase field simulations (2) utilization of non-dissipative spatial discretization. We demonstrate accuracy and robustness improvements from our proposed scheme using numerical tests, including a realistic jet in cross-flow attaining turbulent conditions. Our proposed modifications to the momentum transport equation can be readily extended to other conservative phase field methods.