Scalings and simulation requirements in two-phase flows

Abstract

In this work, important two-phase flow scalings are derived, which enable the quantification of grid-point and time-step requirements as functions of Re, We, and Ca numbers. The adequate grid resolution is determined in the inertia-dominated regime with the aid of high-fidelity simulations of stationary two-phase homogeneous isotropic turbulence by evaluating convergence of total interfacial area, size distribution, SMD, and curvature distribution. Although standards for DNS for single-phase turbulence flow exist, there is a lack of similar guidance in two-phase flows. Therefore, length scale ratios of the Kolmogorov-Hinze to the Kolmogorov scale of \eta_{KH}/\eta \sim We_{L}^{-3/5}Re_{L}^{3/4} in the inertia-dominated regime and the Kolmogorov-viscous to Kolmogorov scale of \eta_{KV}/\eta \sim Ca_{L}^{-1}Re_{L}^{3/4} for the viscous-dominated regime, are constructed. These scalings imply a computational cost increase like We_{L}^{12/5} and Ca_{L}^4, in the inertia-dominated and viscous-dominated regimes, respectively. A novel dimensionless number, coined as the ratio of interface scales (Ris), is proposed to aid in the classification of the turbulence regimes in the presence of an interface. Convergence of the total interfacial area, size distribution, SMD, and curvature distribution are observed for grid resolutions of k_{\max} \eta_{KH} \geq 60$ for second-order schemes. Furthermore, it is observed that this lower bound is the minimum required to capture intermittent events responsible for the increase of instantaneous total interfacial area. This criterion will be a valuable tool for determining grid resolution and time-step requirements a-priori for DNS of two-phase flows and for estimating the corresponding computational cost. This work provides guidelines and best practices for numerical simulations of two-phase flows, which will accelerate physics discovery and model development.