In this work, two-phase flow scalings are derived, which enable the quantification of grid-point and time-step requirements as functions of Reynolds ($\mathrm{Re}$), Weber ($\mathrm{We}$), and capillary ($\mathrm{Ca}$) numbers. The adequate grid resolution is determined in the inertia-dominated regime with the aid of high-fidelity simulations of stationary two-phase, i.e., interface-resolved, homogeneous isotropic turbulence by evaluating convergence of total interfacial area, size distribution, Sauter mean diameter (SMD), and curvature distribution. Although standards for direct numerical simulations (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 ${\eta }_{\mathrm{KH}}/\eta \sim {\mathrm{We}}_{\mathcal{L}}^{-3/5}{\mathrm{Re}}_{\mathcal{L}}^{3/4}$ in the inertia-dominated regime and the Kolmogorov-viscous to Kolmogorov scale of ${\eta }_{\mathrm{KV}}/\eta \sim {\mathrm{Ca}}_{\mathcal{L}}^{-1}{\mathrm{Re}}_{\mathcal{L}}^{3/4}$ for the viscous-dominated regime, are constructed. These scalings imply a computational cost increase like ${\mathrm{We}}_{\mathcal{L}}^{12/5}$ and ${\mathrm{Ca}}_{\mathcal{L}}^4$, in the inertia-dominated and viscous-dominated regimes, respectively. A dimensionless number, referred to as the ratio of interface scales ($\mathrm{Ris}$), defined as $\mathrm{Ris}:={\eta }_{\mathrm{KH}}/{\eta }_{\mathrm{KV}}={\mathrm{We}}_{\mathcal{L}}^{2/5}/{\mathrm{Re}}_{\mathcal{L}}$, 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 $k_{max}{\eta }_{\mathrm{KH}}\ge 60$ for second-order schemes in the inertia-dominated regime. 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.

Close

PrevNext

View figure in article

• Drop & bubble phenomena
• Homogeneous turbulence
• Isotropic turbulence
• Multiphase flows
• Turbulent multiphase flows
• Direct numerical simulations
• Navier-Stokes equation