Capabilities and limitations of smoothed particle hydrodynamics for the simulation of two‐phase flow instabilities

Abstract Smoothed particle hydrodynamics (SPH) is a mesh‐free, Lagrangian particle‐based method that is able to simulate multiphase flows in an economical manner. However, its ability to capture the flow regimes and regime transitions in two phase (liquid‐gas) internal flows, such as pipe or channel flows is not yet generally established. To address this lack in understanding, we first examine a laminar rising bubble case in order to evaluate the fluid‐fluid interface representation and transient interface evolution by the solver. With a focus towards the transition mechanism from a stratified flow regime to a slug flow regime, we investigate the Kelvin–Helmholtz instability (KHI) both qualitatively and quantitatively, initially focusing on a low density ratio () and then extending it to a high density ratio (). For the low density ratio, we conduct an analysis of the temporal evolution and demonstrate that the SPH solver captures the initial exponential growth in qualitative agreement with inviscid linear stability theory (LST) and reference numerical data for shear‐dominated flow with Richardson number . By conducting eight additional simulations for various for the high density ratio, we demonstrate that the numerically obtained parameter value for instability is around , which is in reasonable agreement with the theoretically expected value of . Based on the SPH results obtained for the range , we suggest a simple parameterization of the reduction of the effective growth rate proportional to .