Kelvin-helmholtz instability by SPH

M.S. Shadloo (1) , M. Yildiz (1)

1 Sabanci University - Faculty of Engineering and Natural Sciences

In this paper, we have modeled the Kelvin-Helmholtz Instability (KHI) problem of an incompressible two-phase immiscible fluid in a stratified inviscid shear flow with interfacial tension using Smoothed Particle Hydrodynamics (SPH) method. The time dependent evolution of the two-fluid interface over a wide range of Richardson number (Ri) and for three different density ratios is numerically investigated. The simulation results are compared with analytical solutions in the linear regime. It was observed that the SPH method requires a Richardson number lower than unity (i.e., Ri ≅ 0.8) for the onset of KHI, and that the artificial viscosity plays a significant role in obtaining physically correct simulation results that are in agreement with analytical solutions. The numerical algorithm presented in this work can easily handle a two-phase fluid flow with various density ratios.

Mots clés: Artificial viscosity; Density ratio; Immiscible fluids; Interfacial flows; Kelvin-helmholtz instabilities; Linear regime; Numerical algorithms; Richardson number; Smoothed particle hydrodynamics; Smoothed particle hydrodynamics methods; SPH methods; Time-dependent evolutions; Two-fluid interface; Two-phase fluid flow; Various densities; Algorithms; Mixed convection; Shear flow; Surface tension; Hydrodynamics

Domaines: Mécanique des fluides [physics.class-ph]

M.S. Shadloo, M. Yildiz. Kelvin-helmholtz instability by SPH. Particle-Based Methods II, 2011, Barcelona, Spain. pp.831-842. ⟨hal-02127873⟩