The meshless numerical simulation of Kelvin–Helmholtz instability during the wave growth of liquid–liquid slug flow

Abstract

Kelvin–Helmholtz instability (KHI) occurs at the interface of two fluids, in which the heavier fluid flows at the bottom. In the present numerical work, the KHI was analyzed by solving the modification of two-dimensional (2-D) incompressible Navier–Stokes equations. To capture the interface, the Cahn–Hilliard equation was implemented into the Navier–Stokes equations. The phenomena around the KHI of two and three-component fluids were investigated numerically by using radial basis function (RBF) combined with the domain decomposition method (DDM) in a primitive variable formulation. Here DDM is able to solve the large scale problem. On the other hand the calculation accuracy decreases with the increase of the number of the subdomains. For the above reason, in the present works, the domain was partitioned into 15 x 15 subdomains in order to reduce the decrease in accuracy due to the domain division. Next, fractional step method was used to solve the modification of the Navier–Stokes equations.The numerical results indicate that the procedure used in the present work can easily handle the KHI problem under the variations of the interface thickness, density ratios, and initial velocity differences. Moreover, the interface evolutions obtained from the present method agree well with those of the finite difference method. The effects of the interface thickness, density ratio and magnitude of velocity difference on the KHI were also investigated. The decrease of the interface thickness produces a non-smooth concentration profile, and the increase of the interface thickness produces too much surface diffusion. It was found also that the increase of the density ratio reduces the growth of KHI. The interface rolls up are strongly affected by the initial horizontal velocity difference. Finally, the present study also shows that the RBF method is a reliable method to solve the KHI on the complex domains.