Smoothed particle hydrodynamics modeling of viscous liquid drop without tensile instability

Abstract

a b s t r a c tSmoothed particle hydrodynamics (SPH), as a Lagrangian meshfree particle method, has been applied to modeling viscous liquid drop with surface tension and wetting dynamics. In the SPH model, the van der Waals (vdW) equation of state is usually used to describe the gas-to-liquid phase transition similar to that of a real fluid. However, the attractive forces between SPH particles originated from the cohesive pressure of the vdW equation of state can lead to tensile instability, which is associated with unphysical phenomena such as particle clustering or blowing away. This paper presents an improved SPH method for modeling viscous liquid drop. The inherent tensile instability in SPH is removed by using a hyperbolicshaped kernel function which possesses non-negative second derivatives. A single-step approximation for heat flux is used in modeling viscous liquid drop with smoother temperature field. The formations of viscous liquid drops, both in 2D and 3D, are tested and it clearly demonstrates that the tensile instability can be effectively removed. The improved SPH method is also used to model two other numerical examples including the oscillation and binary collision of liquid drops without tensile instability.

Effects of temperature on spinodal decomposition and domain growth of liquid-vapor systems with smoothed particle hydrodynamics

“…In this procedure only the mean density of the total volume gets below the spinodal curve, but in fact the dynamical process is only a reshaping of an initial squared (or cubed) liquid droplet to a spherical one. This vdW-SPH approach has been the basis for works on various subjects, such as the oscillation and coalescence of droplets, the determination of the surface tension, or modeling multiphase flow in two [32][33][34][35][36][37] and recently also in three dimensions [38,39]. Nugent and Posch pointed out that the attractive and repulsive components of the pressure that are given by the vdW-EOS must be treated separately with different smoothing lengths to obtain sensible results.…”

A modified SPH method to model the coalescence of colliding non‐Newtonian liquid droplets

“…Moreover, by properly deploying particles at specific positions before the analysis, the moving free surface can be naturally tracked regardless of the complicity of particles' movement. In recent years, SPH has been extended to deal with various fluid mechanics problems including underwater explosion, multiphase flows, droplet dynamics, coastal and ocean engineering, viscoelastic flows, etc. It is worth mentioning that SPH has also been applied to simulate the thin film flow, and the potential application is related to lubricant dynamics for the head‐disk interface in the hard disk industry .…”

“…To resolve this problem, they added an artificial stress term that was originally proposed by Monaghan into the momentum equation. The droplet dynamics has also been studied using SPH by Jiang et al and Yang et al…”

Fluid Simulation by the Smoothed Particle Hydrodynamics Method: A Survey

“…Although SPH can model viscous fluids, a problem known as tensile instability can arise due to the cohesive pressure which can cause the particles to cluster or become sparsely distributed. The tensile instability problem is able to be rectified with the use of a hyperbolic-shaped kernel that possesses non-negative second derivatives, which ensures even distribution of particles in the fluid (Yang et al, 2014).…”