Numerical evaluation of virtual mass force coefficient of single solid particles in acceleration

Abstract

• Single solid sphere in acceleration is numerically simulated based on the vorticity-stream function formulation. • Particle acceleration changes significantly the surrounding flow field and the stress tensor on the particle surface. • Virtual mass force coefficient is evaluated from the numerical simulation. • A correlation of total drag coefficient with the Reynolds number and acceleration number is proposed for tentative use in particulate flow simulation. Virtual mass force is an indispensable component in the momentum balance involved with dispersed particles in a multiphase system. In this work the accelerating motion of a single solid particle is mathematically formulated and solved using the vorticity-stream function formulation in an orthogonal curvilinear coordinate system. The total drag coefficient was evaluated from the numerical simulation in a range of the Reynolds number ( Re ) from 10 to 200 and the dimensionless acceleration ( A ) between −2.0 to 2.0. The simulation demonstrates that the total drag is heavily correlated with A , and large deceleration even drops the drag force to a negative value. It is found that the value of virtual mass force coefficient ( C V ) of a spherical particle is a variable in a wide range and difficult to be correlated with A and Re. However, the total drag coefficient ( C DV ) is successfully correlated as a function of Re and A , and it increases as A is increased. The proposed correlation of total drag coefficient may be used for simulation of solid–liquid flow with better accuracy.