Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Abstract

SUMMARYExperimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.

Generalization of the JTZ model to open plane wakes

“…To solve the Navier-Stokes equations, we incorporate a high-order splitting algorithm into the spectral element method, please refer to [20,21] for detail.…”

“…Integrating the Navier-Stokes equations under the boundary conditions given in [21], we obtain velocity field u and vorticity field ω z at Re=250. The drag coefficient C d and Strouhal number Sr are determined as 1.5 and 0.21, respectively, very close to the calculation results of [22,23].…”