Effect of turbulence on the particle settling velocity in the nonlinear drag range

Abstract

Particle settling velocity in the nonlinear drag range is investigated using a Monte Carlo simulation for particles in a low Reynolds number, isotropic, Gaussian, pseudo turbulence. The settling velocity is affected by both the trajectory bias, which enhances the settling velocity, and the nonlinearity of the drag associated with the turbulence, which reduces the settling velocity. The effect of the trajectory bias is important in an almost frozen turbulence when the settling velocity is comparable to the turbulence and particle motion in the creeping-flow regime. For a nonfrozen turbulence, the effect of the trajectory bias on the settling velocity may be overwhelmed by the effect of the nonlinear drag associated with the turbulence. The ensemble average of the second invariant of the turbulence deformation tensor, 〈IId〉, along the particle trajectories is obtained to characterize statistically the trajectory bias and the correlation between the particle concentration and turbulence structure. 〈IId〉 attains its maximum value at zero settling for a given particle inertia. The effect of increasing the settling velocity leads to an exponentially decreasing 〈IId〉 for a large settling rate, and hence a significant reduction in the trajectory bias and the concentration-structure correlation. For very small or large particle inertia, 〈IId〉 vanishes.