EFFECT OF NONLINEAR DRAG ON THE SETTLING VELOCITY OF PARTICLES IN HOMOGENEOUS ISOTROPIC TURBULENCE

We study the average settling velocity of small spherical particles un der gravity through a Gaussian random velocity field generated by Four ier modes with a von Karman energy spectrum. The particles are subject ed to the effects of a linear (Stokes) or nonlinear drag force, inerti a and gravity. It is shown that the effect of drag nonlinearity is a f unction of the particle to fluid density ratio rho(p)/rho(f) and a fun ction of the ratio tau(p)/tau(k) Of the particle time constant to the Kolmogorov timescale of the fluid. Simulations show that as rho(p)/rho (f) decreases from 877 to 2.65 or as tau(p)/tau(k) increases from 1 to 2.74, the drag nonlinearity increases as a result oi the increase in particle Reynolds numbers. Hence the settling velocity changes from la rger to smaller as compared with the still fluid settling velocity, sh owing that one of the major mechanisms governing the fall velocity red uction in a turbulent flow is the drag nonlinearity. The maximum incre ase in settling rate occurs at V-T/upsilon(k) approximate to 2 for rho (p)/rho(f) greater than or equal to 87 (where V-T is the terminal velo city of the particle and upsilon(k) is the Kolmogorov velocity); this is consistent with the results of Wang and Maxey [1993]. The maximum d ecrease in settling rate occurs at V-T/upsilon(k) approximate to 1 for rho(p)/rho(f) approximate to 2.65, consistent with the results of Fun g [1993]. In addition, the role of the spatial and temporal variations of the flow field on the settling rate is investigated. Finally, the Gaussian velocity field is also simulated with an exponential energy s pectrum, and similar results are observed.