On the Importance of the History Force in Dispersion of Particles in von Kármán vortex street

Abstract

Effects of the history (Basset) force on the dispersion of solid particles over a cylinder inside a two-dimensional channel flow associated with von Kármán vortex shedding are investigated. Particles with Stokes numbers (〖St〗_k) of 0.1, 0.5, 1.0 and 5.0 and particle-to-fluid density ratios of 1.1, 10 and 1000 are considered. Clustering (i.e. preferential concentration) of particles is studied qualitatively by visualising particle distributions, and quantitatively by analysing the preference of particles in sampling the vorticity field and by using Voronoϊ tessellation analyses. It is found that the effects of history force on the distribution of particles are noticeable only at moderate particle-to-fluid density ratios and Stokes numbers, though not very significant. Nonetheless, our results suggest that for flows with strong vortices the impact of the history force can be significant. It has also been observed for the first time that inclusion of the history force at high Stokes numbers, i.e. 〖St〗_k=5.0, can increase particle clustering at both moderate and high particle-to-fluid density ratios. At lower Stokes numbers, however, particle clustering decreases when the history force is taken into account. In general, the history force suppresses the influence of particle inertia in all the investigated cases. Finally, the deposition rate of particles, mainly on the front wall of the cylinder, decreases when the history force is included for all cases except when 〖St〗_k=0.1.