COLLISION STATISTICS IN AN ISOTROPIC PARTICLE-LADEN TURBULENT SUSPENSION .1. DIRECT NUMERICAL SIMULATIONS

Direct numerical simulations of heavy particles suspended in a turbule nt fluid are performed to study the rate of inter-particle collisions as a function of the turbulence parameters and particle properties. Th e particle volume fractions are kept small (similar to 10(-4)) so that the system is well within the dilute limit. The fluid velocities are updated using a pseudo-spectral algorithm while the particle forces ar e approximated by Stokes drag. One unique aspect of the present simula tions is that the particles have finite volumes (as opposed to point m asses) and therefore particle collisions must be accounted for. The co llision frequency is monitored over several eddy turnover times. It is found that particles with small Stokes numbers behave similarly to th e prediction of Saffman & Turner (1956). On the other hand, particles with very large Stokes numbers have collision frequencies similar to k inetic theory (Abrahamson 1975). For intermediate Stokes numbers, the behaviour is complicated by two effects: (i) particles tend to collect in regions of low vorticity (high strain) due to a centrifugal effect (preferential concentration); (ii) particle pairs are less strongly c orrelated with each other, resulting in an increase in their relative velocity. Both effects tend to increase collision rates, however the s calings of the two effects are different, leading to the observed comp lex behaviour. An explanation for the entire range of Stokes numbers c an be found by considering the relationship between the collision freq uency and two statistical properties of the particle phase: the radial distribution function and the relative velocity probability density f unction. Statistical analysis of the data, in the context of this rela tionship, confirms the relationship and provides a quantitative descri ption of how preferential concentration and particle decorrelation ult imately affect the collision frequency.