An approach to modeling particle motion in turbulent flows—I. Homogeneous, isotropic turbulence

A model based on time-series analysis concepts is developed for generating the velocity field at particle positions using Eulerian temporal and spatial correlations functions. The particles are then moved in Lagrangian frame in response to the velocity field and body forces. The model was examined by simulating particle motion in homogeneous, isotropic turbulence and two grid-generated turbulent flows of Snyder and Lumley [J. Fluid Mech., 48,41 (1971)], and Wells and Stock [J. Fluid Mech., 136, 31 (1983)]. The predicted asymptotic particle longitudinal and transverse dispersion coefficients are shown to agree with the formula of Csanady [J. atmos. Sci., 20, 201 (1963)]. Comparison is also made for the computed particle fluctuating velocity with the experimental data of Snyder and Lumley and of Wells and Stock. Fairly good agreement is observed. In addition, particle longitudinal dispersion, velocity correlation and corresponding integral time scales are calculated both in presence and absence of particle drift velocity so as to investigate the crossing-trajectory, continuity and particle inertia effects. The trends are in accordance with previous theoretical studies of Reeks [J. Fluid Mech., 83, 529 (1977)], Pismen and Nir [J. Fluid Mech., 84, 193 (1978)] and Nir and Pismen [J. Fluid Mech., 94, 369 (1979)].