Abstract
A Lagrangian stochastic model for the motion of heavy particles has been developed by coupling a stochastic model for the motion of fluid elements to the Stokes equations of motion of a particle in a turbulent flow. The effects of crossing trajectories and continuity are incorporated by generalising Csanady's (1963) ideas developed for stationary homogeneous turbulence; effects of turbulence inhomogeneity and nonstationarity are embodied in the stochastic model for the fluid motion.
The model has been used particularly to examine the effects of turbulence nonstationarity through simulations of the dispersion of heavy particles in the decaying homogeneous turbulence which is obtained by Taylor-transforming grid turbulence. Significant differences from the stationary case occur, mainly as a result of the growth of the turbulent time scale with time.
The importance of the source location in influencing both passive scalar and particle dispersion in grid turbulence is highlighted by the model and can be simply accounted for by nondimensionalisation using the r.m.s. turbulence velocity at the source and the mean travel time from the grid to the source as velocity and time scales, respectively. Reconciliation of the three different experiments of Snyder and Lumley (1971), Wells and Stock (1983) and Ferguson (1986) reporting heavy particle flow and dispersion statistics in wind tunnel grid turbulence has been attempted using this nondimensionalisation. A good correspondence between the various data sets was not obtained because the source in the Wells and Stock, and Ferguson experiments was located at the grid where the self-similar development of the turbulence which underlies the scaling is not appropriate.
The model matches the data for the heaviest particles used by Snyder and Lumley reasonably well. For very light particles, it correctly reverts to the passive scalar limit, while the experimental data in general do not properly approach this limit.
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Sawford, B.L., Guest, F.M. Lagrangian statistical simulation of the turbulent motion of heavy particles. Boundary-Layer Meteorol 54, 147–166 (1991). https://doi.org/10.1007/BF00119417
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DOI: https://doi.org/10.1007/BF00119417