Simulations of spray and particle-laden flows have commonly relied on random walk models to represent dispersion of liquid or solid particles by turbulent motions in the carrier fluid. Particles respond, through a Lagrangian equation of motion, to the mean fluid velocity, computed simultaneously from an Eulerian solution, and to a random fluctuation velocity. In this paper the performance of available models for the case of tracer particles in dilute concentrations is tested. It is demonstrated that several models in wide use do not preserve the required divergence properties of the imposed mean flow. It is found that the method of sampling the fluctuation velocity in these models leads to a spurious component of mean velocity, causing particles to drift relative to the mean flow. Particles concentrate where the turbulence intensity is minimum (at shear layer edges), and are depleted from regions of high turbulence intensity (near the core of the shear layers). The particle concentration may be up more than six times the correct level at the layer edges and less than 40% of the correct level in the shear layer cores. An approximate correction is derived that is the same as that of Wilson et al. [Boundary-Layer Meteorol. 21, 423 (1981)], but with a slightly larger coefficient. It is shown that the effect of fluctuation acceleration has been left out of the model equations, and this leads to a precise correction. To broaden the scope of the work, some recent models that solve a stochastic differential equation for the Lagrangian flow velocity are also considered. One such model is found to give as good an account of the particle number distribution in the shear layers as do the corrected random walk models.

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