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Current particle dispersion models do not accurately predict the particle clustering that occurs in turbulent flow due to interaction of the particles with turbulent eddies. This clustering arises due to the effects of centrifugal forces which act to throw heavy particles out of the turbulent eddies, causing the particles to collect in high-concentration sheets lying between the eddies. The current paper proposes a stochastic vortex structure (SVS) model for simulation of particle clustering and collisions in turbulent flows. A new measure for particle drift relative to the fluid velocity is proposed that is related to the cross product of the fluid acceleration and velocity fields. Tests were conducted comparing the predictions of the SVS model with direct numerical simulation (DNS) and with three different stochastic Lagrangian methods in statistically stationary homogeneous isotropic turbulence with particles having Stokes numbers based on integral length scaling of order unity, assuming one-way fluid-particle coupling. The tests examined different turbulent flow features that are important for particle dispersion and clustering, as well as for prediction of the particle collision rate and collision distribution. The results indicate that the SVS model performs reasonably well for predicting particle concentration heterogeneity and collision rate, and that differences between the SVS and DNS results can be attributed to the fact that the SVS model neglects the small-scale velocity fluctuations within the turbulent flow.