Self-consistency and the use of correlated stochastic separated flow models for prediction of particle-laden flows

Computational fluid dynamics (CFD) is being used increasingly in the design and analysis of particle-laden flows. A significant challenge of this work is in correctly predicting the interaction of the fluid turbulence with the particulate phase. Typically, Lagrangian tracking is used to calculate the particle trajectories with stochastic treatments used to provide an instantaneous turbulent flow field. The stochastic calculations are based on the mean velocities and turbulence quantities calculated by the CFD solver. The current work examines the correlated stochastic separated flow (SSF) model used to synthesize the instantaneous fluid velocity field. Two functional forms of the Eulerian spatial correlation are considered: exponential, and Frenkiel with loop parameter m equal to unity. It is well known that the use of a Frenkiel function is incorrect due to the Markovian nature of the model. Nonetheless, a literature review indicates that the Frenkiel function is still being used in the CFD community. In order to illustrate the implications of this, numerical predictions are compared to Taylor's analytical result for fluid particle dispersion in homogeneous isotropic turbulence. Excellent predictions are obtained with the exponential correlation and recommendations on timestep requirements are made. In contrast, predictions from the Frenkiel model are in poor agreement with Taylor's solution. This poor agreement results from an inconsistency between the effective correlation of fluid velocities arising from the model and the original intended correlation.