Analytical assessment of models for large eddy simulation of particle laden flow

For large eddy simulation of particle-laden flow, the effect of the unresolved scales on the particles needs to be modelled. The present work contains an analysis of three such models, namely approximate deconvolution method (ADM) as proposed by Kuerten (Subgrid modeling in particle-laden channel flow, Phys. Fluids. 18 (2006), p.025108) and two stochastic models proposed by Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulations, J. Turbul. 7 (2006), p.N18) and Simonin, Deutsch and Minier (Eulerian prediction of the fluid/particle correlated Motion in turbulent two-phase flow, Appl. Sci. Res. 51, (1993), pp. 275-283). The purpose of the analysis is twofold. On the one hand, the results serve for model selection in dependence of the application and on the other hand, the analysis shows possibilities for model improvement. The present work contains for each model an analytical computation of averages (first moments) and root-mean square values (second moments) of particle velocity, particle position and fluid velocity seen by the particles. Results indicate that for large Stokes number, ADM yields higher accuracy than the stochastic models analysed, whereas for small Stokes number the stochastic models give higher accuracy. An analytical estimate for the model error is given in dependence of Stokes number and the energy spectrum of the flow. This information can be used for model selection and for reliability prediction. Furthermore, it is shown that both stochastic models contain a deficient convective term, which should be avoided in future model development. The analysis is backed by numerical results from literature.