in Wiley InterScience (www.interscience.wiley.com).Starting from a kinetic theory based two-fluid model for gas-particle flows, we first construct filtered two-fluid model equations that average over small scale inhomogeneities that we do not wish to resolve in numerical simulations. We then outline a procedure to extract constitutive models for these filtered two-fluid models through highly resolved simulations of the kinetic theory based model equations in periodic domains. Two-and three-dimensional simulations show that the closure relations for the filtered two-fluid models manifest a definite and systematic dependence on the filter size. Linear stability analysis of the filtered two-fluid model equations reveals that filtering does indeed remove small scale structures that are afforded by the microscopic twofluid model.

presented a methodology where computational results obtained through highly resolved simulations of a given microscopic two-fluid model (TFM) for gas-particle flows are filtered to deduce models for the residual correlations appearing in the corresponding filtered TFM equations that are appropriate for coarsegrid simulations of gas-particle flows. In the present study, we have performed a large number of highly resolved simulations of a kinetic theory based TFM in two-and three-dimensional periodic domains using this methodology and filtered the results to generate computational data on the filtered drag coefficient, the filtered particle phase pressure, and the filtered particle phase viscosity. These results have been captured in the form of correlations that can readily be employed in coarse-grid simulations of gasparticle flows.

The effect of solid boundaries on the closure relationships for filtered two-fluid models for riser flows was probed by filtering the results obtained through highly resolved kinetic theory-based two-fluid model simulations. The closures for the filtered drag coefficient and particle phase stress depended not only on particle volume fraction and the filter length but also on the distance from the wall. The wall corrections to the filtered closures are nearly independent of the filter length and particle volume fraction. Simulations of filtered model equations yielded grid length independent solutions when the grid length is $half the filter length or smaller. Coarse statistical results obtained by solving the filtered models with different filter lengths were the same and corresponded to those from highly resolved simulations of the kinetic theory model, which was used to construct the filtered models, thus verifying the fidelity of the filtered modeling approach.

In our prior studies ([ Igci Y. Igci Y. AIChE J.20085414311448] and [ Igci Y., Sundaresan S. Igci Y., Sundaresan S. AIChE J. 2010]) we presented a methodology where computational results obtained through highly resolved simulations of a given microscopic two-fluid model (TFM) for gas-particle flows are filtered to deduce constitutive models for the residual correlations appearing in the corresponding filtered TFM equations that are appropriate for coarse-grid simulations of gas-particle flows. We had also analyzed the flow behavior in the vicinity of solid boundaries and proposed wall corrections for these constitutive models. We had ascertained that the filtered models do yield nearly the same time-averaged macroscale flow behavior in vertical channel flows as the underlying kinetic-theory-based TFM, thus verifying the filtered model approach. In the present study, we have performed a set of 3D computational simulations for validation of the filtered TFM against the experimental data on riser flow [ Karri S. Karri S. et al., PSRI Challenge Problem 1, Workshop 3 Modeling Test, at the 8th International Conference on Fluidization, Tour, France, 1995]. It is found that inclusion of wall corrections brings the filtered model predictions closer to the experimental data and that simulations corresponding to different filter lengths yield nearly the same results.

This paper develops a new theoretical framework for analyzing the lift mechanics and stability of skis and snowboards that could have important applications in future ski and snowboard design.