Partial slip boundary conditions for collisional granular flows at flat frictional walls

We derive new boundary conditions (BCs) for collisional granular flows of spheres at flat frictional walls. A new theory is proposed for the solids stress tensor, translational and rotational energy dissipation rate per unit area and fluxes of translational and rotational fluctuation energy. In the theory we distinguish between sliding and sticking collisions and include particle rotation. The predictions are compared with literature results obtained from a discrete particle model evaluated at a given ratio of rotational to translational granular temperature. We find that the new theory is in better agreement with the observed stress ratios and heat fluxes than previous kinetic theory predictions. Finally, we carry out two fluid model simulations of a bubbling fluidized bed with the new BCs, and compare the simulation results with those obtained from discrete particle simulations. The comparison reveals that the new BCs are better capable of predicting solids axial velocity profiles, solids distribution near the walls and granular temperatures. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1853–1871, 2017     

Revisiting Johnson and Jackson boundary conditions for granular flows

In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid‐body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial‐slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle‐wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided. Published 2011 American Institute of Chemical Engineers, 2012     

Evaluation of wall boundary condition parameters for gas–solids fluidized bed simulations

Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas–solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas–solids flow. A model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (Li and Benyahia, AIChE J. 2012;58:2058–2068) is implemented in the open‐source CFD code‐MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial‐slip boundary conditions for the solids phase. Through a series of two‐dimensional numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient. Published 2013 American Institute of Chemical Engineers AIChE J, 59: 3624–3632, 2013     

Validation study on spatially averaged two‐fluid model for gas‐solid flows: II. Application to risers and fluidized beds

In our prior study (Schneiderbauer, AIChE J. 2017;63(8):3544–3562), a spatially averaged two‐fluid model (SA‐TFM) was presented, where closure models for the unresolved terms were derived. These closures require constitutive relations for the turbulent kinetic energies of the gas and solids phase as well as for the subfilter variance of the solids volume fraction. We had ascertained that the filtered model do yield nearly the same time‐averaged macroscale flow behavior in bubbling fluidized beds as the underlying kinetic‐theory‐based two‐fluid model, thus verifying the SA‐TFM model approach. In the present study, a set of 3D computational simulations for validation of the SA‐TFM against the experimental data on riser flow and bubbling fluidized beds is performed. Finally, the SA‐TFM predictions are in fairly good agreement with experimental data in the case of Geldart A and B particles even though using very coarse grids. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1606–1617, 2018