Modification of kinetic theory of granular flow for frictional spheres, Part I: Two-fluid model derivation and numerical implementation

Abstract

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

“…We will now test the performance of our new BCs. For the solids bulk rheology we will use the kinetic theory of rough spheres described by Yang et al, using the same settings as used in the validation case by Yang et al However in the latter work, in the absence of the BCs theory described in this article, the often‐used BCs of Sinclair and Jackson (with a specularity coefficient φ = 0.1) were applied, and adiabatic conditions on the rotational heat flux were assumed. In the following, the simulation results using our new BCs are compared with these previous TFM results, and additionally with results from more detailed DPM simulations, and experimental data obtained from combined PIV‐DIA measurements on a quasi‐2D bubbling fluidized bed containing 3 mm glass particles .…”

“…The results show that our theory works excellent for not too inelastic particles with and smooth to quite frictional walls ( ). We also implemented the new BCs into our in‐house TFM code incorporating bulk particle rheology based on kinetic theory of granular flows of rough spheres by Yang et al Simulations of a pseudo‐2D fluidized bed using this new TFM show that the new BCs are often better capable of predicting solids axial velocity profiles, solids distribution near the walls and granular temperatures than TFM simulations based on Johnson and Sinclair BCs. In very dense zones long enduring particle contacts occur, leading to multi‐particle collisions.…”

“…Here are the translational and rotational shear viscosities, respectively . On the right‐hand side, the components of the local mean contact velocity are expressed in terms of interpolated values of the solids velocities, where the correlation for the average angular velocity which was obtained from DPM simulations is used.…”

“…Since we have calculated the translational fluctuation energy at the wall, the corresponding BCs can be obtained from the balance of the fluctuation energy where is the particle pseudo thermal conductivity and is the pseudo heat flux in this work. In the direction normal to the right wall, the final BC for translational granular temperature in numerical code is where C 2 , D 2 , E 2 are pre‐factors depending on the interpolation method.…”

“…34. v s;y À Á 1;j1 1 2 ;k and v s;y À Á 2;j1 1 2 ;k are solids velocities in computational cells 1 and 2. Since we have calculated the translational fluctuation energy at the wall, the corresponding BCs can be obtained from the balance of the fluctuation energy j t @H t @n 5Q t (36) where j t is the particle pseudo thermal conductivity 27 and Q t is the pseudo heat flux in this work. In the direction normal to the right wall, the final BC for translational granular temperature in numerical code is Figure 6.…”