Revisiting Johnson and Jackson boundary conditions for granular flows

Abstract

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.

Eulerian–Eulerian simulation of dense solid–gas cylindrical fluidized beds: Impact of wall boundary condition and drag model on fluidization

“…In general, it has been determined that low values (∼ 10 −4 − 10 −3 ) are suitable for circulating beds [32,33] while higher values (∼ 0.05-0.5) are appropriate for bubbling beds [15][16][17]30]. This suggests that the choice of φ is dependent on the flow and particle-wall collision properties and may not be universally applicable [1,15,31].…”

“…In Section 5, the developed metrics are first used to estimate the suitable range of φ by comparing simulation predictions with experimental measurements corresponding to different fluidization regimes and then to quantify the sensitivity of the hydrodynamics in both lab-scale (diameter 14.5 cm) and pilot-scale (diameter 30.0 cm) fluidized beds. Finally, a comparison of the predictions using the variable φ model by Li and Benyahia [1] with experimental measurements as well as the suitability of gas-solids drag models are presented. All simulations are performed using MFiX (Multiphase Flow with Interface eXchanges), an open-source code developed at the National Energy Technology Laboratory, USA to describe the hydrodynamics in solid-gas systems.…”

“…the compression and expansion of granular media at the boundaries. While the expressions in [21] are convenient, conditions in bubbling fluidized beds usually operate between these two limits where interpolation is non-trivial and may yield considerable error in the prediction of the slip velocity [1]. The most widely used approach continues to be the Johnson-Jackson model [23] which evaluates the solids slip velocity at the walls based on simple and physically sound arguments.…”

“…Several analytical and semi-empirical models have been developed to evaluate µ and e w in terms of flow parameters such as the impact velocity, impact angle, particle spin and the particle and wall properties [25][26][27][28][29]. While it has been shown that the frictional coefficient significantly affects the collision regime (sliding/non-sliding) [25], fluidization predictions are not sensitive to e w in the range 0.7-1.0 [1,30]. On the other hand, direct experimental measurement of φ is not possible making it a tunable parameter for simulation predictions to fit experimental data.…”

“…In an attempt to determine φ in situ, Li and Benyahia [1] used the classic rigid-body theory in conjunction with the semi-analytical model for oblique collisions by Wu et al [29] to obtain φ in terms of µ and e w through numerical integration. The derived polynomial expression was further used in a series of 2D simulations for bubbling and circulating fluidized beds and found to be consistent with trends in literature [34].…”