(701c) A Modified Frictional Solids Stress Model Fortwo Fluid Modeling of Gas-Solid Fluidized Beds

Two fluid modeling (TFM) has been widely used in simulating large-scale gas-solid fluidized beds due to its computational efficiency. However, TFM needs constitutive relations for solids pressure and solids viscosity to model solids stress. Due to the similarity of the physical picture between particle motion in the kinetic regime and thermal motion of molecules in gas, a kinetic theory of granular flows (KTGF) that is analogous to dense-gas kinetic theory is commonly used to correlate the solids stress in the kinetic regime. In contrast, the theories used to formulate the solids stress in the frictional regime are largely based on the critical state theory of soil mechanics; such efforts, however, are largely empirical as compared to those in the kinetic regime. As a result, TFM with existing frictional solids stress models has been shown to struggle to capture some phenomena associated with fluid-solid transitions. Herein, we propose to modify the Srivastava and Sundaresan model¹ by replacing the frictional solids pressure formulation with the one based off a dilation law² from prior discrete particle simulations. We show that the modified model can successfully capture (1) structured bubbling pattern formed with pulsating the gas flow³ in the bottom inlet, due to rapid, local transitions between solid-like and fluid-like behavior in the grains and (2) granular droplet splitting formed with vibrating the fluidized bed due to local solidification below the droplet⁴.

References:

(1) Srivastava, A.; Sundaresan, S. Analysis of a Frictional–Kinetic Model for Gas–Particle Flow. Powder Technology 2003, 129 (1–3), 72–85. https://doi.org/10.1016/s0032-5910(02)00132-8.

(2) Forterre, Y.; Pouliquen, O. Flows of Dense Granular Media. Annual Review of Fluid Mechanics 2008, 40 (1), 1–24. https://doi.org/10.1146/annurev.fluid.40.111406.102142.

(3) Wu, K.; de Martín, L.; Coppens, M.-O. Pattern Formation in Pulsed Gas-Solid Fluidized Beds – The Role of Granular Solid Mechanics. Chemical Engineering Journal 2017, 329, 4–14. https://doi.org/10.1016/j.cej.2017.05.152.

(4) McLaren, C. P.; Kovar, T. M.; Penn, A.; Muller, C. R.; Boyce, C. M. Gravitational Instabilities in Binary Granular Materials. Proceedings of the National Academy of Sciences of the United States of America 2019, 116 (19), 9263–9268. https://doi.org/10.1073/pnas.1820820116.