A dynamic restitution coefficient model incorporating friction, impact velocity, and temperature effects: Validation in a bubbling fluidized bed

We present a physics-based, dynamic coefficient of restitution (CoR) model for gas–solid flows that explicitly accounts for particle friction, impact velocity, and material temperature-effects neglected in conventional constant-CoR models. In dilute regions, CoR is expressed as a function of impact velocity and temperature; in dense regions, an effective CoR captures collective damping. A smooth transition between regimes is governed by the inertial number, ensuring physical consistency across flow regimes. Integrated into the two-fluid model based on the kinetic theory of granular flow (TFM-KTGF), the model is validated against bubbling fluidized bed experiments and Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations. Results demonstrate marked improvements in predicting solid mass flux, bubble dynamics, and energy dissipation, establishing the model as a robust tool for accurate simulation of complex gas-solid flows.