The assessment of the influence of interaction forces on heat transfer and pressure drop using Eulerian-Lagrangian model with various particle collision approaches

Abstract

This study investigates the impact of critical forces—including linear and rotational drag, gravity, Saffman’s lift, thermophoretic, Brownian, virtual mass, Magnus, pressure, and particle collisions—on pressure drop and the average wall Nusselt number in particle-laden flows using a validated Eulerian-Lagrangian model. The analysis covers a particle Reynolds number range of $0.4<R{e}_p<1.75$ and evaluates four particle interaction models: linear spring, spring-dashpot, Hertzian, and Hertzian-dashpot. Model validation is conducted against benchmark cases, including particle sedimentation, the Segre-Silberberg effect, drafting-kissing-tumbling, Brownian motion (assessed via mean square displacement and diffusion profiles), and the transient thermal response of spherical particles. Heavy (2702 kg/m³) and light particles (500 kg/m³) are studied under gravity directed downward (horizontal channel) and against the flow (vertical channel). The findings reveal that linear and rotational drag are the primary contributors to pressure drop, with their omission resulting in increased Nusselt numbers across all scenarios. Excluding other forces, particularly Saffman’s lift and Magnus, causes moderate reductions in the Nusselt number. The study advocates for the use of spring-dashpot and Hertzian-dashpot models at higher mass flow rates to capture energy dissipation accurately, preventing Nusselt number overestimations of 0.54 %–1.1 % for particle mass flow rates between 0.01 and 0.1 g/s.