An improved direct-forcing immersed boundary method for simulations of flow and heat transfer in particle-laden flows

Abstract

In studies of particle-laden flow, the direct-forcing immersed boundary (IB) method is commonly utilized to fully resolve the flow around the particles. With the use of interpolation functions, the effective diameter of a particle is typically larger than the actual diameter, resulting in an erroneous flow field, an overestimated drag force, and an inaccurately estimated interphase heat transfer rate when the grid resolution is insufficient. Relatively high grid resolutions (typically dp/h > 20) are required to ensure accurate estimations of the momentum and heat transfer between fluid and particles, leading to high computational cost when simulating cases with numerous particles. To address these issues, we propose an improved direct-forcing IB method involving retraction of the Lagrangian points, which considers the interphase momentum and heat transfer simultaneously. The method establishes two sets of Lagrangian points for computing the drag force and heat transfer rate, respectively. Based on the optimal retraction distance of the two sets of Lagrangian points, two retraction functions of the Reynolds number and grid resolution are formulated. Using the developed retraction functions, we simulate the DKT process, non-isothermal flow past three in-line spheres, and gravitational settling of a sphere with variable temperature to validate the improved IB method. It is found that the drag force and Nusselt number can be accurately reproduced using the improved IB method with a relatively small grid resolution (dp/h = 10).