A new drag force and heat transfer correlation derived from direct numerical LBM-simulations of flown through particle packings

Abstract

In the present work a thermal Lattice-Boltzmann method (TLBM) is applied to study convection-diffusion problems and to determine averaged Nusselt numbers for particles being part of differently dense random packings. For the carried out numerical investigations a 3D TLBM framework is derived. Therein the hydrodynamic side is solved with a D3Q19 multiple-relaxation-time (MRT) collision operator and interpolated bounce back schemes. For the thermal side two different collision operators namely Bhatnagar-Gross-Krook (BGK) and MRT are applied and compared against each other. Furthermore, the impact of the LBM mesh structure is examined by comparing a D3Q7 and a D3Q19 model for the thermal side. Thermal diffusion and convection-diffusion problems for plane and curved boundaries are then studied and the results are validated against analytical solutions, when available or compared to established closure correlations. Furthermore, the best collision operator and boundary conditions - regarding numerical accuracy and stability - are selected to investigate convective-diffusive interphase heat transfer inside different static, random particle/fluid systems for varying porosities, Reynolds and Prandtl numbers. Obtained results are compared against published correlations. In addition a new closure correlation for drag forces and particle averaged Nusselt numbers in random particle packings in the range of ε = 0.6 − 1, Rep = 20 − 500 and Pr = 0.5 − 1.5 is proposed.