The study of thermal convection in porous media is of both fundamental and practical interest. Typically, numerical studies have relied on the volume-averaged Darcy–Oberbeck–Boussinesq (DOB) equations, where convection dynamics are assumed to be controlled solely by the Rayleigh number (Ra). Nusselt numbers (Nu) from these models predict Nu–Ra scaling exponents of 0.9–0.95. However, experiments and direct numerical simulations (DNS) have suggested scaling exponents as low as 0.319. Recent findings for solutal convection between DNS and DOB models have demonstrated that the ‘pore-scale parameters’ not captured by the DOB equations greatly influence convection. Thermal convection also has the additional complication of different thermal transport properties (e.g. solid-to-fluid thermal conductivity ratio k_s/k_f and heat capacity ratio σ) in different phases. Thus, in this work we compare results for thermal convection from the DNS and DOB equations. On the effects of pore size, DNS results show that Nu increases as pore size decreases. Mega-plumes are also found to be more frequent and smaller for reduced pore sizes. On the effects of conjugate heat transfer, two groups of cases (Group 1 with varying k_s/k_f at σ = 1 and Group 2 with varying σ at k_s/k_f = 1) are examined to compare the Nu–Ra relations at different porosity (ϕ) and k_s/k_f and σ values. Furthermore, we report that the boundary layer thickness is determined by the pore size in DNS results, while by both the Rayleigh number and the effective heat capacity ratio, $\bar{\phi } = \phi + (1 - \phi )\sigma$ , in the DOB model.

A multiple-time-scaling (MTS) strategy that decouples the time discretization in different domains and enables flexible time-step coarsening, refinement, and stretching in the lattice Boltzmann method (LBM) for the convection diffusion equation is developed. The key in the multiple-time scaling is the satisfaction of physical interface conditions without nested iterations in each time step by implementing appropriate interface schemes for the distribution functions in the LBM. The applicability and second-order accuracy of the MTS-LBM approach is demonstrated with two numerical tests. Our approach greatly expands the avenue and expedites the progress of applying the LBM for modeling complex flows and transport phenomena involving multiphases and multicomponents with large property ratios.

Particle-to-supercritical carbon dioxide (sCO₂) heat exchanger is a critical component in next-generation concentrating solar power (CSP) plants. The inherently low heat transfer between falling particles and sCO₂ imposes a challenge towards economic justification of levelized cost of electricity produced through solar energy. Introduction of integrated porous media with the walls bounding particle flow has the potential to enhance the overall particle-to-sCO₂ heat exchanger performance. This paper presents an experimental study on heat transfer characterization of additively manufactured lattice frame material based on Octet-shaped unit cell with particles and air as working fluids. The lattice structures were additively manufactured in Stainless Steel (SS) 316L and SS420 (with 40% bronze infiltration) via Binder jetting process, where the lattice porosities were varied between 0.75 and 0.9. The mean particle diameters were varied from 266-966 μm. The effective thermal conductivity and averaged heat transfer coefficient were determined through steady-state experiments. It was found that the presence of lattice enhances the effective thermal conductivity by 2-4 times when compared to packed bed of particles alone. Furthermore, for gravity-assisted particle flow through lattice panel, significantly high convective heat transfer coefficients ranging from 200-400 W/m2K were obtained for the range of particle diameters tested. The superior thermal transport properties of Octet-shape-based lattice frame for particle flow makes it a very promising candidate for particle-to-sCO₂ heat exchanger for CSP application.