A hybrid lattice Boltzmann – random walk method for heat transfer in gas–solids systems

The development of accurate and robust heat transfer correlations for gas–solids flows is integral to the development of efficient multiphase unit operations. Direct numerical simulation (DNS) has been shown to be an effective method for developing such correlations. Specifically, the highly-resolved fields present in DNS may be averaged for use at the macroscopic level. Most commonly, particle-resolved immersed boundary or thermal lattice Boltzmann methods are employed. Here we develop a hybrid DNS framework where the hydrodynamics are resolved by the lattice Boltzmann method and the temperature field by random walk particle tracking (Brownian tracers). The random walk algorithm provides an efficient means for simulating scalar transport and can easily handle complex geometries. However, discontinuous fields pose a significant challenge to the random walk framework – e.g., a particle and fluid with different diffusivities. We derive a technique for handling discontinuities via the diffusivity, arising at a particle–fluid interface, and implement said method within the tracer algorithm. In addition, the heat transfer coefficient in the random walk method is defined and a technique for handling phases with different volumetric heat capacities is also developed. Moreover, the present algorithm is shown to correctly characterize intra-particle temperature gradients present in high Biot number systems. Verification of the code is completed against a host of cases: effective diffusivity of a static gas–solids mixture, hot sphere in unbounded diffusion, cooling sphere in unbounded diffusion, and uniform flow past a hot sphere. Predictions made by the new code are observed to agree with analytical solutions, numerical solutions, empirical correlations, and previous works.