Numerical Investigation of Conjugate Heat Transfer and Natural Convection Using the Lattice-Boltzmann Method for Realistic Thermophysical Properties

Abstract

To enable the lattice-Boltzmann method (LBM) to account for temporally constant but spatially varying thermophysical properties, modifications must be made. Recently, many methods have emerged that can account for conjugate heat transfer (CHT). However, there still is a lack of information on the possible physical property range regarding realistic properties. Therefore, two test cases were investigated to gain further insight. First, a differentially heated cavity filled with blocks was used to investigate the influence of CHT on the error and stability of the LBM simulations. Reference finite volume method (FVM) simulations were carried out to estimate the error. It was found that a range between 0.5 to 1.5 is recommended for the fluid relaxation time to balance computational effort, stability, and accuracy. In addition, realistic thermophysical properties of fluids and solids were selected to test whether the lattice-Boltzmann method is suitable for simulating relevant industry-related applications. For a stable simulation, a mesh with 64 times more lattices was needed for the most extreme test case. The second test case was an insulated cavity with a heating pad as the local heat source, which was investigated in terms of the accuracy of a transient simulation and compared to a FVM simulation. It was found that the fluid-phase relaxation time mainly determines the error and that large thermal relaxation times for the solid improve accuracy. Observed deviations from the FVM reference simulations ranged from approximately 20% to below 1%, depending on collision operator and combination of relaxation times. For processes with a large temperature spread, the temporally constant thermophysical properties of the LBM are the primary constraint.

Keywords

• lattice-Boltzmann method
• conjugate heat transfer
• natural convection
• Boussinesq approximation