A coupled Volume Penalization-Thermal Lattice Boltzmann method for thermal flows

In this article, a coupled Volume Penalization-Thermal Lattice Boltzmann method is proposed to solve the thermal flow problem. The temperature Dirichlet boundary condition of the temperature field is ensured by introducing an external thermal penalization heat source term into the energy equation. Coupled with the Lattice Boltzmann-Volume Penalization method, which is used to simulated athermal flow past obstacles, the thermal flow problem can be solved. Besides, performing the Volume Penalization-Thermal Lattice Boltzmann method on a certain point, only the variables of this point are needed, which means the present method can be conducted parallelly. To verify the present method, the heat transfer between two concentric circular cylinders experiment is carried out firstly, in which the accuracy of the present method is also studied. Then natural convection between two concentric circular cylinders and between a cold square outer and a hot cylinder inner is performed to verify the present method further. To validate the ability of the method to solve the forced convection and mixed convection, the flows past a heated circular cylinder and the mixed convection of a heated rotating cylinder in a square enclosure are conducted. Good agreements between the present results and those in the previous literatures are achieved.