Three-dimensional lattice Boltzmann flux solver for simulation of fluid-solid conjugate heat transfer problems with curved boundary.

Abstract

A three-dimensional (3D) lattice Boltzmann flux solver is presented in this work for simulation of fluid-solid conjugate heat transfer problems with a curved boundary. In this scheme, the macroscopic governing equations for mass, momentum, and energy conservation are discretized by the finite-volume method, and the numerical fluxes at the cell interface are reconstructed by the local solution of lattice Boltzmann equation. For solving the 3D fluid-solid conjugate heat transfer problems, the density distribution function (D3Q15 model) is utilized to compute the numerical fluxes of continuity and momentum equations, and the total enthalpy distribution function (D3Q7 model) is introduced to calculate the numerical flux of the energy equation. The connections between the macroscopic fluxes and the local solution of the lattice Boltzmann equation are provided by the Chapman-Enskog expansion analysis. As compared with the lattice Boltzmann method, in which the time step and grid spacing are correlated, the local solution of the lattice Boltzmann equation at each cell interface used in the present scheme is independent of each other. As a result, the drawback of the tie-up between the time step and grid spacing can be effectively removed and the developed method applies very well to nonuniform mesh and curved boundaries. To validate the performance of the developed method, the steady and unsteady natural convection in a finned 3D cavity and in a finned 3D annulus are simulated. Numerical results showed that the present scheme can effectively solve the 3D conjugate heat transfer problems with a curved boundary.