Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number. (September 2019) - Xu, Ao; Shi, Le; Xi, Heng-Dong
Highlights: Three-dimensional thermal LB model achieves isotropy of fourth-order error term. Laminar side-heated convections are simulated with grid up to 257 3 . Turbulent RB convections are simulated with 8 nodes to resolve boundary layers. Abstract: We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-Bénard convection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 10 6 and 10 7, and Prandtl number of 0.71, where the mesh sizes are up to 257 3 ; in Rayleigh-Bénard convection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 10 6, 3 × 10 6, and 10 7, and Prandtl numbers of 0.7 and 7, where the nodes within thermal boundary layer are around 8. Compared with existing benchmark data obtained by other methods, the present LB model can give consistent results.