Numerical simulation of fluid flow and heat transfer inside a rotating disk-cylinder configuration by a lattice Boltzmann model

A simple lattice Boltzmann model for numerical simulation of fluid flow and heat transfer inside a rotating disk-cylinder configuration, which is of fundamental interest and practical importance in science as well as in engineering, is proposed in this paper. Unlike existing lattice Boltzmann models for such flows, which were based on "primitive-variable" Navier-Stokes equations, the target macroscopic equations of the present model for the flow field are vorticity-stream function equations, inspired by our recent work designed for nonrotating flows [S. Chen, J. Tolke, and M. Krafczyk, Phys. Rev. E 79, 016704 (2009); S. Chen, J. Tolke, S. Geller, and M. Krafczyk, Phys. Rev. E 78, 046703 (2008)]. The flow field and the temperature field both are solved by the D2Q5 model. Compared with the previous models, the present model is more efficient, more stable, and much simpler. It was found that, even though with a relatively low grid resolution, the present model can still work well when the Grashof number is very high. The advantages of the present model are validated by numerical experiments.