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A Gas-Kinetic BGK Scheme for Natural Convection in a Rotating Annulus

Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Qinhuai District, Nanjing 210016, China
Author to whom correspondence should be addressed.
Appl. Sci. 2018, 8(5), 733;
Received: 25 March 2018 / Revised: 26 April 2018 / Accepted: 3 May 2018 / Published: 5 May 2018
(This article belongs to the Special Issue Development and Applications of Kinetic Solvers for Complex Flows)
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In this paper, a gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme is developed for simulating natural convection in a rotating annulus, which arises in many scientific and engineering fields. Different from most existing methods for the solution of the incompressible Navier–Stokes (N–S) equations with the Boussinesq approximation, compressible full N–S equations with allowable density variation are concerned. An appropriate BGK model is constructed for the macroscopic equations defined in a rotating frame of reference. In particular, in order to account for the source (non-inertial) effects in the BGK model, a microscopic source term is introduced into the modified Boltzmann equation. By using the finite volume method and assuming the flow is smooth, the time-dependent distribution function is simply obtained, from which the fluxes at the cell interface can be evaluated. For validation, a closed rotating annulus with differentially heated cylindrical walls is studied. A conventional N–S solver with the preconditioner is used for comparison. The numerical results show that the present method can accurately predict the variation of the Nusselt number with the Rayleigh number, but no preconditioning is required due to its delicate dissipation property. The computed instantaneous streamlines and temperature contours are also investigated, and it is verified that the Rayleigh–Bénard convection in a rotating annulus is very similar to that in a classical stationary horizontal enclosure. View Full-Text
Keywords: gas-kinetic scheme; BGK model; source term; natural convection; rotating annulus; Rayleigh–Bénard convection gas-kinetic scheme; BGK model; source term; natural convection; rotating annulus; Rayleigh–Bénard convection

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Zhou, D.; Lu, Z.; Guo, T. A Gas-Kinetic BGK Scheme for Natural Convection in a Rotating Annulus. Appl. Sci. 2018, 8, 733.

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