Study of thermal flows through scalable computation of a discrete unified gas kinetic scheme
Date
2021
Authors
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Publisher
University of Delaware
Abstract
The buoyancy-driven natural convection in an enclosure plays a very important role in both fundamental studies of temperature and velocity structures and practical applications such as geophysical and astrophysical convections, solar energy collection devices, cooling of a nuclear reactor, or electronic equipment. The buoyancy-driven natural convection can be classified into two categories: (1) the Boussinesq flow in which the temperature difference is small so that the density variation can be neglected except in the buoyancy force term; (2) the fully compressible thermal flow in which the temperature difference is large and the changes in fluid density must be explicitly considered. For the latter case, there are very few results available in the literature, and efficient simulation tools remain much desired. Along this direction, mesoscopic CFD methods based on simplified Boltzmann equations have been developed in recent years, to treat compressible thermal flows. In this work, the discrete unified gas-kinetic scheme (DUGKS), a finite-volume discretization of the Boltzmann equation, is developed in order to simulate compressible natural convection. ☐ First, DUGKS with an improved implementation of boundary conditions is applied to study the unsteady three-dimensional natural convection in an air-filled, differentially heated cubical cavity, under the Boussinesq approximation. The focus is on the transition from laminar to unsteady irregular flow in the thermal boundary layer. The simulations are conducted at three Rayleigh numbers: 1.5E9, 1.0E10, and 1.0E11 using nonuniform grids with resolution up to 320^3. The Prandtl number is fixed at 0.71. A detailed analysis is provided of the flow transition and its influence on the rate of heat transfer. Time traces of temperature and velocity, time-averaged flow field, and statistics of fluctuation fields are used to illustrate distinct behaviors in the laminar and turbulent thermal boundary layers, as well as to determine the transition location at different Ra numbers. The variation of the average Nusselt number with Ra is compiled and compared to previous results. ☐ Second, in order to simulate compressible thermal convection, DUGKS should be implemented properly with a consistent treatment including proper implementation of the boundary conditions, an optimized source term to adjust the Prandtl number, a lattice velocity model with adequate Gauss-Hermite quadrature accuracy, and the Hermite expansion of the equilibrium to the fourth-order. Otherwise, errors may arise from each of these implementation details, which are demonstrated by comparing the DUGKS results with results from the convectional CFD solvers. ☐ Third, two-dimensional compressible natural convection flows in a square cavity are simulated using our redesigned DUGKS. A systematic approach of deriving the temperature and velocity boundary conditions based on the Chapman-Enskog analysis is developed. The fully compressible Navier-Stokes equations can be accurately recovered by the current kinetic model. Results on steady and unsteady thermal convections are provided and compared with the literature results, showing an excellent agreement of flow structures, velocity and temperature profiles, and the resulting Nusselt number. The transition to the unsteady thermal boundary layer in compressible natural convection is also explored. To allow simulation of natural convection with curved solid boundaries, we incorporate the immersed boundary method into DUGKS. Natural convection in a cavity with hot cylinders is simulated and compared with the literature results. ☐ Finally, a D3Q77A9 lattice velocity model is developed to provide a Gauss-Hermite quadrature of ninth-order accuracy in three dimensions, which allows efficient and adequate representation of compressible thermal flows in DUGKS. This lattice velocity model enables successful simulations of three-dimensional thermal flows and three-dimensional compressible turbulence. ☐ Overall, this dissertation work extends the design of DUGKS, expands the application domain of DUGKS, and advances our understanding of thermal convection flows.
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Keywords
Boundary condition, Compressible flow, DUGKS, Instability mechanism, Natural convection, Numerical modeling