| This work investigates the single-relaxation-time Lattice Boltzmann Method and how to develop it into a full hydrodynamic and thermal modeling scheme. First the single- relaxation time isothermal Lattice Boltzmann Method is outlined, beginning with the fundamentals of the lattice model and then proceeding through the necessary governing equations for the two-dimensional, nine-directional lattice. The governing equations are then presented in a discretized form to be used for simulation, followed by treatment of boundary conditions. Fluid and dimensional properties are explained in terms of both lattice units and physical units via conversion factors. Next is an introduction to thermal Lattice Boltzmann, discussing the changes as well as going through new governing equations pertaining to the internal energy density distribution function. Then the thermal scheme is shown in discretized form along with thermal boundary conditions and updated hydrodynamic boundary conditions. Fluid properties are reviewed alongside thermal properties, as they are essential to know when designing a simulation. Finally, results are shown for some two-dimensional channel flow geometries with hot and cold surfaces: a uniform-width channel, a channel that undergoes sudden expansion, and a channel featuring sudden contraction. The flow within the channel could be dominated by the density stratification or the forced flow introduced at the inlet. These mixed flows of natural and forced convection are characterized by the Reynolds and Rayleigh numbers, the Rayleigh numbers above critical value to allow for formation of natural convection 2 cells when experiencing low-Reynolds flows. The results are presented as contour plots of temperature and stream function. |
