Thermal Lattice Boltzmann Simulation for Rarefied Flow in Microchannels
Bayazitoglu, Yildiz; Chapman, Walter G.
Doctor of Philosophy
This dissertation provides a detailed description of a new thermal lattice Boltzmann model capable of simulating temperature and velocity gradients within micro/nano-channels and vertical cavities in rarefied flow extending to the high end of the transition flow regime. The lattice Boltzmann method was selected to perform this study due to its applicability to the rarefied conditions expected in such small scale scenarios. An introduction is first included to provide details on the origins and derivation of the lattice Boltzmann method, including the various aspects that are required to successfully perform a simulation, namely boundary conditions, lattice velocity sets, methods to determine relaxation times, and strategies for capturing velocity as well as temperature fields. This is followed by a description of the thermal lattice Boltzmann method used as the basis for this study, as well as the determination of the method used to incorporate effects of walls on the calculation of the relaxation times. The applicability of this method is validated by incorporating two wall-distance functions based on exponential and power law relationships and simulating isothermal as well as thermally-affected cases. Next, a novel wall-distance function is derived to extend the applicability of our thermal lattice Boltzmann model to the entire transition flow regime. The method through which the function is derived is thoroughly described, and the resulting function compared against reference data based on Molecular Dynamics as well as existing functions available in the literature. The resulting function is validated by simulating cases representing conduction as well as convection applications. Finally, the resulting thermal lattice Boltzmann model is utilized to determine the effect of Knudsen number on natural convection within vertical cavities. In order to successfully simulate natural convection cases representing the conduction, asymptotic, and boundary layer regimes, a method to determine the magnitude of the external force due to density gradients is first derived starting from the Boussinesq approximation. The resulting model is first validated by simulating classic natural convection cases in the continuum flow regime. The model is then utilized to simulate natural convection cases in the conduction regime for Kn up to 1.0, well within the transition flow regime. The results included in this thesis demonstrate that our thermal lattice Boltzmann model can accurately capture the velocity and temperature gradients expected in continuum, slip, and transition flow regimes. Lastly, the contributions of this thesis to the development of lattice Boltzmann models is summarized, as well as potential future research topics.