Date of Award
Open Access Dissertation
Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)
Administrative Home Department
Department of Mechanical Engineering-Engineering Mechanics
Committee Member 1
Franz X. Tanner
Committee Member 2
Committee Member 3
Derivation of an unambiguous incompressible form of the lattice Boltzmann equation is pursued in this dissertation. Further, parallelized implementation in developing application areas is researched. In order to achieve a unique incompressible form which clariﬁes the algorithm implementation, appropriate ansatzes are utilized. Through the Chapman-Enskog expansion, the exact incompressible Navier-Stokes equations are recovered. In initial studies, fundamental 2D and 3D canonical simulations are used to evaluate the validity and application, and test the required boundary condition modiﬁcations. Several unique advantages over the standard equation and alternative forms found in literature are found, including faster convergence, greater stability, and higher ﬁdelity for relevant ﬂows. Direct numerical simulation and large eddy simulation of transitional and chaotic ﬂows are one application area explored with the derived incompressible form. A multiple relaxation time derivation is performed and implemented in a 2D cavity (direct simulation) and a 3D cavity (large eddy simulation). The Kolmogorov length scale, a function of Reynolds number, determines grid resolution in the 2D case. Comparison is made to the extensive literature on laminar ﬂows and the Hopf bifurcation, and ﬁnal transition to chaos is predicted. Steady and statistical properties in all cases are in good agreement with literature. In the 3D case the relatively new Vreman subgrid model provides eddy viscosity modeling. By comparing the center plane to the direct numerical simulation case, both steady and unsteady ﬂows are found to be in good agreement, with a coarse grid, including prediction of the Hopf bifurcation. Multiphysics pore scale ﬂow is the other main application researched here. In order to provide the substrate geometry, a straightforward algorithm is developed to generate random blockages producing realistic porosities and passages. Combined with advection-diﬀusion equations for conjugate heat transfer and soot particle transport, critical diesel particulate ﬁltration phenomena are simulated. To introduce additional ﬁdelity, a model is added which accounts for deposition caused by a variety of molecular and atomic forces. Detailed conclusions are presented to lay the groundwork for future extensions and improvements. Predominantly, higher lattice velocity large eddy simulation, improved parallelization, and ﬁlter regeneration.
Murdock, John R., "TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD", Open Access Dissertation, Michigan Technological University, 2017.