Date of Award
2024
Document Type
Open Access Dissertation
Degree Name
Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)
Administrative Home Department
Department of Mechanical Engineering-Engineering Mechanics
Advisor 1
Song-Lin Yang
Committee Member 1
Jeffrey S. Allen
Committee Member 2
Chunpei Cai
Committee Member 3
Gowtham
Abstract
The present study addresses the compressibility error inherent in the standard Lattice Boltzmann Method (LBM) and LBM’s restriction to uniform Cartesian meshes. To mitigate the compressibility error, an incompressible LBM (iLBM) model has been incorporated into the finite volume framework using a cell-centered finite volume approach, leveraging the simplicity of the LBM algorithm for irregularly shaped flow domains with unstructured meshes. Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) and linear reconstruction (LR) schemes have been used to compute convective fluxes across the cell interfaces with boundary conditions implemented using the second-order accurate Non-Equilibrium Extrapolation (NEE) method.
The finite volume iLBM (FV-iLBM) model has been validated using canonical flow problems, demonstrating its applicability and precision. While simulating Womersley flow, it has outperformed the standard LBM model by limiting the compressibility error, thus, highlighting its accuracy in handling unsteady flow phenomena. Despite MUSCL scheme’s substantial non-physical numerical diffusion, the FV-iLBM model, in conjunction with the LR scheme has simulated lid-driven flow in a 2D square cavity effectively, capturing velocity profiles and vortex structures accurately. The FV-iLBM approach has also successfully simulated external flow over National Advisory Committee for Aeronautics (NACA) 0012 airfoil, capturing unsteady vortex shedding with pressure coefficient profiles aligning well with the existing literature. Despite losing the benefits of local computations and exact treatment of advective terms, the FV-iLBM model’s ability to manage irregular geometries and limit compressibility error is significant.
The FV-iLBM model, with its ability to mitigate compressibility errors, has been effectively used to simulate pulsatile blood flow through arterial stenosis and aneurysms. It accurately captured the dynamics of pulsating non-Newtonian blood flow, revealing significant pressure drop, increased velocity at stenosis throats, and heightened wall shear stress. The model’s investigations showed that higher Reynolds and Womersley numbers amplify flow instabilities and wall shear stress, increasing the risk of endothelial damage. It also found that the size of upstream stenoses significantly influence downstream flow conditions. Furthermore, the simulation of pulsatile non-Newtonian blood flow in aneurysmal arteries highlighted flow separation, recirculation, and shear stress fluctuations with larger aneurysms resulting in more pronounced disturbances.
Recommended Citation
Dongre, Akshay S., "Modeling Pulsatile Flows Using Truly Incompressible Finite Volume Lattice Boltzmann Model", Open Access Dissertation, Michigan Technological University, 2024.