Numerical studies on complex axisymmetric flows using axisymmetric lattice Boltzmann method

Morakabi, Farokh (2023) Numerical studies on complex axisymmetric flows using axisymmetric lattice Boltzmann method. Doctoral thesis (PhD), Manchester Metropolitan University.

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Abstract

The lattice Boltzmann method (LBM) has proven to be an effective numerical technique for computational fluid dynamics (CFD). It has numerous advantages over traditional computational methods such as finite element and finite difference approaches. The method’s simplicity, easy treatment of boundary conditions, and parallel programming features make it ideal for solving large-scale real-world problems. In this thesis, the development and use of a lattice Boltzmann model for both steady and unsteady two-dimensional axisymmetric flows are presented. Three-dimensional (3D) Navier-Stokes equations describe axisymmetric flows, which can be solved using the three-dimensional (3D) lattice Boltzmann method. Such 3D equations become 2D axisymmetric flow equations when cylindrical coordinates are used. The cavity flow benchmark has been used in our study to verify the axisymmetric lattice Boltzmann revised model(AxLAB®) for more complex axisymmetric flows in a cylindrical container. Also, systematic research on vortex breakdown has been done in a closed cylindrical container with one or two rotating lids. Furthermore, an investigation was carried out into unsteady-periodic flow in the cavity to see how the flow behaviour can be predicted. To the author’s knowledge, this is the first numerical study to determine the periodicity of such flows. The formation of vortex breakdowns, their frequency, and the locations of stagnation points as the flow pattern enlarges are all explained in depth. In addition, the second-order bounce-back technique is introduced to the model for no-slip boundary conditions to increase the accuracy of the AxLAB®. The magnitude of the maximum axial velocities along the cylinder axis, their locations, and the locations of stagnation points have all been analysed to demonstrate the advantages of the described method. The most recent experimental and numerical approaches are then used to compare the results, indicating that the new method provides more accurate results in detail. Also, a more advanced version of AxLAB® is developed to model turbulent flows. By incorporating the conventional subgrid-scale stress (SGS) model into the axisymmetric lattice Boltzmann equation in a way that is consistent with lattice gas dynamics, the turbulent flow is effectively and naturally represented. By using the model to simulate two common engineering scenarios, (i) pipe flow through an abrupt axisymmetric constriction, and (ii) axisymmetric separated-reattached flow, the model is proven to be accurate. Analysis of the axial velocity profile and the reattachment length reveals how much more comparable the outcomes are to other experimental and computational methods, particularly in the region close to the wall domain, as a result of using the second-order bounce back method for the wall boundary conditions. The result demonstrates that the second-order bounce-back method in the upgraded AxLAB® is straightforward and has a higher level of accuracy than AxLAB® in its ability to predict axisymmetric turbulent flows as well as laminar flows.