Assessment of lattice boltzmann approach for non-newtonian fluid flow simulation (PhD)

Abstract

The study of non-Newtonian fluids forms a vital subject in modern technology with various applications in sectors such as petroleum engineering, paints and chemical industries, molten plastic and molding, drilling fluids, food processing, bio-medical fluids, and polymer fabrication. Numerous materials, for example, blood, paints, drilling mud, toothpaste, certain oils, polymer dissolves, and different emulsions, have shown non-Newtonian fluid behavior. The analysis of the flow of non-Newtonian fluids in various geometries is essential. The assessment and characterization of models for the non-Newtonian fluid properties and underpinning the flow behaviour is a necessity. This thesis is carried out using a kinetic theory based lattice Boltzmann method (LBM), which provides a stable and efficient numerical simulation approach for the non-Newtonian fluid flows. Firstly, the well-known Bhatnagar-Gross-Krook (BGK) approximation based lattice Boltzmann(LB) method, also referred to as the lattice-BGK (LBGK) approach, is applied to simulate both Newtonian and non-Newtonian fluids (i.e., for shear-thinning and shear-thickening fluids; wherein the viscosity is modeled using the power-law model). The standard example benchmark flow over two-dimensional wall-driven enclosures is used. The wall-driven enclosure (representing the wall- or boundary-shear) is considered with a corrugated bottom to ensure the effect of fluid-shear on the flow structure. The LBGK algorithm is first validated for the Newtonian flows and then assessed for the non Newtonian fluid flows. The Newtonian flow inside a corrugated enclosure is analyzed in detail. The influences of various parameters such as the flow Reynolds number, number of corrugations for the bottom wall of the cavity, corrugation heights, and power-law index have been analyzed. The results for non-Newtonian flows show numerical instability for the shear-thinning power-law fluid flow (i.e., when the power-law index is less than 1.0). This led to the use of an advanced LB collision model, namely, the multiple relaxation time (MRT), to enhance the numerical stability and accuracy, particularly for the shear-thinning fluid flow simulation. The standard, central processing units (CPUs) based distributed memory parallel MRT-LB algorithm using MPI bindings is developed. This enabled the computations on the Institute’s high-performance computing (HPC) cluster. The effect of different values of the non-hydrodynamic relaxation parameters of the MRT model is examined. This assessment is performed to establish the stability window for the numerical problem which is under consideration. It is concluded that the values of the relaxation parameters corresponding to the non-hydrodynamic moments should be between 1.0 and 1.5. This enabled an accurate prediction of the flow structures inside the wall-driven corrugated enclosures. Next, the MRT-LB algorithm is coupled with non-Newtonian fluid flow models apart from the conventional power-law model, namely, Carreau, Carreau-Yasuda, and Cross models. These couplings are analyzed using conventional two-dimensional benchmark problems; namely, lid-driven cavity flow, lid-driven cavity flow with an embedded cylinder at the center of the cavity, flow through a straight channel and flow over a circular cylinder embedded asymmetrically in a confined channel. Then, the results are compared with the previously known analytical and computational results for non-Newtonian fluids, and new benchmark results are given. Lastly, the non-Newtonian power-law fluid flow structures over the obstacle(s) are studied. The obstacle(s) are placed inside a lid-driven two-dimensional cavity and embedded in a confined channel. For a single circular or square obstacle inside a lid-driven cavity, the influences of various parameters such as flow Reynolds number, obstacle size, and power-law index are examined. It is found that these parameters have a significant impact on the flow characteristics, the vortex formations, and the drag coefficient. Next, the effect of two square obstacles arranged side-by-side or tandem manner inside the cavity is analyzed. Lastly, the fluid flow over the multiple square obstacles embedded inside the cavity and the channel is examined. This study concludes that the LBM with the MRT collision model is a promising technique to simulate the non-Newtonian fluid flows.