Abstract
A modified power-law (MPL) viscosity model of non-Newtonian fluid flow has been used for the multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) and then validated with the benchmark problems using the graphics process unit (GPU) parallel computing via Compute Unified Device Architecture (CUDA) C platform. The MPL model for characterizing the non-Newtonian behavior is an empirical correlation that considers the Newtonian behavior of a non-Newtonian fluid at a very low and high shear rate. A new time unit parameter (λ) governing the flow has been identified, and this parameter is the consequence of the induced length scale introduced by the power law. The MPL model is free from any singularities due to the very low or even zero shear-rate. The proposed MPL model was first validated for the benchmark study of the lid-driven cavity and channel flows. The model was then applied for shear-thinning and shear-thickening fluid flows through a backward-facing step with relatively low Reynolds numbers, Re = 100–400. In the case of shear-thinning fluids (n=0.5), laminar to transitional flow arises while Re≥300, and the large vortex breaks into several small vortices. The numerical results are presented regarding the velocity distribution, streamlines, and the lengths of the reattachment points.
Highlights
The study of non-Newtonian fluids has received prodigious attention from the researchers in many branches of science because of the ubiquitous presence of non-Newtonian fluids in nature.Examples include shampoo, toothpaste, ketchup, whipped cream, biological fluids, industrial fluids, polymer solutions, Oobleck, and body armor, to name a few
We introduce the modified power-law model to characterize the non-Newtonian viscosity for the internal flow
A new modified power-law viscosity model has been proposed for the lattice Boltzmann method and successfully applied for the 2D laminar flows in a lid-driven cavity, channel, and backward-facing step that are shown in Figure 1a–c, respectively
Summary
The study of non-Newtonian fluids has received prodigious attention from the researchers in many branches of science because of the ubiquitous presence of non-Newtonian fluids in nature. The present study intended to employ the modified power-law viscosity model to investigate the non-Newtonian fluid flow in a complex benchmark problem; the lattice Boltzmann method (LBM). In this approach, the lid-driven cavity flow, channel flow, and backward-facing step (BFS) flow are utilized for the present study as the computational fluid dynamics (CFD) community considered these models a benchmark problem examining the accuracy and efficiency of any numerical method. Wu and Shao [51] investigated numerical simulation of steady two-dimensional incompressible lid-driven cavity flows (Re = 100–500) using a multi-relaxation-time (MRT) model in the parallel lattice Boltzmann Bhatnager–Gross–Krook method (LBGK). To the best of the author’s knowledge, no study has considered a comprehensive investigation of the non-Newtonian power-law fluids in a backward-facing step flow with the lattice Boltzmann simulation approach. The present simulations have been done using the state-of-the-art GPU parallel computing using the CUDA C platform
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