Multiple-relaxation-time lattice Boltzmann simulation of viscoplastic Bingham nanofluids in a suddenly expanded channel: a systematic numerical study

The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is used in a suddenly expanded channel to demonstrate the flow of viscoplastic Bingham nanofluid with Al\(_2\)O\(_3\) nanoparticles. The geometry has two sections namely, inlet and outlet, and the corresponding heights are denoted by h and H, respectively. The length of the entire channel is 20H, and the expanded channel has a height of 16H. The purpose of the MRT-LBM simulation is to investigate the impact of changing the Bingham number (\( 0 \le Bn \le 200\)), keeping the Reynolds number (Re) fixed for different volume fractions (\(\phi =\) 0.00 and 0.04). In addition, the consequences of variations in the Reynolds number (\( 50 \le Re \le 1000 \)) at constant Bingham number (Bn) are also studied for those two different volume fractions. The results demonstrate that with fixed \(Bn=2\), \(Re=400\) is the point where the flow pattern and recirculation regions are exactly the same for both volume fractions. An increase in Re causes the recirculation regions to grow for a fixed Bn for both volume fractions as Re’s rise increases the velocity and decreases the viscous force. Bn’s increment with Re and volume fraction unchanged lowers the recirculation region’s size due to a rise in viscous force. Higher Re and lower Bn cause the more significant recirculation regions to break down into smaller areas. Incrementing the volume fraction lowers size of the recirculation region. An unstable flow was observed for higher Bn (e.g., \(Bn \ge 100\)) and lower Bn (e.g., \(0 \le Bn \le 10\)) when \(Re \ge 500\) for both volume fractions in maximum cases. Unstable flow for lower Bn makes the recirculation regions asymmetric, and when Re is high, the recirculation regions break down for the base fluid (\(\phi =0.00\)). When \(Re=300\) and \(Bn=2\), the length of the recirculation region of the upper wall decreases by \(28.58\%\), and the length of the lower wall falls a bit less by \(26.37\%\) when \(\phi \) is increased from 0.00 to 0.04. For \(x/h=2\), the nanoparticle mixed fluid’s velocity (\(\phi =0.04\)) never gets a negative magnitude till the final position for \(Re=700\). In most situations, an increased volume fraction increases the skin-friction effect on both walls.