Numerical study of the Bingham fluid flow in a cylindrical enclosure with exact Bingham model

In the present paper, the non-iterative PISO algorithm and finite volume method are employed to solve the exact Bingham fluid flow. The OpenFOAM solver, i.e., icoFoam, is modified to achieve this goal. The accuracy of numerical procedures is obtained by reproducing the results of Chupin and Dubois (Comput Math Appl 72:1263–1286, 2016. doi:10.1016/j.camwa.2016.06.026). Then, the Bingham fluid flow in a cylindrical enclosure with the rotating top wall is numerically studied by the modified solver for the following ranges of conditions: Reynolds number, $$ 1 \le \text{Re} \le 1000 $$, Bingham number, $$ 0 \le {\text{Bn}} \le 1000 $$ and aspect ratio (AR) of 1, 1/2, 1/4, 1/8 and 1/16. The variation of yielded regions percentage with Re and Bn is plotted for AR = 0.5 and 1. It is found that Reynolds number change in the range $$ 1 \le {\text{Re}} \le 10{\text{Bn}} $$ has no significant effect on the size and shape of the unyielded regions for constant Bn and AR = 1. The effect of Re, Bn and AR on the primary ($$ Q_{p}^{*} $$) and secondary ($$ Q_{s}^{*} $$) volumetric flow rate is also discussed. A correlation is proposed in terms of Re and Bn to approximate the torque coefficient ($$ C_{\text{T}} $$) for $$ 1\le {\text{Re}} \le 1 0 0,\,\, 0\le {\text{Bn}} \le 1000\, $$ and different aspect ratios.