Effect of orientation on the drag of a cone settling in a Bingham plastic fluid
Pragya Mishraa, A.K. Tiwaria,b, R.P. Chhabraa,*
Effects of the orientation and apex angle on the settling velocity of conical particles in Bingham plastic fluids are numerically investigated over a Reynolds number range of 1 ≤ Re ≤ 100, Bingham number range of 0 ≤ Bn ≤ 100, and cone angle range of 20° ≤ α ≤ 150°. Governing equations (of continuity and momentum) are solved numerically using the finite element method to obtain velocity and pressure fields that are postprocessed to obtain values of the drag coefficient. Furthermore, the effect of cone orientation on the flow field is visualized and explored in terms of streamline contours and the morphology of yielded/unyielded regions. Finally, the obtained values of drag are correlated via a simple predictive expression in terms of the modified Reynolds number. The effect of the cone angle on drag is found to be moderate because the drag force acting on the lateral surface is a small fraction of the overall drag.
Bingham number; Reynolds number; Yielded/unyielded regions; Drag