Steady flow of a power-law non-Newtonian fluid across an unconfined square cylinder

A two-dimensional flow of a non-Newtonian power-law fluid directed normally to a horizontal cylinder with a square cross section is considered in the present paper. The problem is investigated numerically with a finite volume method by using the commercial code Ansys Fluent with a very large computational domain so that the flow could be considered unbounded. The investigation covers the power-law index from $0.1$ to $2.0$ and the Reynolds number range from $0.001$ to $45.000$. It is found that the drag coefficient for low Reynolds numbers and low power-law index $(n\le 0.5)$ obeys the relationship $C_D=A/\mathrm{Re}$. An equation for the quantity $A$ as a function of the power-law index is derived. The drag coefficient becomes almost independent of the power-law index at high Reynolds numbers and the wake length changes nonlinearly with the Reynolds number and power-law index.