Correspondence between the number of no-slip critical points and nature of rear stagnation point of a symmetric object

Abstract

For flow around an isolated object, the points of zero vorticity/shear stress located at fluid-solid interface, i.e., the separation, reattachment points inclusive of forward and rear stagnation points are refered to as no-slip critical points. The total number, n (≥ 2), of such points is an even number. For flow past a diamond-section object, it is shown here that a change of the value of n by 2 alters the nature of its rear stagnation point. The rear stagnation point acts as a separation point for n = 2, 6, 10, etc. and as an attachment point for n = 4, 8, 12, etc. A pair of hypothetical mean wakes is proposed and their viability discussed with reference to results available in literature. Concerning flow past two in-line diamond cylinders, the formation of an "anti-wake"at the leading edge of the downstream cylinder renders its forward stagnation point to act as a separation point, which, otherwise for an isolated object, invariably serves as an attachment point. The forebody and afterbody of a symmetric object act as independent entities in influencing the nature of no-slip stagnation points.