POD analysis of a finite-length cylinder near wake

Abstract

The near wake of a wall-mounted finite-length square cylinder with an aspect ratio of 7 is investigated based on the proper orthogonal decomposition (POD) of the PIV data measured in three spanwise planes, i.e., z/d = 6, 3.5 and 1.0, near the cylinder free end, mid-span and fixed end (wall), respectively. The Reynolds number based on free-stream velocity (U∞) and cylinder width (d) is 9,300. A two-dimensional (2D) square cylinder wake is also measured and analyzed at the same Reynolds number for the purpose of comparison. The structures of various POD modes show marked differences between the two flows. While the coefficients, a1 and a2, of the POD modes 1 and 2 occur within an annular area centered at a1 = a2 = 0 in the 2D wake, their counterparts are scattered all over the entire circular plane at z/d = 1.0 and 3.5 of the finite-length cylinder wake. Flow at z/d = 6 is dominated by POD mode 1, which corresponds to symmetrical vortex shedding and accounts for 54.0 % of the total turbulent kinetic energy (TKE). On the other hand, the POD modes 1 and 2, corresponding to anti-symmetrical vortex shedding, are predominant, accounting for about 45.0 % of the total TKE, at z/d = 3.5 and 1. It has been found that the flow structure may be qualitatively and quantitatively characterized by the POD coefficients. For example, at z/d = 6, a larger a1 corresponds to a smaller length of flow reversal zone and a stronger downwash flow. At z/d = 3.5 and 1, two typical flow modes can be identified from a1 and a2. While large a1 and/or a2 correspond to anti-symmetrical vortex shedding, as in a 2D cylinder wake, small a1 and a2 lead to symmetrical vortex shedding. Any values between the large and small a1 and/or a2 correspond to the flow structure between these two typical flow modes. As such, the probability of occurrence of a flow structure may be determined from the distribution of the POD coefficients.