Numerical study on uniform-shear flow over a circular disk at low Reynolds numbers

Abstract

Uniform shear flows over a circular disk of aspect ratio 10 (thickness/diameter) at low Reynolds numbers are numerically investigated with the main focus on the effect of inlet shear on the wake evolutions. The Reynolds numbers considered are Re = 140, 160, and 180 based on the inlet center velocity uc and disk diameter d. The non-dimensional shear rate k(=∇ud/uc) is varied from 0 to 0.09. The bifurcations leading to unsteady states with hairpin vortex shedding occur much earlier in uniform shear. In most cases, wake evolutions occurring as the shear rate increases in uniform shear are similar to those as the Reynolds number increases in uniform flow. A new wake mode termed as dragonfly-wings (DW) mode is captured at Re = 180 and k = 0.01 and 0.03. At DW mode, hairpin vortex structures are shed from diametrically opposite orientations, but with irregularity in strength and shape, i.e., three different vortex loops are observed in the wake, and produce three peaks at low frequencies in the frequency spectrum of the drag. The planar-symmetry plane for standing-wave and zig-zig modes is determined by both the initial conditions and the direction of the uniform shear. It is found that with increasing inlet shear rate, the non-dimensional shedding frequency remains nearly constant for the low shear rates (k < 0.1). Time-averaged drag and lift coefficients slightly increase with increasing inlet shear rate. Finally, the hysteretic property of the DW mode transition is examined and further investigated using the Landau mode, indicating that DW mode transition is non-hysteretic (supercritical).