Excitation of shear layer instability in flow past a cylinder at low Reynolds number

Abstract

SUMMARYThe instability of the separated shear layer for ow past a cylinder, in two dimensions, is investigated for low Reynolds numbers (Re 6 350). The line of symmetry, downstream of the cylinder, in the wake is forced to be a streamline. This hypothetical situation allows slip of velocity along the wake centreline but prevents any ow normal to it. With this arrangement the ow is completely stable for Re 6 250. It suppresses the primary instability of the wake that is responsible for the von Karman vortex shedding. Unlike the conventional splitter plate such an arrangement does not have a wake of its own. At Re = 300 and above the wake instability and the shear layer instability are observed. The uctuations due to the instabilities are intermittent in nature. The shear layer frequency is smaller than the frequency of the von Karman vortex shedding for the regular ow past a cylinder. It is also found that ow past half a cylinder, with symmetry conditions at the wake centreline, at Re = 300 is stable. However, when a secondary cylinder with one-ÿfth the diameter of the half-cylinder is placed close to it, the vortex shedding from the smaller cylinder again leads to instability of the separated shear layer of the half-cylinder. This suggests that although the separated shear layer is stable, at such low Re, the shear layer instability can be excited by some other disturbances. It is found that even at such low Re, the normalized shear layer frequency follows the Re 0:67 power law. All the computations have been carried out using a stabilized ÿnite element formulation.

Instability of the separated shear layer in flow past a cylinder: Forced excitation

“…This results in larger amplitude oscillations in the velocity field as is seen from the time history shown in Figure 8. This behaviour is very similar to the one observed in our earlier work [8] where the separated shear layer for a steady inflow is excited by a smaller secondary cylinder.…”

“…The values for the same, reported by Fornberg [20], are 0.726 and 20.40D, respectively. For more details on the steady-state flow past a cylinder and for the performance of the present algorithm for unsteady flows, the interested reader is referred to our earlier papers [8,13,14].…”

Numerical Investigation of the Evolution of Vortex Instability in a 2-D Compressible Flow over a Cylinder

“…Mittal [12] published aerodynamic coefficients for 2-D unsteady flow simulations over a cylinder at Reynolds numbers of 50, 100, 200, 300 in terms of time averaged mean and root-mean-square amplitude. Since the periodic wave forms are nearly sinusoidal, Mittal's root-mean-square values can easily be converted to peak amplitude through a multiplication with 2 ; a comparison of calculated and directly quoted value for peak lift at 100 Re = was less than 1%.…”

“…A number of instability modes have been identified with cylinder flow associated with its wake, separated shear layer, boundary layer, and three-dimensional instabilities along its span [11][12][13]. Each mode adds a time varying component to the flow and can generally be observed above a critical Reynolds number (Re).…”

Numerical Study on Flow Characteristics Around Curved Riser

“…에 대한 Miliou et al(2003)의 연구를 시작으로, Miliou et al (2007)은 환형(Ring shape)의 1/4 형상에 수평 원형 실린더를 이 은 굽은 실린더(Curved cylinder, Fig. 1 (Franke et al, 1990;Mittal, 2005;Li et al, 2009). (Fig.…”