Periodic Wake Behind a Circular Cylinder at Low Reynolds Numbers

Abstract

SummaryThe effects of free-stream turbulence and of sinusoidal free-stream pulsations of controlled frequencies and amplitudes on the periodic wake of a circular cylinder are investigated experimentally by employing hot-wire and smoke visualisation techniques. In addition, the effects of cylinder yaw and mild favourable and adverse pressure gradients on the vortex shedding mechanism have been explored.The data relating frequency to mean velocity follow Berger’s relation; this relation is uninfluenced by free-stream turbulence intensities up to 8 per cent. As the longitudinal turbulence intensity increases from 0.3 to 8 per cent, the downstream distance Lp behind the cylinder over which the hot-wire signal is periodic decreases progressively, indicating that the otherwise steady periodic wake interacts non-linearly with the three-dimensional free-stream turbulence and undergoes either transition or rapid diffusion by turbulence, depending on both the Reynolds number and the turbulence intensity. For a given turbulence intensity, Lp decreases also with increasing Reynolds number.The shedding frequency behind a yawed cylinder does not vary as the cosine of the yaw angle ϕ for ϕ < 50°; the signal switches intermittently between periodic and irregular form as the yaw is increased from 0 to 70°. Mild pressure gradients (favourable as well as adverse) do not affect the shedding frequency; this is confirmed by smoke visualisation, which also shows that the pressure gradient changes the longitudinal vortex spacing downstream; the measured frequency is that determined by the local Reynolds number corresponding to the Berger relation.Sinusoidal streamwise pulsations of controlled frequencies, and of amplitudes up to 10 per cent of free-stream velocity, have no effect on the natural shedding frequency; this is confirmed by smoke visualisation of the cylinder wake. However, the wake signal is amplitude-modulated at a frequency equal to the difference between the pulsation frequency and the natural shedding frequency corresponding to the free-stream mean velocity. The vortices are diffused faster in the presence of pulsation. When the pulsation amplitude is increased beyond 20 per cent, the hot-wire signal frequency in the wake equals the driving frequency; the frequency in the wake centre is also that of the pulsation. The effect of free-stream pulsation on the periodic wake is different from that due to longitudinal or transverse cylinder vibration, when lock-in has been observed.It appears that free-stream disturbances – random or periodic – cannot account for the “Tritton jump”.