Effect of frequency lock-in on the dynamic response and heat transfer from a circular cylinder at low Reynolds number

Abstract

Numerical analyses are carried out to investigate the flow physics and heat transfer from an undamped freely oscillating circular cylinder at low Reynolds numbers, for an incompressible, constant property, Newtonian fluid. Mass ratio is fixed at 10, while the Prandtl number is 7. Natural frequency of the system is set equal to the vortex shedding frequency of a stationary circular cylinder at Reynolds number of 100. New results pertaining to the oscillation trajectory shapes, vortex formation length, influenced wake width and average Nusselt number in view of the pre lock-in, lock-in and post lock-in flow regimes are presented and discussed in detail. Recirculation bubble behind the cylinder disappears for large oscillation amplitudes during lock-in; while a pair of counter-rotating vortices, having opposite rotational directions to what might be expected, is observed behind the cylinder in the mean vorticity field, which alters the shape of the cylinder trajectory. Average drag coefficient is shown to be directly proportional to the vortex formation length while it is inversely related to the influenced wake width. Streamwise oscillations are noted to be more sensitive to the increasing Reynolds number during lock-in, as compared to the transverse oscillations. Progressively increasing space and time-averaged Nusselt number values comparably higher than stationary cylinder are observed as Reynolds number increases. The behavior of time-averaged-local Nusselt number varies with position around the surface of the cylinder. The maximum local Nusselt number on the surface of the cylinder is also seen to vary both in magnitude as well as location on the surface of the cylinder in a direct correspondence with the oscillation amplitudes of the cylinder. Moreover, a regression correlation is proposed which relates Reynolds number, root-mean-squared streamwise and transverse oscillation amplitudes and Strouhal number with the space and time-averaged Nusselt number.