Investigation of the effect of external periodic flow pulsation on a cylinder wake using linear stability analysis

Abstract

The aim of this paper is to investigate the receptivity of cylinder wake to external periodic flow pulsation at low Reynolds number using linear stability analysis. The inlet flow pulsation appears as a forcing term in the linearised equation set. The full non-linear N-S equations as well as the linearised set for small perturbations around the time-averaged flow are solved using an in-house finite volume solver. The results are first validated against reference data for growth rate and frequency of the most unstable eigenmode for flow past a fixed cylinder with steady base flow at various Reynolds numbers. A special numerical technique is developed to separate the components of the solution in the wake that vary with the natural shedding frequency and the external pulsating frequency. The developed approach requires temporal integration over one period of vortex shedding and solution of a 4×4 linear system at every cell of the domain. The results show that both cross-stream and streamwise velocity components in the near cylinder region are strongly affected by flow pulsation, and its effect is spatially localised in the near wake. Increasing the pulsation frequency reduces the spatial extent within which pulsation plays an important role. A symmetric shedding pattern is established and at every period of external pulsation, two pairs of symmetric vortices are shed from the top and bottom of the cylinder. The width of the wake periodically widens and narrows, which is similar to “wake breathing” observed in a streamwise oscillating cylinder.