Multiscale instabilities of Magnus–Robins effect for compressible flow past rotating cylinder

Abstract

In the present research, the instability suffered by flow past a rotating cylinder with very high rotation rates is studied. Special emphasis is given on exploring the effects of compressibility by solving two-dimensional Navier–Stokes equations. The first account of this instability has been provided in “T. K. Sengupta, K. Gupta, and M. T. Nair, “Lift generation and limiting mechanism via unsteady flow development for Magnus-Robins effect,” Proceedings of the 8th Asian Congress of Fluid Mechanics, Shenzhen, China (1999).” Subsequently, there have been other efforts on the same with different numerical models based on incompressible and compressible flow formulation. Apart from the efforts reported by the present group, other reported results did not identify this as a phenomenon of flow instability. The perceived temporal variations of lift and drag by both the incompressible and compressible flow formulation have been correlated with each other, without highlighting the role of compressibility in triggering the flow instability. Here, we report the sensitive dependence of the temporal instability on the accuracy of the simulation for the growth of the disturbance field during the transient monotonic variations of lift and drag. Of specific interest is the role of compressibility in promoting the disturbance growth and limiting the maximum lift that is generated. The compressibility effects have been incorporated by considering lower Mach numbers for the oncoming uniform flow, so that nowhere in the flow field there is the formation of a supersonic pocket.