Global stability analysis of axisymmetric boundary layer on a rotating circular cylinder

Abstract

In this manuscript, we comprehensively investigated the global stability of the incompressible axisymmetric boundary layer (ABL) developed on a rotating circular cylinder. A finite length of a rotating cylinder was considered in an axial stream of incompressible fluid. The rotation of a cylinder produces centrifugal force in the radial direction, which produces a pressure gradient (PG) in the radial direction. The axial flow (U∞) develops shear in the BL which has a stabilization effect on the BL. Thus, the Reynolds number (Re) and rotation rate (S) are two important control parameters of the BL and they are calculated based on a cylinder radius. The spectral collocation method has been used to discretize the linearized Navier–Stokes equations (LNS) and Arnold’s iterative algorithm for the numerical solution of the 2D eigenvalues problem. The computations were performed for Reynolds numbers Re= 2600, 5200, and 20,800, rotation rates S=0.5, 1.0, and 2.0 for azimuthal wave-numbers N = 0, 1, 2, and 3. Thus, the effects of S, Re, and N were studied on the stability of the rotating ABL. The temporal and spatial properties of the small disturbances were studied to understand the effect of shear and centrifugal force by varying S and Re. The increased rotation of a cylinder makes the BL unstable while increased axial flow stabilizes the ABL. The small disturbances are found globally unstable for N = 1 at a small Re with an even small S.