Global stability analysis of axisymmetric boundary layer over a circular cone

Abstract

Abstract This paper presents linear biglobal stability analysis of axisymmetric boundary layer over a circular cone. An incompressible flow over a sharp circular cone is considered with zero angle of attack. The base flow velocity profile is fully non-parallel and non-similar. Linearized Navier-Stokes (LNS) equations are derived for disturbance flow quantities using the standard procedure. The LNS equations are discretized using Chebyshev spectral collocation method. The governing equations along with boundary conditions form a general eigenvalues problem. The numerical solution of general eigenvalues problem is obtained using ARPACK subroutine, which uses Arnoldis iterative algorithm. The global temporal modes are computed for the range of Reynolds number and semi-cone angles(α)for the axisymmetric mode(N=0). The flow is found temporally and spatially stable for 1° semi-cone angle and the range of Reynolds numbers considered. However, flow becomes temporally unstable and spatially stable with the increase in semi-cone angle(α). The wave-like behaviour of the disturbances is found at small semi-cone angles (α).