Global stability analysis of axisymmetric boundary layer: Effect of axisymmetric forebody shapes

This paper presents the effect of axisymmetric forebody shapes on the global stability characteristics of axisymmetric boundary layer developed on a circular cylinder. Axisymmetric forebodies like sharp-cone, ellipsoid, and paraboloid with a fineness ratio (FR) of 2.5, 5.0 and 7.5 are considered. The boundary layer starts to develop at a stagnation point on the forebody geometry and grows in spatial directions. The inflow velocity component is parallel to the axis of the cylinder, and hence the angle of attack is zero. The base flow is axisymmetric, non-parallel and non-similar. The linearised Navier–Stokes equations are derived in the cylindrical polar coordinates for the disturbance flow components. The discretised linearised Navier–Stokes equations along with appropriate boundary conditions form a general eigenvalue problem and it has been solved using Arnoldi’s algorithm. The global temporal modes have been computed by solving the two-dimensional eigenvalue problem. The extent of a favourable pressure gradient developed in streamwise direction depends on the shape of axisymmetric forebody. The temporal and spatial growth of the disturbances has been computed for axisymmetric (N= 0) mode for different Reynolds numbers (Re). The forebody shapes have a significant effect on the base flow and stability characteristics at low Re.