Instability of Rotating-Cone Boundary Layer in Axial Inflow

Abstract

Boundary-layer instability on a rotating cone induces coherent spiral vortices that are linked to the onset of laminar–turbulent transition. This type of transition is relevant to several aerospace systems with rotating components, e.g., aeroengine nose cones. Because a variety of options exist for the nose-cone shapes, it is important to know how their shape affects the boundary-layer transition phenomena. This study investigates the effect of varying cone angle on the boundary-layer instability on rotating cones facing axial inflow. It is found that increasing cone angle has a stabilizing effect on the boundary layer over rotating cones in axial inflow. The parameter space of Reynolds number Re
_l and local rotational speed ratio S is experimentally explored to find the spiral vortex growth on rotating cones of half angle ψ 22.5°, 45°, and 50°. The previously addressed cases of ψ 15° and 30° are also revisited. Increasing half-cone angle is found to have a stabilizing effect on the boundary layer on the rotating cones with ψ ≲ 45°; i.e., the spiral vortex growth is delayed to higher Re
_l and S. This effect diminishes when the half-cone angle increases from ψ 45° to 50°. The spiral vortex angle ϵ decreases with increasing rotational speed ratio S for all the investigated cones, irrespective of the half-cone angle. However, the instability on the broader cones is found to induce shorter azimuthal wavelengths.