Linear Instability Analyses of Supersonic and Hypersonic Flows over Rotating Cones

Abstract

Rotating objects are present in numerous real-world applications. The state of the boundary layer significantly effects the skin friction drag and thermal load of aeronautical objects in highspeed flow. To understand and predict the laminar-to-turbulent boundary-layer transition on rotating configurations, the prevailing boundary-layer instabilities involved in the transition process need to be known depending on the rotation speed and inflow velocity. Basic research on the influence of rotation on boundary-layer instabilities has focused mainly on simple geometries such as rotating disks and cones. However, even for such simple geometries, the effect of rotation on boundary-layer instabilities is not yet fully understood, especially for compressible inflow. Recently, Song & Dong [1] numerically studied the impact of rotation on the instability characteristics of the 1st-Mode, the crossflow-, and centrifugal instability for the boundary layer on a 7° half-opening angle cone subjected to supersonic axial flow. This work extends the study to more half-opening angles, rotation speeds, and to hypersonic axial inflow velocity. The aim is to investigate whether rotation has a stabilizing or destabilizing effect on the primary instability mechanisms as a function of half-opening angle and inflow velocity using local linear stability theory. Furthermore, the influence of the Coriolis and centrifugal force terms (in combination: rotation terms) appearing in the linearized disturbance equations on the instability characteristics is of particular interest as well as the metric terms, which represent effects of surface curature and conical divergence.