Stability of a nonorthogonal stagnation flow to three-dimensional disturbances

Abstract

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant-density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have applications to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, we examine the stability of this nonorthogonal flow to self-similar, three-dimensional disturbances. Stability characteristics of the flow are given as a function of the parameters of this study: ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wave number and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case. By use of this scaling, it can be shown that decreasing the angle of attack decreases the wave number and the magnitude of the temporal decay rate, thus making nonlinear effects important. For small wave numbers, it is shown that cooling the plate decreases the temporal decay of the least-stable mode, while heating the plate has the opposite effect. For moderate to large wave numbers, density variations have little effect except that there exists a range of cool plate temperatures for which these disturbances are extremely stable.