Supersonic Starting Flow by Accelerated Sinking Movement to Large Angle of Attack

The classic linear Heaslet–Lomax problem, which is concerned with the indicial response of a supersonic airfoil experiencing a sudden small step motion, was recently extended to nonlinear cases where the sudden step motion is of high amplitude or equivalently a high angle of attack is suddenly achieved. Here in this paper, the more practical case of starting flow is considered where the high angle of attack is achieved through an accelerated sinking movement over a finite time interval. The problem is classified into fast sinking motion, middle-speed sinking motion, and slow sinking motion, for which the flow and force evolution exhibit different behaviors. The acceleration is shown to generate unsteady pressure waves that feed the major shock wave and expansions wave. A nonlinear indicial approach based on application of weighted Duhamel superposition principle to nonlinear starting flow model is built. This nonlinear model is shown to compare well with computational fluid dynamics simulation. The physics related to various stages of force evolution is discussed.