Hypersonic starting flow at high angle of attack

Abstract

Compressible starting flow at small angle of attack (AoA) involves small amplitude waves and time-dependent lift coefficient and has been extensively studied before. In this paper we consider hypersonic starting flow of a two-dimensional flat wing or airfoil at large angle of attack involving strong shock waves. The flow field in some typical regions near the wing is solved analytically. Simple expressions of time-dependent lift evolutions at the initial and final stages are given. Numerical simulations by compuational fluid dynamics are used to verify and complement the theoretical results. It is shown that below the wing there is a straight oblique shock (OSW) wave, a curved shock wave (CSW) and an unsteady horizontal shock wave (USW), and the latter moves perpendicularlly to the wing. The length of these three parts of waves changes with time. The pressure above OSW is larger than that above USW, while across CSW there is a significant drop of the pressure, making the force nearly constant during the initial period of time. When, however, the Mach number is very large, the force coefficient tends to a time-independent constant, proportional to the square of the sine of the angle of attack.