Unified unsteady supersonic/hypersonic theory of flow past double wedge airfoils (Q800154)

A unified theory for the unsteady supersonic flow past double wedge airfoils is developed. The method is applicable for any supersonic Mach number and arbitrary angle of attack and airfoil thickness but restricted to slow pitching oscillations with small amplitude. The nonstationarity is established as a perturbation of the well known stationary supersonic flow. Therefore the usual equations of stationary supersonic gas dynamics including those of an oblique shock wave are given for the three existing flow regimes, namely the flow at the front part of the body with an attached shock wave, the Prandtl-Meyer expansion flow at the upper edge and the flow at the rearward part of the body. The foundations of those terms of the equations describing the nonstationarity are given in a quoted previous paper of the author [Z. Angew. Math. Phys. 29, 414-427 (1978; Zbl 0393.76035)]. The resulting equations for the nonstationary flow in the present case are discussed in detail however distinguishing in-phase and out-of-phase flow quantities for instance. The equations are solved for the three flow regimes mentioned above using different coordinate systems. There exists some connection with the limit case of hypersonic flow because the so called shock-expansion method is used, i.e. pressure waves being reflected at the shock wave are neglected partially. Therefore the method gives exact results in the case of high Mach numbers, when the reflected waves do not reach the body and it is a good approximation for low supersonic Mach numbers. The results are confirmed by numerical examples and by comparisons with quoted experiments and other approximation theories in view of the stiffness and damping-in-pitch derivatives.