On the Unsteady Supersonic Cascade With a Subsonic Leading Edge—An Exact First Order Theory—Part 1

This paper presents, in two parts, the theoretical predictions of the aerodynamic forces acting on slowly oscillating airfoils in a supersonic cascade with a subsonic leading edge. The analysis is based on the assumption of an inviscid, two-dimensional and linearized flow. In the first part of the paper, the flow field ahead of the cascade is considered. An initial value problem is posed and, from the periodicity requirement in the cascade, the problem is reformulated in terms of integral equations. Solution of the integral equations, accurate to the first order of a frequency parameter, are obtained in closed form. In the limit of the steady flow, the unsteady flow analysis yields a mathematical verification of the unique incidence effect. Based on this proof, a simple rule is presented for the airfoil suction surface contour satisfying steady flow requirement ahead of the cascade. The complete aeroelastic problem, including the solution for the flow field between the blades and the trailing interference zone, is treated in Part 2.