Velocity field near a wing?Fuselage combination at an angle of attack in a supersonic stream

Abstract

To investigate interference between the wing and fuselage at supersonic flight velocities, one can, besides numerical methods based on the exact equations of motion, make effective use of the theory of small perturbations [1]. This is the direction adopted, in particular, in [2–4], in which the problem is solved in the framework of linear theory. In [5], the results obtained in the first approximations are corrected by taking into account the following term in the expansion of the potential function in a series in a small parameter. The present paper considers the velocity field near an arbitrarily profiled wing with supersonic edges and the features due to the presence of the fuselage. A general expression is found for the singular term of the asymptotic expansion of the solution of the linear equation in the neighborhood of the Mach cone with apex at the point of intersection of the leading edge of the wing with the surface of the fuselage. A uniformly exact solution for the linear differential equation for the additional velocity potential is constructed. The position and intensity of the shock wave on the upper surface of the wing are determined. Analytic dependences and quantitiative estimates are obtained for the local downwashes below the wing in the region of the flow where the linear theory leads to the largest errors. The obtained results are important for the correct determination of the aerodynamic characteristics of aircraft in the three-dimensional velocity field produced by the wing-fuselage combination.