Investigation of pressure-discontinuity system with one and two triplets,taking into account equilibrium physicochemical transformations of air

It is known that the interaction of pressure discontinuities preceding the projecting elements of a supersonic object considerably increase the pressure in the interaction region [1–3]. Existing methods of estimating this excess pressure at the leading edge of the projecting element are based on the calculation of the configuration of pressure-discontinuity intersections with two or one triple points for a perfect gas with a constant adiabatic modulus . The calculation reduces to the successive solution of two transcendental equations for the determination of the angles of slope of the discontinuities at the node points [2, 4]. The present paper states the formulation of the problem and results of flow calculations in pressure-discontinuity configurations with triple points, taking into account the equilibrium dissociation of air. The Predvoditelev approximation is used to calculate the thermodynamic function of the pressure p, as proposed in [5]. The formulation of the problem is considered for the calculation of the flow taking into account the equilibrium dissociation of air in the interference region of pressure discontinuities with two and one triple points — interactions of types I and II, according to the classification of [4]. Some results of the computer solution of the resulting system of equations are given both for a flow of cold unperturbed air (the interaction region w of the leading shock wave of an object with its projecting elements) and for a flow of hot dissociating air (the interaction region O with the boundary-layer breakaway region at the surface of the supersonic object). It is shown that, both in region w and in region O, the relative pressure is considerably affected not only by the velocity and the angle of the incident pressure discontinuity but also by the density of the incoming flow (the flight altitude of the object). Depending on this parameter, the relative pressure in the interaction region may be less or more than the pressure calculation for a perfect gas with = 1.4 to analogous flow conditions. The results obtained indicate the need to take account of the real properties of air in determining the mechanical and thermal loads in the interaction region of the pressure discontinuities at the surface of projecting elements of a hypersonic object.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 111–116, September–October, 1978.