A hypersonic chemically nonequilibrium viscous shock layer oh wings with a catalytic surface

Abstract

Within the framework of the theory of a hypersonic viscous shock layer a study is made of flow round wings of infinite span with blunt leading edges at various angles of attack and slip.Account is taken of multicomponent diffusion, and homogeneous chemical reactions, including dissociation-recombination reactions and exchange reactions. On the shock wave the generalized Rankine--Hugoniot conditions are given, and on the surface of the body conditions which allow for heterogeneous catalytic reactions of the first order with reaction rate constants depending [i] or not depending [2] on the temperature.The cases of an ideally catalytic and a noncatalytic surface are also considered.The surface of the body is assumed to be heatinsulated.A numerical study was made of the problem in a broad range of variation in the angles of attack and slip for different cases of prescribed constants representing the rates of the heterogeneous reactions.The conditions of the flow corresponded to the motion of a body which possess a lifting force along the trajectory of entry into the Earth's atmosphere [3]. The dependences are given of the equilibrium temperature of the surface along the stagnation line of the wing on the height of the flight and the distribution of this temperature along the surface of wings with parabolic and hyperbolic contours. It is shown that for flow regimes with a relatively high degree of dissociation in cases when the proportion of atoms recombined on the surface of the body is small, the dependences of the heat flow and the temperature of the surface on the angle of slip are of a nonmonotonic nature.Studies have been made previously in [4,5] of a viscous shock layer on wings of infinite span and for homogeneous gas flow. The authors of [6,7] considered a viscous shock layer with nonequilibrium homogeneous and heterogeneous reactions in the neighborhood of the stagnation line of a circular cylinder with a flow round it in the transverse direction [6], and on the surface of a delta wing with blunt leading edges, with flmv around it at angles of attack [7]. Within the framework of boundary layer theory the flow around the wings, allowing for slip, was considered in [8,9].A considerable number of studies have been devoted to axisymmetric flows in a viscous shock layer in the presence of nonequilibrium chemical reactions (see, for example, [10,11]). I. Formulation of the ProblemWe shall consider flow at angles of attack and slip around wings of infinite span with a blunt leading edge and rectilinear generator.We decompose the velocity vector of the oncoming flow into two components, one of which, W~ = V~ sin ~, is directed along the generator, the other, U~ = V~ cos ~, lies in the plane of the orthogonal generator; ~ is the angle of slip, formed by the vectors V~ and U~, and the angle of attack a is the angle between some plane (for example, the plane of symmetry of the wing, if it is symmetrical) and the vector U~.Let the equation of the wing contour in the Cartesian system of coordinates {yi} have the form y3...