Supersonic radial flow past sharp-nosed cones

Abstract

Axisymmetric and three-dimensional gas flows past sharp cones are studied both analytically and numerically for the case in which the supersonic oncoming stream is of source type . The effect of the governing parameters, such as the distance from the source to the cone, the specific heat ratio, the cone angle, and the angle of attack, on the flow is studied . Asymptotic laws governing the flow at large distances from the cone vertex are established .The conical flow theory is a well-studied part of supersonic gasdynamics which is described in a number of monographs (for example, [1,2]) . Many results concerning supersonic flows past conical bodies were obtained by numerical methods (for example, [3]) . If a conical body is immersed in a nonuniform gas flow, for instance in a radial flow, a scale length appears in the flow past the cone, so that it ceases to be self-similar . In that case conical flow exists only in a small vicinity of the sharp nose ; farther on the flow rearranges itself into a new limiting state which stabilizes at large distances from the body vertex .Supersonic source flows past sharp-nosed bodies were studied in [4][5][6][7] by means of approximate methods . These studies were restricted to the case of slender bodies in a hypersonic stream, so that the solutions obtained are valid only at small distances from the sharp nose . Some examples of the numerical solution of the problem can be found in [8,9] (the case of flow past two-dimensional sharp airfoils was considered in [8]) .The present work continues the study of nonuniform flow past bodies immersed in an underexpanded jet emerging from a sonic nozzle [10,11] . The flow in such a jet, as well as the flow in a supersonic underexpanded jet, can be satisfactorily approximated by source flow, at any rate, in a near-axis flow region . Source flow also simulates some other supersonic gas flows, for example, the flow in the divergent part of a Laval nozzle . Therefore, the main properties of radial source flow past a particular body having been established, it is to be expected that the same properties will be inherent in flows of a rather wide class past the same body .