The Flow in an Axially-Symmetric Supersonic Jet from a Nearly-Sonic Orifice into a Vacuum

Abstract

The numerical method of characteristics is used to calculate the flow in a steady supersonic jet of air issuing from a slightly supersonic circular orifice into a vacuum. The calculations are entirely numerical, and no recourse is made to graphical methods. The characteristic equations for steady supersonic flow with rotational symmetry are first derived, and then special consideration is given to the flow near the axis of symmetry, where the normal step-by,step numerical process breaks down. In the calculation, the Mach angle in the plane of the orifice is taken as 85 deg to obviate the difficulties of a sonic orifice at which the initial characteristics would be perpendicular to the flow, and the potential equation parabolic. The results should be practically the same as for a sonic orifice. An alternative method of dealing with a sonic boundary-plane would have been the use of analytical solutions for the initial flow in this region (cf. Ref. 3). The results of the calculations are presented in diagrams. The solution is a universal solution in so far that it applies to any similar jet, flowing into any external pressure, in that region bounded by the orifice and the first wave front which registers the existence of an external pressure outside the jet. This fact allows the calculated pressure distribution along the axis of symmetry to be compared with experimental measurements in air jets with finite pressure ratios, and good agreement is obtained.