On the Structure of Jets from Highly Underexpanded Nozzles Into Still Air

A method for calculating the position of the first normal shock, or Mach disc, in the jet behind a highly underexpanded nozzle is presented. In the calculation for a sonic orifice, the axial pressure distribution on the centerline of the flow behind the orifice, calculated by the method of characteristics, is used to define a fictitious nozzle extension, and the shock is then assumed to exist at that point where atmospheric pressure would be attained behind the shock—i.e., the shock is assumed to exist at the end of the fictitious nozzle extension. Physical arguments are then employed to extend this calculation to nozzles with supersonic exit Mach Numbers. The results compare favorably with experimental data. An approximate method for computing the jet boundary up to the point of maximum jet area is given, and the results are compared both with photographs of actual jets and with jet boundaries calculated by the method of characteristics. Favorable agreement exists at relatively low nozzle pressure ratios.