Mach Disk from Underexpanded Axisymmetric Nozzle Flow
The flowfield associated with the underexpanded ax {symmetric nozzle freejet flow including the appearance of a Mach disk has been studied. It is shown that the location and size of the Mach disk are governed by the appearance of a triple-point shock configuration and the condition that the central core flow will reach a state of "choking at a throat." It is recognized that coalescence of waves requires special attention and the reflected wave, as well as the vorticity generated from these wave interactions, have to be taken accurately into account. The theoretical results obtained agreed well with the experimental data. Nomenclature cv = specific heat at constant volume M = Mach number M* = Mach number based on speed of sound at critical condition N = number of divisions on the starting characteristic line p = pressure r = radial coordinate s = entropy x = horizontal coordinate a = Mach angle y = ratio of specific heats (= 1.4 here for air) 9 = flow angle Subscripts a = ambient condition c = centerline of symmetry e = nozzle exit i = incident wave / = lower side of slipline md = Mach disk o = stagnation state r = reflected shock wave sk = imbedded shock wave u = upper side of slipline I, II = characteristic of family I or family II