Hysteresis Phenomena of Mach Disk in an Underexpanded Jet

When the high-pressure gas is exhausted to the vacuum chamber from the nozzle exit, the underexpanded supersonic jet with the Mach disk is generally formed. The jet structure has been studied as a fundamental phenomenon of the supersonic fluid mechanics, and numerous works have been done theoretically as well as experimentally. However, they are on the steady jet as the ratio of reservoir stagnation pressure to back pressure is fixed. Recently the existence of hysteresis for a dual solution domain is become known from regular to Mach reflection of a shock wave in two-dimensional super flow. The purpose of this study is to clear the hysteresis phenomenon of Mach disk formation for an underexpanded supersonic jet induced by the variation of pressure ratio. When the exit Mach number change from 1 to 2.5, the axisymmetric conservational equation is solved by a TVD scheme. A quasi-steady approach is employed to calculate the entire hysteresis loop for the diameter and position of the Mach disk.