Exhaust of Underexpanded Jets from Finite Reservoirs

Abstract

The response of an underexpanded jet to a depleting finite reservoir is examined with experiments and simulations. An open-ended shock-tube facility with a variable reservoir length is used to obtain images of nitrogen- and helium-jet structures at successive instances during the blowdown from initial pressure ratios of up to 250. The reservoir and ambient pressures are simultaneously measured to obtain the instantaneous pressure ratio. We estimate the time scales for jet formation and reservoir depletion as a function of the specific heat ratio of the gas and the initial pressure ratio. The jet structure formation time scale is found to become approximately independent of the pressure ratio for ratios greater than 50. In the present work, no evidence of time dependence in the Mach disk shock location is observed for rates of pressure decrease associated with isentropic blowdown of a finite reservoir while the pressure ratio is greater than 15. The shock location in the finite-reservoir jet can be calculated from an existing empirical fit to infinite-reservoir jet data evaluated at the instantaneous reservoir pressure. For pressure ratios below 15, however, the present data deviate from a compilation of data for infinite-reservoir jets. A new fit is obtained to data in the lower-pressure regime. The self-similarity of the jet structure is quantified, and departure from similarity is noted to begin at pressure ratios lower than about 15, approximately the same ratio that limits existing empirical fits