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 heliumjet 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.

Inferring Compressible Fluid Dynamics From Vent Discharges During Volcanic Eruptions

“…Thus, whatever surface charges survive the transit across normal shock are likely to be too few in number to produce electric fields capable of contending with the increased dielectric strength in overlying repressurized subsonic flow. In Figure , note that the extent of electrical discharges agree best geometrically with the volume of rarefaction when the elevation of the Mach disk (equation ) is described by C = 0.41 and α = 0.66 (Orescanin et al, ; Orescanin & Austin, ). That these parameters provide the best fit for the experimental data is to be expected given that they characterize supersonic jets emanating from a finite reservoir.…”

“…Upon emerging from the conduit, the jet undergoes Prandtl‐Meyer expansion to form a barrel shock structure (Figure b). With increasing distance from the vent, the flow accelerates to elevated Mach numbers and decreases rapidly in both density and pressure (Kieffer, ; Ogden et al, ; Orescanin et al, ; Orescanin & Austin, ). This pressure drop with distance from an underexpanded nozzle has been described in detail by Owen and Thornhill () and Adamson and Nicholls () using the method of characteristics (The analysis of the pressure variation in volcanic jets explored here makes use of their numerical models [Figure a]).…”

“…This pressure drop with distance from an underexpanded nozzle has been described in detail by Owen and Thornhill () and Adamson and Nicholls () using the method of characteristics (The analysis of the pressure variation in volcanic jets explored here makes use of their numerical models [Figure a]). Indeed, the pressure in the expanding flow may drop below atmospheric by up to one or two orders of magnitude (Ogden et al, ; Orescanin et al, ; Orescanin & Austin, ). At some distance, however, this rarefaction terminates abruptly in a normal shock (Mach disk).…”

“…For jets sourced from large pressurized (infinite) reservoirs, C takes values ranging between 0.67 (Orescanin et al, ) and 0.85 (Ogden et al, ), and α = 0.5. For finite reservoirs with overpressure factors smaller than 15, experimental work suggests that C is closer to 0.41 and α = 0.66 (Orescanin & Austin, ). While details of this model may change as the pseudo‐gas assumption is relaxed, the general form of this relationship should remain valid.…”

Characterization of Supersonic Gas Jets for High-Resolution Laser Ionization Spectroscopy of Heavy Elements

“…where c is the speed of light and v is the velocity of the atoms seeded into the argon flow. ν 0 is the frequency of the electron transition for the atoms at rest or moving perpendicular to the observation axis for the transition from the hyperfine level F ¼ 1 of the 4s 2 S 1=2 ground state to the hyperfine level F ¼ 2 0 of the 4p 2 P 1=2 excited state in 63 Cu (see Fig. 5), which was measured in an atomic beam unit (ABU) prior to the PLIF experiments.…”