Impulse Generated by a Shock Tube in a Vacuum

Detonation tube specific impulse increases with decreasing ambient pressure for fully-filled conditions in a sub-atmospheric environment. In the present study, we use an open-end shock tube to simulate a detonation tube and investigate the dependence of the specific impulse on the propellant fraction, i.e., partial filing, in vacuum operation. The impulse is experimentally determined by hanging the shock tube in a ballistic pendulum arrangement inside a vacuum chamber. The shock tube driver section has a fixed length of 0.1 m and is filled to 1 MPa with various gases including helium, hydrogen, nitrogen, argon, and sulfur hexafluoride. The pressure inside the vacuum chamber is 5 Pa. The shock tube had constant area and different lengths (0-1.2 m) of the open-end driven sections (extension tubes) are used to vary the fraction or gas filling the shock tube (fill fraction) between 7.8% and 100%. The specific impulse is a weak function of extension tube length but varies strongly with the gas type. Dimensional analysis is used to correlate the data and we show that similar to data from detonation tubes, it is possible to correlate specific impulse with a single parameter that takes into account the lime scale for depressurization. The specific impulse is predicted using the method or characteristics ignoring two-dimensional and rarified gas effects at the tube exit. In agreement with the experiments, the specific impulse is predicted to increase slightly with extension tube length and vary inversely with the square root of the molecular weight of the gas. The specific impulse observed for SF₆ is about 25% higher that observed for the other gases with the same extension tube lengths, indicating an effect or vibration-translational energy exchange on the exhaust velocity.