On the maximum attainable temperature in Hartmann-Sprenger tubes

The paper describes the Hartmann-Sprenger tube which constitutes a repetitive shock tube in which shock waves travel up and down the tube at nearly the acoustic frequency. During each cycle, shock wave irreversibilities and frictional heating increase the mean temperature of the gas; if the tube material is a perfect insulator, the heat cannot escape from the gas, and the maximum temperature of the gas becomes questionable. As the temperature gradient of the gas increases, a smaller fraction of the compression waves will steepen and the shock strength will decrease at each cycle. The theory which gives the steepening distance of a compression wave train in a gas with arbitrary temperature distribution ahead of the waves is applied to the case of the Hartmann-Sprenger tube, so that the maximum attainable gas temperature and the corresponding end wall temperature are derived.