End-Wall Heat-Transfer Effects on the Trajectory of a Reflected Shock Wave

Abstract

The trajectory of a reflected shock wave has been measured near the end wall where the motion is perturbed by the displacement effect of heat transfer to the wall. In this experiment an x, t diagram of the reflection of an Ms = 4.08 shock wave was constructed by measuring shock arrival times with small probes. The parameter that measures the (negative) displacement thickness of the end-wall thermal layer, a ``Reynolds number'' R based on the shock velocity, the time after reflection, and the thermal diffusivity was varied between 9 and 600. In this range the measured deviation of the shock trajectory from ideal varied from 1½ to 17 shock thicknesses. The shock velocity was determined by differentiating a least-squares fit of the data to a fourth-order polynomial in R−½. In the range of the experiments the shock accelerated from a velocity that was 20% below ideal to one that was within 4% of ideal. Experiment agrees with boundary-layer theory above R = 150 for the shock trajectory and above R = 25 for the shock velocity, and implies that the exponent of the power-law dependence of the thermal conductivity on temperature is 0.81 ± 0.02. The small deviation of the shock velocity from boundary-layer theory predicted for R < 100 by higher-order theory is not observed, though since this theory falls just within the estimated experimental error this result is somewhat qualified. In any case, the unexpected agreement with first-order theory at small R indicates that molecular effects, such as temperature jump, do not play a large role when the shock is more than ten shock thicknesses from the end wall.