The reduction of test time in low pressure shock tubes, due to a laminar wall boundary layer, has been analytically investigated.In previous studies by Roshko and Hooker the flow was considered in a contact surface fixed co-ordinate system. In the present study it was assumed that the shock moves with uniform velocity, and the flow was investigated in a shock fixed co-ordinate system. Unlike the previous studies, the variation of free stream conditions between the shock and contact surface was taken into account. It was found that P, a parameter defined by Roshko, is considerably larger than the estimates made byRoshko and Hooker except for very strong shocks. Since test time is proportional to V 2 , previous estimates of test time are too large, particularly for weak shocks. The present estimates for P appear to agree with existing experimental data to within about 10 percent for shock Mach numbers greater than 5. In other respects, the basic theory is in general agreement with the previous results of Roshko.

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Shock tube flow nonuniformity is investigated in the limit where the shock and contact surface have reached their maximum separation. Ideal gases are considered. It is found that all fluid properties increase in value between the shock and contact surface. The nonuniformity is greatest when γ (ratio of specific heats) is large and Ms (shock Mach number) is low. For γ = 53 and Ms ≥ 3, the static temperature, density, and pressure increase by about 8, 12, and 20%, respectively; the stagnation temperature increases by about 35%, and the stagnation pressure, dynamic pressure, and stagnation point heat transfer increase by about a factor of 2. These results apply to turbulent as well as laminar boundary layers. The variation of flow properties with distance behind the shock, as well as particle time of flight, is given for both wholly laminar and wholly turbulent wall boundary layers. These results are particularly important for chemical rate and heat transfer studies.

The laminar wall boundary layer behind a strong shock moving with nonuniform velocity into a stationary fluid has been investigated. In particular, two-dimensional and axisymmetric boundary layers behind plane, cylindrical, and spherical shocks which move according to the power law xs = Ctm have been considered. The wall boundary layers associated with blast waves are special cases of the class of problems treated herein. It was assumed that the fluid is a perfect gas, that viscosity is proportional to temperature, and that the wall surface temperature is small relative to the temperature in the free stream. The resulting boundary-layer equations were simplified by expanding the dependent variables in powers of a nondimensional distance measured from the shock. The zero-order flow corresponds, at each instant, to a two-dimensional boundary layer behind a shock wave moving with uniform velocity. Numerical solutions of the first-order equations have been found for several cases of interest, and the results for wall shear and heat transfer have been tabulated and discussed.