On the flow in a reflected-shock tunnel

Abstract

The performance of a shock tunnel operated by the reflected-shock technique is examined theoretically neglecting viscous effects and high-temperature real-gas effects. Particular attention is given to disturbances to the flow at the nozzle entry caused by waves reflected from the contact surface when the operating conditions depart from those for 'tailoring'. For unheated hydrogen driving air, the results suggest that the first disturbance reflected from the contact surface is weak enough to be tolerated only within a small range of primary-shock Mach number, Ms1 (e.g., 5.7 < Ms1 < 6.3 if the pressure at entry to the nozzle is to remain constant to ± 10 per cent). Within this range, running times much longer than those obtained in 'straight-through' shock tunnels are predicted, the limitation usually being imposed by the arrival of the expansion wave originating at the diaphragm. Outside this range of Mach number, the uniform-flow duration between the arrival at the nozzle entry of the primary shock and the first disturbance reflected from the contact surface is shown to be approximately equal to the time between the arrival of the primary shock and the contact surface in a 'straight-through' shock tunnel. At first sight it appears, therefore, that the advantages of reflected-shock operation are confined to a very narrow range of shock Mach number, unless a heated driver gas is used in order to vary the Mach number for 'tailoring'. Further analysis suggests, however, that subsequent disturbances in the multiple wave reflection process between the contact surface and the end of the tube are relatively weak over a useful range of shock Mach number. Thus, if the flow after the arrival of the early reflected disturbances is used for test purposes, long running times seem possible in theory without severe restrictions to the shock Mach number. Experiments have been made in a shock tube and a shock tunnel to provide data for comparisons with the results of the simple theory. If allowance is made for viscous effects on the motion of the contact surface, fair agreement is found for the disturbances reflected and transmitted by the contract surface, and for the arrival of the expansion wave. It is, however, observed that the pressure gradient in the multiple reflection process increases when the shock Mach number is raised substantially above the 'tailored' value, and a limit to the usable flow duration may result. A striking feature of the results is a fall of pressure at the end of the tube immediately after reflection of the primary shock. This is attributed to attenuation of the reflected shock resulting from its interaction with the boundary layer on the wall of the tube. Further research is required to check this explanation, and to investigate the effects of Reynolds number and of the cross-sectional shape and size of the tube. The effects of the tail and reflected head of the expansion wave originating at the main diaphragm are discussed. It is shown that the arrival of the reflected head at the nozzle entry may impose a severe limitation to the duration of uniform conditions at low'shock Mach number, and that the arrival of the tail may limit the flow duration at high shock Mach number. Unless means can be devised to suppress the expansion wave, it is demonstrated that it is desirable to have alternative diaphragm positions in a tube required to operate over a range of shock Mach number. It is concluded that running times of order 10 milliseconds at a shock Mach number of 4, falling to, perhaps, 1 millisecond at a shock Mach number of 8 seem possible in a shock tunnel of reasonable size by using reflected-shock operation with unheated hydrogen driving air. Because of the simplifying assumptions of the theoretical investigations, and the deficiencies of the apparatus used for the experiments, the present investigation must, however, be regarded as preliminary in character. Further research is required to check and extend the findings, and topics particularly requiring investigation are listed in the Paper.