A-to-Z Guide to Thermodynamics,
Heat & Mass Transfer, and Fluids Engineering
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Shock tubes are devices for studying the flow of high-temperature and high-velocity compressible gas.

A high-temperature supersonic gas flow is initiated in a shock tube as a result of rupture of a diaphragm separating two gases in high-pressure and low-pressure chambers. An unsteady rarefaction wave passes into the "driver" gas in the high-pressure chamber with a velocity a few kilometers per second. This results in the drivers gas flowing into the low pressure gas, pushing the gas in the low pressure chamber ahead of it. The shock wave propagates in the low-pressure chamber ahead of this flow of the studied gas. The velocity of the driven gas flow is equal to that of the driver gas flow. The wave (x − t) pattern, the schematic of the shock tube, and distribution of pressures p and temperatures T along the tube axis are presented in Figure 1. The parameters are denoted by 0 in the low-pressure chamber of the shock tube, 1 behind the incident shock wave, 2 behind the contact surface, 3 in the rarefaction wave, 4 in the high-pressure chamber, and 5 behind the reflected wave. In order to generate a shock wave with the specified pressure ratio p1/p0 in a shock tube, it is necessary to provide the pressure ratio p4/p0 over the shock tube diaphragm, which satisfies the relation

where a is the velocity of sound, γ the adiabatic exponent, u1 the velocity of gas flow behind the shock wave producing the pressure ratio p1/p0. Varying the length of high- and low-pressure chambers, we can find a regime of shock tube operation under which the shock wave reflected from an end meets the tail of the rarefaction wave and the head of the reflected rarefaction wave at a fixed point. This regime known as the "joined" contact surface regime ensures the maximum time of undisturbed state behind the reflected wave. The maximum flow parameters achieved in shock tubes depend on the design of the high-pressure chamber. According to this, shock tubes can be devided into four groups.

(1) Shock tubes with an inert gas in the high-pressure chamber. In this case a driver gas is hydrogen or helium at a pressure ranging from several to a hundred atmospheres and of ambient initial temperature. For pressures in the low-pressure chamber from 1 to 100 mmHg, the shock wave velocities range from 0.5 to 6 km/s. The temperature behind the shock wave is from 1000 to 10,000 K. The length of the high pressure gas zone, depending on the tube length and the shock wave velocity, is from several centimeters in laboratory tubes, whose length does not exceed 10 meters, to a meter in test shock tubes 50 to 100 meters long.

(2) Shock tubes with an explosive in the high-pressure chamber. In this case, in the high-pressure chamber, a hydrogen-oxygen-helium mixture or a solid explosive charge are used to increase the initial temperature of a driver gas. The gas temperature behind the shock wave amounts to 20,000 K in an inert gas and 15,000 K in a dissociating gas.

(3) Electrically driven shock tubes. These are tubes in which a discharge chamber with discharge-heated gas is used instead of the high-pressure chamber. Electrically driven shock tubes are designed with and without diaphragms because the parameters of the driver gas increase sharply as a result of discharge. In these shock tubes the velocity of the shock waves varies from 10 km/sec at initial pressures of several millimeters Hg to 100 km/sec at initial pressures fractions of a millimeter Hg. Gas temperature reaches a few tens of thousands of degrees.

(4) Shock tubes with shock wave enhancement. Shock tubes in this category use for shock wave enhancement the interaction of waves arising in transition of a shock wave to sections with different pressure and cross section, the category also includes shock tubes with two diaphragms.

In steady propagation of a shock wave in a shock tube the flow parameters behind the shock wave such as temperature, pressure, density, and velocity are unambiguously determined by the conservation laws using the shock wave velocity and the gas state, if the degree of approach to equilibrium is unknown, then determination of flow parameters requires, in addition to determination of the shock wave velocity, the measurement of one or several more gas parameters behind the shock wave or the time distribution of these parameters. These parameters include:

1. density distribution behind the shock wave (interferometer method, photoelectric shadow method, absorption of an electron beam, absorption of x-rays),

2. distribution of flow velocity (by the velocity of displacement of a weak disturbance introduced by transient heating of a wire placed in the flow or by electrical discharge),

3. distribution of the gas temperature (by spectral methods) or the electron temperature (by optical methods or by radiation emission),

4. distribution of the flow Mach numbers (by measuring the direction of the Mach lines resulting from interaction of the supersonic flow behind the shock wave with an obstacle in the tube),

5. distribution of pressures (by the readings of piezoelectric transducers),

6. composition of the gas dissociating behind the shock wave (by absorption of ultraviolet or infrared radiation),

7. electrophysical properties of gas such as concentration of unbound electrons and collision frequency (by microwave, optical, electromagnetic, and probe methods),

8. the shock wave velocity measured by either visualization of its propagation in a transparent section of the tube or by the time-of-flight method, i.e., measuring the time interval between the readings of two transducers responding to the shock wave at two points of the tube (use is made of pressure transducers, photoelectric glow sensors, ionization sensors, and thin-film resistance thermometers),

9. heat fluxes to the shock tube wall determined by calorimetric transducers or by measuring the time dependence of the wall temperature using a thin-film resistance thermometer.

A fraction of the gas mass flowing in the shock tube passes from the center to the boundary layer. The thickness of the boundary layer near the shock wave front is zero, then it grows toward the contact surface, and the gas outflow to the boundary layer grows, respectively.

Growth of the boundary layer is interrupted as soon as the gas outflow across it becomes equal to the gas inflow across the shock wave front. Owing to this, the shock wave and the contact surface velocities become equal, the plug size reaches maximum and remains unchanged. The flow becomes steady as in the steady bow shock distance from the blunt body in a supersonic flow, when the gas inflow across the shock wave front becomes equal to the outflow across sonic lines and, to the flow along the side surfaces of the body. The gas flow between the shock wave front and the contact surface is isentropic. The gas velocity behind the shock is determined in accordance with the conservation laws depending on the velocity of the shock wave front.

The range of problems of heat and mass transfer to be solved on shock tubes covers an analysis of dynamic and thermal loads of intricately shaped bodies exposed to blast waves, heat transfer by radiation under joint action of radiation and convection, fluid dynamics of jet flows, interaction of jets, investigation of gas outflow (heated by the shock wave) from the jet at the tube end, and heat transfer during external flow around bodies.

REFERENCES

Gaydon, A. G. and Hurle, I. R. (1963) The Shock Tube in High Temperature Chemical Physics, Chapman and Hall.

Warren, W. R. and Harris, G. J. (1970) A Critique of High-Performance Shock Tube Driving Techniques, Shock Tubes, 143-176, Toronto Univ. Press.

Korobeinikov, V. P. (1989) Ed., Unsteady Interaction of Shock and Detonation Waves in Gases, Hemisphere Publ. Corp.

References

1. Gaydon, A. G. and Hurle, I. R. (1963) The Shock Tube in High Temperature Chemical Physics, Chapman and Hall.
2. Warren, W. R. and Harris, G. J. (1970) A Critique of High-Performance Shock Tube Driving Techniques, Shock Tubes, 143-176, Toronto Univ. Press.
3. Korobeinikov, V. P. (1989) Ed., Unsteady Interaction of Shock and Detonation Waves in Gases, Hemisphere Publ. Corp.