Interaction of Reflected Shock Waves with Solid or Liquid Particulates
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When performing shock-tube experiments with a gaseous mixture containing small particles, uncertainties can arise in the knowledge of the test conditions. Of particular importance is the accuracy of the test temperature when conducting chemistry and spectroscopic measurements behind the reflected shock wave. The primary uncertainty in an aerosol-laden flow field arises from the thermal and momentum (i.e., drag) relaxation of the particles, since a finite amount of time is required for the particles to achieve the temperature and speed of the shocked carrier gas. The net result is a transient relaxation zone leading to a final, equilibrium temperature and pressure of the gas/particle mixture that differ from the temperature and pressure if the particles were not present. The duration and magnitude of the effects depend on several factors, including the particle-to-gas mass loading ratio (), the average particle diameter, the material properties of the condensed phase, and the shock speed. A one-dimensional model of the gas dynamics was compiled from models in the literature and used to estimate how the presence of the particles ultimately affects the uncertainty in reflected-shock test temperature over a range of temperatures from 1500 to 4000 K, from 0 to 10, particle diameters from 0.1 to 100 m, and two characteristic powders: silica and titania. When compared to a pure-gas shock wave at the same velocity, the equilibrium temperature in a gas/particle mixture is lower, the static pressure is higher, and the mixture specific heat ratio is lower. For example, a shock speed providing 3000 K, 1.0 atm behind the reflected shock wave in pure argon results in a temperature and pressure of 2735 K and 1.33 atm in a mixture of SiO 2 and Ar at = 0.10. The duration of the particle relaxation time can be several hundred microseconds or longer, depending on the particle size and loading. Even for as low as 0.001, this relaxation time can be a significant fraction of the total test time since the test time is usually on the order of only a few milliseconds. In general, the relaxation zone introduces uncertainties in the equilibrium temperature as high as 10% for 0.10 and depends strongly on the material composition.
