Electron Beam Measurements of the Shock Wave Structure: Part I. The Inference of Intermolecular Potentials from Shock Wave Experiments. Part II. The Influence of Accommodation on Reflecting Shock Waves

Citation

Steinhilper, Eric Anthony (1972) Electron Beam Measurements of the Shock Wave Structure: Part I. The Inference of Intermolecular Potentials from Shock Wave Experiments. Part II. The Influence of Accommodation on Reflecting Shock Waves. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/AWTA-PA12. https://resolver.caltech.edu/CaltechETD:etd-09042007-094927

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A technique has been developed in which accurate measurements of shock wave structure and an exact molecular theory of shock waves are used to determine intermolecular potentials. Shock wave density profiles in neon, argon, krypton, and xenon are measured in the GALCIT 17-inch diameter shock tube. The theory is a numerical molecular simulation technique (developed by G. Bird of the University of Sidney) in which the only adjustable parameter is the intermolecular potential. Parameters for the exp-6 and Lennard-Jones potentials are determined by matching the experimental shock wave density profiles with those predicted by the Monte Carlo simulation technique. The experimental data are taken at shock Mach number of about 8; consequently, these results fall in an energy range midway between the molecular beam measurements and low temperature transport property results. After the potentials for neon, argon, krypton, and xenon have been determined, they are tested for conformity to the Law of Corresponding States. Plots of the potentials in corresponding states coordinates, [...] vs.[...], show that the exp-6 potential model issuperior to the Lennard-Jones. This is an important result, because for the first time this statement can be made on the basis of one set of measurements. Previously it had been necessary to adduce molecular beam results in order toprove that the inverse twelfth-power repulsive part of the Lennard-Jones potential is too strong. Comparisons show that the exp-6, Lennard-Jones, simple repulsive, and hard sphere molecular potentials predict the experimental shock structure with successively decreasing accuracy. However, their accuracy is sufficient that any one of the potentials would predict any flow accurately enough to give an indication of the relative importance of the parameters governing the flow. This point is emphasized by the need for both the most precise experimental measurements and the use of the Law of Corresponding States in order to provide the basis for ranking the potentials. Moreover, changing the potentials has given a better understanding of the mechanisms by which intermolecular forces influence shock structure. Measurements of density profiles during the reflection of thick shock waves in argon from the end wall of the GALCIT 17-inch diameter shock tube were reported previously. A mass balance using these profiles had revealed that as much as 20% of the gas which should have been between the end wall and the reflected shock was simply not present. Comparison with theory was not possible because no theory incorporated a loss of mass. Currently available theories for the reflection process include a Monte Carlo flow simulation technique for a thermally accommodating wall. It is found that this technique can correctly predict either the reflected shock trajectory or the thermal layer near the wall, but the inability to duplicate both implies that there is a second important effect which we assume to be adsorption. Additional experiments are conducted in neon which has a lower thermal accommodation coefficient than argon. If thermal accommodation is the only wall boundary condition, then according to the Monte Carlo calculations the shock should reflect faster in neon, and the thermal layer should be thinner. However, the measured density profiles show that the reflected shock trajectory is nearly the same as in argon but that there is only half as much "missing" mass. Thus, the neon results provide the most significant confirmation of adsorption. Because this unexpected violation of the continuity equation was observed, a comprehensive review of instrumental effects and the data reduction technique is made. Several hypothetical effects are shown to have no influence on the loss of mass. However, improving the mass balance calculations accounts for approximately 25% of the missing mass. Correcting for multiple scattering of the electron beam accounts for another 10%, but this correction applies only at the highest densities. Therefore, the "missing" mass of the previous experiment is verified but is reduced somewhat in magnitude.

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