The structure of shock waves propagating through heavy noble gases: temperature dependence
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ORIGINAL ARTICLE
The structure of shock waves propagating through heavy noble gases: temperature dependence F. C. Dias1
· F. Sharipov1
Received: 10 September 2019 / Revised: 28 July 2020 / Accepted: 8 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The structure of planar shock waves propagating through argon, xenon, and krypton is calculated using the direct simulation Monte Carlo method for Mach numbers 2, 5, and 10. The upstream temperature considered in the present paper varies from 30 to 8000 K, depending on the gas species and Mach number. Both quantum and classical approaches to the intermolecular collisions based on ab initio potential are used. The distributions of density and temperature inside the shock wave are reported. The density slope is calculated as a function of the upstream temperature and Mach number with the numerical error less than 0.5%. The dependence of the density slopes on the upstream temperature is studied. It is shown that the slope behaviors of the heavy gases are qualitatively similar to each other, but they are completely different from those for helium. Keywords Direct simulation Monte Carlo · Planar shock wave · Ab initio potential · Quantum scattering
1 Introduction Planar shock waves in a single gas are commonly used to evaluate numerical methods and approximate techniques in kinetic theory. The structure of shock waves propagating through monatomic single gases was analyzed by means of various theoretical methods [1–15] and also by experimental techniques [16–21]. As was shown previously [10,13], structures of shock waves calculated theoretically agree much better with experimental results when realistic intermolecular potentials are applied to describe the intermolecular collisions. Moreover, the structure of shock waves is sensitive to the gas species [13] and to chemical composition in the case of a mixture [14].
Communicated by S. O’Byrne. This paper is based on work that was presented at the 32nd International Shock Wave Symposium, Singapore, July 14–July 19, 2019. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00193-020-00965-w) contains supplementary material, which is available to authorized users.
B 1
F. Sharipov [email protected] Departamento de Física, Universidade Federal do Paraná, Curitiba 81531-980, Brazil
In our previous paper [15], we observed that the structure of shock waves propagating through helium and neon depends also on the upstream temperature. Such a dependence is determined by the quantum effect in the interatomic collisions. However, the influence of the upstream temperature on shock waves in heavy gases when the quantum effects are negligible has not been studied yet. In practice, the upstream temperature of shock wave propagating through a gas can vary in a wide range. For instance, radiative shock waves in xenon and krypton at high temperatures were investigated experimentally and theoretically due to their importance in astrophysical research [22–26
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