To the problem of modeling gas flows behind the front of a strong shock wave using an effective adiabatic index
DOI:
https://doi.org/10.21638/11701/spbu01.2020.111Abstract
In problems with strong shock waves (the problem of a strong explosion, the motion of bodies with high supersonic speeds, the problem of supersonic piston expansion), a significant increase in temperature occurs in the perturbed region of the flow. Therefore, when determining the parameters of the gas flow behind the front of a strong shock wave, it is necessary to take into account the real properties of the gas. This greatly complicates the construction of approximate analytical solutions. However, studies show that the influence of the real properties of the gas on the gas-dynamic parameters of the flow can be taken into account by changing the adiabatic index, that is, by introducing an effective adiabatic
exponent. If the gas behind the shock wave is in a state of thermodynamic equilibrium, then the effective adiabatic index changes little in the entire flow zone. This makes it possible to simulate the flow behind the shock wave front by some perfect gas, the adiabatic index of which is determined depending on the Mach number and the thermodynamic state of the gas by the shock front. To obtain more accurate solutions to problems with strong shock waves, the model must allow a break in the adiabatic index at the shock wave. In the present work, an explicit expression is obtained for the gas parameters behind the front of an intense shock wave under the assumption that the adiabatic index undergoes discontinuity during the transition of gas particles through the surface of the shock wave. The plane and axisymmetric case are considered.
Keywords:
modeling, shock wave, hypersonic flows, adiabatic index discontinuity
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Литература
Лунев В. В. Гиперзвуковая аэродинамика. М.: Машиностроение, 1975.
Зельдович Я. Б., Райзер Ю. Н. Физика ударных волн и высокотемпературных гидродинамических явлений. М.: Наука, 1966.
Теленин Г. Ф., Липницкий Ю. М. Нестационарное сверхзвуковое обтекание затупленных тел с отошедшей ударной волной // Изв. АН СССР. Механика жидкости и газа. 1966. № 4. C. 19–29.
Запрянов З. Д. Численное исследование сверхзвукового обтекания плоских и осесимметричных затупленных тел при M → ∞ и γ → 1 // Изв. АН СССР. Механика жидкости и газа. 1967. № 4. C. 164–167.
Лебедев М. Г., Миносцев В. Б., Теленин Г. Ф., Тиняков Г. П. Приближенный метод учета влияния реальности газа при гиперзвуковом обтекании сегментальных тел // Изв. АН СССР. Механика жидкости и газа. 1969. № 2. C. 107–111.
Vallerani E. An “ideal equivalent gas method” for the study of shock waves in supersonic real gas flow // Meccanica. 1969. Vol. 4, no. 3. P. 234–249.
Гвоздева Л. Г., Предводителева О. А. Экспериментальное исследование маховского отражения ударных волн при скорости 1000–3000 м/сек в углекислом газе, аргоне и воздухе // Докл. АН СССР. 1965. Т. 163, № 5. C. 1088–1091.
Тарнавский Г. А., Шпак С. И. Способы расчета эффективного показателя адиабаты при компьютерном моделировании гиперзвуковых течений // Сибирский журнал индустриальной математики. 2001. Т. IV, № 1(7) C. 177–196.
Седов Л. И. Методы подобия и размерности в механике. 8-е изд. М.: Наука, 1977.
Taylor G. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I // Proc. Royal Society of London. Ser. A. 1950. Vol. 201. Issue 1065. P. 192–196. https://doi.org/10.1098/rspa.1950.0052
Гиро Ж. Основные вопросы теории гиперзвуковых течений. М.: Мир, 1965.
Богатко В. И., Потехина Е. А. Об учете конечности чисел Маха при обтекании плоских и осесимметричных тел, движущихся с большой переменной скоростью // Вестн. С.-Петерб. ун-та. Сер. 1. Математика. Механика. Астрономия. 1995. Вып. 2, № 8. C. 49–53.
Полянский О.Ю. О моделировании течений реального газа в ударных волнах с помощью совершенного газа // Труды ЦАГИ. 1983. Вып. 2177. С. 130–137.
Цибаров В. А. Кинетический метод в теории газовзвесей. СПб.: Изд-во С.-Петерб. ун-та, 1997.
Богатко В. И., Потехина Е. А. Некоторые замечания об учете реальных свойств газа за фронтом ударной волны // Ученые зап. ЛГУ. Газодинамика и теплообмен. 1977. № 393. С. 152–156.
Черный Г. Г. Течения газа с большой сверхзвуковой скоростью. М.: Физматгиз, 1959.
Su F. Y., Olfe D. B. Radiative transferee effects on reflected shock waves. I. Transparent gas // Phys. Fluids. 1971. Vol. 14, no. 12. P. 2636–2644.
References
Lunev V. V., Hypersonic aerodynamics (Mashinostroenie Publ., Moscow, 1975). (In Russian)
Zel’dovich Y. B., Raizer Y. P., Physics of Shock Waves and Hightemperature Hydrodynamic Phenomena (Academic Press, New York, 1967).
Telenin G. F., Lipnitsky Yu. M., “Unsteady supersonic flow around blunt bodies with a departing shock wave”, Izv. USSR Academy of Sciences. Fluid and gas mechanics (4), 19–29 (1966). (In Russian)
Zapryanov Z. D., “Numerical study of supersonic flow around flat and axisymmetric blunt bodies as M → ∞ and γ → 1”, Izv. USSR Academy of Sciences. Fluid and gas mechanics (4), 164–167 (1967). (In Russian)
Lebedev M. G., Minostsev V. B., Telenin G. F., Tinyakov G. P., “An approximate method for taking into account the influence of gas reality during hypersonic flow around segmental bodies”, Izv. USSR Academy of Sciences. Fluid and gas mechanics (2), 107–111 (1969). (In Russian)
Vallerani E., “An “ideal equivalent gas method” for the study of shock waves in supersonic real gas flow”, Meccanica 4(3), 234–249 (1969).
Gvozdeva L. G., Predvoditeleva O. A., “An experimental study of the Mach reflection of shock waves at a speed of 1000–3000 m/s in carbon dioxide, argon and air”, Dokl. USSR Academy of Sciences 163(5), 1088–1091 (1965). (In Russian)
Tarnavsky G. A., Shpak S. I., “Methods for calculating the effective adiabatic index in computer simulation of hypersonic flows”, Siberian Journal of Industrial Mathematics IV(1–7), 177–196 (2001). (In Russian)
Sedov L. I., Similarity and Dimensional Methods in Mechanics (Academic Press, New York, 1959).
Taylor G., “The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I”, Proc. Royal Society of London. Ser. A. 201, issue 1065, 192–196 (1950). https://doi.org/10.1098/rspa.1950.0052
Guiraud J.-P., Topics in hypersonic flow theory (Stanford University Press, Stanford, California, 1963).
Bogatko V. I., Potekhina E. A., “About registration of the Mach number finiteness in a near moving flow with a high variable velocity plane and axisymmetrical bodies”, St. Petersburg University. Mechanics Bulletin (2), 1–5 (1995).
Polyansky O. Yu., “On the simulation of real gas flows in shock waves using perfect gas”, Proceedings of TsAGI (2177), 130–137 (1983). (In Russian)
Tsibarov V. A., Kinetic method in the theory of gas suspensions (St. Petersburg University Press, St. Petersburg, 1997). (In Russian)
Bogatko V. I., Potekhina E. A., “Some comments on taking into account the real properties of the gas behind the shock front”, Scientists app. LSU. Gas dynamics and heat transfer (393), 152–156 (1977). (In Russian)
Chernyi G. G., Gas flows with a high supersonic velocity (Fizmatgiz Publ., Moscow, 1959). (In Russian)
Su F. Y., Olfe D. B., “Radiative transfere effects on reflected shock waves. I. Transparent gas”, Phys. Fluids 14(12), 2636–2644 (1971).
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