Effects of non-monotony of aerodynamic characteristics of a plate in hypersonic rarefied gas flow

DOI: 10.34759/trd-2020-110-9


Vuong V. T.1*, Gorelov S. L.2**, Rusakov S. V.2***

1. Moscow Institute of Physics and Technology, 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia
2. Central Aerohydrodynamic Institute named after N.E. Zhukovsky, TsAGI, 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia

*e-mail: tienbom@mail.ru
**e-mail: gorelovsl@yandex.ru
***e-mail: sv_vidukova@yandex.ru


The study of rarefied gas flows allows revealing a number of effects that are not observed in the continuous flows. Despite the fact that the studies in this field are being conducted for more than 50 years, some properties of such flows are far from being well studied. For example, effects of non-monotony of aerodynamic characteristics for a plate in the hypersonic rarefied gas flow by Reynolds numbers have been previously studied in the works [1, 2]. However, behavior of these characteristics depending on different angels of attack has not been studied up to now. Thorough studies of these effects by the direct simulation Monte Carlo (DSMС) technique depending on the key parameters such as Reynolds numbers, angle of attack, temperature factors and temperatures ratio of the plate surfaces were conducted in the presented work. It was revealed that with equal temperatures of the plate sides, the friction coefficients remained non-monotonous up to the angle of attack of 10 degrees, and up to 30 degrees by the pressure coefficient. Based on the obtained calculations, approximate analytical dependences of the coefficients of friction, pressure and lifting force on the angles of attack and temperature factors in a wide range of Reynolds numbers are proposed. These dependencies were applied for aerodynamic characteristics determining for arbitrary shape bodies in the framework of the local interaction hypothesis, and performed comparison demonstrated good conformance with the other authors’ data and experiment. At small angles of attack and different temperatures of the plate sides the lift coefficient changes its sign depending on the Reynolds numbers, and there are values of the angle of attack an temperatures ratio on the plates surfaces, at which the lift coefficient equals to zero.


plate flow-around in a rarefied gas flow, Reynolds number, direct simulation Monte Carlo (DSMС) technique, gas rarefaction effects


  1. Erofeev A.I., Perepukhov V.A. Uchenye zapiski TsAGI, 1976, vol. VII, no. 1, pp. 102 – 106.

  2. Gorelov S.L., Erofeev A.I. Uchenye zapiski TsAGI, 1979, vol. X, no. 2. pp. 59 – 64.

  3. Kogan M.N. Dinamika razrezhennogo gaza (Rarefied Gas Dynamics), Moscow, Nauka, 1967, 440 p.

  4. Yanitskii V.E. Stokhasticheskie modeli sovershennogo gaza iz konechnogo chisla chastits (Stochastic ideal gas models for finite number of particles), Moscow, VTs AN SSSR, 1988, 55 p.

  5. Gusev V.N., Erofeev A.I., Klimova T.V., Perepukhov V.A., Ryabov V.V., Tolstykh A.I. Trudy TsAGI, 1977, no. 1855, pp. 43, available at: https://cloud.mail.ru/public/5gEy/3XP57XuKZ

  6. Ivanov M.S., Rogazinskii S.V. Metod pryamogo statisticheskogo modelirovaniya v dinamike razrezhennogo gaza (Direct Simulation Monte Carlo Technique in Rarefied Gas Dynamics), Novosibirsk, VTs SO AN SSSR, 1988, 118 p.

  7. Egorov I.V., Erofeev A.I. Uchenye zapiski TsAGI, 1997, vol. XXVIII, no. 2, pp. 23 – 40.

  8. Nikolaev V.S. Uchenye zapiski TsAGI, 1981, vol. XII, no. 4, pp. 143 – 150.

  9. Vyong Van T’en, Gorelov S.L. Trudy MAI, 2018, no. 10, available at: http://trudymai.ru/eng/published.php?ID=93327

  10. Koshmarov Yu.A., Ryzhov Yu.A. Prikladnaya dinamika razrezhennogo gaza (Applied Rarefied Gas Dynamics), Moscow, Mashinostroenie, 1977, 184 p.

  11. Chernyi G.G. Techeniya gaza s bol’shoi sverkhzvukovoi skorost’yu (Gas flows at high supersonic speeds), Moscow, Fizmatgiz, 1959, 220 p.

  12. Bird G.A. Molecular gas dynamics and the direct simulation of gas flows, Clarendon press, Oxford, 1994, 458 p.

  13. Berd G. Molekulyarnaya gazovaya dinamika (Molecular Gas Dynamics), Moscow, Mir, 1981, 320 p.

  14. Bird G.A. Monte Carlo simulation of gas flows, Annual Review of Fluid Mechanics, 1978, vol. 10, pp. 11 – 31.

  15. Shidlovskii V.P. Vvedenie v dinamiku razrezhennogo gaza (Introduction to the Rarefied Gas Dynamics), Moscow, Nauka, 1965, 220 p.

  16. Egorov I.V., Erofeev A.I. Uchenye zapiski TsAGI, 1997, no. 2, pp. 23 – 39.

  17. Shen C. Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows, Springer, Berlin Heidelberg, New York, 2005, 406 p.

  18. Al’pert Ya.L., Gurevich A.V., Pitaevskii L.P. Iskusstvennye sputniki v razrezhennoi plazme (Artificial satellites in rarefied plasma), Moscow, Nauka, 1964, 384 p.

  19. Barantsev R.G. Vzaimodeistvie razrezhennykh gazov s obtekaemymi poverkhnostyami (Interaction between rarefied gases and flown-around surfaces), Moscow, Nauka, 1975, 344 p.

  20. Lunev V.V. Giperzvukovaya aerodinamika (Hypersonic aerodynamics), Moscow, Mashinostroenie, 1975, 328 p.

  21. William W. Liou, Yichuan Fang. Microfluid Mechanics: Principles and Modeling, The McGraw-Hill Companies, Inc, 2006, 353 p.

  22. Berezko M.E., Nikitchenko Yu.A., Tikhonovets A.V. Trudy MAI, 2017, no. 94, available at: http://trudymai.ru/eng/published.php?ID=80922

  23. Ryzhov Yu.A., Nikitchenko Yu.A., Paramonov I.V. Trudy MAI, 2012, no. 55, available at: http://trudymai.ru/eng/published.php?ID=30027&eng=N

  24. Bykov L.V., Nikitin P.V., Pashkov O.A. Trudy MAI, 2014, no. 78, available at: http://trudymai.ru/eng/published.php?ID=53445

  25. Khatuntseva O.N. Trudy MAI, 2019, no. 104, available at: http://trudymai.ru/eng/published.php?ID=102091

  26. Nikitchenko Yu.A. Trudy MAI, 2014, no. 77, available at: http://trudymai.ru/eng/published.php?ID=52938


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