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Mathematical Modeling of Gas Effusion into a Vacuum

  • MECHANICS OF MACHINES
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Abstract

The effusion of gas through a small rectangular opening into a vacuum is studied using methods of mathematical modeling. The distribution functions of gas particles flowing out of an opening and the moments of these functions, i.e., fields of gas particle concentrations and velocities, are obtained. The dependence of effusion on the volume from which the gas escapes is investigated.

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REFERENCES

  1. Ponomareva, V.L., Kosmonavtika v lichnom izmerenii (Cosmonautics in the Personal Dimension), Moscow: Kosmoskop, 2016.

  2. Kubarev, Yu.V., Flights to Mars, electric propulsion engines of the present and future, Nauka Tekhnol. Prom-sti, 2006, no. 2, p. 19.

  3. Dushman, S. and Lafferty, J.M.,Scientific Foundations of Vacuum Technique, New York: Wiley, 1962.

    Google Scholar 

  4. Saksaganskii, G.L., Molekulyarnye potoki v slozhnykh vakuumnykh strukturakh (Molecular Flows in Complex Vacuum Structures), Moscow: Atomizdat, 1980.

  5. Anan’in, A.A., Zanin, A.N., and Semkin, N.D., Modeling of gas leakage from a spacecraft module, Izmerit. Tekh., 2001, no. 4, p. 29.

  6. Zanin, A.N., Device for recording the place of air leakage from the module of the space station, Cand. Sci. (Tech. Sci.) Dissertation, Samara: Samara State Aerospace Univ., 2009.

  7. Nesterov, S.B., Vasil’ev, Yu.I., and Androsov, A.V., Raschet slozhnykh vakuumnykh sistem (Calculation of Complex Vacuum Systems), Moscow: MEI, 2001.

  8. Nesterov, S.B., Astashina, M.A., Neznamova, L.O., and Vasil’ev, Yu.K., Tasks and methods for studying a rarefied gas medium near a spacecraft, Vakuum. Tekh. Tekhnol., 2007, vol. 18, no. 3, p. 183.

    Google Scholar 

  9. Astashina, M.A., Molecular flows in complex objects taking into account gas evolution of surfaces, Cand. Sci. (Tech. Sci.) Dissertation, Moscow: Mosc. Power Eng. Inst., 2009.

  10. Rozanov, L.N. and Skryabnev, A.Yu., Gas flow through a round pipe at large pressure drops, Vakuum. Tekh. Tekhnol., 2010, vol. 20, no. 1, p. 3.

    Google Scholar 

  11. Skryabnev, A.Yu., Vacuum measuring method for monitoring the tightness of large technical objects, Cand. Sci. (Tech. Sci.) Dissertation, St. Petersburg: SPb. State Polytech. Univ., 2012.

  12. Tang, M.J., Cox, R.A., Kalberer, M., Compilation and evaluation of gas phase diffusion coefficients ofreactive trace gases in the atmosphere: Vol. 1. Inorganic compounds, Atmos. Chem. Phys., 2014, no. 14, p. 9233.

  13. Krewinkel, R., A review of gas turbine effusion cooling studies, Int. J. Heat Mass Transfer, 2013, vol. 66, p. 706.

    Article  Google Scholar 

  14. Schumacher, J.C., Zupanc, F.J., and Dudebout, R., Segmented effusion cooled gas turbine engine combustor, US Patent no. 7546737B2, 2006.

  15. Wahlbeck, P.G., Effusion. VII. The failure of isotropy of a gas in an effusion cell and the transition region, J. Chem. Phys., 2003, vol. 55, no. 1709 (1971).

  16. Malhotra, M. and Kumar, S., Thermal gas effusion from diamond-like carbon films, Diamond Relat. Mater., 1997, vol. 6, no. 12, p. 1830.

    Article  Google Scholar 

  17. Bronson, T.J., Zupanc, F.J., Yankowich, P., Rudrapatna, N., Effusion cooled dual wall gas turbine combustors, US Patent US9897320B2, 2010.

  18. Iczkowski, R.P., Margrave, J.L., and Robinson, S.M., Effusion of gases through conical orifices, J. Phys. Chem., 1963, no. 67, no. 2, p. 229.

  19. Kotel’nikov, V.A., Ul’danov, S.V., and Kotel’nikov, M.V., Protsessy perenosa v pristenochnykh sloyakh plazmy (Transfer Processes in the Parietal Layers of Plasma), Moscow: Nauka, 2004.

  20. Kotel’nikov, V.A., Kotel’nikov, M.V., and Gidaspov, V.Yu., Matematicheskoe modelirovanie obtekaniya tel potokami stolknovitel’noi i besstolknovitel’noi plazmy (Mathematical Modeling of Bodies Flowing in Collisional and Collisionless Plasma Flows), Moscow: Fizmatlit, 2010.

  21. Kotel’nikov, M.V., Kotel’nikov, V.A., and Morozov, A.V., Matematicheskoe modelirovanie vzaimodeistviya potoka razrezhennoi plazmy s poperechnym magnitnym polem (Mathematical Modeling of the Interaction of a Rarefied Plasma Flow with a Transverse Magnetic Field), Moscow: MAI, 2015.

  22. Kotel’nikov, V.A., Gurina, T.A., Demkov, V.P., and Popov, G.A., Matematicheskoe modelirovanie elektrodinamiki letatel’nogo apparata v razrezhennoi plazme (Mathematical Modeling of the Electrodynamics of an Aircraft in a Rarefied Plasma), Moscow: Nats. Akad. Prikl. Nauk RF, 1999.

  23. Kotel’nikov, M.V. and Kotel’nikov, V.A., An advanced method of characteristics, Mat. Model., 2017, vol. 29, no. 5, p. 85.

    MathSciNet  MATH  Google Scholar 

  24. Kotel’nikov, M.V. and Nguen, S.Tk., The technique of using computer graphics in computational experiments, Tr. MAI, 2011, no. 53.

  25. Savel’ev, I.V., Kurs fiziki (Course of Physics), Moscow: Nauka, 1989, Vol. 1.

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Authors and Affiliations

  1. Blagonravov Mechanical Engineering Research Institute, Russian Academy of Sciences, 101990, Moscow, Russia

    V. A. Kotelnikov, M. V. Kotelnikov & G. S. Filippov

  2. Moscow Aviation Institute, 125993, Moscow, Russia

    V. A. Kotelnikov, M. V. Kotelnikov, G. S. Filippov & M. A. Platonov

Authors
  1. V. A. Kotelnikov
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  2. M. V. Kotelnikov
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  3. G. S. Filippov
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  4. M. A. Platonov
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Correspondence to M. V. Kotelnikov, G. S. Filippov or M. A. Platonov.

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Translated by L. Trubitsyna

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Kotelnikov, V.A., Kotelnikov, M.V., Filippov, G.S. et al. Mathematical Modeling of Gas Effusion into a Vacuum. J. Mach. Manuf. Reliab. 49, 197–205 (2020). https://doi.org/10.3103/S1052618820030061

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  • DOI: https://doi.org/10.3103/S1052618820030061

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