Conditions of optimality of classical ejectors in the frame of different theories of critical mode


DOI: 10.34759/trd-2023-130-05

Аuthors

Eremin A. M.

Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), Zhukovsky, Moscow region, Russia

e-mail: chief.ere2011@yandex.ru

Abstract

In this article explores conditions for the optimality of a gas ejector in various theories of the critical mode. Explored three theories: Millionshikov—Ruabinkov theory, Vasiliev theory and Pearson, Holyday and Smith theory. System of equations of critical mode has been investigated on extremum by Lagrange method. New conditions of optimality have been obtained. For theories of Millionshikov—Ruabinkov and Pearson these condition for the optimality is blocking in pipe with flexible boundary and which corresponds to subsonic speed of gas in the place of blocking. New condition for the optimality for Vasiliev theory is equality of static pressures in mixed jets in the place of blocking. In the frame of each theory for a number of values of the reduced speed of active gas has been calculated values of compression ratio for k=0,1 and σ=10. Examination of these figures shows that in the case of classical condition of blocking λ2=1 point with equal static pressures at the entrance of ejector responds to the maximum of compression ratio. In the case of blocking in the pipe with flexible boundaries point with equal static pressures at the entrance of ejector responds to the inflection point of compression ratio curve, but maximum of compression ratio responds to the sonic speed of gas in the entrance of ejector. In the frame of Vasiliev theory has been obtained that the case of equal static pressure in the place of blocking responds to the maximum of compression ratio and this case is different from critical mode. Also has been obtained that in frame of Pearson theory exists the condition of optimality, which differ from the condition of optimality by Vasiliev theory by the presence of an additional term. Although obtained condition is mathematically correct, calculations show that it can’t be realized in real ejector.

Keywords:

gas ejector, compression ratio, ejection coefficient, conditions of optimality, Lagrange method, conditional extremum

References

  1. Vasil’ev Yu.N. Gazovye ezhektory so sverkhzvukovymi soplami. Sbornik rabot po issledovaniyu sverkhzvukovykh gazovykh ezhektorov (Gas ejectors with supersonic nozzles. Compilation of work about research of supersonic gas ejectors), Zhukovskii, TsAGI, 1961, pp. 134–212.
  2. Arkadov Yu.K. Novye gazovye ezhektory i ezhektsionnye protsessy (New gas ejectors and ejection processes), Moscow, Fizmatlit, 2001, 336 p.
  3. Arkadov Yu.K., Zernov V.I., Shmukler B.Yu. Uchenye zapiski TsAGI, 1992, vol. 23, no. 3, pp. 54-59.
  4. Samoilova N.V. Trudy TsAGI, 1982, no. 2150, pp. 3-18.
  5. Zhulev Yu.G., Potapov Yu.F. Trudy TsAGI, 1978, no. 1958, pp. 3-20.
  6. Ganich G.A., Neimark R.V. Trudy TsAGI, 1978, no. 1958, pp. 30–37.
  7. Pis’mennyi V.L. Trudy MAI, 2003, no. 11. URL: https://trudymai.ru/eng/published.php?ID=34476
  8. Pis’mennyi V.L. Trudy MAI, 2003, no. 12. URL: https://trudymai.ru/eng/published.php?ID=34456
  9. Khristianovich S.A. O raschete ezhektora. Promyshlennaya aerodinamika: sbornik statei (About calculation of ejector. Industrial aerodynamics: collection of articles.), Moscow, Izd-vo BNT NKAP, 1944, pp. 3–17.
  10. Millionshchikov M.D., Ryabinkov G.M. Gazovye ezhektory bol’shikh skorostei. Sb. rabot po issledovaniyu sverkhzvukovykh gazovykh ezhektorov (Gas ejectors of high velocities. Compilation of work about research of supersonic gas ejectors), Zhukovskii, BNI TsAGI, 1961, pp. 5–31.
  11. Taganov G.I., Mezhirov I.I. K teorii kriticheskogo rezhima gazovogo ezhektora: sbornik rabot po issledovaniyu sverkhzvukovykh gazovykh ezhektorov (On theory of critical mode of gas ejector. Compilation of work about research of supersonic gas ejectors), Zhukovskii, BNI TsAGI, 1961, pp. 33–40.
  12. Nikol’skii A.A., Shustov V.I. Kriticheskie rezhimy gazovykh ezhektorov bol’shikh perepadov davlenii: sbornik rabot po issledovaniyu sverkhzvukovykh gazovykh ezhektorov (Critical modes of gas ejectors with high differential pressure. Compilation of work about research of supersonic gas ejectors), Zhukovskii, BNI TsAGI, 1961, pp. 41–47.
  13. Keenan J.H., Neumann E.P. A Simple Air Ejector, Journal of Applied Mechanics, 1942, vol. 9(2), pp. 75–81.
  14. Fabri J., Siestrunck R. Supersonic Air Ejectors, Advances in Applied Mechanics, 1958, vol. 5, pp. 1-35.
  15. Chow W.L., Addy A.L. Interaction between Primary and Secondary Streams of Supersonic Ejector Systems and Their Performance Characteristics, AIAA Journal, 1964, vol. 2, no. 4, pp. 686–695. DOI:10.2514/3.2403
  16. Pearson H., Holliday J.B., Smith S.F. A theory of the cylindrical ejector propelling nozzle, Journal of the Royal Aeronautical Society, 1958, vol. 62, no. 574, pp. 746-751.
  17. Larina E.V., Tsipenko A.V. Trudy MAI, 2017, no. 97. URL: https://trudymai.ru/eng/published.php?ID=87135
  18. Eremin A.M. Uchenye zapiski TsAGI, 2020, vol. LI., no. 2, pp. 39–46.
  19. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov (Mathematical handbook), Moscow, Nauka, 1984, 831 p.
  20. Abramovich G.N. Prikladnaya gazovaya dinamika (Applied gas dynamic), Moscow, Nauka, 1976, 888 p.

Download

mai.ru — informational site MAI

Copyright © 2000-2024 by MAI

 Вход