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Limit Energy Theorem for Gas Flow Systems


The paper presents a review of research dealing with the limit energy theorem for fast gas flow systems (FGFS’s) [19, 21, 23, 24, 38] where no mechanical work is performed. FGFS’s include gas-discharge lasers and plasmatrons, chemical gas reactors, vortex tubes, acoustic systems, various gas mixing devices, astrophysical objects, etc. The analysis shows that these flow systems do not belong to the Carnot class. In contrast to the Carnot cycle efficiency, the efficiency of energy conversion in FGFS’s depends on the properties of the working medium, and the conventional FGFS cycle is essentially irreversible. For the chosen class of FGFS’s, the theorem yields a more strictly formulated second law of thermodynamics. Implications of the theorem for various fields of physics and engineering are discussed.

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  1. 1.

    Sedov, L.I., Mekhanika sploshnykh sred (Mechanics of Continuous Media) Moscow: Nauka, 1970, vol.1.

  2. 2.

    Kirillin, V.A., Sychev, V.V., and Sheindlin, A.E., Tekhnicheskaya termodinamika (Engineering Thermodynamics) Moscow: Energoatomizdat, 1983.

    Google Scholar 

  3. 3.

    Carnot, S., Reflections on the Motive Power of Heat, New York: Wiley, 1890.

    MATH  Google Scholar 

  4. 4.

    Kvasnikov, I.A., Termodinamika i statisticheskaya fizika, Tom 1, Teoriya ravnovesnykh sistem: Termodinamika (Thermodynamics and Static Physics, vol. 1, Theory of Equilibrium Systems: Thermodynamics), 2nd ed., Moscow: URSS, 2002.

    Google Scholar 

  5. 5.

    Spasskii, B.I. and Sarangov, Ts.S., On the History of the Discovery of the Carnot Theorem, Sov. Phys. Usp., 1979, vol. 12, pp. 684–687.

    ADS  Article  Google Scholar 

  6. 6.

    Brodyanskii, V.M., Sadi Karno 1796–1832 (Sadi Carnot 1796–1832), Moscow: Nauka, 1993.

    MATH  Google Scholar 

  7. 7.

    Hawking, S.W., Black Hole Explosions?, Nature, 1974, vol. 248, no. 5443, pp. 30/31.

    ADS  Article  MATH  Google Scholar 

  8. 8.

    Hawking, S.W., Particle Creation by Black Holes, Comm. Math. Phys., 1975, vol. 43, no. 3, pp. 199–220.

    ADS  MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Bekenstein, J.D., Black Holes and Entropy, Phys. Rev. D, 1973, vol. 7, no. 8, pp. 2333–2346.

    ADS  MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Bekenstein, J.D., UniversalUpper Bound on the Entropy-to-Energy Ratio for Bounded Systems, Phys. Rev. D, 1981, vol. 23, no. 2, pp. 287–298.

    ADS  MathSciNet  Article  Google Scholar 

  11. 11.

    Hawking, S.W., Black Holes and Thermodynamics, Phys. Rev. D, 1976, vol. 13, no. 2, pp. 191–197.

    ADS  Article  Google Scholar 

  12. 12.

    Martin, N., Mathematical Theory of Entropy, Eddison-Wesley, 1981.

    Google Scholar 

  13. 13.

    Zel’dovich, Ya.B. and Novikov, I.D., Relyativistskaya astrofizika (Relativistic Astrophysics), Moscow, 1967.

    Google Scholar 

  14. 14.

    Taganov, I.N. and Shkaratan, O.I., Investigation of Social Structures by the Entropy AnalysisMethod, Vopr. Filos., 1969, vol. 5, pp. 74–82.

    Google Scholar 

  15. 15.

    Stakhov, A., The Generalized Principle of the Golden Section and Its Applications in Mathematics, Science, and Engineering, Chaos, Solit. Fractals, 2005, vol. 26, no. 2, pp. 263–289.

    MathSciNet  Article  MATH  Google Scholar 

  16. 16.

    Stakhov, A., Fundamentals of a New Kind of Mathematics Based on the Golden Section, Chaos, Solit. Fractals, 2005, vol. 27, no. 5, pp. 1124–1146.

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Volov, V.T., On One Class of Conditional Entropy, Obozr. Prikl. Promyshl. Mat., 2001, vol. 12, no. 4, pp. 929–930.

    Google Scholar 

  18. 18.

    Bridyanskii, V.M. and Semenov, A.M., Termodinamicheskie osnovy kriogennoi tekhniki (Thermodynamic Basis of Cryogenic Engineering), Moscow: Energiya 1980.

    Google Scholar 

  19. 19.

    Volov, V.T., Limit Energy Theorem for a Flow Rate Thermal Machine, Dokl. Akad. Nauk, 2001, vol. 381, no. 4, pp. 387–389.

    Google Scholar 

  20. 20.

    Merkulov, A.P., Vikhrevoi effekt i ego primenenie v tekhnike (Vortex Effect and Its Application in Engineering), Moscow: Mashinostroenie, 1969.

    Google Scholar 

  21. 21.

    Volov, V.T., Proc. Conf. Heat and Mass Reansfer and Hydrodynamics in Swirled Flows, Moscow: MEI, 2011.

    Google Scholar 

  22. 22.

    Volov, V.T., Modeli szhimaemykh zakruchennykh potokov gaza i plazmy (Models of Compressible Swirled Gas and Plasma Flows), Samara: Samara Scientific Center, 2011.

    Google Scholar 

  23. 23.

    Shmelev, V.M., Margolin, A.D., Vasilik, N.Ya., Krupkin, V.G., Volov, V.T., and Volov, D.B., Ballistic Plasma Generator with a Vortex Chamber for Pumping Solid-State Lasers, Teplofiz. Vys. Temp., 1998, vol. 36, pp. 548–551.

    Google Scholar 

  24. 24.

    Volov, V.T., A Thermodynamic Analysis of the Efficiency of Transformation of Flow Processes inHeat Engines with a Flow-ThroughWorking Medium, Therm. Engin., 2003, vol. 50, no. 12, pp. 1026–1030.

    Google Scholar 

  25. 25.

    Landau, L.D. and Lifshits, E.M., Gidrodinamika (Hydrodynamics), Moscow: Nauka, 1986.

    Google Scholar 

  26. 26.

    Zel’dovich, Ya.B. and Raizer, Yu.B., Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavlenii (Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena), Moscow: Nauka, 1966.

    Google Scholar 

  27. 27.

    Vulis, L.A., Termodinamika gazovykh potokov (Thermodynamics of Gas Flows), Moscow: Gosenergoizdat, 1950.

    Google Scholar 

  28. 28.

    Behera, U., Paul, P.J., Kasthurirengan, S., Karunanithi, R., Ram, S.N., Dinesh, K., and Jacob, B., CFD Analysis and Experimental Investigations towards Optimizing the Parameters of Ranque–Hilsch Vortex Tube, Int. J. Heat Mass Transfer, 2005, vol. 48, pp. 1961–1973.

    Article  Google Scholar 

  29. 29.

    Burtsev, S.A., ExploringWays to Improve Efficiency of Gasdynamic Energy Separation, High Temp., 2014, vol. 52, no. 1, pp. 12–18.

    Article  Google Scholar 

  30. 30.

    Burtsev, S.A. and Leontiev, A.I., Study of the Influence of Dissipative Effects on the Temperature Stratification in Gas Flows (Review), High Temp., 2014, vol. 52, no. 2, pp. 297–307.

    Article  Google Scholar 

  31. 31.

    Leontiev, A.I. and Burtsev, S.A., Device for Separation of Vortex Gas-Dynamic Energy, Dokl. Phys., 2015, vol. 60, no. 10, pp. 476–478.

    ADS  Article  Google Scholar 

  32. 32.

    Burtsev, S.A., Karpenko, A.P., and Leontiev, A.I., A Method for Distributed Production of Liquefied Natural Gas at Gas-Distribution Stations, High Temp., 2015, vol. 54, no. 4, pp. 573–576.

    Article  Google Scholar 

  33. 33.

    Leontiev, A.I. and Burtsev, S.A., Intensification of Heat Exchange in a Device for Gas-Dynamic Energy Separation, Dokl. Phys., 2016, vol. 61, no. 11, pp. 543–545.

    ADS  Article  Google Scholar 

  34. 34.

    Leontiev, A.I. and Burtsev, S.A., Cycle of a Closed Gas-Turbine Plant with a Gas-Dynamic Energy-Separation Device, Dokl. Phys., 2017, vol. 62, no. 9, pp. 443–445.

    ADS  Article  Google Scholar 

  35. 35.

    Kapitz, M. et al., Experimental Study of the Influence of the Prandtl Number on the ConvectiveHeat Transfer from a Square Cylinder, Int. J. Heat Mass Transfer, 2018, vol. 120, pp. 471–480.

    Article  Google Scholar 

  36. 36.

    Qian, Z., Wang, Q., and Cheng, J., Analysis of Heat and Resistance Performance of Plate Fin-and-Tube Heat Exchanger with Rectangle-Winglet Vortex Generator, Int. J. Heat Mass Transfer, 2018, vol. 124, pp. 1198–1211.

    Article  Google Scholar 

  37. 37.

    Chimres, N., Wang, C.C., andWongwises, S., Optimal Design of the Semi-Dimple Vortex Generator in the Fin and Tube Heat Exchanger, Int. J. HeatMass Transfer, 2018, vol. 120, pp. 1173–1186.

    Article  Google Scholar 

  38. 38.

    Isaev, S.A. et al., Intensification of a Laminar Flow in a Narrow Microchannel with Single-Row Inclined Oval-Trench Dimples, Techn. Phys. Lett., 2018, vol. 44, no. 5, pp. 398–400.

    ADS  Article  Google Scholar 

  39. 39.

    Volov, V.T., Estimation of Energy Release in System of Close Double Stars on the Basis of the Limit Energy Theorem for Gas Flow Systems, in Nelineinye polya i relyativistskaya statistika v teorii gravitatsii i kosmologii (Nonlinear Fields and Relativistic Statistics in the Theory of Gravitation and Cosmology), Ignat’ev, Yu.G., Ed., Kazan: Kazan Federal University, 2013, pp. 39–42.

    Google Scholar 

  40. 40.

    Unruh, W.G., Notes on Black-Hole Evaporation, Phys. Rev. D., vol. 14, no. 4, pp. 870–892.

  41. 41.

    Burdakov, V.P. et al., Termodinamika. Chast’ 2. Spezial’nyi kurs (Thermodynamics, part 2, Special Course), Moscow: Drofa, 2009.

    Google Scholar 

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Volov, V.T. Limit Energy Theorem for Gas Flow Systems. J. Engin. Thermophys. 27, 489–500 (2018).

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