Engineering Journal: Science and InnovationELECTRONIC SCIENCE AND ENGINEERING PUBLICATION
Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
  • Русский
  • Английский
Article

Pressure effects on aerodynamic losses and load capacity of the lubrication layer for various noble gases

Published: 08.07.2025

Authors: Verenin M.A.

Published in issue: #7(163)/2025

DOI: 10.18698/2308-6033-2025-7-2458

Category: Mechanics | Chapter: Mechanics of Liquid, Gas, and Plasma

Gas lubrication is widely used in industry; therefor, its mathematical simulation becomes an urgent research problem. Computing a gas flow requires correct determination of its thermophysical properties, which inevitably raises a question of the macroscopic parameters influence on them, including the pressure and temperature. In particular, results of numerous experiments demonstrate that the increasing pressure causes diversity in the viscosity values from the Chapman-Enskog theory forecasts. The presented study proposes the existing methodology for accounting for the high-pressure effect on properties of the inert gases binary mixtures to be applied to computation of the most important characteristics of the gas lubricating layer, including the aerodynamic losses and the bearing capacity. The paper provides quantitative assessment of the indicated effects in the temperature range of 400…1200K and pressure of 1…7 MPa. The considered method could be applied in compiling and optimizing the program codes to solve the gas lubrication problems.

EDN ACUUZO


References
[1] Leibenzon L.S., ed. Gidrodinamicheskaya teoriya smazki [Hydrodynamic theory of lubrication]. Moscow, Gostekhizdat Publ., 1934.
[2] Loitsyansky L.G. Mekhanika zhidkosti i gaza [Mechanics of liquid and gas]. Moscow, Nauka Publ., 1970.
[3] Schlichting H. Boundary-Layer Theory. Springer, 1954 [In Russ.: Shlikhting G. Teoriya pogranichhnogo sloya. Moscow, Nauka Publ., 1974].
[4] Gross W.A. Gas film lubrication. New York, London, Wiley, 1962.
[5] Constantinescu V.N. Gas lubrication. New York, American Society of Mechanical Engineers, 1969.
[6] Turchak L.I., Shidlovsky V.P. Teoreticheskoe i chislennoe issledovanie protsessov gazovoy smazki na osnove uravneniy aerogidrodinamiki [Theoretical and numerical study of the gas lubrication processes based on the aerohydrodynamic equations]. Izvestiya RAN. Mekhanika zhidkosti i gaza — Fluid Dynamics. A Journal of Russian Academy of Sciences, 2001, no. 5, pp. 24–34.
[7] Turchak L.I., Shidlovsky V.P. Prostranstvennaya zadacha teorii gazovoy smazki i eye reshenie s pomoshchyu metoda srashchivaemykh asimptomaticheskikh razlozheniy [A three-dimensional problem of gas lubrication theory and its solution by method of matched asymptotic expansions]. Zhurnal vychislitelnoy i matematicheskoy fiziki — Computational Mathematics and Mathematical Physics, 2002, vol. 42, no. 12, pp. 1875–1880.
[8] Turchak L.I., Shidlovsky V.P. Matematicheskoe modelirovanie problem gazovoy smazki [Mathematical modeling of gas lubrication problems]. Zhurnal vychislitelnoy i matematicheskoy fiziki — Computational Mathematics and Mathematical Physics, 2011, vol. 51, no. 2, pp. 329–348.
[9] Zvonarev P.N. Razrabotka metoda rascheta radialnykh uprugogazodinamicheskikh podshipnikov s predvaritelno napryazhennymi lepestkami dlya malykh turbomashin nizkotemperaturnykh ustanovok: Dis. … kand. tekhn. nauk [Development of a calculation method for the radial elastic-gas-dynamic bearings with the prestressed petals for a small turbomachine of the low-temperature installations: Diss. … Cand. Sc. (Eng.)]. Moscow, 2005. (in Russ).
[10] Sytin A.V. Reshenie kompleksnoy zadachi rascheta kharakteristik radialnykh lepestkovykh gazodinamicheskikh podshipnikov: Dis. … kand. tekh. nauk [Solution to complex problem of calculating characteristics of the radial petal gas-dynamic bearings: Diss. … Cand. Sc. (Eng.)]. Orel; 2008. (in Russ).
[11] Bonello P., Pham H. The efficient computation of the nonlinear dynamic response of a foil air bearing rotor system. J. Sound Vib, 2014, vol. 333, pp. 3459–3478. https://doi.org/10.1016/j.jsv.2014.03.001
[12] Nikolaev V.S., Tishchenko I.V. Matematicheskoe modelirovanie dinamiki rotora turbomashiny na lepestkovykh gazodinamicheskikh podshipnikakh pri vozdeystvii vibratsii [Mathematical modeling of the rotor dynamics of a turbomachine on gas foil bearings subjected to vibration]. Kholodilnaya tekhnika — Refrigeration Technology, 2022, vol. 111, no. 3, pp. 165–179. DOI: 10.17816/RF111753
[13] Le Lez S., Arghir M., Frene J. Nonlinear numerical prediction of gas foil bearing stability and unbalance response. Journal of Engineering for Gas Turbines and Power, 2009, vol. 131 no. 1.
[14] Kim D. Parametric studies on static and dynamic performance of air foil bearings with different top foil geometries and bump stiffness distributions. Journal of tribology, 2007, vol. 129, no. 2, pp. 354–364. https://doi.org/10.1115/1.2540065
[15] Peshti Y.V. Gazovaya smazka [Gas lubricant]. Moscow, BMSTU Press, 1993. (in Russ).
[16] Koroteev A.S., Gotovtsev K.V., Zakharenkov L.E., Karevsky A.V., Lovtsov A.S., Oshev Yu.A. et. al. Sovmestnoe funktsionirovanie elektroraketnykh dvigateley i sistemy gazoturbinnogo preobrazovaniya energii v sostave energodvigatelnoy ustanovki kosmicheskogo naznacheniya [Joint operation of electric propulsion and closed Brayton cycle power conversion unit as parts of space power and propulsion system]. Izvestiya RAN. Energetika — Proceedings of the Russian Academy of Sciences. Power Engineering, 2020, no. 1, pp. 3–20.
[17] Akimov V.N., Zakharenkov L.E., Karevsky A.V., Kuvshinova E.Y., Semenkin A.V. Osobennosti postroyeniya i vozmozhnye primeneniya moshchnykh yadernykh energodvigatelnykh ustanovok perspektivnykh kosmicheskikh apparatov [Features of construction and possible use of powerful nuclear power plants of advanced spacecraft]. Inzhenerny zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2019, issue 6. https://doi.org/10.18698/2308-6033-2019-6-1889
[18] Akimov V.N., Koroteev A.A., Koroteev A.S. Yadernaya kosmicheskaya energetika: vchera, segodnya, zavtra [Nuclear space power engineering: yesterday, today, tomorrow]. Izvestiya RAN. Energetika — Proceedings of the Russian Academy of Sciences. Power Engineering, 2012, no. 1, pp. 3–11.
[19] Koroteev A.S., Oshev Yu.A., Popov S.A., Karevsky A.V., Solodukhin A.E., Zakharenkov L.E., Semenkin A.V. Yadernaya energodvigatelnaya ustanovka kosmicheskogo apparata [Nuclear power propulsion system of a spacecraft]. Izvestiya RAN. Energetika — Proceedings of the Russian Academy of Sciences. Power Engineering, 2015, no. 5, pp. 45–59.
[20] Andrianov D.I., Zakharenkov L.E., Karevsky A.V., Popov A.V., Popov S.A., Semenkin A.V., et al. Moshchnye energodvigateknye ustanovki kosmicheskogo naznacheniya s gazoturbinnym preobrazovaniem energii po zamknutomu tsiklu Braytona i osobennosti ikh eksperimentaknoy otrabotki [Space power propulsion systems with gas turbine power conversion system of closed Brayton cycle of high power and characteristic features of their experimental testing]. Inzhenerny zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2016, iss. 7 (55). https://doi.org/10.18698/2308-6033-2016-7-1518
[21] Egorov K.S., Stepanova L.V. Teplofizicheskie svoystva smesey blagorodnykh gazov s nizkimi chislami Prandlya [Thermophysical properties of noble gas mixtures with low Prandtl number]. Inzhenerny zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2019, iss. 3. https://doi.org/10.18698/2308-6033-2019-3-1858
[22] Tournier J.M., El-Genk M.S., Gallo B.M. Best Estimates of Binary Gas Mixtures Properties for Closed Brayton Cycle Space Application. AIAA-2006-4154.
[23] Tournier J.P., Mohamed S.E. Properties of noble gases and binary mixtures for closed Brayton Cycle application. Energy Conversion and Management, 2008, vol. 49, pp. 469–492.
[24] El-Genk M.S., Tournier J.M. Selection of noble gas binary mixtures for brayton space nuclear power systems. AIAA-2006-59986.
[25] Dorfman L.A. Gidrodinamicheskoe soprotivlenie i teplootdacha vrashchayushchikhsya tel [Hydrodynamic resistance and heat transfer of solids of revolution]. Moscow, Fizmatlit Publ., 1960.
[26] Afanasyev A.A., Kovalev A.V. K opredeleniyu momenta sil treniya diska, vrashchyayushchegosya v ogranichennom prostranstve, zapolnennom vyazkoy neszhimaemoy zhidkostyu [About finding friction torque of a disk rotating in limited space filled with viscous incompressible fluid]. Vestnik VGU. Seriya: fizika, matematika — Proceedings of Voronezh State University. Series: Physics, Mathematics, 2014, no. 4.
[27] Hirschfelder J.O., Curtiss C.F., Bird R.B. Molecular theory of gases and liquids. New York, John Wiley & Sons Inc., London, Chapman and Hall, 1954.
[28] Hairer E., Wanner G. Solving ordinary differential equations II. Stiff and differential algebraic problems. Springer, Berlin, 1991 [In Russ.: Khayrer E., Vanner G. Reshenie obyknovennykh differentsialnykh uravneniy. Zhestkie i differentsialno-algebraicheskie zadachi. Moscow, Mir Publ., 1999].
[29] Hairer E., Wanner G. Radau Methods. Springer Berlin Heidelberg, 2015, pp. 1213–1216. https://doi.org/10.1007/978-3-540-70529-1_139
[30] Hairer E., Wanner G. Stiff differential equations solved by Radau methods. Journal of Computational and Applied Mathematics, 1999, vol. 111, pp. 93–111. https://doi.org/10.1016/S0377-0427(99)00134-X
[31] Polikarpov A.V., Vikulov A.P., Zotov S.N., Kostenko A.A., Galperin I.I., Labutin A.D. Bezmaslyanyi tsentrobezhnyi elektrokompressor na lepestkovykh gazodinamicheskikh podshipnikakh [Oil-free centrifugal electric compressor with foil gas-dynamic bearings]. Kholodilnaya tekhnika — Refrigeration Technology, 2020, vol. 109, no. 2, pp. 36–34. https://doi.org/10.17816/RF104085
[32] Schedukhin S.I., Polikarpov A.V., Vikulov A.P., Zotov S.N., Rozenoer T.M., Kostenko A.A., Voronov A.A. Bezmaslyanyi turbodetander prirodnogo gaza na lepestkovykh gazodinamicheskikh podshipnikakh [Oil-free turbo-expander for natural gas using leaf gas-dynamic bearings]. Kholodilnaya tekhnika — Refrigeration technology, 2017, vol. 106, no. 6, pp. 46–50. https://doi.org/10.17816/RF99254