Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura
A constant wall temperature microbearing gas flow
Апстракт
U radu je analizirano neizotermsko dvodimenzijsko stišljivo strujanje gasa u mikroležaju konstantnih i jednakih temperatura zida. Vrednost Knudsenovog broja je između 10-3 i 10-1, što odgovara režimu strujanja sa klizanjem. Ovaj režim strujanja definiše se jednačinama kontinuuma: Navije-Stoksovom i jednačinom energije i graničnim uslovom klizanja i temperaturskog skoka na zidu. Strujanje gasa je dozvučno, pa se mali parametar definiše kao ε = κM2/Re. Osim toga pretpostavljeno je se poprečni presek mikrokanala menja sporo, što dovodi do spore promene svih veličina u pravcu strujanja. Rešenje je dobijeno perturbacionom metodom. Prva aproksimacija predstavlja rešenje za slučaj strujanja gasa bez klizanja, dok se u drugoj aproksimaciji javlja uticaj klizanja i inercije. Dobijena su analitička rešenja za raspodelu pritiska, brzine i temperature u mikroležaju pri umereno velikim vrednostima Rejnoldsovog broja.
A non-isothermal two-dimensional compressible gas flow in a slider microbearing with constant and equal wall temperature is investigated in this paper analytically. The slip flow is defined by the Navier-Stokes and energy continuum equations along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3 to 10-1, which corresponds to the slip flow. The gas flow is subsonic and the ratio κM2/Re is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of inertia as well as rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are obtained.
Кључне речи:
slip flow / non-isothermal / microbearing / low Mach number / inertia / high Reynolds number / analytical solutionИзвор:
FME Transactions, 2010, 38, 2, 71-77Издавач:
- Univerzitet u Beogradu - Mašinski fakultet, Beograd
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Stevanović, Nevena AU - Milićev, Snežana PY - 2010 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1027 AB - U radu je analizirano neizotermsko dvodimenzijsko stišljivo strujanje gasa u mikroležaju konstantnih i jednakih temperatura zida. Vrednost Knudsenovog broja je između 10-3 i 10-1, što odgovara režimu strujanja sa klizanjem. Ovaj režim strujanja definiše se jednačinama kontinuuma: Navije-Stoksovom i jednačinom energije i graničnim uslovom klizanja i temperaturskog skoka na zidu. Strujanje gasa je dozvučno, pa se mali parametar definiše kao ε = κM2/Re. Osim toga pretpostavljeno je se poprečni presek mikrokanala menja sporo, što dovodi do spore promene svih veličina u pravcu strujanja. Rešenje je dobijeno perturbacionom metodom. Prva aproksimacija predstavlja rešenje za slučaj strujanja gasa bez klizanja, dok se u drugoj aproksimaciji javlja uticaj klizanja i inercije. Dobijena su analitička rešenja za raspodelu pritiska, brzine i temperature u mikroležaju pri umereno velikim vrednostima Rejnoldsovog broja. AB - A non-isothermal two-dimensional compressible gas flow in a slider microbearing with constant and equal wall temperature is investigated in this paper analytically. The slip flow is defined by the Navier-Stokes and energy continuum equations along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3 to 10-1, which corresponds to the slip flow. The gas flow is subsonic and the ratio κM2/Re is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of inertia as well as rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are obtained. PB - Univerzitet u Beogradu - Mašinski fakultet, Beograd T2 - FME Transactions T1 - Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura T1 - A constant wall temperature microbearing gas flow EP - 77 IS - 2 SP - 71 VL - 38 UR - https://hdl.handle.net/21.15107/rcub_machinery_1027 ER -
@article{ author = "Stevanović, Nevena and Milićev, Snežana", year = "2010", abstract = "U radu je analizirano neizotermsko dvodimenzijsko stišljivo strujanje gasa u mikroležaju konstantnih i jednakih temperatura zida. Vrednost Knudsenovog broja je između 10-3 i 10-1, što odgovara režimu strujanja sa klizanjem. Ovaj režim strujanja definiše se jednačinama kontinuuma: Navije-Stoksovom i jednačinom energije i graničnim uslovom klizanja i temperaturskog skoka na zidu. Strujanje gasa je dozvučno, pa se mali parametar definiše kao ε = κM2/Re. Osim toga pretpostavljeno je se poprečni presek mikrokanala menja sporo, što dovodi do spore promene svih veličina u pravcu strujanja. Rešenje je dobijeno perturbacionom metodom. Prva aproksimacija predstavlja rešenje za slučaj strujanja gasa bez klizanja, dok se u drugoj aproksimaciji javlja uticaj klizanja i inercije. Dobijena su analitička rešenja za raspodelu pritiska, brzine i temperature u mikroležaju pri umereno velikim vrednostima Rejnoldsovog broja., A non-isothermal two-dimensional compressible gas flow in a slider microbearing with constant and equal wall temperature is investigated in this paper analytically. The slip flow is defined by the Navier-Stokes and energy continuum equations along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3 to 10-1, which corresponds to the slip flow. The gas flow is subsonic and the ratio κM2/Re is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of inertia as well as rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are obtained.", publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd", journal = "FME Transactions", title = "Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura, A constant wall temperature microbearing gas flow", pages = "77-71", number = "2", volume = "38", url = "https://hdl.handle.net/21.15107/rcub_machinery_1027" }
Stevanović, N.,& Milićev, S.. (2010). Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura. in FME Transactions Univerzitet u Beogradu - Mašinski fakultet, Beograd., 38(2), 71-77. https://hdl.handle.net/21.15107/rcub_machinery_1027
Stevanović N, Milićev S. Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura. in FME Transactions. 2010;38(2):71-77. https://hdl.handle.net/21.15107/rcub_machinery_1027 .
Stevanović, Nevena, Milićev, Snežana, "Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura" in FME Transactions, 38, no. 2 (2010):71-77, https://hdl.handle.net/21.15107/rcub_machinery_1027 .