Abstract
Porous gas bearings (PGBs) have a proactive application in aerospace and turbomachinery. This study investigates the gas lubrication performance of a PGB with the condition of velocity slip boundary (VSB) owing to the high Knudsen number in the gas film. The Darcy-Forchheimer laws and modified Navier-Stokes equations were adopted to describe the gas flow in the porous layer and gas film region, respectively. An improved bearing experimental platform was established to verify the accuracy of the derived theory and the reliability of the numerical analysis. The effects of various parameters on the pressure distribution, flow cycle, load capacity, mass flow rate, and velocity profile are demonstrated and discussed. The results show that the gas can flow in both directions, from the porous layer to the gas film region, or in reverse. The load capacity of the PGB increases with an increase in speed and inlet pressure and decreases with an increase in permeability. The mass flow rate increases as the inlet pressure and permeability increase. Furthermore, the simulation results using VSB are in agreement with the experimental results, with an average error of 3.4%, which indicates that the model using VSB achieves a high accuracy. The simulation results ignoring the VSB overrate the load capacity by 16.42% and undervalue the mass flow rate by 11.29%. This study may aid in understanding the gas lubrication mechanism in PGBs and the development of novel gas lubricants.
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Abbreviations
- C ij :
-
Inertial resistance coefficient matrix
- c p :
-
Constant pressure specific heat (J/(kg·K)−1)
- D ij :
-
Viscous resistance coefficient matrix
- div:
-
Divergeence sign
- F :
-
Volumetric force (N)
- h :
-
Thickness of porous layer (mm)
- L :
-
Bearing length (mm)
- \(\nabla {p_i}\) :
-
Internal pressure decrease of porous (Pa)
- p :
-
Pressure (Pa)
- m :
-
Mass flow rate (kg/s)
- N:
-
Rotational speed (rpm)
- R 1 :
-
Inner radius (mm)
- R 2 :
-
Outer radius (mm)
- U :
-
Tangential velocity (m/s)
- V :
-
Normal velocity (m/s)
- x, y, z :
-
Cartesian coordinates
- α :
-
Permeability factor
- λ :
-
Mean free path (mm)
- l :
-
Characteristic length (mm)
- σ :
-
Molecular diameter (mm)
- κ :
-
Boltzmann constant
- ζ :
-
Dynamic viscosity ((N·s)/m2)
- ρ :
-
Gas density (kg/m3)
- v :
-
Velocity component in Cartesian coordinates (m/s)
- u, v, w :
-
Velocity in the three directions of the Cartesian coordinates (m/s)
- γ :
-
Porosity
- ϕ x, ϕ y, ϕ z :
-
Viscous permeability (m2)
- ψ x, ψ y, ψ z :
-
Inertial permeability (m2)
References
Feng K, Wu Y H, Liu W H, Zhao X Y, Li W J. Theoretical investigation on porous tilting pad bearings considering tilting pad motion and porous material restriction. Precis Eng 53: 26–37 (2018)
Wu Y H, Feng K, Zhang Y, Liu W H, Li W J. Nonlinear dynamic analysis of a rotor-bearing system with porous tilting pad bearing support. Nonlinear Dyn 94(2): 1391–1408 (2018)
Kumar V. Porous metal bearings—A critical review. Wear 63(2): 271–287 (1980)
Sneck H J. A survey of gas-lubricated porous bearings. J Lubr Technol 90(4): 804–809 (1968)
Majumdar B C. Gas-lubricated porous bearings: A bibliography. Wear 36(3): 269–273 (1976)
Heller S, Shapiro W, Decker O. A porous hydrostatic gas bearing for use in miniature turbomachinery. S L E Trans 14(2): 144–155 (1971)
Devitt D, San A L, Jeung SH.Carbon-graphite gas bearings for turbomachinery. In Proceedings of the 30th ASPE Annual Meeting, Hyatt Regency Austin, Austin, USA, 2015: 218–222.
Information. https://www.newwayairbearings.com/technology/technical-resources/new-way-techincal-reports/technical-report-6-air-bearings-for-high-power-turbomachinery/, 2014.
Lee C C, You H I. Geometrical design considerations on externally pressurized porous gas bearings. Tribol Trans 53(3): 386–391 (2010)
Lee C C, You H I. Characteristics of externally pressurized porous gas bearings considering structure permeability. Tribol Trans 52(6): 768–776 (2009)
Chang C W, Chen C K. Chaotic response and bifurcation analysis of a flexible rotor supported by porous and nonporous bearings with nonlinear suspension. Nonlinear Anal: Real World Appl 10(2): 1114–1138 (2009)
Cui H L, Wang Y, Yue X B, Huang M, Wang W. Effects of manufacturing errors on the static characteristics of aerostatic journal bearings with porous restrictor. Tribol Int 115: 246–260 (2017)
Cui H L, Wang Y, Yue X B, Huang M, Wang W, Jiang Z Y. Numerical analysis and experimental investigation into the effects of manufacturing errors on the running accuracy of the aerostatic porous spindle. Tribol Int 118: 20–36 (2018)
Kurotani Y, Tanaka H. A novel physical mechanism of liquid flow slippage on a solid surface. Sci Adv 6(13): eaaz0504 (2020)
Nicoletti R, Silveira Z C, Purquerio B M. Modified Reynolds equation for aerostatic porous radial bearings with quadratic forchheimer pressure-flow assumption. J Tribol 130(3): 031701 (2008)
Rao T V V L N, Rani A M A, Awang M, Nagarajan T, Hashim F M. Stability analysis of double porous and surface porous layer journal bearing. Tribol - Mater Surfaces Interfaces 10(1): 19–25 (2016)
Prakash J, Gururajan K. Effect of velocity slip in an infinitely long rough porous journal bearing. Tribol Trans 42(3): 661–667 (1999)
Kalavathi G K, Dinesh P A, Gururajan K. Influence of roughness on porous finite journal bearing with heterogeneous slip/no-slip surface. Tribol Int 102: 174–181 (2016)
Le N T P, Roohi E, Tran T N. Comprehensive assessment of newly-developed slip-jump boundary conditions in highspeed rarefied gas flow simulations. Aerosp Sci Technol 91: 656–668 (2019)
Jebauer S, Czerwińska J. Implementation of Velocity Slip and Temperature Jump Boundary Conditions for Microfluidic Devices. Warsaw (Poland): Instytut Podstawowych Problemów Techniki PAN, 2007.
Su J C T, You H I, Lai J X. Numerical analysis on externally pressurized high-speed gas-lubricated porous journal bearings. Ind Lubr Tribol 55(5): 244–250 (2003)
Wang N Z, Chen H Y. A two-stage multiobjective optimization algorithm for porous air bearing design. Tribol Int 93: 355–363 (2016)
Jiang S Y, Lin S Y, Xu C D. Static and dynamic characteristics of externally pressurized porous gas journal bearing with four degrees-of-freedom. J Tribol 140(1): 011702 (2018)
Cui Y W. Thermal characteristic analysis and rotordynamic experimental study of aerostaticporous journal bearings. Ph.D. Thesis. Changsha (China): Hunan University, 2017.
Saha N, Majumdar B C. Study of externally-pressurized gas-lubricated two-layered porous journal bearings: A steady state analysis. Proc Inst Mech Eng Part J: J Eng Tribol 216(3): 151–158 (2002)
Paidoussis M, Price S, de Langre E. Fluid-structure Interactions. Cambridge (UK): Cambridge University Press, 2009.
Ji F Z, Bao Y P, Zhou Y, Du F R, Zhu H J, Zhao S, Li G, Zhu X F, Ding S T. Investigation on performance and implementation of Tesla turbine in engine waste heat recovery. Energy Convers Manag 179: 326–338 (2019)
Jin Y Z, Chen F, Xu J M, Yuan X Y. Nonlinear dynamic analysis of low viscosity fluid-lubricated tilting-pad journal bearing for different design parameters. Friction 8(5): 930–944 (2020)
Hu Y Q, Meng Y G. Numerical modeling and analysis of plasmonic flying head for rotary near-field lithography technology. Friction 6(4): 443–456 (2018)
Lin W. A slip model for rarefied gas flows at arbitrary Knudsen number. Appl Phys Lett 93(25): 253103 (2008)
Liang H, Guo D, Luo J B. Film forming behavior in thin film lubrication at high speeds. Friction 6(2): 156–163 (2018)
Zhang S H, Qiao Y J, Liu Y H, Ma L R, Luo J B. Molecular behaviors in thin film lubrication—Part one: Film formation for different polarities of molecules. Friction 7(4): 372–387 (2019)
Tang Z Q, Zhou D D, Jia T, Pan D, Zhang C W. Investigation of lubricant transfer and distribution at head/disk interface in air-helium gas mixtures. Friction 7(6): 564–571 (2019)
Ma L R, Luo J B. Thin film lubrication in the past 20 years. Friction 4(4): 280–302 (2016)
Gao M, Li H Y, Ma L R, Gao Y, Ma L W, Luo J B. Molecular behaviors in thin film lubrication—Part two: Direct observation of the molecular orientation near the solid surface. Friction 7(5): 479–488 (2019)
Beskok A, Karniadakis G E, Trimmer W. Rarefaction and compressibility effects in gas microflows. J Fluids Eng 118(3): 448–456 (1996)
Bailey NY, Hibberd S, Power H. Evaluation of the minimum face clearance of a high-speed gas-lubricated bearing with Navier slip boundary conditions under random excitations. J Eng Math 112(1): 17–35 (2018)
Zhang X B, Ding S T, Du F R, Ji F Z, Guo S G. Numerical simulation on aerodynamic performance of ram air turbine based on mixed flow field. In Proceedings of the ASME 2018 International Mechanical Engineering Congress and Exposition, Pittsburgh, PA, USA, 2018: 88304.
Zhu J C, Chen H, Chen X D. Large eddy simulation of vortex shedding and pressure fluctuation in aerostatic bearings. J Fluids Struct 40: 42–51 (2013)
Wang W, He Y Y, Zhao J, Mao J Y, Hu Y T, Luo J B. Optimization of groove texture profile to improve hydrodynamic lubrication performance: Theory and experiments. Friction 8(1): 83–94 (2020)
Leclercq T, de Langre E. Vortex-induced vibrations of cylinders bent by the flow. J Fluids Struct 80: 77–93 (2018)
Ji F Z, Zhang X B, Du F R, Ding S T, Zhao Y H, Xu Z, Wang Y, Zhou Y. Experimental and numerical investigation on micro gas turbine as a range extender for electric vehicle. Appl Therm Eng 173: 115236 (2020)
Oshkai P, Velikorodny A. Flow-acoustic coupling in coaxial side branch resonators with rectangular splitter plates. J Fluids Struct 38: 22–39 (2013)
Lam K, Lin Y F, Zou L, Liu Y. Investigation of turbulent flow past a yawed wavy cylinder. J Fluids Struct 26(7–8): 1078–1097 (2010)
Zhang W M, Yan H, Peng Z K, Meng G. Finite volume modeling of gas flow in microbearings with rough surface topography. Tribol Trans 59(1): 99–107 (2016)
Ji F Z, Pan Y, Zhou Y, Du F R, Zhang Q, Li G. Energy recovery based on pedal situation for regenerative braking system of electric vehicle. Veh Syst Dyn 58(1): 144–173 (2020)
Cha M, Glavatskih S. Nonlinear dynamic behaviour of vertical and horizontal rotors in compliant liner tilting pad journal bearings: Some design considerations. Tribol Int 82: 142–152 (2015)
Wu Y H. Theoretical analysis and experimental investigation on rotordynamic performance of a rigid rotor supported on porous tiliting pad bearings. Ph.D. Thesis. Changsha (China): Hunan University, 2019.
Cui H L. Study on the influence mechanism of the dynamic characteristics of porous aerostatic bearings. Ph.D. Thesis. Mianyang (China): China Academy of Engineering Physics, 2018.
Wu Y S, Pruess K, Persoff P. Gas flow in porous media with klinkenberg effects. Transp Porous Media 32(1): 117–137 (1998)
Joseph J, Kuntikana G, Singh D N. Investigations on gas permeability in porous media. J Nat Gas Sci Eng 64: 81–92 (2019)
Balasoiu A M, Braun M J, Moldovan S I. A parametric study of a porous self-circulating hydrodynamic bearing. Tribol Int 61: 176–193 (2013)
Zhou Y, Xing T, Song Y, Li Y J, Zhu X F, Li G, Ding S T. Digital-twin-driven geometric optimization of centrifugal impeller with free-form blades for five-axis flank milling. J Manuf Syst 58: 22–35 (2021)
Wu J, Wen B, Zhou Y, Zhang Q, Ding S T, Du F R, Zhang S G. Eddy current sensor system for blade tip clearance measurement based on a speed adjustment model. Sensors 19(4): 761 (2019)
Xu Z, Ji F Z, Ding S T, Zhao Y H, Zhang X B, Zhou Y, Zhang Q, Du F R. High-altitude performance and improvement methods of poppet valves 2-stroke aircraft diesel engine. Appl Energy 276: 115471 (2020)
Zhou Y, Shao L T, Zhang C, Ji F Z, Liu J, Li G, Ding S T, Zhang Q, Du F R. Numerical and experimental investigation on dynamic performance of bump foil journal bearing based on journal orbit. Chinese J Aeronaut 34(2): 586–600 (2021)
Hsu T C, Chen J H, Chiang H L, Chou T L. Lubrication performance of short journal bearings considering the effects of surface roughness and magnetic field. Tribol Int 61: 169–175 (2013)
Xu Z, Ji F Z, Ding S T, Zhao Y H, Zhou Y, Zhang Q, Du F R. Digital twin-driven optimization of gas exchange system of 2-stroke heavy fuel aircraft engine. J Manuf Syst 58: 132–145 (2021)
Information. https://www.iso.org/standard/50461.html, 1995.
Acknowledgements
This study was funded by the National Natural Science Foundation of China (Grant Nos. 51775025 and 51175018), China Automobile Industry Innovation and Development Joint Fund (Grant No. U1664257), China Key Research and Development plan (Grant Nos. 2017YFB0102102 and 2018YFB0104100), and the Beijing Natural Science Foundation (Grant No. 3113030).
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Xiangbo ZHANG. He received his B.S. degree from Henan University of Science and Technology in 2012. He is currently a Ph.D. student at the School of Energy and Power Engineering, Beihang University, China. His research is related to power machinery and engineering, including high-speed rotor system and micro gas turbine engine.
Shuiting DING. He received his B.S. degree in thermal engine power from Beihang University in 1990, and his Ph.D. degree in aerospace propulsion theory and engineering from Beihang University in 1998. He is currently a professor in Beihang University. His research interests include aviation engine system safety and airworthiness, air system of aero engine, and new energy system.
Farong DU. He received his B.S. degree from Henan University of Science and Technology in 1984. He is currently an associated professor in Beihang University. His research interests include aviation power system, high-speed rotor system, and micro gas turbine engine.
Fenzhu JI. She received her Ph.D. degree in vehicle engineering from Beihang University in 2006. She is currently an associated professor in Beihang University. Her research interests include automobile engine design theory & design method and new energy electric vehicle design technology.
Zheng XU. He received his B.S. degree in thermal energy and power engineering from Beihang University in 2014. He is currently a Ph.D. student in power machinery and engineering in Beihang University. His research interests include aviation power system, power characteristics at high altitude, and engine gas exchange process.
Jiang LIU. He received his Ph.D. degree in vehicle engineering from Beihang university in 2013. He is currently a CEO in Richen Power. His research interests include micro-hybird aviation power system.
Qi ZHANG. He received his B.S. degree from University of Electronic Science and Technology of China in 2001, and his Ph.D. degree in vehicle engineering from Beihang University in 2015. He is currently a lecturer in Beihang University. His research interests include micro-hybird aviation power system, brushless DC motor drive, and generator rectification.
Yu ZHOU. He received his B.S. degree in transportation science from Harbin Institute of Technology in 2003, and his Ph.D. degree in vehicle engineering from Beihang University in 2007. He is currently an associated professor in Beihang University. His research interests include high-speed rotor system dynamics and aerodynamic thermal characteristics.
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Zhang, X., Ding, S., Du, F. et al. Investigation into gas lubrication performance of porous gas bearing considering velocity slip boundary condition. Friction 10, 891–910 (2022). https://doi.org/10.1007/s40544-021-0503-7
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DOI: https://doi.org/10.1007/s40544-021-0503-7