Pressure, temperature, and heat flux in high speed lubrication flows of pressurized gases

• Published in: Tribology international Vol. 129; pp. 468 - 475
• Main Authors: Chien, S.Y., Cramer, M.S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.01.2019; Elsevier BV
• Subjects: Analytical model; Bulk modulus; Compressibility; Film thickness; Fluid mechanics; Gas lubricated bearing; Gas lubrication; Heat flux; Heat transfer; Lubrication; Pressure distribution; Reynolds equation; Supercritical gases; Temperature distribution; Thermal expansion; Analytical model; Fluid mechanics; Gas lubricated bearing; Supercritical gases
• ISSN: 0301-679X; 1879-2464
• DOI: 10.1016/j.triboint.2018.08.030

We present approximate solutions to the compressible Reynolds equation and the corresponding temperature equation which are valid for large speed numbers in the dense and supercritical gas regime. The flows are taken to be two-dimensional, steady, compressible, single-phase and laminar. New results include explicit formulas for pressure, density, temperature, and heat flux in terms of the speed number, film thickness function, and the material functions. We have found that the first correction for finite speed number will depend on the local values of the effective bulk modulus and thermal expansion coefficient. Our approximations are compared to numerical solutions to the exact Reynolds theory. It was found that the first order approximation is necessary to obtain realistic pressure and temperature distributions. •Explicit solutions to the compressible Reynolds theory for high-speed gas bearings are provided.•Solutions are valid for temperatures and pressures corresponding to ideal, dense, and supercritical gases.•Effective bulk modulus plays a key role.•Effect of finite speed number increases with increasing pressure.•Temperature variation at adiabatic walls differs significantly from that of the lowest order theory.