Abstract
We consider steady, laminar, compressible lubrication flows in a high-speed two-dimensional journal bearing governed by the appropriate Reynolds equation. The thermodynamic states correspond to pressurized gases and are in the single-phase regime. Simple explicit formulas for the load capacity, power loss, and attitude angle are derived by applying the virial (or small density) expansions of pressure and shear viscosity to results developed in previous studies. The present virial approximation was compared to the exact numerical solutions to the Reynolds equation. It was shown that the results based on our virial expansions are quite accurate at thermodynamic states corresponding to dense and supercritical gases. The first virial correction is seen to significantly improve predictions based on the ideal gas theory.
Highlights
The canonical equation governing many lubrication flows is the Reynolds equation [1]
Conditions under which the Reynolds equation is valid are satisfied in many devices [6,7,8,9,10]
We only present results for reference thermodynamic states having 2B∆ ≤ 0.5
Summary
The canonical equation governing many lubrication flows is the Reynolds equation [1]. Since its introduction in the late 19th Century, it has been generalized to include the effects of three-dimensional unsteady flow, turbulence, non-Newtonian constitutive laws, two-phase flow, and wall slip [2,3,4,5]. An important motivation for the use of the Reynolds equation is that it provides a relatively simple, computationally-efficient, and -reproducible context in which to examine physical effects and mathematical models. Recent interest in novel power systems have motivated the use of gases rather than highly viscous oils [11,12,13,14,15]. The advantages of gases over liquids include weight reduction, elimination of complications associated with fouling due to leaks and complications due to phase changes, and the compatibility with working fluids of the parent power system
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