Virial Approximation for Load and Loss in High-Speed Journal Bearings Using Pressurized Gases

Chien, Ssu-Ying; Cramer, M. S.

doi:10.3390/fluids4010027

Cited by 2 publications

(2 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Chien & Cramer (2019 a , b , c ) derived the approximate solutions to the Reynolds and corresponding temperature equations of Chien et al. (2017) for high-speed high-pressure lubrication flows between non-concentric cylinders.…”

Section: Introductionmentioning

confidence: 99%

“…the viscosity, bulk modulus and thermal expansivity (Chien & Cramer 2019 b ). The approximations for global parameters, including the total force and total friction loss, were also developed in Chien & Cramer (2019 a , b ). While the numerical and analytic results of Chien & Cramer (2019 a , b , c ) delineate the effects of pressurization for a simple two-dimensional configuration, the complication due to the three dimensionality of the flow has not yet been investigated in their analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Compressible high-pressure lubrication flows in thrust bearings

Chien

Cramer

2022

J. Fluid Mech.

View full text Add to dashboard Cite

We present a detailed derivation of the Reynolds equation and its corresponding energy equation for three-dimensional, steady, laminar, compressible flows of single-phase Navier–Stokes fluids in thrust bearings. These equations are shown to be valid over most of the dense and supercritical gas regime except for the vicinity of the thermodynamic critical point. It is shown that the primary thermodynamic function governing the lubrication flow of high-pressure gases is the effective bulk modulus defined as the ratio of the bulk modulus to the shear viscosity. Numerical solutions to our Reynolds equation are obtained using a finite difference scheme for both moderate and high-speed flows. Approximate solutions to our Reynolds equation for high-speed flows are also derived through a perturbation analysis. It is found that boundary layers form on three out of four edges of the thrust pad. At the inner and outer radii of the pad, the flow is governed by a nonlinear heat equation. As the main flow leaves the pad, the flow is governed by a nonlinear relaxation equation. These three boundary layer solutions are rendered consistent by the construction of boundary layer solutions in the corner regions. A composite solution is developed which provides a single approximation and has the same accuracy as the individual approximations in their respective regions of validity.

show abstract