Derivation of Modified Reynolds Equation—A Porous Media Model

1999 ◽  
Vol 121 (4) ◽  
pp. 823-829 ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Porous Media ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Fluid Film ◽  
Stress Jump ◽  
Darcy Model ◽  
Viscous Shear ◽  
Porous Media Model ◽  
Modified Reynolds Equation ◽  
Film Interface

In this study, a porous media model is developed which can be applied to thin film lubrication problems. The microstructure of bearing surfaces is modeled as porous layers attached to the impermeable substrate. The Brinkman-extended Darcy equations and Stokes’ equations are utilized to model the flow in the porous region and fluid film region, respectively. The stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included in deriving the modified Reynolds equation. The present model can correct and modify a previous study based on the Darcy model with slip-fiow effects or another based on the Brinkman-extended Darcy model with stress continuity at the porous media/fluid film interface. In the results, the effects of material properties: viscosity ratio (αi2), thickness of porous layer (Δi), permeability (Ki), stress jump parameter (βi), on the velocity distributions, and performance of one-dimensional converging wedge problems are discussed.

Derivation of Modified Reynolds Equation: A Porous Media Model With Effects of Electrokinetics

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Porous Media ◽  
Charge Density ◽  
Apparent Viscosity ◽  
Reynolds Equation ◽  
Debye Length ◽  
Porous Film ◽  
Fluid Film ◽  
Stress Jump ◽  
Viscous Shear ◽  
Modified Reynolds Equation

A lubrication theory that includes the effects of electrokinetics and surface microstructure is developed. A porous layer attached to the impermeable substrate is used to model the microstructure on a bearing surface. The Brinkman-extended Darcy equations and Stokes equations are modified by considering the electrical body force and utilized to model the flow in porous media and fluid film, respectively. The stress jump boundary conditions on the porous media/fluid film interface and the effects of viscous shear and electric double layer (EDL) are also considered when deriving the modified Reynolds equation. Under the usual assumptions of lubrication and Debye–Hückel approximation for low surface potential, the velocity distributions, the apparent viscosity, and the modified Reynolds equation are then derived. The apparent viscosity is expressed explicitly as functions of the Debye length, the electroviscosity, the charge density, the stress jump parameter, and the porous parameters (permeability, porosity, and porous film thickness). The considerations of EDL near the interface and the charge density of the flow in the porous media increase the apparent viscosity. The existence of porous film also increases the apparent viscosity as well. Both effects are important for flow within microspacing and lubrication problems. The apparent viscosity and the performance of 1D slider bearings are analyzed and discussed. The results show that the apparent viscosity and the load capacity increase as the permeability decreases, the stress jump parameter decreases, the charge density increases, the inverse Debye length decreases, or the porosity decreases.

Lubrication of journal bearings—influence of stress jump condition at the porous-media/fluid film interface

2002 ◽  
Vol 35 (5) ◽  
pp. 287-295 ◽  
Author(s):  
Ming-Da Chen ◽  
Kuo-Ming Chang ◽  
Jau-Wen Lin ◽  
Wang-Long Li
Keyword(s):  
Porous Media ◽  
Jump Condition ◽  
Journal Bearings ◽  
Fluid Film ◽  
Stress Jump ◽  
Film Interface

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

2007 ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Mathematical Modeling ◽  
Porous Medium ◽  
Linear Model ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Dimensional Parameter ◽  
Pressure Flow ◽  
Darcy Model ◽  
Linear Effects ◽  
Modified Reynolds Equation

The mathematical modeling of aerostatic porous bearings, represented by the Reynolds equation, depends on the assumptions for the flow in the porous medium. One proposes a modified Reynolds equation based on the quadratic Forchheimer assumption, which can be used for both linear and quadratic conditions. Numerical results are compared to those obtained with the linear Darcy model. It is shown that, the non-dimensional parameter Φ, related to non-linear effects, strongly affects the bearing dynamic characteristics, but for values of Φ > 10, the results tend to those obtained with the linear model.

Static characteristics of hydrostatic doubled-layered porous journal bearings with slip flow including additives percolation into pores under coupled stress lubrication

2017 ◽  
Vol 232 (8) ◽  
pp. 927-939 ◽  
Author(s):  
Shitendu Some ◽  
Sisir K Guha
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Journal Bearings ◽  
Static Characteristics ◽  
Governing Equations ◽  
Modified Reynolds Equation ◽  
Film Interface ◽  
Coupled Stress ◽  
Steady State Performance

A theoretical analysis of the steady-state characteristics of finite hydrostatic double-layered porous journal bearings dealing with the effects of slip flow at the fine porous layer–film interface and percolation of additives into pores under the coupled stress fluid lubrication is presented. Based on the Beavers–Joseph’s criterion for slip flow, the modified Reynolds equation applicable to finite porous journal bearings lubricated with coupled stress fluids have been derived. The governing equations for flow in the coarse and fine layers of porous medium incorporating the percolation of polar additives of lubricant and the modified Reynolds equation are solved simultaneously using finite difference method satisfying appropriate boundary conditions to obtain the steady-state performance characteristics for various parameter namely percolation factor, slip coefficient, bearing feeding parameter, coupled stress parameter, and eccentricity ratio. The results are exhibited in the form of graphs, which may be useful for design of such bearing.

Tribological Study of a Slider Bearing in the Supersonic Regime

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Florence Dupuy ◽  
Benyebka Bou-Saïd ◽  
Mathieu Garcia ◽  
Grégory Grau ◽  
Jérôme Rocchi ◽  
...  
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slider Bearing ◽  
Navier Stokes Equations ◽  
Supersonic Regime ◽  
Two Dimensional Flow ◽  
Modified Reynolds Equation ◽  
The One

Aerodynamic slider bearings are currently used in various types of turbomachinery. Many such systems perform at increasingly faster speeds and may operate in the supersonic regime. Although there is extensive research on compressible lubrication extrapolated to high-speeds, very little of it addresses the potential supersonic nature of the flow. It is well known in compressible flow that many of the tendencies of subsonic flow actually reverse themselves as the singularity at Mach one is traversed. Thus, examination of this high-speed regime may yield some unanticipated results. The behavior of a thin film of air in the supersonic regime is studied in the two-dimensional flow case with rigid sliding surfaces. The one-dimensional bearing studied has a dual profile consisting of an inlet region converging wedge of constant slope and an exit region of constant gap. Two approaches are compared: the solution of a modified Reynolds equation, and the solution to a version of Navier–Stokes equations adapted to thin films. The results show that the modified Reynolds equation approach, which is useful to describe the behavior of lubricating fluids at high subsonic speeds may be inadequate in the supersonic regime. The present studies show the absence of shock and expansion wave phenomena for cases in which the film thickness ratio does not exceed 0.01.

Hybrid Porous Gas Journal Bearings: Steady State Solution Incorporating the Effect of Velocity Slip

1984 ◽  
Vol 106 (3) ◽  
pp. 322-328 ◽  
Author(s):  
K. C. Singh ◽  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Load Capacity ◽  
Velocity Slip ◽  
Steady State Solution ◽  
Static Characteristic ◽  
Journal Bearings ◽  
Mass Rate ◽  
Modified Reynolds Equation

A theoretical analysis is presented to predict the steady state performance characteristics of externally pressurized rotating gas journal bearings incorporating the effect of velocity slip at the porous interface. The governing equation for flow in the porous media and the modified Reynolds equation derived from the Navier-Stokes equations satisfying the velocity slip boundary condition, are solved simultaneously for film pressure distribution. Due to the nonlinearity of modified Reynolds equation the solution is obtained by perturbation method using finite difference technique. The dimensionless load capacity, attitude angle and mass rate of flow are computed numerically for different operating parameters. The effect of slip on the static characteristic is discussed. Comparison of the results with similar available solution for the no-slip case shows good agreement.

scholarly journals Effect ofL/DRatio on the Performance of Two-Lobe Pressure Dam Bearing: Micropolar Lubricated

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Sanyam Sharma ◽  
C. M. Krishna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Aspect Ratio ◽  
Micropolar Fluid ◽  
High Speed ◽  
Reynolds Equation ◽  
Dynamic Performance ◽  
Performance Characteristics ◽  
Fluid Film ◽  
Modified Reynolds Equation

Two-lobe pressure dam bearings are commonly used in high speed rotating machineries. Their use is considered more stable than plain cylindrical bearings. Such bearings have a dam in the upper half whereas the lower half is provided with a relief track. Performance of two-lobe pressure dam bearings under micropolar fluid is evaluated. Finite element method is used to solve the modified Reynolds equation. Fluid film pressures are obtained by solving modified Reynolds equation. Thus pressure obtained is used to find performance characteristics of this bearing. The dynamic performance characteristics are studied at variousL/Dratios. ThreeL/Dratios are considered 1.6, 2.0, and 2.4 for the analysis purpose. Results obtained are presented for various micropolar parameters. Results show that stability of two-lobe pressure dam bearings increases with decrease in aspect ratio (L/D).

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