Derivation of Modified Reynolds Equation—A Porous Media Model

Li, Wang Long

doi:10.1115/1.2834141

Cited by 34 publications

(25 citation statements)

References 20 publications

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“…The resulting inequality condition given in equation (14), here called the parametric compatibility condition, is used to find valid physical parametric ranges for the present modified Reynolds equation. For the case studies performed in this study, the two parameters of a and b are varied in previously reported ranges, 27,28 whereas the range of K is to be confined to satisfy the parametric compatibility condition. Note that this condition is sufficient but not necessary for the unique determination of the parameters G 1 , G 2 , and G 3 .…”

Section: Appendixmentioning

confidence: 99%

“…To make up for this gap, he proposed the Brinkman- On the other hand, Ochoa-Tapia and Whitaker 26,27 performed both theoretical and empirical studies on the stress jump condition and effective viscosity in the boundary layer between the porous medium and the free flow region by introducing a volume averaging technique. Li 28 proposed a fluid flow model to solve the thin-film lubrication problem on porous media by extensively using the Brinkman-extended-Darcy equation incorporated with the stress jump condition and the viscosity ratio.…”

Section: Introductionmentioning

confidence: 99%

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Lubrication characteristics of a textured porous sliding bearing

Lee

Jang

Wang

et al. 2015

Advances in Mechanical Engineering

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This study investigates the lubrication characteristics of a textured bearing sliding on a porous layer. To properly implement the porous layer effect in the bearing, the Brinkman-extended-Darcy model is employed, which results in a modified Reynolds equation. This equation is then evaluated to examine the effects of the porous layer's material and geometric properties on the lubrication characteristics through the use of (semi-)analytic and numerical approaches. The cavitation effect is reflected in the numerical treatment of the model equation, and an adaptive finite difference scheme is employed to efficiently model the bearing system with finite dimples that may be far smaller than the overall bearing dimensions. Along with the variation trends of the bearing performance with respect to the material and geometric properties of the porous layer, the pattern effects of textured surfaces on the bearing performance indices (load capacity and equivalent friction coefficient) are also thoroughly investigated. Here, the pattern comprised a set of regularly spaced identical dimples either in semi-spherical or semi-ellipsoidal shape, and the effects of size and orientation of the dimples are comprehensively explored to separately identify their influence on the bearing performance indices.

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Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lubrication characteristics of a textured porous sliding bearing

Lee

Jang

Wang

et al. 2015

Advances in Mechanical Engineering

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“…The geometry of eccentric and asymmetric film thickness in this study is illustrated in Figure 2, where e is the eccentricity, γ 1 and γ 2 are the tilt angles, and x = 0 is the reference point at the oil entrance. From Figures 1 and 2, the film thickness equation can be written in the following dimensionless form (15) where…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In the present study, both the porous media model, which was developed by Tichy 14 and modified by Li,15 and the couple stress model are utilised to study the effects of lubricant additives on the performance of misaligned conical-cylindrical bearings. A modified form of Reynolds equation using the Brinkman-extended Darcy model with stress jump boundary condition at the porous media/fluid interface and the couple stress model is derived.…”

Section: Introductionmentioning

confidence: 99%

Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings

Elsharkawy

2007

Lubrication Science

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Conical-cylindrical bearings are used in electrohydraulic servo systems to improve the control accuracy, eliminate the static friction and increase the normal load-carrying capacity. A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the performance of misaligned conical-cylindrical bearings is proposed in this study. In this model, the non-Newtonian behaviour resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilised to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. The misalignment of the cylinder rod is also considered. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry and non-Newtonian behaviour of the lubricant on the steadystate performance characteristics such as pressure distribution, load-carrying capacity and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load-carrying capacity and reduce the coefficient of friction as compared to the Newtonian lubricants. Furthermore, the misalignment of the piston rod has significant effects on the performance of conical-cylindrical bearings. Copyright

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“…Meanwhile, theoretical consideration of fluid flow in porous media has received great attention in recent years. Most of the earlier studies [3,5] were based on Darcy's law which states that the volume-averaged velocity is proportional to the pressure gradient. The Darcy model is shown to be valid under the conditions of low velocities and small porosity [12].…”

mentioning

confidence: 99%

On Temporal Stability Analysis for Hydromagnetic Flow in a Channel Filled with a Saturated Porous Medium

Makinde

Mhone

2008

Flow Turbulence Combust

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In this paper, a linear stability analysis is presented to trace the time evolution of an infinitesimal, two-dimensional disturbance imposed on the base flow of an electrically conducting fluid in a channel filled with a saturated porous medium under the influence of a transversely imposed magnetic field. An eigenvalue problem is obtained and solved numerically using the Chebyshev collocation spectral method. The critical Reynolds number Re c , the critical wave number α c and the critical wave speed c c are obtained for a wide range of the porous medium shape factor parameter S and Hartmann number H. It is found that an increase in the magnetic field intensity and a decrease in porous medium permeability have a stabilizing effect on the fluid flow.

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Derivation of Modified Reynolds Equation—A Porous Media Model

Cited by 34 publications

References 20 publications

Lubrication characteristics of a textured porous sliding bearing

Lubrication characteristics of a textured porous sliding bearing

Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings

On Temporal Stability Analysis for Hydromagnetic Flow in a Channel Filled with a Saturated Porous Medium

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