On the effects of two-dimensional Reynolds roughness in hydrodynamic lubrication

1978 ◽  
Vol 364 (1716) ◽  
pp. 89-106 ◽  
Keyword(s):  
Surface Roughness ◽  
Numerical Computation ◽  
Autocorrelation Function ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
The Other ◽  
Roughness Height ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Dimensional Surface

The hydrodynamic lubrication of rough surfaces is analysed with the Reynolds equation, whose application requires the roughness spacing to be large, and the roughness height to be small, compared with the thick­ness of the fluid film. The general two-dimensional surface roughness is considered, and results applicable to any roughness structure are obtained. It is revealed analytically that two types of term contribute to roughness effects: one depends on the shape of the autocorrelation function and the other does not. The former contribution was neglected by previous workers. The numerical computation of an example shows that these two contributions are comparable in magnitude.

A Lubrication Equation Incorporating Two-Dimensional Roughness Effects, With Emphasis on the Patterned Data Islands of a Recording Disk

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Multiple Scale ◽  
Industrial Applications ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Design And Optimization ◽  
Lubrication Equation ◽  
Wide Range ◽  
Level Of Understanding ◽  
Dimensional Surface

Current industrial applications require a consideration of two-dimensional surface roughness effects in design and optimization of fluid bearings. Although the influence of striated surface roughness on fluid lubrication is now at a fairly mature level of understanding, the knowledge and understanding of two-dimensional roughness effects is not nearly at the same level as that achieved over the past several decades for one-dimensional striations. The subject of this paper includes the formulation of a practical “roughness averaged” lubrication equation that is appropriate for two-dimensional surface roughness and applicable over a wide range of Knudsen numbers. After derivation by multiple-scale analysis, the resulting lubrication equation is specialized to treat the patterned data islands located on a storage medium as a two-dimensional roughness pattern, and then used to determine the effect of this roughness on the air-bearing interface between recording head slider and disk. The roughness averaged lubrication equation is solved numerically by a variable-grid finite-difference algorithm, and computed results are included for several bearing geometries.

scholarly journals Surface Roughness Effects in Hydrodynamic Lubrication: The Flow Factor Method

1983 ◽  
Vol 105 (3) ◽  
pp. 458-463 ◽  
Author(s):  
J. H. Tripp
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Flow Model ◽  
Hydrodynamic Lubrication ◽  
Perturbation Expansion ◽  
Ensemble Averaging ◽  
Roughness Effects ◽  
Average Flow ◽  
Point Correlation ◽  
Average Flow Model

The average flow model of Patir and Cheng [1, 2] for obtaining an average Reynolds equation in the presence of two dimensional surface roughness is extended and generalized. Expectation values of the flow factors appearing in the formalism are calculated by means of a perturbation expansion of the pressure in a nominal parallel film. Terms in the series are evaluated using the unperturbed Green function, which permits ensemble averaging to be performed directly on the solution. Calculations are carried to second order, which involves only two point correlation functions of the two rough surfaces. Perturbation results agree well with results of the earlier numerical simulation until surface contact becomes important when both approaches are inadequate. The theory displays the dependence of the flow factors on the roughness parameters in simple closed form, leading to improved understanding of the average flow method.

An Evaluation of the Average Flow Model [1] for Surface Roughness Effects in Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 360-366 ◽  
Author(s):  
J. L. Teale ◽  
A. O. Lebeck
Keyword(s):  
Surface Roughness ◽  
Flow Model ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Important Conclusion ◽  
Average Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Average Flow Model

The average flow model presented by Patir and Cheng [1] is evaluated. First, it is shown that the choice of grid used in the average flow model influences the results. The results presented are different from those given by Patir and Cheng. Second, it is shown that the introduction of two-dimensional flow greatly reduces the effect of roughness on flow. Results based on one-dimensional flow cannot be relied upon for two-dimensional problems. Finally, some average flow factors are given for truncated rough surfaces. These can be applied to partially worn surfaces. The most important conclusion reached is that an even closer examination of the average flow concept is needed before the results can be applied with confidence to lubrication problems.

Wavefronts, light rays and caustic associated with the refraction of a plane wavefront by a conospherical lens

2021 ◽  
Author(s):  
José Israel Galindo-Rodríguez ◽  
Gilberto Silva-Ortigoza
Keyword(s):  
Optical Axis ◽  
Spherical Surface ◽  
Bessel Beam ◽  
Optical Element ◽  
The Other ◽  
Two Dimensional ◽  
Light Rays ◽  
Plane Wavefront ◽  
The Relationship ◽  
Dimensional Surface

Abstract The aim of the present work is to introduce a lens whose faces are a conical surface and a spherical surface. We illuminate this lens by a plane wavefront and its associated refracted wavefronts, light rays and caustic are computed. We find that the caustic region has two branches and can be virtual, real or one part virtual and the other real, depending on the values of the parameters characterizing the lens. Furthermore, we present a particular example where one of the branches of the caustic region is constituted by two segments of a line, one part is real and the other one virtual. The second branch is a two-dimensional surface with a singularity of the cusp ridge type such that its Gaussian curvature is different from zero. It is important to remark that for this example, the two branches of the caustic are disconnected. Because of this property and the result obtained by Berry and Balazs on the relationship between the acceleration of an Airy beam and the curvature of its corresponding caustic, we believe that using this optical element one could generate a scalar optical accelerating beam in the region where the caustic is a two-dimensional surface of revolution, and at the same time a scalar optical beam with similar properties to the Bessel beam of zero order in the region were the real caustic is a segment of a line along the optical axis.

Calculation of Surface Roughness Effects on Air-Riding Seals

2002 ◽  
Author(s):  
C. Guardino ◽  
J. W. Chew ◽  
N. J. Hills
Keyword(s):  
Surface Roughness ◽  
Compressible Flows ◽  
Reynolds Equation ◽  
Incompressible Flows ◽  
Numerical Solutions ◽  
Cfd Analysis ◽  
Roughness Effects ◽  
Stationary Wall ◽  
Comparative Results ◽  
Effect Of Surface

The effects of surface roughness on air-riding seals are investigated here using the Rayleigh-pad as an example. Both incompressible and compressible flows are considered using both CFD analysis and analytical/numerical solutions of the Reynolds equation for various 2D or 3D roughness patterns on the stationary wall. A ‘unit-based’ approach for incompressible flows has also been employed and is shown to be computationally much less expensive than the full-geometry solution. Results are presented showing the effect of surface roughness on the net lift force. The effects of varying the Reynolds number are demonstrated, as well as comparative results for static stiffness.

Measurements and Prediction of the Effects of Surface Roughness on Profile Losses and Deviation in a Turbine Cascade

1998 ◽  
Vol 120 (1) ◽  
pp. 20-27 ◽  
Author(s):  
R. J. Kind ◽  
P. J. Serjak ◽  
M. W. P. Abbott
Keyword(s):  
Surface Roughness ◽  
Three Dimensional ◽  
Leading Edge ◽  
Computational Method ◽  
Roughness Height ◽  
Surface Boundary ◽  
Turbine Cascade ◽  
Suction Surface ◽  
Roughness Effects ◽  
Profile Losses

Measurements of pressure distributions, profile losses, and flow deviation were carried out on a planar turbine cascade in incompressible flow to assess the effects of partial roughness coverage of the blade surfaces. Spanwise-oriented bands of roughness were placed at various locations on the suction and pressure surfaces of the blades. Roughness height, spacing between roughness elements, and band width were varied. A computational method based on the inviscid/viscous interaction approach was also developed; its predictions were in good agreement with the experimental results. This indicates that good predictions can be expected for a variety of cascade and roughness configurations from any two-dimensional analysis that couples an inviscid method with a suitable rough surface boundary-layer analysis. The work also suggests that incorporation of the rough wall skin-friction law into a three-dimensional Navier–Stokes code would enable good predictions of roughness effects in three-dimensional situations. Roughness was found to have little effect on static pressure distribution around the blades and on deviation angle, provided that it does not precipitate substantial flow separation. Roughness on the suction surface can cause large increases in profile losses; roughness height and location of the leading edge of the roughness band are particularly important. Loss increments due to pressure-surface roughness are much smaller than those due to similar roughness on the suction surface.

A unified theory of surface roughness

1984 ◽  
Vol 393 (1804) ◽  
pp. 133-157 ◽  
Keyword(s):  
Surface Roughness ◽  
Rough Surface ◽  
Random Noise ◽  
Sampling Interval ◽  
The Other ◽  
Real Surface ◽  
Unified Theory ◽  
Two Dimensional ◽  
Minor Degree ◽  
A Minor

The properties of the peaks and summits of a rough surface are predicted on the assumption that the surface is two-dimensional random noise. The important result is that, in non-dimensional form, the answers depend only to a minor degree on the parameters describing the surface or on the sampling interval used: on the other hand the absolute values are strongly dependent on the sampling interval. Experimental results on a real surface agree remarkably well with the predictions.

scholarly journals Hydrodynamic lubrication of rough surfaces

1982 ◽  
Vol 383 (1785) ◽  
pp. 439-446 ◽  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Rough Surfaces ◽  
Homogenization Method ◽  
Squeeze Film ◽  
Spatial Average

Using the two-space homogenization method we derive an averaged Reynolds equation that is correct to O (< H 6 > — < H 3 > 2 ), where H is the total film thickness and the angle brackets denote a spatial average. Applications of this mean Reynolds equation to a squeeze-film bearing with a sinusoidal or an isotropic surface roughness are discussed.

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