Averaged Reynolds Equation Extended to Gas Lubrication Possessing Surface Roughness in the Slip Flow Regime: Approximate Method and Confirmation Experiments

1989 ◽  
Vol 111 (3) ◽  
pp. 495-503 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo ◽  
H. Ota
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Approximate Method ◽  
Flow Regime ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Roughness Effects ◽  
Gas Lubrication ◽  
Slip Flow Regime ◽  
Average Film Thickness

The average film thickness theory is extended to gas lubrication possessing surface roughness in the slip flow regime. A simplified averaged Reynolds equation is derived and its applicability is confirmed through comparing with experiments. This averaging equation makes use of the mixed average film thickness defined as Havem = αHm + (1 − α)Hmˆ, where m = 1, 2 and 3; α indicates the mixing ratio; and H¯ and Hˆ denote the arithmetically and harmonically averaged film thicknesses. The experiments were performed using computer flying heads having precisely photolithography-fabricated longitudinal, transverse or checkered pattern roughnesses under submicron spacing conditions. From the excellent agreement obtained between the calculated and experimental results, it can be concluded that the assumption that velocity slippage occurs along the surface even if roughnes is present is justified, and that the approximate method is applicable for determining the surface roughness effects in the slip flow regime.

Roughness Effect on the Heat Transfer Coefficient for Gaseous Flow in Microchannels

2010 ◽  
Author(s):  
Metin B. Turgay ◽  
Almila G. Yazicioglu ◽  
Sadik Kakac
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Nusselt Number ◽  
Flow Regime ◽  
Viscous Dissipation ◽  
Slip Flow ◽  
Roughness Height ◽  
Working Fluid ◽  
Axial Conduction ◽  
Slip Flow Regime

Effects of surface roughness, axial conduction, viscous dissipation, and rarefaction on heat transfer in a two–dimensional parallel plate microchannel with constant wall temperature are investigated numerically. Roughness is simulated by adding equilateral triangular obstructions with various heights on one of the plates. Air, with constant thermophysical properties, is chosen as the working fluid, and laminar, single-phase, developing flow in the slip flow regime at steady state is analyzed. Governing equations are solved by finite element method with tangential slip velocity and temperature jump boundary conditions to observe the rarefaction effect in the microchannel. Viscous dissipation effect is analyzed by changing the Brinkman number, and the axial conduction effect is analyzed by neglecting and including the corresponding term in the energy equation separately. Then, the effect of surface roughness on the Nusselt number is observed by comparing with the corresponding smooth channel results. It is found that Nusselt number decreases in the continuum case with the presence of surface roughness, while it increases with increasing roughness height in the slip flow regime, which is also more pronounced at low-rarefied flows (i.e., around Kn = 0.02). Moreover, the presence of axial conduction and viscous dissipation has increasing effects on heat transfer with increasing roughness height. Even in low velocity flows, roughness increases Nusselt number up to 33% when viscous dissipation is considered.

Hydrothermal performance analysis of various surface roughness configurations in trapezoidal microchannels at slip flow regime

2020 ◽  
Vol 28 (6) ◽  
pp. 1522-1532 ◽  
Author(s):  
Davood Toghraie ◽  
Ramin Mashayekhi ◽  
Mohammadreza Niknejadi ◽  
Hossein Arasteh
Keyword(s):  
Surface Roughness ◽  
Performance Analysis ◽  
Flow Regime ◽  
Slip Flow ◽  
Slip Flow Regime

Surface Roughness Effects on Fluid Flow between Two Rotating Cylinders

2015 ◽  
Vol 642 ◽  
pp. 275-280
Author(s):  
Sutthinan Srirattayawong ◽  
Shian Gao
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Profile ◽  
Fluid Film ◽  
Real Surface ◽  
Contact Center ◽  
Roughness Effects ◽  
Fluid Film Thickness ◽  
Lubricant Viscosity

In general, the thin fluid film problems are explained by the classical Reynolds equation, but this approach has some limitations. To overcome them, the method of Computational Fluid Dynamics (CFD) is used in this study, as an alternative to solving the Reynolds equation. The characteristics of the two cylinders contact with real surface roughness are investigated. The CFD model has been used to simulate the behavior of the fluid flows at the conjunction between two different radius cylinders. The non-Newtonian fluid is employed to calculate the lubricant viscosity, and the thermal effect is also considered in the evaluation of the lubricant properties. The pressure distributions, the fluid film thickness and the temperature distributions are investigated. The obtained results show clearly the significance of the surface roughness on the lubricant flow at the contact center area. The fluctuated flow also affects the pressure distribution, the temperature and the lubricant viscosity in a similar pattern to the rough surface profile. The surface roughness effect will decrease when the film thickness is increased.

Application of Average Flow Model to Thin Film Gas Lubrication

1993 ◽  
Vol 115 (1) ◽  
pp. 185-190 ◽  
Author(s):  
T. Makino ◽  
S. Morohoshi ◽  
S. Taniguchi
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Mean Free Path ◽  
Perturbation Approach ◽  
Roughness Effects ◽  
Load Carrying ◽  
Gas Lubrication ◽  
Induced Flow ◽  
Average Film Thickness ◽  
Average Flow Model

The flow factors for the average Reynolds equation introduced by Patir and Cheng (1978, 1979) are extended to be valid for thin film gas lubrication. The effects of molecular mean free-path on the roughness-induced flow factors are included on the assumption that the local compressibility is small. The derivation of flow factors is carried out by means of the perturbation approach developed by Tripp (1983). The results are expressed in terms of Knudsen number, Peklenik parameter and nondimensional film thickness defined as the ratio of average film thickness and standard deviation of composite roughness. Two-dimensional roughness effects on the load-carrying capacity of a gas lubricated finite slider are also investigated.

DDC Lubrication: A New Concept in Tribology

1992 ◽  
Vol 114 (1) ◽  
pp. 181-185 ◽  
Author(s):  
K. To̸nder
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Gap Function ◽  
Upper And Lower Bounds ◽  
Roughness Effects ◽  
Cavity Depth ◽  
Roughness Amplitude ◽  
Previously Treated ◽  
The Mean ◽  
Expansion Scheme

A new lubrication concept is presented, Deep Disconnected Cavities. It differs from the lubrication of microcavities, previously treated by other authors, by the deepness of the cavities. The validity of Reynolds’ equation and nonturbulent conditions are assumed. By a Taylor expansion scheme, it is shown that the roughness effects are expressible in terms of roughness factors modifying the Reynolds equation, similar to those proposed by Patir and Cheng (1978). Unlike those established for ordinary roughness, the DDC factors are independent of local film thickness and roughness amplitude (cavity depth), and may therefore be used to modify standard hydro-dynamic parameters. By a different mathematical approach, involving upper and lower bounds on the various hydrodynamic quantities, it is found that Reynolds’ equation and all the other hydrodynamic expressions may be written just as for smooth surfaces, with the following modifications: 1. The film thickness should be expressed by the minimum gap function, and not by the mean gap function. 2. There are, in general, three effective viscosities, lower than the physical one, two of which are associated with the x and y directions respectively and appear in the modified Reynolds equation as well as in the flow terms. The third one appears only in the expression for shear stress.

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