Coupled Nonlinear Effects of Random Surface Roughness and Rarefaction on Slip Flow in Ultra-Thin Film Gas Bearing Lubrication

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Wen-Ming Zhang ◽  
Guang Meng ◽  
Zhi-Ke Peng ◽  
Di Chen
Keyword(s):  
Thin Film ◽  
Surface Roughness ◽  
Knudsen Number ◽  
Numerical Solutions ◽  
Slip Flow ◽  
Surface Profile ◽  
Linearized Boltzmann Equation ◽  
Rarefaction Effect ◽  
Gas Bearing ◽  
Ultra Thin Film

A mathematical model of gaseous slip flow in ultra-thin film gas bearings is numerically analyzed incorporating effects of surface roughness, which is characterized by fractal geometry. The Weierstrass-Mandelbrot (W-M) function is presented to represent the multiscale self-affine roughness of the surface. A modified Reynolds equation incorporating velocity slip boundary condition is applied for the arbitrary range of Knudsen numbers in the slip and transition regimes. The effects of bearing number, Knudsen number, geometry parameters of the bearing and roughness parameters on the complex flow behaviors of the gas bearing are investigated and discussed. Numerical solutions are obtained for various bearing configurations under the coupled effects of rarefaction and roughness. The results indicate that roughness has a more significant effect on higher Knudsen number (rarefaction effect) flows with higher relative roughness. Surface with larger fractal dimensions yield more frequency variations in the surface profile, which result in an obviously larger incremental pressure loss. The Poiseuille number increases not only with increasing of rarefaction effect but also with increasing the surface roughness. It can also be observed that the current study is in good agreement with solutions obtained from the linearized Boltzmann equation.

Thin Spacing Analysis for Head-Tape Interface

1996 ◽  
Vol 118 (4) ◽  
pp. 800-806 ◽  
Author(s):  
Kazuo Sakai ◽  
Yasumasa Nagawa ◽  
Koetsu Okuyama ◽  
Takao Terayama
Keyword(s):  
Surface Roughness ◽  
Boltzmann Equation ◽  
Flow Model ◽  
Slip Flow ◽  
First Order ◽  
Lubrication Equation ◽  
Linearized Boltzmann Equation ◽  
Deformation Equation ◽  
High Density Magnetic Recording ◽  
Average Flow Model

Very thin head-tape spacing, combining contact and floating conditions, is investigated for high density magnetic recording. A generalized lubrication equation, based on a linearized Boltzmann equation, is coupled with the tape deformation equation for analysis. Tape-surface roughness is also taken into account in the lubrication equation. The average flow model is adopted to analyzing tape-surface roughness. For very thin spacing conditions, it is found that the spacing based on the linearized Boltzmann equation is smaller than that based on first-order slip flow, and larger than that based on second-order slip flow. It is also found that considering tape-surface roughness reduces the calculated minimum spacing. Analytical results agreed with the experimental ones.

Comparison of Moving and Stationary Surface Roughness Effects on Bearing Performance, With Emphasis on High Knudsen Number Flow

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Knudsen Number ◽  
Multiple Scale ◽  
Air Bearing ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Wide Range ◽  
Transverse Roughness ◽  
Number Flow ◽  
Gas Bearing

Low clearance gas bearing applications require an understanding of surface roughness effects at increased levels of Knudsen number. Because very little information has been reported on the relative air-bearing influence of roughness location, this paper is focused on a comparison of the effects of moving and stationary striated surface roughness under high Knudsen number conditions. First, an appropriate lubrication equation will be derived based on multiple-scale analysis that extends the work of White (2010, “A Gas Lubrication Equation for High Knudsen Number Flows and Striated Rough Surfaces,” ASME J. Tribol., 132, p. 021701). The resulting roughness averaged equation, applicable for both moving and stationary roughness over a wide range of Knudsen numbers, allows an arbitrary striated roughness orientation with regard to both (1) the direction of surface translation and (2) the bearing coordinates. Next, the derived lubrication equation is used to analyze and compare the influences produced by a stepped transverse roughness pattern located on the moving and the stationary bearing surface of a wedge bearing geometry of variable inclination. Computed results are obtained for both incompressible and compressible lubricants, but with an emphasis on high Knudsen number flow. Significant differences in air-bearing performance are found to occur for moving versus stationary roughness.

Stress-density ratio slip-corrected Reynolds equation for ultra-thin film gas bearing lubrication

2002 ◽  
Vol 14 (4) ◽  
pp. 1450-1457 ◽  
Author(s):  
Eddie Yin-Kwee Ng ◽  
Ningyu Liu ◽  
Xiaohai Mao
Keyword(s):  
Thin Film ◽  
Reynolds Equation ◽  
Density Ratio ◽  
Gas Bearing ◽  
Ultra Thin Film

Experimental Investigation of Gas Flow in Microchannels

2004 ◽  
Vol 126 (5) ◽  
pp. 753-763 ◽  
Author(s):  
Stephen E. Turner ◽  
Lok C. Lam ◽  
Mohammad Faghri ◽  
Otto J. Gregory
Keyword(s):  
Surface Roughness ◽  
Experimental Investigation ◽  
Mach Number ◽  
Friction Factor ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Reynolds Numbers ◽  
Channel Length ◽  
Limiting Case

This paper presents an experimental investigation of laminar gas flow through microchannels. The independent variables: relative surface roughness, Knudsen number and Mach number were systematically varied to determine their influence on the friction factor. The microchannels were etched into silicon wafers, capped with glass, and have hydraulic diameters between 5 and 96 μm. The pressure was measured at seven locations along the channel length to determine local values of Knudsen number, Mach number and friction factor. All measurements were made in the laminar flow regime with Reynolds numbers ranging from 0.1 to 1000. The results show close agreement for the friction factor in the limiting case of low Ma and low Kn with the incompressible continuum flow theory. The effect of compressibility is observed to have a mild (8 percent) increase in the friction factor as the Mach number approaches 0.35. A 50 percent decrease in the friction factor was seen as the Knudsen number was increased to 0.15. Finally, the influence of surface roughness on the friction factor was shown to be insignificant for both continuum and slip flow regimes.

Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip-Flow Model and Considering Surface Accommodation Coefficient

1993 ◽  
Vol 115 (2) ◽  
pp. 289-294 ◽  
Author(s):  
Y. Mitsuya
Keyword(s):  
Thin Film ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Second Order ◽  
Flow Models ◽  
Gas Lubrication ◽  
Modified Reynolds Equation ◽  
Ultra Thin Film

A 1.5-order modified Reynolds equation for solving the ultra-thin film gas lubrication problem is derived by using an accurate higher-order slip-flow model. This model features two key differences from the current second-order slip-flow model. One is the involvement of an accommodation coefficient for momentum. The other is that the coefficient of the second-order slip-flow term is 4/9 times smaller than that for the current model. From the physical consideration of momentum transfer, the accommodation coefficient is found to have no affect on the second-order slip-flow term. Numerical calculations using the 1.5-order modified Reynolds equation are performed. The results are compared with those obtained using three kinds of currently employed modified Reynolds equations: those employing the first- and second-order slip-flow models and those utilizing the Boltzmann equation. These comparisons confirm that the present modified Reynolds equation provides intermediate characteristics between those derived from the first- and second-order slip-flow models, and produces an approximation closer to the exact solution resulting from the Boltzmann-Reynolds equation.

scholarly journals Numerical Investigation of Thin Film Spreading Driven by Surfactant Using Upwind Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
E. Momoniat ◽  
M. M. Rashidi ◽  
R. S. Herbst
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Time Derivative ◽  
Surface Profile ◽  
Coupled System ◽  
Upwind Scheme ◽  
Upwind Schemes ◽  
Free Surface Profile

Numerical solutions of a coupled system of nonlinear partial differential equations modelling the effects of surfactant on the spreading of a thin film on a horizontal substrate are investigated. A CFL condition is obtained from a von Neumann stability analysis of a linearised system of equations. Numerical solutions obtained from a Roe upwind scheme with a third-order TVD Runge-Kutta approximation to the time derivative are compared to solutions obtained with a Roe-Sweby scheme coupled to a minmod limiter and a TVD approximation to the time derivative. Results from both of these schemes are compared to a Roe upwind scheme and a BDF approximation to the time derivative. In all three cases high-order approximations to the spatial derivatives are employed on the interior points of the spatial domain. The Roe-BDF scheme is shown to be an efficient numerical scheme for capturing sharp changes in gradient in the free surface profile and surfactant concentration. Numerical simulations of an initial exponential free surface profile coupled with initial surfactant concentrations for both exogenous and endogenous surfactants are considered.

Reduction of Wind Disturbance by Optimizing the Drive Current of Pt Ultra-thin Film Hydrogen Sensor

2020 ◽  
Vol 140 (4) ◽  
pp. 92-96
Author(s):  
Yuto Goda ◽  
Hiroto Shobu ◽  
Kenji Sakai ◽  
Toshihiko Kiwa ◽  
Kenji Kondo ◽  
...  
Keyword(s):  
Thin Film ◽  
Hydrogen Sensor ◽  
Wind Disturbance ◽  
Drive Current ◽  
Ultra Thin Film
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