Numerical Solution to Reynolds Equation for Micro Gas Journal Bearings

2012 ◽  
Vol 466-467 ◽  
pp. 991-994
Author(s):  
Qin Yang ◽  
Hai Jun Zhang
Keyword(s):  
Boundary Condition ◽  
Reynolds Equation ◽  
Effective Means ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
First Order ◽  
Slip Boundary ◽  
Pressure Profiles ◽  
The Finite Difference Method ◽  
Modified Reynolds Equation

Reynolds equation for gas bearings is a nonlinear partial differential one and its analytical solution usually is difficult to obtain. Therefore numerical method is an effective means to investigate the performance of gas-lubricated journal bearings. In this paper, firstly the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution for micro gas journal bearings under different reference Knudsen numbers. Numerical analysis shows that the pressure profiles for micro gas journal bearings decrease obviously with the reference Knudsen number increasing.

Study on the Performance of Gas Journal Bearings for Power MEMS

2011 ◽  
Vol 483 ◽  
pp. 635-639
Author(s):  
Hai Jun Zhang ◽  
Qin Yang
Keyword(s):  
Boundary Condition ◽  
Knudsen Number ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Slip Boundary ◽  
Attitude Angle ◽  
Pressure Profiles ◽  
Power Mems ◽  
Modified Reynolds Equation

Gas journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in Power MEMS deriving from the extremely shallow structures. With the reference Knudsen number being included, the modified Reynolds equation for gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The boundary condition for modified Reynolds equation is given. The numerical method is employed to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles of gas journal bearings for Power MEMS under different reference Knudsen numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with the reference Knudsen number increasing, and the attitude angle changes conversely. Moreover, when the eccentricity ratio is smaller, the effect of gas rarefaction on the attitude angle is less.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

Numerical Simulation of Newtonian Fluid Flow in a T-Channel with no Slip/Slip Boundary Conditions on a Solid Wall

2017 ◽  
Vol 743 ◽  
pp. 480-485
Author(s):  
Evgeny Borzenko ◽  
Olga Dyakova
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Solid Wall ◽  
Simple Procedure ◽  
Slip Boundary Condition ◽  
Navier Slip ◽  
Slip Boundary ◽  
Pressure Profiles ◽  
Slip Yield Stress ◽  
Solid Walls

The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three fluid interaction models with solid walls are considered: no slip boundary condition, Navier slip boundary condition and slip boundary condition with slip yield stress. The fluid flow is provided by uniform pressure profiles at the boundary sections of the channel. The problem is numerically solved using a finite difference method based on the SIMPLE procedure. Characteristic flow regimes have been found for the described models of liquid interaction with solid walls. The estimation of the influence of the Reynolds number, pressure applied to the boundary sections and the parameters of these models on the flow pattern was performed. The criterial dependences describing main characteristics of the flow under conditions of the present work have been demonstrated.

The half-wetted bearing. Part 1: Extended Reynolds equation

2003 ◽  
Vol 217 (1) ◽  
pp. 1-14 ◽  
Author(s):  
H. A. Spikes
Keyword(s):  
Boundary Condition ◽  
Solid Surface ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Critical Shear Stress ◽  
Slip Boundary Condition ◽  
Low Friction ◽  
Slip Boundary ◽  
Lubrication Condition ◽  
Bearing Part

Recent research has shown that, when a liquid is partially wetting or non-wetting against a very smooth solid surface, the conventional no-slip boundary condition can break down. Under such circumstances, the Reynolds equation is no longer applicable. In the current paper, the Reynolds equation is extended to consider the sliding, hydrodynamic lubrication condition where the lubricant has a no-slip boundary condition against the moving solid surface but can slip at a critical shear stress against the stationary surface. It is shown that such a ‘half-wetted’ bearing is able to combine good load support resulting from fluid entrainment with very low friction due to very low or zero Couette friction.

Investigating the effect of different slip zone locations on the lubrication performance of textured journal bearings

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Arif ◽  
Saurabh Kango ◽  
Dinesh Kumar Shukla
Keyword(s):  
Boundary Condition ◽  
Carrying Capacity ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Load Carrying Capacity ◽  
Inflow Rate ◽  
Content Type ◽  
Surface Textures ◽  
Slip Boundary ◽  
Load Carrying

Purpose This study aims to purpose the suitable location of slip boundary condition and microscale surface textures to enhance the tribological performance of the hydrodynamic journal bearings. Design/methodology/approach Mass conserving Elrod cavitation algorithm with considering slip boundary condition has been used for predicting the static performance characteristics (load carrying capacity, coefficient of friction and volumetric inflow rate) of finite cylindrical shape textured journal bearings. Findings It has been observed that the full textured bearing with slip boundary condition in between 0°–180° circumferential region gives a significant reduction in the lubricant rupture zone. However, the introduction of textures up to the interface of slip and the no-slip region is increasing the load-carrying capacity and reduces the shear stress. This reduction in shear stress with combined slip and surface textures is effective in increasing the volumetric inflow rate of the lubricant. Practical implications The combined effect of slip boundary condition and surface texturing is increasing the scope of liquid lubricants in hydrodynamic journal bearings and further contributing toward the development of small-scale rotating machines. Originality/value The study related to the use of mass conserving Elrod cavitation algorithm for finding the optimum location of slip and surface texture zones has been found rare in the literature. Previous studies show that the mass conserving Elrod cavitation algorithm gives realistic results for textured bearings and its findings show good agreement with the experimental observations.

A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

2014 ◽  
Vol 6 (06) ◽  
pp. 811-829 ◽  
Author(s):  
X. Wang ◽  
C. Shu ◽  
J. Wu ◽  
L. M. Yang
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Delta Function ◽  
Slip Boundary Condition ◽  
Immersed Boundary ◽  
First Order ◽  
Slip Boundary ◽  
Boltzmann Method

AbstractA boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

Rarefaction Effect on the Characteristics of Micro Gas Journal Bearings

2009 ◽  
Author(s):  
Haijun Zhang ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

Journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in MEMS deriving from the extremely shallow structures. Thus, the micro gas journal bearings are characterized by a very small length-diameter ratio, defined as the ratio of the bearing length to its diameter and a paradoxically large bearing clearance ratio, defined as the ratio of the average radial clearance to the bearing radius. Given the definition of the reference Knudsen number for micro gas journal bearings, the range of the reference Knudsen number is illustrated according to the viscosity values of air under different temperatures. With the reference Knudsen number being included, the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution, load capacities and attitude angles for micro gas journal bearings under different reference Knudsen numbers, bearing numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with gas rarefaction strengthened, and the attitude angle changes conversely. Moreover, when the bearing number is smaller, the effect of gas rarefaction on the non-dimensional load capacity and attitude angle is less.

A kinetic-theory based first order slip boundary condition for gas flow

2007 ◽  
Vol 19 (8) ◽  
pp. 086101 ◽  
Author(s):  
Sheng Shen ◽  
Gang Chen ◽  
Robert M. Crone ◽  
Manuel Anaya-Dufresne
Keyword(s):  
Boundary Condition ◽  
Kinetic Theory ◽  
Gas Flow ◽  
Slip Boundary Condition ◽  
First Order ◽  
Slip Boundary

A Kinetic Theory-Based First-Order Slip Boundary Condition for Gas Micro/Nano-Flows with Heat Transfer

2010 ◽  
Vol 224 (11) ◽  
pp. 2390-2395 ◽  
Author(s):  
R Kamali ◽  
A Kharazmi ◽  
M Akbari
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Kinetic Theory ◽  
Slip Boundary Condition ◽  
Constant Heat Flux ◽  
Interactive Effects ◽  
Constant Wall Temperature ◽  
First Order ◽  
Slip Boundary ◽  
Thermal Boundary Conditions

A kinetic theory-based first-order slip boundary condition for micro/nano-gas flows with heat transfer is presented analytically using the Chapman—Enskog solution of the Boltzmann equation. This slip model is investigated by studying heat transfer for laminar Newtonian fluid in a Poiseuille flow. The problem is solved for two different thermal boundary conditions, namely, constant heat flux and constant wall temperature with different Knudsen numbers. The interactive effects of the Knudsen number on the Nusselt numbers are determined analytically, and for both cases, the temperature profile and the Nusselt number are compared with previous published results.

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