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.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
3D Simulations ◽  
Slip Boundary ◽  
Wall Shear

This study forms part of a program to develop a micro-electro-mechanical systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump, the flow can still be treated as a continuum; however, the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant nondimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases, slip-flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001 and 0.1 with reasonable agreement found. The method of specifying the wall shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional (2D) simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear, and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition, it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified-shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional (3D) simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring 3D simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present, this relationship was far weaker.

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.

Hygro-thermo-mechanical vibration of two vertically aligned single-walled boron nitride nanotubes conveying fluid

2021 ◽  
pp. 107754632110065
Author(s):  
Yalda Zarabimanesh ◽  
Pouyan Roodgar Saffari ◽  
Peyman Roudgar Saffari ◽  
Nima Refahati
Keyword(s):  
Boundary Condition ◽  
Boron Nitride ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Slip Boundary Condition ◽  
Boron Nitride Nanotubes ◽  
Strain Gradient Theory ◽  
Slip Boundary ◽  
Vertically Aligned ◽  
Nonlocal Strain Gradient

The nonlocal strain gradient theory, when combined with the first-order shear deformation theory, provides many capabilities in size-dependent structures. The aim of the present study is evaluation of the free vibration behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes in hygrothermal environments considering slip boundary condition based on Knudsen number. These two adjacent nanotubes are coupled in the context of linear deformation through van der Waals interaction according to Lennard–Jones potential function. Actually, the contribution of the present work, compared with those previously reported, is investigating the simultaneous effect of hygrothermal loading and slip boundary condition on the dynamic behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes. As an additional step to achieve a more accurate model of low-scale structures, both hardening and softening effects of materials are taken as important variables in the nonlocal strain gradient approach. To derive the motion equations and associated boundary conditions, Hamilton’s variational principle is used. The equations are then solved with the aid of differential quadrature method. Numerical studies are also performed to depict the effects of a number of parameters such as boundary conditions, size scale, aspect ratio, inter-tube distance, and temperature alteration on the variations of dimensionless eigenfrequency and critical flow velocity.

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.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2013 ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Three Dimensional ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Three Dimensional Simulations

This study forms part of a program to develop a micro-electro-mechanical-systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump the flow can still be treated as a continuum however the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant non-dimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases slip flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001–0.1 with reasonable agreement found. The method of specifying the wall-shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring three-dimensional simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present this relationship was far weaker.

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