A phenomenological lubrication model for the entire Knudsen regime
نویسندگان
چکیده
Rarefied gas flows in thin film slider bearings are studied in a wide range of Knudsen numbers (Kn) at low Mach number (Ma) with the objective of developing simple physics-based semi-analytical models. A recently developed modified slip boundary condition for steady plane Couette flows and a generalized high-order velocity slip boundary condition, developed and validated earlier for pressure-driven flows, are used to derive a modified slip-corrected Reynolds lubrication equation in the entire Knudsen regime. In particular, we present results of velocity profiles, pressure distribution and load capacity for various slider-bearing configurations. In addition, we outline a method to accurately predict the drag force induced by air resistance to the track-access-motion of the sliders. The new model is validated by comparisons with numerical solutions of the generalized lubrication equation based on the two-dimensional linearized Boltzmann equation and direct simulation Monte Carlo (DSMC) results available in the literature. The model predicts the velocity profiles, pressure distribution, load capacity and skin friction with good accuracy for a wide range of Knudsen numbers for low subsonic compressible flows.
منابع مشابه
Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime
A complete mathematical description of oscillatory Couette flows within the framework of kinetic theory is not available in the literature. Motivated by this and their vast engineering applications, we present a parametric study of time-periodic oscillatory Couette flows using the unsteady direct simulation Monte Carlo ~DSMC! method. Computations are performed as a function of the Knudsen ~Kn! ...
متن کاملUsing Burnett Equations to Derive an Analytical Solution to Pressure-Driven Gas Flow and Heat Transfer in Micro-Couette Flow
The aim of the present study is deriving an analytical solution to incompressible thermal flow in a micro-Couette geometry in the presence of a pressure gradient using Burnett equations with first- and second-order slip boundary conditions. The lower plate of the micro-Couette structure is stationary, whereas the upper plate moves at a constant velocity. Non-dimensional axial velocity and tempe...
متن کاملFriction factor for aerosol fractal aggregates over the entire Knudsen range.
We develop an approach for computing the hydrodynamic friction tensor and scalar friction coefficient for an aerosol fractal aggregate in the transition regime. Our approach involves solving the Bhatnagar-Gross-Krook equation for the velocity field around a sphere and using the velocity field to calculate the force on each primary sphere in the aggregate due to the presence of the other spheres...
متن کاملReport: a Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales
Rarefied gas flows in channels, pipes, and ducts with smooth surfaces are studied in a wide ( ) ( ) range of Knudsen number Kn at low Mach number M with the objectiv e of dev eloping simple, physics-based models. Such flows are encountered in microelectromechanical systems ( ) MEMS , in nanotechnology applications , and in low-pressure env ironments. A new general boundary condition that accoun...
متن کاملMethodology for the Control of Wear of Journal Bearing Operating in Mixed Lubrication Regime
The journal bearings subjected to heavy load and slow speed operates in mixed lubrication regime causing contact between the interacting surfaces and resulting in wear. The complexity of wear behavior and lack of unifying theory/model make wear control very challenging. In the present research work, a methodology is outlined for the minimization of the wear of journal bearing operating in mixed...
متن کامل