Subsonic gas flow in a straight and uniform microchannel

2002 ◽  
Vol 472 ◽  
pp. 125-151 ◽  
Author(s):  
YITSHAK ZOHAR ◽  
SYLVANUS YUK KWAN LEE ◽  
WING YIN LEE ◽  
LINAN JIANG ◽  
PIN TONG
Keyword(s):  
Gas Flow ◽  
Theoretical Calculations ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Perturbation Expansions ◽  
Slip Boundary ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
Flow Effects

A nonlinear equation based on the hydrodynamic equations is solved analytically using perturbation expansions to calculate the flow field of a steady isothermal, compressible and laminar gas flow in either a circular or a planar microchannel. The solution takes into account slip-flow effects explicitly by utilizing the classical velocity-slip boundary condition, assuming the gas properties are known. Consistent expansions provide not only the cross-stream but also the streamwise evolution of the various flow parameters of interest, such as pressure, density and Mach number. The slip-flow effect enters the solution explicitly as a zero-order correction comparable to, though smaller than, the compressible effect. The theoretical calculations are verified in an experimental study of pressure-driven gas flow in a long microchannel of sub-micron height. Standard micromachining techniques were utilized to fabricate the microchannel, with integral pressure microsensors based on the piezoresistivity principle of operation. The integrated microsystem allows accurate measurements of mass flow rates and pressure distributions along the microchannel. Nitrogen, helium and argon were used as the working fluids forced through the microchannel. The experimental results support the theoretical calculations in finding that acceleration and non-parabolic velocity profile effects were found to be negligible. A detailed error analysis is also carried out in an attempt to expose the challenges in conducting accurate measurements in microsystems.

A Friction Factor Correlation for Gas Flow in Parallel Plate Microchannels by Considering Combined Effects of Compressibility and Rarefaction

2008 ◽  
Author(s):  
Xiaohong Yan ◽  
Qiuwang Wang
Keyword(s):  
Friction Factor ◽  
Velocity Gradient ◽  
Parallel Plate ◽  
Gas Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Combined Effects ◽  
Slip Boundary

The effects of compressibility and rarefaction for gas flow in microchannels have been extensively studied separately. However, these two effects are always combined for gas flow in microchannels. In this paper, the two-dimensional compressible Navier-Stokes equations are solved for gas flow in parallel plate channels with a slip boundary condition to study the combined effects of compressibility and rarefaction on the friction factor. The numerical methodology is based on the control volume finite difference scheme. It is found that the effect of compressibility increases the velocity gradient near the wall which then increases the friction factor. On the other hand, increasing the velocity gradient near the wall leads to a much larger slip velocity and implies a stronger rarefaction effect and a corresponding decrease in the friction factor. These two opposite effects make the effect of compressibility on friction factor for slip flow weaker than that for no-slip compressible flow. A correlation among fRe, Kn and Ma is presented. The correlation is validated with available experimental and analytical results.

scholarly journals Slip Flow of Kerosene Oil Based SWCNT Nanofluid over Stretching Sheet with Radiation and Suction/Injection Effects

2021 ◽  
Vol 6 (3) ◽  
pp. 860-877
Author(s):  
Susheela Chaudhary ◽  
Kiran Kunwar Chouhan ◽  
Santosh Chaudhary
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Skin Friction Coefficient ◽  
Single Wall Carbon Nanotubes ◽  
Local Skin ◽  
Slip Boundary ◽  
Similarity Transformations

Present study numerically investigates a two dimensional steady laminar boundary layer nanofluid flow of single-wall carbon nanotubes (SWCNTs) immersed into kerosene oil, due to a linearly stretched sheet. Flow is subjected to the slip boundary condition and suction/injection effects. Employing suitable similarity transformations, governing PDEs of the arising problem are converted into coupled nonlinear non-dimensional ordinary differential equations. A set of obtained ODEs with assisting boundary conditions is solved numerically by applying finite element method (FEM). Effect of pertinent factors, velocity slip parameter, suction/injection parameter and solid volume fraction parameter on non-dimensional velocity and temperature profiles are characterized graphically. In addition, physical emerging parameters, local Nusselt’s number and local skin friction coefficient are computed and presented via table. Furthermore, derived numerical values of shear stress and heat flux at the surface are compared with previously published results.

Liquid Leak Predictions in Micro- and Nanoporous Gaskets

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Experimental Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Gas Leak ◽  
Flow Through

In recent years, quite few experimental and theoretical studies have been conducted to predict gas leak rate through gaskets. However, a very limited work is done on liquid leak rates through gaskets. The slip flow model is used to predict liquid flow through porous gaskets based on measurements of gas flow at different pressures. In fact, an extrapolation of the porosity parameter approach (Grine, L., and Bouzid, A., 2009, “Correlation of Gaseous Mass Leak Rates Through Micro and Nano-Porous Gaskets,” ASME Paper No. PVP2009-77205) used to correlate leak rates between different gases is used to predict liquid leak rates. In the present article, an analytical-computational methodology based on the number and pore size to predict liquid micro- and nanoflows in the slip flow regime through gaskets is presented. The formulation is based on the Navier–Stokes equations associated with slip boundary condition at the wall. The mass leak rates through a gasket considered as a porous media under various experimental conditions of fluid media, pressure, and gasket stress were conducted on a special gasket test rig. Gaseous and liquid leaks are measured and comparisons with the analytical predictions are made.

scholarly journals Numerical Study of Nanoparticle Deposition in a Gaseous Microchannel under the Influence of Various Forces

Micromachines ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 47
Author(s):  
Fubing Bao ◽  
Hanbo Hao ◽  
Zhaoqin Yin ◽  
Chengxu Tu
Keyword(s):  
Drag Force ◽  
Particle Deposition ◽  
Gas Flow ◽  
Numerical Study ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Deposition Efficiency ◽  
Nanoparticle Deposition ◽  
Thermophoretic Force ◽  
Slip Boundary

Nanoparticle deposition in microchannel devices inducing contaminant clogging is a serious barrier to the application of micro-electro-mechanical systems (MEMS). For micro-scale gas flow fields with a high Knudsen number (Kn) in the microchannel, gas rarefaction and velocity slip cannot be ignored. Furthermore, the mechanism of nanoparticle transport and deposition in the microchannel is extremely complex. In this study, the compressible gas model and a second-order slip boundary condition have been applied to the Burnett equations to solve the flow field issue in a microchannel. Drag, Brownian, and thermophoretic forces are concerned in the motion equations of particles. A series of numerical simulations for various particle sizes, flow rates, and temperature gradients have been performed. Some important features such as reasons, efficiencies, and locations of particle deposition have been explored. The results indicate that the particle deposition efficiency varies more or less under the actions of forces such as Brownian force, thermophoretic force, and drag force. Nevertheless, different forces lead to different particle motions and deposition processes. Brownian or thermophoretic force causes particles to move closer to the wall or further away from it. The drag force influence of slip boundary conditions and gas rarefaction changes the particles’ residential time in the channel. In order to find a way to decrease particle deposition on the microchannel surface, the deposition locations of different sizes of particles have been analyzed in detail under the action of thermophoretic force.

A New Slip Model for Gas Lubrication

Tribology ◽  
2006 ◽  
Author(s):  
Sheng Shen ◽  
Robert M. Crone ◽  
Gang Chen ◽  
Manuel Anaya-Dufresne
Keyword(s):  
Gas Flow ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Rarefied Gas ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Slip Model ◽  
Slip Boundary ◽  
Physical Mechanisms ◽  
Gas Lubrication

In this paper, a new slip boundary condition is derived using the solution of the Boltzmann equation. The physical mechanisms of velocity slip in rarefied gas flow are discussed and emphasized. The Poiseuille flow rates predicted by the new slip model show better agreements with those calculated from the existing slip models such as 1st, 2nd, and 1.5th slip order. Based on the new slip model, a new modified Reynolds equation is also proposed to predict the pressure field in gas lubrication problem.

Prediction of Liquid and Gas Leak Rates in Packed Stuffing Boxes

2019 ◽  
Author(s):  
Ali Salah Omar Aweimer ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Axial Stress ◽  
Slip Flow ◽  
Experimental Tests ◽  
Theoretical Models ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Packing Rings

Abstract The prediction of gas and liquid leak rate through packed stuffing boxes subjected to gas flow is a subject of very few studies in the literature. For better prediction of leakage, the change of porosity with length due to the non-uniform axial stress must be accounted for. There are few theoretical models on the prediction of leak rates in packing rings with capillary models. However, a model that incorporates the change of the capillary area with stress gives a better prediction. In this paper, the first slip flow model is used to predict gas and liquid flow considering the straight capillaries and capillaries having an area dependent on the axial stress in the packing rings. An approach that uses an analytical-computational methodology based on the number and the size of pores obtained experimentally is adopted to predict gas and liquid leak rates in uniform and non-uniform compressed yarned packings. The Navier-Stokes equations associated with slip boundary condition at the wall are used to predict leakage. Experimental tests with helium, argon, nitrogen and air for gazes and water and kerosene for liquids will be used to validate the models. The porosity parameters characterization will be conducted experimentally with helium at a reference gas at different gland stresses and pressures.

Correlation of Gaseous Mass Leak Rates Through Micro and Nano-Porous Gaskets

2009 ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Slip Flow ◽  
Experimental Studies ◽  
Slip Boundary Condition ◽  
Molecular Flow ◽  
Mass Spectrometers ◽  
Flow Rates ◽  
First Order ◽  
Slip Boundary

The present work deals with theoretical and experimental studies of gaseous flow through tight gasket. The paper presents an innovative approach to accurately predict and correlate leak rates of several gases through nano-porous gaskets. The new approach is based on the calculation of the gasket porosity parameters (DH, N) using a model based on a first order slip flow regime. The model assumes the flow to be continuum but employs a slip boundary condition on the channel wall. Experimental measured gas flow rates were performed on gaskets with a microscopic flow rate range and isothermal steady conditions. The flow rate is accurately measured using multi-gas mass spectrometers. The gasket porosity parameters in the developed leakage rate formula were obtained experimentally for a reference gas (helium) for each stress level. In the presence of these statistical properties of a porous media the leak rates for different gases can be predicted with reasonable accuracy. It was found that the approach that considers the slip flow with the first order combined to the molecular flow covers the prediction of flow rates at the microscopy level and down to 10−8 mg/s very well.

Correlation of Gaseous Mass Leak Rates Through Micro- and Nanoporous Gaskets

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Slip Flow ◽  
Experimental Studies ◽  
Slip Boundary Condition ◽  
Molecular Flow ◽  
Equivalent Thickness ◽  
Flow Rates ◽  
First Order ◽  
Slip Boundary

The present work deals with the theoretical and experimental studies of gaseous flow through tight gaskets. The paper presents an innovative approach to accurately predict and correlate leak rates of several gases through nanoporous gaskets. The new approach is based on the calculation of the gasket porosity parameters (D and N) using a model based on a first order slip flow regime. The model assumes the flow to be continuum but employs a slip boundary condition on the leak path wall. Experimental measured gas flow rates were performed on gaskets with a microscopic flow rate range and isothermal steady conditions. The flow rate is accurately measured using multigas mass spectrometers. The gasket porosity parameters used in the developed leakage rate formula were experimentally obtained for a reference gas (helium) for each stress level. In the presence of the statistical properties of a porous gasket, the leak rates for different gases can be predicted with reasonable accuracy. It was found that the approach that considers the slip flow with the first order combined to the molecular flow covers the prediction of flow rates at the microscopy level and down to 10−8 mg/s very well. Tightness hardening is the result of the saturation of the gasket combined porosity parameters or the equivalent thickness of the void layer.

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.

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

2008 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Slip Flow ◽  
Tube Length ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Rarefaction Effect ◽  
Wide Range ◽  
Poiseuille Number ◽  
Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

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