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.

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.

Numerical Analysis of Rarefaction and Compressibility Effects in Bent Microchannels

2010 ◽  
Author(s):  
O. Rovenskaya ◽  
G. Croce
Keyword(s):  
Gas Flow ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Outer Wall ◽  
Slip Boundary Condition ◽  
Central Line ◽  
Navier Stokes ◽  
Strong Impact ◽  
First Order ◽  
Slip Boundary

Numerical investigation of a gas flow through microchannels with a sharp, 90 degrees bend is carried out using Navier-Stokes (N-S) equations with the classical Maxwell first-order slip boundary condition, including the tangential gradient effect due to the wall curvature, and Smoluchowski first order temperature jump definition. The details of the flow structure near the corner are analyzed, investigating the competing effects of rarefaction and compressibility on the channel performances. The flow characteristics in terms of velocity profiles, slip velocity distribution along inner and outer wall, pressure, average Mach number along central line of the channel have been presented. The results showed that impact of the bend on the channel performances is smaller at high rarefaction levels. The behaviour of pressure and velocity away from the bend is similar to that of a straight microchannel; however, the asymmetry in the flow at the bend, with high velocities and high velocity gradients on its inner side, has a strong impact on wall slip velocities. The presence of a recirculation is detected on both the inner and outer walls of the corner for larger Reynolds. However, rarefaction may delay the onset of recirculation. It is also observed that the mass flux through a bend microchannel can even be slightly larger than that through a straight microchannel of the same length and subjected to the same pressure difference.

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.

COMPARISON OF GAS SLIP MODELS WITH SOLUTIONS OF LINEARIZED BOLTZMANN EQUATION AND DIRECT SIMULATION OF MONTE CARLO METHOD

2007 ◽  
Vol 18 (02) ◽  
pp. 203-216 ◽  
Author(s):  
G. H. TANG ◽  
Y. L. HE ◽  
W. Q. TAO
Keyword(s):  
Friction Factor ◽  
Flow Rate ◽  
Slip Flow ◽  
Flow Analysis ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Slip Regime ◽  
Linearized Boltzmann Equation

Analytical solutions of the Navier–Stokes equation based on a locally fully-developed flow assumption with various gas slip models are presented and comparisons for velocity profile, flow rate, friction factor, and pressure distribution are performed. The effect of the second-order coefficient in the slip boundary condition becomes significant as the Knudsen number increases. Most slip models are limited to slip regime or marginally transition regime and break down around Kn = 0.1 while Sreekanth's model, followed by Mitsuya's model, gives a good agreement with the linearized Boltzmann solutions from slip regime up to Kn = 2 for flow rate and friction factor predictions. These two models should be of great use for slip flow analysis in micro-electro-mechanical systems (MEMS) and, in particular, in situations where the flow rate and flow resistance are of interest.

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.

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.

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.

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

Experimental and Numerical Study of the Pressure Drop in Transonic Micronozzle Flows Across Multiple Flow Regimes

2016 ◽  
Author(s):  
Juan E. Gomez Herrera ◽  
Rodion Groll
Keyword(s):  
Pressure Drop ◽  
Mass Flow ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Lower Mass ◽  
Flow Rates ◽  
Slip Boundary ◽  
Accommodation Coefficients ◽  
Mass Flow Rates

In the present work, the behavior of a millimeter-scale cold-gas thruster operating with the noble gases neon, argon, krypton and xenon is investigated both experimentally and numerically. In the experimental setup, the cold-gas thruster operates under vacuum conditions and the pressure drop in the system is measured at several fixed mass flow rates ranging between 0.178 mg/s and 3.568 mg/s. The estimated Knudsen numbers for all the studied cases are above the continuum flow limit 0.01. At the higher mass flow rates the studied flows are in the slip-flow regime while at the lower mass flow rates, the transition regime is reached. The experimental pressure results are compared with numerical simulations based on the compressible Navier-Stokes equations with a no-slip boundary condition and with simulations based on the Direct Simulation Monte Carlo (DSMC) method. At high values of Kn, the pressure results of the Navier-Stokes based simulations show high deviations from both the DSMC and the experimental results. This is a consequence of the discrepancy between the no-slip boundary condition used for the Navier-Stokes simulations and gas rarefaction effects in the micronozzle becoming dominant at the lower mass flow rates. Based on the comparison between the experimental results and the Navier-Stokes based simulations, a Knudsen-dependent correcting function with four gas-independent accommodation coefficients is developed. The accommodation coefficients allow the accurate estimation of the actual pressure drop along the nozzle based on usually computationally inexpensive Navier-Stokes simulations with no-slip boundary conditions. The flexibility of the proposed approach is advantageous for the study of experimental setups operating at a large range of mass flow rates, where several flow regimes might exist, provided that a rigorous numerical distinction between continuum, slip-flow and transition regime is not essential.

Analysis of the Diameter of Microbubbles Formed in a Cross Flow Microchannel

2009 ◽  
Author(s):  
T. J. John ◽  
B. Mathew ◽  
H. Hegab
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Liquid Flow Rate ◽  
Fluid Velocity ◽  
Cross Flow ◽  
Slip Boundary Condition ◽  
Force Balance ◽  
Gas Channel ◽  
Slip Boundary ◽  
The Moment

Two microfluidic devices for generating microbubbles are considered in the study presented in this paper. The first device consists of a liquid channel and a gas channel that is perpendicular to each other. In this device, the microbubble diameter varies inversely with the liquid flow rate (i.e. with flow velocity) but at the expense of high pressure drop. This device is modified by introducing a solid structure in front of the orifice to become the second device. This modification causes an increase in fluid velocity only in front of the orifice. In this paper a model is developed for determining the diameter of microbubbles generated in both of these devices. The model is developed by balancing the forces acting on the microbubble during growth and at the moment of detachment from the orifice. The detachment of the microbubble is assumed to happen when the sum of all detaching forces equals the net attaching force acting on the microbubble during the growth. Non-slip boundary condition is assumed on the walls of the channels in this model. Based on these assumptions a mathematical model is developed and solved numerically for different values of liquid and gas flow rate to obtain the microbubble diameter at the moment of detachment. A MATLAB® code is developed for solving the force balance equation. The superiority of the second device over the first one is validated by comparing the results obtained from the models in both cases.

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