Mass Flow Measurements of Gases in Deep-RIE Microchannels

2002 ◽  
Author(s):  
Jaesung Jang ◽  
Yabin Zhao ◽  
Steven T. Wereley ◽  
Lichuan Gui
Keyword(s):  
Experimental Data ◽  
Aspect Ratio ◽  
Mass Flow ◽  
Gas Flow ◽  
Pressure Ratio ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Effective Diameter ◽  
Flow Measurements ◽  
Pressure Distributions

We present mass flow measurements and pressure distributions in near unity aspect ratio microchannels using Deep Reactive Ion Etching (RIE). Almost all of the previous papers have dealt with only wide channels for gas flow measurements. We also adopt Spin-On-Glass (SOG) to bond Pyrex glass to silicon. Using the first order slip flow formula and experimental data, we extracted the tangential momentum accommodation coefficient (TMAC) of 0.425 for the case of SOG and Si microchannels and air, and the effective diameter of 57.67μm. Increased mass flow from the incompressible flow case is mostly due to compressibility rather than rarefaction, which is expected from the fact that the Knudsen number is 0.00115, the borderline of slip flows. The deviations from the linear incompressible pressure distributions get larger with increasing inlet pressures, and the dimensionless streamwise locations of maximum deviations are between 0.5 and 0.6, which is slightly downstream from the middle of the channels. It is notable that these experimental data are much closer to simulation results than the previous experiments in microchannels. The inlet pressure drops are almost linear with respect to pressure ratio of inlet to outlet. This type of near unity aspect ratio microchannel is more effective for heat exchangers than previous thin, wide channels.

scholarly journals Exact solutions for the axial pressure drop in isothermal channels with maxwell slip flow

2018 ◽  
Author(s):  
Alex Christian Hoffmann ◽  
Stamatina Karakitsiou ◽  
Bodil Holst
Keyword(s):  
Mass Flow ◽  
Gas Flow ◽  
Cylindrical Channel ◽  
Rectangular Channel ◽  
Slip Flow ◽  
Order Relation ◽  
Pressure Profile ◽  
Accommodation Coefficient ◽  
Parallel Plates ◽  
Axial Pressure

Expressions for the axial pressure profiles in a cylindrical channel and between parallel plates or a rectangular channel with large aspect ratio, with Maxwell slip gas flow are derived from first principles. The resulting expressions, which only involve the inlet and outlet pressures and the channel dimensions, will be useful in modelling or simulations of channel flows at Knudsen numbers in the range 0.001–0.1, such as in MEMS and NEMS. The expression for a cylindrical channel is validated by deriving from it an expression for the channel mass flow, which is shown to agree with a known expression for the mass flow through cylindrical channels with Maxwell slip flow. The expression for flow between parallel plates is found to agree with the zeroth order relation derived by Arkilic et al. using perturbation analysis. The effect of the accommodation coefficient on the pressure profile in a cylindrical channel is shown.

Laminar Forced Convection in Annular Microchannels With Slip Flow Regime

2009 ◽  
Author(s):  
Arman Sadeghi ◽  
Abolhassan Asgarshamsi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Graphical Form ◽  
Uniform Temperature

Fluid flow and heat transfer at microscale have attracted an important research interest in recent years due to the rapid development of microelectromechanical systems (MEMS). Fluid flow in microdevices has some characteristics which one of them is rarefaction effect related with gas flow. In this research, hydrodynamically and thermally fully developed laminar rarefied gas flow in annular microducts is studied using slip flow boundary conditions. Two different cases of the thermal boundary conditions are considered, namely: uniform temperature at the outer wall and adiabatic inner wall (Case A) and uniform temperature at the inner wall and adiabatic outer wall (Case B). Using the previously obtained velocity distribution, energy conservation equation subjected to relevant boundary conditions is numerically solved using fourth order Runge-Kutta method. The Nusselt number values are presented in graphical form as well as tabular form. It is realized that for the case A increasing aspect ratio results in increasing the Nusselt number, while the opposite is true for the case B. The effect of aspect ratio on Nusselt number is more notable at smaller values of Knudsen number, while its effect becomes slighter at large Knudsen numbers. Also increasing Knudsen number leads to smaller values of Nusselt number for the both cases.

An Investigation on Micro Slip Flows in Micro Channels

2010 ◽  
Author(s):  
Gh. Reza Salehi ◽  
Masoud JalaliBidgoli ◽  
Saeed ZeinaliDanaloo ◽  
Kazem HasanZadeh
Keyword(s):  
Flow Rate ◽  
Pressure Ratio ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Flow Rate Ratio ◽  
Numerical Representation ◽  
Micro Channel ◽  
Parallel Plates ◽  
Dimensionless Numbers ◽  
Micro Channels

In this paper, distributions of velocity and flow rate of micro channels are studied. Moreover, the parameters which influence them were also discussed, as well as their effects and relevant curves. In the Analytical study, the governing equation in specific micro flows is obtained. This equation is specifically investigated for slip flow in two micro parallel plates (micro channel).At the next step numerical representation shows the influence of the related parameters in micro channel flow such as Knudsen number, thermal -accommodation coefficient, mass flow rate ratio and pressure ratio (outlet to inlet), Tangential Momentum Accommodation Coefficient with relative curves, and flow rate distribution in slippery state to no slip state has been compared as the another part of this solution. Finally, the results of investigating parameters and dimensionless numbers in micro channels are reviewed.

Three-Dimensional Simulation of Gas Flow in Microducts

2005 ◽  
Author(s):  
Abhishek Agrawal ◽  
Amit Agrawal
Keyword(s):  
Aspect Ratio ◽  
Knudsen Number ◽  
Gas Flow ◽  
Flow Direction ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Theoretical Development ◽  
Width Ratio ◽  
Two Dimensional

Three-dimensional lattice Boltzmann method based simulations of a microduct have been undertaken in this paper. The objective is to understand the different physical phenomena occurring at these small scales and to investigate when the flow can be treated as two-dimensional. Towards this end, the Knudsen number and aspect ratio (depth to width ratio) are varied for a fixed pressure ratio. The pressure in the microduct is non-linear with the non-linearity in pressure reducing with an increase in Knudsen number. The pressure and velocity behaves somewhat similar to two-dimensional microchannels even when the aspect ratio is unity. The slip velocity at the impenetrable wall has two components: along and perpendicular to the flow. Our results show that the streamwise velocity near the centerline is relatively invariant along the depth for aspect ratio more than three, suggesting that the microduct can be modeled as a two-dimensional microchannel. However, the velocity component along the depth is never identically zero, implying that the flow is not truly two-dimensional. A curious change in vector direction in a plane normal to the flow direction is observed around aspect ratio of four. These first set of three-dimensional results are significant because they will help in theoretical development and flow modeling at micro scales.

Review of Critical Flowmeters for Gas Flow Measurements

1962 ◽  
Vol 84 (4) ◽  
pp. 447-457 ◽  
Author(s):  
B. T. Arnberg
Keyword(s):  
Mass Flow ◽  
Flow Measurement ◽  
Gas Flow ◽  
Flow Measurements ◽  
Flow Rates ◽  
Real Gas ◽  
Discharge Coefficients ◽  
Critical Nozzles ◽  
Mass Flow Rates ◽  
Flow Functions

Critical flowmeters for accurately measuring the mass flow rates of nonreacting real gases were reviewed. Discussions were presented on theoretical flow functions, on parameters for correlating discharge coefficients, and on the importance of real gas properties. The performance characteristics of critical nozzles and orifices of several designs were reviewed. Approaches were discussed to problems which must be researched before the fullest potential of this type of flow measurement can be realized.

Study for the Gas Flow Through a Critical Nozzle

2003 ◽  
Author(s):  
Heuy Dong Kim ◽  
Jae Hyung Kim ◽  
Kyung Am Park
Keyword(s):  
Reynolds Number ◽  
Mass Flow ◽  
Gas Flow ◽  
Critical Pressure ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Nozzle Throat ◽  
Critical Nozzle ◽  
Flow Through ◽  
Diffuser Angle

The critical nozzle is defined as a device to measure the mass flow with only the nozzle supply conditions, making use of flow choking phenomenon at the nozzle throat. The discharge coefficient and critical pressure ratio of the gas flow through the critical nozzle are strongly dependent on Reynolds number, based on the diameter of nozzle throat and nozzle supply conditions. Recently a critical nozzle with small diameter is being extensively used to measure mass flow in a variety of industrial fields. For low Reynolds numbers, prediction of the discharge coefficient and critical pressure is very important since the viscous effects near walls significantly affect the mass flow through critical nozzle, which is associated with working gas consumption and operation conditions of the critical nozzle. In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through critical nozzle. In order to investigate the effect of the working gas and turbulence model on the discharge coefficient, several kinds of gases and several turbulence models are employed. The Reynolds number effects are investigated with several nozzles with different throat diameter. Diffuser angle is varied to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the standard k-ε turbulence model with the standard wall function gives a best prediction of the discharge coefficient. The discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that diffuser angle affects the critical pressure ratio.

Computational study of the gas flow through a critical nozzle

2003 ◽  
Vol 217 (10) ◽  
pp. 1179-1189 ◽  
Author(s):  
H-D Kim ◽  
J-H Kim ◽  
K-A Park ◽  
T Setoguchi ◽  
S Matsuo
Keyword(s):  
Reynolds Number ◽  
Mass Flow ◽  
Gas Flow ◽  
Critical Pressure ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Nozzle Throat ◽  
Critical Nozzle ◽  
Flow Through ◽  
Diffuser Angle

The critical nozzle is defined as a device to measure the mass flow with only the nozzle supply conditions making use of the flow choking phenomenon at the nozzle throat. The discharge coefficient and critical pressure ratio of the gas flow through the critical nozzle are strongly dependent on the Reynolds number, based on the diameter of the nozzle throat and nozzle supply conditions. Recently a critical nozzle with a small diameter has been extensively used to measure mass flow in a variety of industrial fields. For low Reynolds numbers, prediction of the discharge coefficient and critical pressure is very important since the viscous effects near walls significantly affect the mass flow through the critical nozzle, which is associated with working gas consumption and operation conditions of the critical nozzle. In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through the critical nozzle. In order to investigate the effect of the working gas and turbulence model on the discharge coefficient, several kinds of gases and several turbulence models are employed. The Reynolds number effects are investigated with several nozzles with different throat diameters. The diffuser angle is varied in order to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the standard k-ε turbulence model with the standard wall function gives the best prediction of the discharge coefficient. The discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that the diffuser angle affects the critical pressure ratio.

Experimental and Numerical Investigations on the Leakage Flow Characteristics of the Labyrinth Brush Seal

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Jun Li ◽  
Bo Qiu ◽  
Zhenping Feng
Keyword(s):  
Experimental Data ◽  
Pressure Ratio ◽  
Flow Characteristics ◽  
Leakage Rate ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Blow Down ◽  
Pressure Distributions ◽  
Brush Seal ◽  
Brush Seals

The leakage rate of the labyrinth brush seal was experimentally measured and numerically investigated in this paper. Four different rotational speeds of 0, 1500, 2400 and 3000 rpm were utilized to investigate the effects on the leakage rate of the labyrinth brush seal. In addition, five different pressure ratios and two initial clearances were also adopted to study the influences of pressure ratio and clearance size on the leakage rate of the labyrinth brush seal. The leakage rates of the experimental labyrinth brush seal at different rotational speeds, pressure ratios, and initial clearances were also predicted using Reynolds-averaged Navier-Stokes (RANS) solutions coupling with a non-Darcian porous medium model. The rotor centrifugal growth and bristle blow-down effects were considered in the present numerical research. The rotor centrifugal growth at different rotational speeds was calculated using the finite element method (FEM). The variation of the sealing clearance size with rotor centrifugal growth and bristle blow-down was analyzed. The numerical leakage rate was in good agreement with the experimental data. The effects of rotational speeds, pressure ratios, and clearance sizes on the leakage flow characteristics of brush seals were also investigated based on the experimental data and numerical results. The detailed leakage flow fields and pressure distributions of the brush seals were also presented.

Incompressible Criterion and Pressure Drop for Gaseous Slip Flow in Circular and Noncircular Microchannels

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Zhipeng Duan
Keyword(s):  
Mach Number ◽  
Simple Model ◽  
Pressure Drop ◽  
Compressible Flows ◽  
Gas Flow ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Gaseous Slip Flow ◽  
Practical Engineering ◽  
Poiseuille Number

Slip flow in various noncircular microchannels has been further examined, and a simple model for a normalized Poiseuille number is proposed. As for slip flow, no solutions or graphical and tabulated data exist for most geometries; the developed simple model fills this void and can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution, and pressure drop of slip flow in noncircular microchannels by the research community for the practical engineering design of microchannels. The incompressible flow criterion for gas flow in microchannels is given. A Mach number less than 0.3 is not sufficient to ensure that the flow is incompressible. Compressibility depends on the product of two dimensionless parameters: L/L(DRe)(DRe) and Ma (Arkilic et al., 1997, “Gaseous Slip Flow in Long Microchannels,” J. Microelectromech. Syst., 6(2), pp. 167–178). Some flows where Ma < 0.3 are low speed compressible flows. A fresh general pressure drop model for isothermal low Mach number compressible flow in microchannels is proposed. If the pressure drop is less than 10% of the outlet pressure, the flow can be considered as incompressible for practical engineering applications. This paper improves and extends previous studies on slip flow in noncircular microchannels.

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.

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