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.

Compressibility and Rarefaction Effects on Pressure Drop in Rough Microchannels

2006 ◽  
Author(s):  
Giulio Croce ◽  
Paola D’Agaro ◽  
Alessandro Filippo
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Drop ◽  
Slip Flow ◽  
Major Effect ◽  
Flow Conditions ◽  
Fully Developed Flow ◽  
Compressibility Effect ◽  
Wide Range ◽  
Poiseuille Number

A numerical analysis of the flow field in rough microchannel is carried out with a finite volume compressible solver, including generalized Maxwell slip flow boundary conditions suitable for arbitrary geometries. Roughness geometry is modeled as a series of triangular shaped obstructions. Relative roughness from 0% to 2.65% were considered. Since for truly compressible flow we have no fully developed flow condition, the simulation is performed over the whole length of the channel. A wide range of Mach number is considered, from nearly incompressible to chocked flow conditions. Flow conditions with Reynolds number up to around 200 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from very low value to 0.0249. Performance charts are presented in terms of both average and local Poiseuille number as a function of local Kn, Ma and Re. In particular, it appears that roughness strongly decreases the reduction in pressure loss due to rarefaction. Thus, roughness effect is stronger at high Kn. Furthermore, compressibility effect has a major effect on pressure drop, as soon as local Mach number exceed 0.3.

Models for Gaseous Slip Flow in Circular and Noncircular Microchannels

2010 ◽  
Author(s):  
Zhipeng Duan ◽  
M. M. Yovanovich
Keyword(s):  
Simple Model ◽  
Friction Factor ◽  
Common Duct ◽  
Slip Flow ◽  
Rectangular Duct ◽  
Circular Sector ◽  
Circular Segment ◽  
Practical Engineering ◽  
Annular Sector ◽  
Poiseuille Number

Slip flow in noncircular microchannels has been examined and a simple model for normalized Poiseuille number is proposed to predict the friction factor and Reynolds number product fRe for slip flow. The developed model for normalized Poiseuille number has an accuracy of 4.2 percent for all common duct shapes. As for slip flow, no solutions or graphical and tabulated data exist for most geometries, the developed simple model can be used to predict friction factor, mass flow rate, and pressure distribution of slip flow in noncircular microchannels for the practical engineering design of microchannels such as rectangular, trapezoidal, double-trapezoidal, triangular, rhombic, hexagonal, octagonal, elliptical, semielliptical, parabolic, circular sector, circular segment, annular sector, rectangular duct with unilateral elliptical or circular end, annular, and even comparatively complex doubly-connected microducts.

Compressibility and Rarefaction Effect on Heat Transfer in Rough Microchannels

2007 ◽  
Author(s):  
Giulio Croce ◽  
Paola D’Agaro
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Mach Number ◽  
Pressure Drop ◽  
Fluid Dynamic ◽  
Slip Flow ◽  
Flow Conditions ◽  
Rarefied Flow ◽  
Wide Range ◽  
Poiseuille Number

High pressure drop and high length to hydraulic diameter ratios yield significant compressibility effects in microchannel flows, which compete with rarefaction phenomena at the smaller scale. In such regimes, flow field and temperature field are no longer decoupled. In presence of significant heat transfer, and combined with the effect of viscous dissipation, this yields to a quite complex thermo-fluid dynamic problem. A finite volume compressible solver, including generalized Maxwell slip flow and temperature jump boundary conditions suitable for arbitrary geometries, is adopted. Roughness geometry is modeled as a series of triangular shaped obstructions, and relative roughness from 0% to 2.65% were considered. The chosen geometry allows for direct comparison with pressure drop computations carried out, in a previous paper, under adiabatic conditions. A wide range of Mach number is considered, from nearly incompressible to chocked flow conditions. Flow conditions with Reynolds number up to around 300 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from very low value to around 0.05, and the competing effects of rarefaction, compressibility and roughness are investigated in detail. Compressibility is found to be the most dominant effect at high Mach number, yielding even inversion of heat flux, while roughness has a strong effect in the case of rarefied flow. Furthermore, the mutual interaction between heat transfer and pressure drop is highlighted, comparing Poiseuille number values for both cooled and heated flows with previous adiabatic computations.

Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Snežana S. Milićev ◽  
Nevena D. Stevanović
Keyword(s):  
Mach Number ◽  
Friction Factor ◽  
Cross Section ◽  
Gas Flow ◽  
Variable Cross Section ◽  
Molecular Flow ◽  
Variable Cross ◽  
General Boundary Condition ◽  
Poiseuille Number ◽  
Isothermal Gas

Abstract The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,” J. Microscale Thermophys. Eng., 3, pp. 43–77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.

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.

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&ndash;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.

Friction Factor Correlations of Slip Flow in Micro-Tubes

2007 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Mohammad Faghri
Keyword(s):  
Mach Number ◽  
Friction Factor ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Arbitrary Lagrangian Eulerian ◽  
Constant Wall Temperature ◽  
Wide Range ◽  
Exit Mach Number ◽  
Poiseuille Number ◽  
Energy Equations

Poiseuille number, the product of friction factor and Reynolds number (f·Re) for quasi-fully developed flow in a micro-tube was obtained in slip flow regime. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers with two thermal boundary conditions: CWT (constant wall temperature) and CHF (constant heat flux), respectively. The tube diameter ranges from 3 to 10μm and the tube aspect ratio is 200. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at the atmospheric pressure. In slip flow, Mach and Knudsen numbers are systematically varied to determine their effects on f·Re. The correlation for f·Re is obtained from numerical results. It was found that f·Re is mainly a function of Mach number and Knudsen number and is different from the values obtained by 64/(1+8Kn) for slow flow. The obtained f·Re correlations are applicable to both no-slip and slip flow regimes.

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.

Experimental Investigation of Microscale Effects in Perforated Plate Aerodynamics

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Ryszard Szwaba ◽  
Tomasz Ochrymiuk ◽  
Tomasz Lewandowski ◽  
Justyna Czerwinska
Keyword(s):  
Experimental Investigation ◽  
Compressible Flows ◽  
Large Scale ◽  
Gas Flow ◽  
Perforated Plate ◽  
Quadratic Function ◽  
Accommodation Coefficient ◽  
Turbulence Transition ◽  
Wide Range ◽  
Strong Relation

This paper contains an extensive analysis of the flow in microholes based on an experimental investigation. Experiments of the gas flow past a perforated plate with microholes (110μm) were carried out. A wide range of pressure differences between the inlet and the outlet were investigated for that purpose. Two distinguishable flow regimes were obtained: the laminar flow with the slip effects and the turbulence transition regime for a very low Reynolds number. The results are in good agreement with the theory, simulations, experiments for large scale perforated plates, and compressible flows in microtubes. The relation between the mass flow rate and the Knudsen, Reynolds, and Mach numbers for the laminar and transitional regime was obtained. It is a quadratic function of the Reynolds and Knudsen numbers (ReKn) based on the hole's diameter. The value of the first order tangential momentum accommodation coefficient was estimated. It shows a strong relation to the inlet Knudsen number.

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