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.

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.

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.

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.

Estimation of Leak Flow Rates Through Narrow Cracks

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Jae-Heon Lee
Keyword(s):  
Friction Factor ◽  
Gas Flow ◽  
Slip Flow ◽  
Nonlinear Ordinary Differential Equation ◽  
Opening Displacement ◽  
Flow Rates ◽  
Choked Flow ◽  
Runge Kutta Method ◽  
Wide Range ◽  
Leak Before Break

The estimation of the gaseous leak flow rates through a narrow crack is important for a leak-before-break analysis as a method of nondestructive testing. Therefore, the methodology to estimate the gaseous leak flow rates in a narrow crack for a wide range of flow conditions, from no-slip to slip flow and from unchoked to choked flow, by using f⋅Re (the product of friction factor and Reynolds number) correlations obtained for a microchannel, was developed and presented. The correlations applied here were proposed by the previous study (Hong, et al., 2007, “Friction Factor Correlations for Gas Flow in Slip Flow Regime,” ASME J. Fluids Eng., 129, pp. 1268–1276). The detail of the calculation procedure was appropriately documented. The fourth-order Runge–Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure, and the regular-Falsi method was employed to find the inlet Mach number. An idealized crack, whose opening displacement ranges from 2 μm to 50 μm, with the crack aspect ratio of 200, 1000, and 2000, was chosen for sample estimation. The present results were compared with both numerical simulations and available experimental measurements. The results were in excellent agreement. Therefore, the gaseous leak flow rates can be correctly predicted by using the proposed methodology.

Experimental Investigation of the Air Flow Behavior and Heat Transfer Characteristics in Microchannels With Different Channel Lengths

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Zhi Tao ◽  
Zhibing Zhu ◽  
Haiwang Li
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Flow Behavior ◽  
Channel Length ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Poiseuille Number ◽  
Channel Lengths

This paper attempts to experimentally investigate the influence of channel length on the flow behavior and heat transfer characteristics in circular microchannels. The diameters of the channels were 0.4 mm and the length of them were 5 mm, 10 mm, 15 mm, and 20 mm, respectively. All experiments were performed with air and completed with Reynolds number in the range of 300–2700. Results of the experiments show that the length of microchannels has remarkable effects on the performance of flow behavior and heat transfer characteristics. Both the friction factor and Poiseuille number drop with the increase of channel length, and the experimental values are higher than the theoretical ones. Moreover, the channel length does not influence the value of critical Reynolds number. Nusselt number decrease as the increase of channel length. Larger Nusselt numbers are obtained in shorter channels. The results also indicate that in all cases, the friction factor decreases and the Poiseuille number increases with the increase of the Reynolds number. It is also observed that the value of critical Reynolds number is between 1500 and 1700 in this paper, which is lower than the value of theoretical critical Reynolds number of 2300.

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 Pressure Losses at Moderate Reynolds Numbers in Diamond-Shaped Cylinders Arrays: Application to Microregenerators

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
A. Sochinskii ◽  
D. Colombet ◽  
M. Medrano Muñoz ◽  
F. Ayela ◽  
N. Luchier
Keyword(s):  
Numerical Simulations ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Apex Angle ◽  
Circular Cylinders ◽  
Collective Effects ◽  
Pressure Losses ◽  
Compact Heat Exchangers ◽  
Poiseuille Number

Abstract Cylinders with an elliptical, oblong, lenticular, sinus, or diamond transveral shape are very interesting geometries for the design of compact heat exchangers. This work investigates the role of the porosity and of the apex angle of diamond-shaped cylinders networks on the pressure losses, at moderate Reynolds numbers, inside microheat regenerators. The design of the geometry under test has been chosen so that the cross section of the flow remains almost constant along the path of the flow between cylinders. Experiments have been performed at 1 ⩽ Re ⩽ 30 and a porosity range 0.40&lt;ε&lt;0.90 for an apex angle of α=33deg. Numerical simulations have been conducted using the same Reynolds and porosity ranges but varying the apex angle 33deg ⩽ α ⩽ 90deg. Experimental measurements and dimensional analysis have shown that the friction factor can be affected by the porosity. Two-dimensional numerical simulations confirmed that the friction factor increases with the porosity but also with the apex angle. An analysis at the scale of a channel flanked by adjacent cylinders has provided an original correlation able to describe easily the evolution of the Poiseuille number and the collective effects on the drag coefficient as a function of α and ε. Such a diamond-shaped design is found to induce much lower Poiseuille numbers than those expected from conventional stacked spheres, woven wires, and circular cylinders arrays. The findings of this study can help for better understanding the optimization of low pressure drop regenerators and how to reduce associated hydraulic power.

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