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.

Gaseous Slip Flow Mixed Convection in Vertical Microducts With Constant Axial Energy Input

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Arman Sadeghi ◽  
Mostafa Baghani ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Cross Sections ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Slip Boundary Conditions ◽  
First Order ◽  
Slip Boundary

The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary conditions are then applied to the solution using the point matching technique. The results show that both the Nusselt number and the pressure drop parameter are increasing functions of the Grashof to Reynolds ratio. It is also found that, with the exception of the H2 Nusselt number of the triangular duct, which shows an opposite trend, both the Nusselt number and the pressure drop are decreased by increasing the Knudsen number. Furthermore, the pressure drop of the H2 case is found to be higher than that obtained by assuming an H1 thermal boundary condition.

Method of Submerged Stokeslets for Slip Flow About Ensembles of Particles

2008 ◽  
Vol 8 (7) ◽  
pp. 3790-3801
Author(s):  
Shunliu Zhao ◽  
Alex Povitsky
Keyword(s):  
Boundary Conditions ◽  
Self Assembly ◽  
Slip Flow ◽  
Chemical Vapor ◽  
Partial Slip ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Singularity Method ◽  
Low Reynolds Number Flows ◽  
Micro Pump

A boundary singularity method with submerged Stokeslets is applied to the low Reynolds number flows about a set of spheres. Newtonian fluid is considered with no slip or partial slip boundary conditions at the wall. The validity of the method for Stokes flows about representative sets of spheres is investigated. The considered cases include (i) a uniform flow about a stationary set of particles typical for filtration and chemical vapor deposition, (ii) a flow induced by particles moving toward each other typical for self-assembly processes and (iii) a flow induced by spinning particles typical for micro-pump applications. The dependence of the flowfield on the number of Stokeslets is investigated in order to establish the needed number of Stokeslets. Comparison of flow field for the no-slip (Kn = 0) and partial-slip boundary conditions (Kn = 0.1) shows that the partial slip at the particles' surface significantly affect the velocity field and pressure distribution.

Second-Order Gaseous Flow Models in Long Circular and Noncircular Microchannels and Nanochannels

2011 ◽  
Author(s):  
Zhipeng Duan
Keyword(s):  
Boundary Conditions ◽  
Pressure Distribution ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Second Order ◽  
Slip Boundary Conditions ◽  
Gaseous Flow ◽  
Slip Boundary ◽  
Poiseuille Number

Gaseous flow in circular and noncircular microchannels has been examined and a simple analytical model with second-order slip boundary conditions for normalized Poiseuille number is proposed. The model is applicable to arbitrary length scale. It extends previous studies to the transition regime by employing the second-order slip boundary conditions. The effects of the second-order slip boundary conditions are analyzed. As in slip and transition regimes, 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, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels by the research community 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. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier-Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. The transition regime is a varying mixture of different transport mechanisms and the mixed degree relies on the magnitude of the Knudsen number. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given. This paper demonstrates that with some relatively simple ideas from knowledge, observation, and intuition, one can predict some fairly complex flows.

Gaseous Slip Flow in a Micro-Channel

2003 ◽  
Author(s):  
Shou-Shing Hsieh ◽  
Huang-Hsiu Tsai ◽  
Chih-Yi Lin ◽  
Ching-Fang Huang ◽  
Cheng-Ming Chien
Keyword(s):  
Gas Flow ◽  
Perturbation Methods ◽  
Flow Model ◽  
Slip Flow ◽  
Micro Channel ◽  
Slip Boundary Conditions ◽  
Nitrogen Gas ◽  
Slip Boundary ◽  
Mass Flow Rates ◽  
Good Agreement

An experimental and theoretical study of low Reynolds number compressible gas flow in a micro channel is presented. Nitrogen gas was used. The channel was microfabricated on silicon wafers and were 50 μm deep, 200 μm wide and 24000 μm long. The Knudsen number ranged from 0.001 to 0.02. Pressure drop were measured at different mass flow rates in terms of Re and found in good agreement with those predicted by analytical solutions in which a 2-D continuous flow model with first slip boundary conditions are employed and solved by perturbation methods.

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