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.

Friction Factor Correlations of Gas Slip Flow in Concentric Micro Annular Tubes

2009 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Friction Factor ◽  
Cross Sections ◽  
High Speed ◽  
Slip Flow ◽  
Arbitrary Lagrangian Eulerian ◽  
Slip Boundary ◽  
Exit Mach Number ◽  
Fast Flow ◽  
Energy Equations ◽  
Compressibility Effects

A concentric micro annular passage is a basic and important micro-geometry of micro-fluidic-systems from simple heat exchangers to the most complicated nuclear reactors. Therefore, the product of friction factor and Reynolds number (f·Re) for quasi-fully developed high speed and slip flow in a concentric micro annular tubes of Re<1000 and Ma<1.0 was obtained numerically. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations with slip boundary conditions were solved for both isothermal flow and no-heat conduction flow conditions. The outer tube radius ranged from 5 to 40 μm with the radius ratios of 0.2, 0.5 and 0.8. The ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1 to 1.0. The outlet pressure was fixed at the atmospheric pressure. The value of f·Re for compressible slip flow in concentric micro annular tubes were obtained. The detail of the incompressible slip f·Re is documented and its value defined as a function of r* and Kn is represented. The results show that in the case of fast flow, the values of f·Re for compressible slip flow is higher than those for incompressible slip flow due to compressibility effects. Also, the f·Re correlation for compressible slip flow is obtained from that of compressible no-slip flow and incompressible slip flow as a function of Mach and Knudsen numbers and radius ratio. In addition, a f·Re correlation from the values of f·Re obtained for micro-channel, micro-tube, and micro annular tube referred in author’s previous works that is applicable to micro-geometries whose cross-sections are parallel, rectangular, circular and annular, is proposed.

Friction Factor Correlations for Gas Flow in Slip Flow Regime

2007 ◽  
Vol 129 (10) ◽  
pp. 1268-1276 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Stephen E. Turner ◽  
Mohammad Faghri
Keyword(s):  
Friction Factor ◽  
Flow Regime ◽  
Gas Flow ◽  
Slip Flow ◽  
Channel Height ◽  
Inlet Temperature ◽  
Arbitrary Lagrangian Eulerian ◽  
Knudsen Numbers ◽  
Wide Range ◽  
Slip Flow Regime

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

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.

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.

Effect of Compressibility on Gaseous Flows in a Micro-Tube

2003 ◽  
Author(s):  
Yutaka Asako ◽  
Kenji Nakayama
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Distribution ◽  
Flow Characteristics ◽  
Fused Silica ◽  
Two Dimensional ◽  
Arbitrary Lagrangian Eulerian ◽  
Gaseous Flow ◽  
Gaseous Flows ◽  
Energy Equations

The product of friction factor and Reynolds number (f·Re) of gaseous flow in the quasi-fully developed region of a micro-tube was obtained experimentally and numerically. The tube cutting method was adopted to obtain the pressure distribution along the tube. The fused silica tubes whose nominal diameters were 100 and 150 μm, were used. Two-dimensional compressible momentum and energy equations were solved to obtain the flow characteristics in micro-tubes. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The both results agree well and it was found that (f·Re) is a function of Mach number.

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.

Mach Number on Outlet Plane of a Straight Micro-Tube

2013 ◽  
Author(s):  
Y. Asako ◽  
D. Kawashima ◽  
T. Yamada ◽  
C. Hong
Keyword(s):  
Mach Number ◽  
Turbulent Flow ◽  
Gas Flow ◽  
Flow Characteristics ◽  
Ideal Gas ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Downstream Region ◽  
Laminar And Turbulent Flow ◽  
Energy Equations

The Mach number and pressure on the outlet plane of a straight micro-tube were investigated numerically for both laminar and turbulent flow cases. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The LB1 turbulence model was used for the turbulent flow case. The compressible momentum and energy equations with the assumption of the ideal gas were solved. The computational domain is extended to the downstream region from the micro-tube outlet. The back pressure was given to the outside of the downstream region. The computations were performed for a tube whose diameter ranges from 50 to 500 μm. The average Mach number on the outlet plane of the fully under-expanded flow depends on the tube diameter and ranges from 1.16 to 1.25. The flow characteristics of the under-expanded gas flow in a straight micro-tube were revealed.

Experimental Investigation of Pressure Side Flow Separation on the T106C Airfoil at High Suction Side Incidence Flow

2016 ◽  
Author(s):  
Stephan Stotz ◽  
Reinhard Niehuis ◽  
Yavuz Guendogdu
Keyword(s):  
Mach Number ◽  
Wind Tunnel ◽  
Separation Bubble ◽  
Suction Side ◽  
Pressure Side ◽  
Blade Passage ◽  
Wide Range ◽  
Profile Losses ◽  
Exit Mach Number ◽  
Side Flow

The objective of this work is to study the influence of a pressure side separation bubble on the profile losses and the development of the bubble in the blade passage. For the experimental investigations the T106 profile is used, with an increased loading due to an enlarged pitch to chord ratio from 0.799 to 0.95 (T106C). The experiments were performed at the high-speed cascade wind tunnel of the Institute of Jet Propulsion at the University of the Federal Armed Forces Munich. The main feature of the wind tunnel is to vary Reynolds and Mach number independently to achieve realistic turbomachinery conditions. The focus of this work is to determine the influence of a pressure side separation on the profile losses and hence the robustness to suction side incidence flow. The cascade is tested at four incidence angles from 0° to −22.7° to create separation bubbles of different sizes. The influence of the Reynolds number is investigated for a wide range at constant exit Mach number. Therefore a typical exit Mach number for low pressure turbines in the range of 0.5–0.8 is chosen in order to consider compressible effects. Furthermore, two inlet turbulence levels of about 3% and 7.5% have been considered. The characteristics of the separation bubble are identified by using the profile pressure distributions, whereas wake traverses with a five hole probe are used to determine the influence of the pressure side separation on the profile losses. Further, time-resolved pressure measurements near the trailing edge as well as single hot wire measurements in the blade passage are conducted to investigate the unsteady behavior of the pressure side separation process itself and also its influence on the midspan passage flow.

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