Semi-local friction factor of turbulent gas flow through rectangular microchannels

Hong, Chungpyo; Nakamura, Takaki; Asako, Yutaka; Ueno, Ichiro

doi:10.1016/j.ijheatmasstransfer.2016.02.080

Cited by 16 publications

(13 citation statements)

References 9 publications

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“…They proposed local fRe correlations as a function of Mach number and Knudsen number corresponding to compressibility and rarefaction effects for quasi-fully developed laminar flow. Their local fRe correlations were in excellent agreement with the experimental data of Hong et al, [9,20]. They also reported pressure variations and mass flow rate for microchannel gas flow using the fRe correlations [21,22].…”

Section: Introductionsupporting

confidence: 75%

Average Friction Factor for Laminar Gas Flow in Microtubes

Hong¹,

Asako²,

Faghri³

et al. 2020

CFDL

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The average friction factor in micro tubes will help the design engineers to estimate the pressure loss in micro flow devices. The aim of the present study is to obtain numerically average Darcy and Fanning friction factors and Mach numbers between the inlet and outlet of gas flows through adiabatic microtubes. This paper presents the average Poiseuille numbers, (fdRe)ave & (ffRe)ave, between the inlet and outlet, those are obtained from numerical results for laminar gas flow in microtubes with diameters of 50, 100 and 150 m and aspect ratios (i.e. length/diameter) of 100, 200 and 400, respectively. Axis-symmetric compressible momentum and energy equations were solved with the Arbitrary-Lagrangian-Eulerian (ALE) method. The stagnation pressure was chosen in such a way that the outlet Mach number ranged from 0.1 to 1.0. The outlet pressure was fixed at atmospheric condition. As a result, the average Darcy and Fanning friction factors between the inlet and outlet were obtained and compared with Moody's chart. The (fdRe)ave and (ffRe)ave were also obtained and presented as a function of average Mach number and were compared with the local fRe correlations proposed in the previous study.

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Section: Introductionsupporting

confidence: 75%

Average Friction Factor for Laminar Gas Flow in Microtubes

Hong¹,

Asako²,

Faghri³

et al. 2020

CFDL

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“…To validate the adopted numerical scheme, a MC with hydraulic diameter of 203 μm (MC2) is simulated and numerical friction factors are compared with experiments of Hong et al [19]. The width and height of the MC are 1020 μm and 112.7 μm respectively giving it an aspect ratio of 0.11.…”

Section: Numerical Methodologymentioning

confidence: 99%

“…The width and height of the MC are 1020 μm and 112.7 μm respectively giving it an aspect ratio of 0.11. Length of the channel in numerical model is taken as 100 mm while it is 26.9 mm in experiments performed by [19]. Moreover, dimensions of the inlet manifold are slightly different in experimental settings than those adapted in numerical model.…”

Section: Numerical Methodologymentioning

confidence: 99%

“…By incorporating temperature gradient along the length of MC, it was shown numerically that local friction factor for nitrogen gas in microtubes (MTs) is in good agreement with conventional theory not only in laminar but also in the high-speed turbulent flow regime. Hong et al [19] later measured local pressure at five axial positions of rectangular MCs and considered gas temperature change for the experimental calculation of semi-local friction factors (i.e., between two closely placed pressure ports). Semi-local turbulent friction factors considering Fanno flow were in good agreement with Blasius law whereas they were lower when gas was considered isothermal.…”

Section: Introductionmentioning

confidence: 99%

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A Comparison of Data Reduction Methods for Average Friction Factor Calculation of Adiabatic Gas Flows in Microchannels

2019

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In this paper, a combined numerical and experimental approach for the estimation of the average friction factor along adiabatic microchannels with compressible gas flows is presented. Pressure-drop experiments are performed for a rectangular microchannel with a hydraulic diameter of 295 μ m by varying Reynolds number up to 17,000. In parallel, the calculation of friction factor has been repeated numerically and results are compared with the experimental work. The validated numerical model was also used to gain an insight of flow physics by varying the aspect ratio and hydraulic diameter of rectangular microchannels with respect to the channel tested experimentally. This was done with an aim of verifying the role of minor loss coefficients for the estimation of the average friction factor. To have laminar, transitional, and turbulent regimes captured, numerical analysis has been performed by varying Reynolds number from 200 to 20,000. Comparison of numerically and experimentally calculated gas flow characteristics has shown that adiabatic wall treatment (Fanno flow) results in better agreement of average friction factor values with conventional theory than the isothermal treatment of gas along the microchannel. The use of a constant value for minor loss coefficients available in the literature is not recommended for microflows as they change from one assembly to the other and their accurate estimation for compressible flows requires a coupling of numerical analysis with experimental data reduction. Results presented in this work demonstrate how an adiabatic wall treatment along the length of the channel coupled with the assumption of an isentropic flow from manifold to microchannel inlet results in a self-sustained experimental data reduction method for the accurate estimation of friction factor values even in presence of significant compressibility effects. Results also demonstrate that both the assumption of perfect expansion and consequently wrong estimation of average temperature between inlet and outlet of a microchannel can be responsible for an apparent increase in experimental average friction factor in choked flow regime.

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“…Compared to the well-known laminar incompressible parabolic profile derived from the Poiseuille theory [8], flatter profiles result in altered velocity gradients at the wall and thus, by definition, in larger wall shear stresses and growing friction factors. In the literature, the evaluation of the compressible friction factor was addressed in [9] for the laminar case and in [10] for turbulent flow. These works are based on pressure and temperature experimental measurements and do not deal with the local velocity profile change in shape.…”

Section: Introductionmentioning

confidence: 99%

Velocity profile development and friction in compressible micro-flows

Cavazzuti

Corticelli

Karayiannis

2019

Second International Conference on Material Science, Smart Structures and Applications: Icmss-2019

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From Poiseuille theory, it is known that incompressible laminar fully-developed flow of a Newtonian fluid in a constant cross-section channel is characterised by steady parabolic velocity profiles after a fully-developed flow condition is attained. In turbulent fully-developed flow the velocity profiles are non-parabolic and become more flat for higher Reynolds numbers. When the incompressible hypothesis does not hold, as in the case of high velocity ideal gas flow, the velocity profile becomes flatter, as if more turbulent, due to the superposition of compressibility and turbulence effects, if applicable. This is typical in microchannel flows, where pressure gradients are high and the gas is rapidly accelerating, eventually up to the sound velocity. As the flow accelerates the effects of compressibility grow stronger and the velocity profile keeps changing shape. The radial velocity component does not zero as in fully-developed flow but reverses after the entrance effects have damped out and grows with the Mach number. A net mass transfer toward the walls is thus generated making the velocity profile more flat. This affects the friction factor which is no longer constant, being proportional to the normal-to-wall velocity gradient, and needs to be evaluated. In the present work, the compressible friction factor is numerically investigated and correlations are proposed based on the velocity profile shape evolution as a function of the Mach number. This, together with other considerations on the velocity profile shape change, is shown to enhance the predictive capability of the Fanno theory for compressible flows.

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Semi-local friction factor of turbulent gas flow through rectangular microchannels

Cited by 16 publications

References 9 publications

Average Friction Factor for Laminar Gas Flow in Microtubes

Average Friction Factor for Laminar Gas Flow in Microtubes

A Comparison of Data Reduction Methods for Average Friction Factor Calculation of Adiabatic Gas Flows in Microchannels

Velocity profile development and friction in compressible micro-flows

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