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Analysis of laminar-to-turbulent transition for isothermal gas flows in microchannels

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Abstract

In this work the laminar-to-turbulent transition in microchannels of circular cross-section is studied experimentally. In order to single out the effects of relative roughness, compressibility and channel length-to-diameter ratio on the Reynolds number at which transition occurs, experimental runs have been carried out on circular microchannels in fused silica—smooth for all purposes—and in stainless steel (which possess a high surface roughness), with a diameter between 125 and 180 μm and a length of 5–50 cm through which nitrogen flows. For each tube the friction factor has been computed. The values of the critical Reynolds number have been determined plotting the Poiseuille number (i.e., the product of the friction factor, f, times the Reynols number, Re) as a function of the average Mach number between inlet and outlet. The transitional regime was found to start no earlier than at values of the Reynolds number around 1,800–2,000. It has been observed that surface roughness has no effect on the hydraulic resistance in the laminar region for a relative roughness lower than 4.4%, and that friction factor obeys the Poiseuille law, if it is correctly computed taking compressibility into account. It is found that recent correlations for the prediction of the critical Reynolds number in microchannels that link the relative roughness of the microtubes to the critical Reynolds number do not agree with the present results.

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Abbreviations

A :

Cross-sectional area (m2)

C :

Local loss coefficient

D :

Inner diameter (m)

F :

Friction factor

L :

Microchannel length (m)

\( \dot{m} \) :

Mass flow rate (kg s−1)

Ma :

Mach number

P :

pressure (Pa)

R :

gas constant (J kg−1 K−1)

Re :

Reynolds number

T :

temperature (K)

Δ:

difference

δ :

relative uncertainty (%)

ε :

roughness (m)

γ :

specific heat ratio (cp/cv)

μ :

dynamic viscosity (kg m−1 s−1)

ρ :

density (kg m−3)

avg:

average

cf:

constricted flow

cr:

critical

Ex:

exit

h:

hydraulic

in:

inlet

m:

measured

n:

net

no:

nominal

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Acknowledgments

This work has been funded by the Italian Ministry of Research in the framework of the PRIN 2007 action on Microfluidics.

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Authors and Affiliations

  1. DIENCA, Università degli Studi di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Gian Luca Morini, Marco Lorenzini & Sandro Salvigni

  2. Dipartimento di Ingegneria Industriale, Università di Parma, Via G.P. Usberti 181A, 43100, Parma, Italy

    Marco Spiga

  3. DIENCA, Università degli Studi di Bologna, Via Terracini 34, 40131, Bologna, Italy

    Marco Lorenzini

Authors
  1. Gian Luca Morini
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  2. Marco Lorenzini
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  3. Sandro Salvigni
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  4. Marco Spiga
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Correspondence to Marco Lorenzini.

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Morini, G.L., Lorenzini, M., Salvigni, S. et al. Analysis of laminar-to-turbulent transition for isothermal gas flows in microchannels. Microfluid Nanofluid 7, 181–190 (2009). https://doi.org/10.1007/s10404-008-0369-2

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  • DOI: https://doi.org/10.1007/s10404-008-0369-2

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