Time-dependent methodology for non-stationary mass flow rate measurements in a long micro-tube

Experimental and numerical analysis at arbitrary rarefaction conditions
  • Marcos Rojas-CárdenasEmail author
  • Ernane Silva
  • Minh-Tuan Ho
  • César J. Deschamps
  • Irina Graur
Research Paper


This paper reports the experimental and numerical analysis of time-dependent rarefied gas flows through a long metallic micro-tube. The experimental methodology was conceived on the basis of the constant volume technique and adapted to measure the evolution with time of a transient mass flow rate through a micro-tube. Furthermore, the characteristic time of each experiment, extracted from the pressure measurements in each reservoir, offered a clear indication on the dynamics of the transient flow as a function of the gas molecular mass and its rarefaction level. The measured pressure evolution with time at the inlet and outlet of the micro-tube was compared to numerical results obtained with the BGK linearized kinetic equation model. Finally, we present an original methodology to extract stationary mass flow rates by using the tube conductance, which can be associated with the characteristic time of the experiment, measured for different mean pressures between two tanks. The results were obtained in a wide range of rarefaction conditions for nitrogen (\(N_2\)). A brief comparison is offered with respect to R134a (CH2FCF3), too, a heavy polyatomic gas which is typically used in the refrigeration industry.


Micro-flows Transient flows MEMS Gas rarefaction Kinetic theory 



This work has been partially (authors M.-T. Ho and I. Graur) carried out in the framework of the Labex MEC (ANR-10-LABX-0092) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French Government program managed by the French National Research Agency (ANR). Additionally, the authors E. Silva and C. J. Deschamps thank the support of EMBRACO, CNPq and EMBRAPII Unit Polo/UFSC. Finally, the author M. Rojas-Cárdenas would like to acknowledge the financial support provided by the EU network program H2020 under Grant MIGRATE No. 643095.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institut Clément Ader (ICA)Université de Toulouse, CNRS, INSA, ISAE-SUPAERO, Mines Albi, UPSToulouseFrance
  2. 2.Polo Research Laboratories for Emerging Technologies in Cooling and ThermophysicsFederal University of Santa CatarinaFlorianópolisBrazil
  3. 3.CNRS, IUSTI UMR 7343Aix-Marseille UniversitéMarseilleFrance
  4. 4.James Weir Fluids Laboratory, Department of Mechanical and Aerospace EngineeringUniversity of StrathclydeGlasgowUK

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