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Non-equilibrium thermal transport and entropy analyses in rarefied cavity flows

Published online by Cambridge University Press:  14 February 2019

Vishnu Venugopal ,
Divya Sri Praturi Open the ORCID record for Divya Sri Praturi [Opens in a new window]  and
Sharath S. Girimaji
Vishnu Venugopal
Affiliation:
Aerospace Engineering Department, Texas A&M University, College Station, TX 77843, USA
Divya Sri Praturi*
Affiliation:
Aerospace Engineering Department, Texas A&M University, College Station, TX 77843, USA
Sharath S. Girimaji
Affiliation:
Aerospace Engineering Department, Texas A&M University, College Station, TX 77843, USA Ocean Engineering Department, Texas A&M University, College Station, TX 77843, USA
*
†Email address for correspondence: [email protected]
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Abstract

Thermal transport in rarefied flows far removed from thermodynamic equilibrium is investigated using kinetic-theory-based numerical simulations. Two numerical schemes – unified gas kinetic scheme (UGKS) and direct simulation Monte Carlo (DSMC) – are employed to simulate transport at different degrees of rarefaction. Lid-driven cavity flow simulations of argon gas are performed over a range of Knudsen numbers, Mach numbers and cavity shapes. Thermal transport is then characterized as a function of lid Mach number and Knudsen number for different cavity shapes. Vast deviations from the Fourier law – including thermal transport aligned along the direction of temperature gradient – are observed. Entropy implications are examined using Sackur–Tetrode and Boltzmann $H$-theorem formulations. At low Knudsen and Mach numbers, thermal transport is shown to be amenable to both entropy formulations. However, beyond moderate Knudsen and Mach numbers, thermal transport complies only with the Boltzmann $H$-theorem entropy statement. Two extended thermodynamic models are compared against simulation data and found to account for some of the observed non-equilibrium behaviour.

JFM classification

Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 995 - 1025
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Copyright
© 2019 Cambridge University Press 

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