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Efficient simulation of non-classical liquid–vapour phase-transition flows: a method of fundamental solutions

Published online by Cambridge University Press:  01 June 2021

Anirudh S. Rana Open the ORCID record for Anirudh S. Rana [Opens in a new window] ,
Sonu Saini ,
Suman Chakraborty Open the ORCID record for Suman Chakraborty [Opens in a new window] ,
Duncan A. Lockerby Open the ORCID record for Duncan A. Lockerby [Opens in a new window]  and
James E. Sprittles Open the ORCID record for James E. Sprittles [Opens in a new window]
Anirudh S. Rana*
Affiliation:
Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan, India
Sonu Saini
Affiliation:
Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan, India
Suman Chakraborty
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, India
Duncan A. Lockerby
Affiliation:
School of Engineering, University of Warwick, CoventryCV4 7AL, UK
James E. Sprittles
Affiliation:
Mathematics Institute, University of Warwick, CoventryCV4 7AL, UK
*
†Email address for correspondence: [email protected]
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Abstract

Classical continuum-based liquid–vapour phase-change models typically assume continuity of temperature at phase interfaces along with a relation which describes the rate of evaporation at the interface (Hertz–Knudsen–Schrage, for example). However, for phase-transition processes at small scales, such as the evaporation of nanodroplets, the assumption that the temperature is continuous across the liquid–vapour interface leads to significant inaccuracies (McGaughey et al., J. Appl. Phys., vol. 91, issue 10, pp. 6406–6415; Rana et al., Phys. Rev. Lett., vol. 123, 154501), as might the adoption of classical constitutive relations that lead to the Navier–Stokes–Fourier (NSF) equations. In this paper, to capture the notable effects of rarefaction at small scales, we adopt an extended continuum-based approach utilising the coupled constitutive relations (CCRs). In CCR theory, additional terms are invoked in the constitutive relations of the NSF equations originating from the arguments of irreversible thermodynamics as well as being consistent with the kinetic theory of gases. The modelling approach allows us to derive new fundamental solutions for the linearised CCR model, to develop a numerical framework based upon the method of fundamental solutions (MFS) and enables three-dimensional multiphase micro-flow simulations to be performed at remarkably low computational cost. The new framework is benchmarked against classical results and then explored as an efficient tool for solving three-dimensional phase-change events involving droplets.

JFM classification

Micro-/Nano-fluid dynamics: Non-continuum effects Phase change: Condensation/evaporation Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A35
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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