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Efficient simulation of non-classical liquid-vapour phase-transition flows : a method of fundamental solutions
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Rana, Anirudh S., Saini, Sonu, Chakraborty, Suman, Lockerby, Duncan A. and Sprittles, James E. (2021) Efficient simulation of non-classical liquid-vapour phase-transition flows : a method of fundamental solutions. Journal of Fluid Mechanics, 919 . A35. doi:10.1017/jfm.2021.405 ISSN 0022-1120.
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Official URL: https://doi.org/10.1017/jfm.2021.405
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.
| Item Type: | Journal Article | ||||||||||||
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||||||
| Publisher: | Cambridge University Press | ||||||||||||
| ISSN: | 0022-1120 | ||||||||||||
| Official Date: | 25 July 2021 | ||||||||||||
| Dates: |
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| Volume: | 919 | ||||||||||||
| Article Number: | A35 | ||||||||||||
| DOI: | 10.1017/jfm.2021.405 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Journal of Fluid Mechanics [http://doi.org/10.1017/jfm.2021.405. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © Cambridge University Press | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Copyright Holders: | © The Author(s), 2021. Published by Cambridge University Press | ||||||||||||
| Date of first compliant deposit: | 26 April 2021 | ||||||||||||
| Date of first compliant Open Access: | 1 June 2022 | ||||||||||||
| RIOXX Funder/Project Grant: |
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