Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-dfw9g Total loading time: 0.485 Render date: 2022-08-19T08:23:30.958Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

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*
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: anirudh.rana@pilani.bits-pilani.ac.in

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.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
3
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

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

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *