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

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, suc...

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Bibliographic Details
Published in:Journal of fluid mechanics 2021-06, Vol.919, Article A35
Main Authors: Rana, Anirudh S., Saini, Sonu, Chakraborty, Suman, Lockerby, Duncan A., Sprittles, James E.
Format: Article
Language:English
Subjects:
Boundary conditions
Computational fluid dynamics
Computer applications
Constitutive relationships
Continuity (mathematics)
Evaporation
Evaporation rate
Flow simulation
Fluid mechanics
Gases
Heat
Interfaces
JFM Papers
Kinetic theory
Mathematical models
Partial differential equations
Phase change
Phase transitions
Rarefaction
Temperature
Three dimensional flow
Transition flow
Vapor phases
Velocity
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2021.405