TY - JOUR

T1 - Non-equilibrium condensation

AU - Graur, Irina A.

AU - Batueva, Marina A.

AU - Wolf, Moritz

AU - Gatapova, Elizaveta Ya

N1 - Funding Information: The study was supported by Russian Science Foundation (Project no. 20-19-00722). Publisher Copyright: © 2022 Elsevier Ltd

PY - 2022/12/1

Y1 - 2022/12/1

N2 - The condensation process today requires more accurate, efficient and well-tested modeling approaches. In this article the numerical simulations of monatomic vapor condensation on its liquid phase have been carried out by applying the S-model kinetic equation, the Molecular Dynamics approach and the Moment Method. A good agreement is found between the results obtained by these three methods for monatomic gases. The Moment Method has great potential for efficient estimation of condensation fluxes by respecting the conservation of mass, momentum and energy through the Knudsen layer. This method has no analytical solution in the case of condensation, unlike the evaporation process, and the three conservation equations must be solved numerically (the Python tool is provided in Supplementary). Similar to evaporation, the nonlinear form of Schrage's analytic expression requires information about the third parameter, additionally to two needed in the case of condensation, while linear Schrage's formula overestimates the condensation rate for small condensation velocities and underestimates it for higher ones. We have tested our approaches by comparison with experimental data for the condensation of mercury for a wide range of Mach numbers, up to 0.85. The existence of an inverted temperature gradient has been showed numerically as well as the reason of its appearance and its evolution for different experimental conditions. The methodology for extracting the condensation coefficient based on the results of the Moment method is proposed. Obtained by this way condensation coefficients were found to be close to unity and decreasing with increasing vapor pressure and temperature.

AB - The condensation process today requires more accurate, efficient and well-tested modeling approaches. In this article the numerical simulations of monatomic vapor condensation on its liquid phase have been carried out by applying the S-model kinetic equation, the Molecular Dynamics approach and the Moment Method. A good agreement is found between the results obtained by these three methods for monatomic gases. The Moment Method has great potential for efficient estimation of condensation fluxes by respecting the conservation of mass, momentum and energy through the Knudsen layer. This method has no analytical solution in the case of condensation, unlike the evaporation process, and the three conservation equations must be solved numerically (the Python tool is provided in Supplementary). Similar to evaporation, the nonlinear form of Schrage's analytic expression requires information about the third parameter, additionally to two needed in the case of condensation, while linear Schrage's formula overestimates the condensation rate for small condensation velocities and underestimates it for higher ones. We have tested our approaches by comparison with experimental data for the condensation of mercury for a wide range of Mach numbers, up to 0.85. The existence of an inverted temperature gradient has been showed numerically as well as the reason of its appearance and its evolution for different experimental conditions. The methodology for extracting the condensation coefficient based on the results of the Moment method is proposed. Obtained by this way condensation coefficients were found to be close to unity and decreasing with increasing vapor pressure and temperature.

KW - Kinetic equations

KW - Liquid-vapor interface

KW - Molecular dynamics

KW - Non-equilibrium condensation

UR - http://www.scopus.com/inward/record.url?scp=85137374021&partnerID=8YFLogxK

U2 - 10.1016/j.ijheatmasstransfer.2022.123391

DO - 10.1016/j.ijheatmasstransfer.2022.123391

M3 - Article

AN - SCOPUS:85137374021

VL - 198

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

M1 - 123391

ER -