A self-consistent kinetic model for droplet heating and evaporation

S. S. Sazhin, I. N. Shishkova, Mansour Al Qubeissi

Research output: Contribution to journalArticle

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Abstract

A new kinetic model for heating and evaporation of Diesel fuel droplets is suggested. The model is based on the introduction of the kinetic region in the immediate vicinity of the heated and evaporating droplets, where the dynamics of molecules are described in terms of the Boltzmann equations for vapour components and air, and the hydrodynamic region. The effects of finite thermal conductivity and species diffusivity inside the droplets and inelastic collisions in the kinetic region are taken into account. Diesel fuel is approximated by n-dodecane or a mixture of 80% n-dodecane and 20% p-dipropylbenzene. In both cases, the evaporation coefficient is assumed equal to 1. The values of temperature and vapour density at the outer boundary of the kinetic region are inferred from the requirement that both heat flux and mass flux of vapour (or vapour components) in the kinetic and hydrodynamic regions in the vicinity of the interface between these regions should be equal. Initially, the heat and mass fluxes in the hydrodynamic region are calculated based on the values of temperature and vapour density at the surface of the droplet. Then the values of temperature and vapour density at the outer boundary of the kinetic region, obtained following the above-mentioned procedure, are used to calculate the corrected values of hydrodynamic heat and mass fluxes. The latter in their turn lead to new corrected values of temperature and vapour density at the outer boundary of the kinetic region etc. It is shown that this process quickly converges for the cases analysed in the paper, and it leads to self-consistent values for both heat and mass fluxes. The model is applied to the analysis of heating and evaporation of Diesel fuel droplets with initial radii and temperature equal to 5 μm and 300 K, immersed into gas with temperatures in the range 800–1200 K and pressure equal to 30 bar. It is shown that in all cases the kinetic effects lead to a decrease in droplet surface temperature and an increase in the evaporation time. The kinetic effects on the droplet evaporation time are shown to increase with increasing gas temperatures. Publisher statement: NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Heat and Mass Transfer. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Heat and Mass Transfer, [79, (2015)] DOI: 10.1016/j.ijheatmasstransfer.2015.10.039 © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Original languageEnglish
Pages (from-to)1206–1217
Number of pages12
JournalInternational Journal of Heat and Mass Transfer
Volume93
DOIs
Publication statusPublished - 7 Feb 2016

Fingerprint

Evaporation
evaporation
Heating
Kinetics
heating
Density of gases
kinetics
vapors
Mass transfer
diesel fuels
Heat flux
heat flux
Hydrodynamics
Diesel fuels
hydrodynamics
Temperature
Vapors
mass transfer
temperature
Gases

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Heat and Mass Transfer. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Heat and Mass Transfer, [79, (2015)] DOI: 10.1016/j.ijheatmasstransfer.2015.10.039

© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

  • Boltzmann equation
  • Diesel fuel droplet
  • n-dodecane
  • p-dipropylbenzene
  • Heat/mass transfer
  • Kinetic effects

Cite this

A self-consistent kinetic model for droplet heating and evaporation. / Sazhin, S. S.; Shishkova, I. N.; Al Qubeissi, Mansour.

In: International Journal of Heat and Mass Transfer, Vol. 93, 07.02.2016, p. 1206–1217.

Research output: Contribution to journalArticle

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N1 - NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Heat and Mass Transfer. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Heat and Mass Transfer, [79, (2015)] DOI: 10.1016/j.ijheatmasstransfer.2015.10.039 © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

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N2 - A new kinetic model for heating and evaporation of Diesel fuel droplets is suggested. The model is based on the introduction of the kinetic region in the immediate vicinity of the heated and evaporating droplets, where the dynamics of molecules are described in terms of the Boltzmann equations for vapour components and air, and the hydrodynamic region. The effects of finite thermal conductivity and species diffusivity inside the droplets and inelastic collisions in the kinetic region are taken into account. Diesel fuel is approximated by n-dodecane or a mixture of 80% n-dodecane and 20% p-dipropylbenzene. In both cases, the evaporation coefficient is assumed equal to 1. The values of temperature and vapour density at the outer boundary of the kinetic region are inferred from the requirement that both heat flux and mass flux of vapour (or vapour components) in the kinetic and hydrodynamic regions in the vicinity of the interface between these regions should be equal. Initially, the heat and mass fluxes in the hydrodynamic region are calculated based on the values of temperature and vapour density at the surface of the droplet. Then the values of temperature and vapour density at the outer boundary of the kinetic region, obtained following the above-mentioned procedure, are used to calculate the corrected values of hydrodynamic heat and mass fluxes. The latter in their turn lead to new corrected values of temperature and vapour density at the outer boundary of the kinetic region etc. It is shown that this process quickly converges for the cases analysed in the paper, and it leads to self-consistent values for both heat and mass fluxes. The model is applied to the analysis of heating and evaporation of Diesel fuel droplets with initial radii and temperature equal to 5 μm and 300 K, immersed into gas with temperatures in the range 800–1200 K and pressure equal to 30 bar. It is shown that in all cases the kinetic effects lead to a decrease in droplet surface temperature and an increase in the evaporation time. The kinetic effects on the droplet evaporation time are shown to increase with increasing gas temperatures. Publisher statement: NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Heat and Mass Transfer. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Heat and Mass Transfer, [79, (2015)] DOI: 10.1016/j.ijheatmasstransfer.2015.10.039 © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

AB - A new kinetic model for heating and evaporation of Diesel fuel droplets is suggested. The model is based on the introduction of the kinetic region in the immediate vicinity of the heated and evaporating droplets, where the dynamics of molecules are described in terms of the Boltzmann equations for vapour components and air, and the hydrodynamic region. The effects of finite thermal conductivity and species diffusivity inside the droplets and inelastic collisions in the kinetic region are taken into account. Diesel fuel is approximated by n-dodecane or a mixture of 80% n-dodecane and 20% p-dipropylbenzene. In both cases, the evaporation coefficient is assumed equal to 1. The values of temperature and vapour density at the outer boundary of the kinetic region are inferred from the requirement that both heat flux and mass flux of vapour (or vapour components) in the kinetic and hydrodynamic regions in the vicinity of the interface between these regions should be equal. Initially, the heat and mass fluxes in the hydrodynamic region are calculated based on the values of temperature and vapour density at the surface of the droplet. Then the values of temperature and vapour density at the outer boundary of the kinetic region, obtained following the above-mentioned procedure, are used to calculate the corrected values of hydrodynamic heat and mass fluxes. The latter in their turn lead to new corrected values of temperature and vapour density at the outer boundary of the kinetic region etc. It is shown that this process quickly converges for the cases analysed in the paper, and it leads to self-consistent values for both heat and mass fluxes. The model is applied to the analysis of heating and evaporation of Diesel fuel droplets with initial radii and temperature equal to 5 μm and 300 K, immersed into gas with temperatures in the range 800–1200 K and pressure equal to 30 bar. It is shown that in all cases the kinetic effects lead to a decrease in droplet surface temperature and an increase in the evaporation time. The kinetic effects on the droplet evaporation time are shown to increase with increasing gas temperatures. Publisher statement: NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Heat and Mass Transfer. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Heat and Mass Transfer, [79, (2015)] DOI: 10.1016/j.ijheatmasstransfer.2015.10.039 © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

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KW - Diesel fuel droplet

KW - n-dodecane

KW - p-dipropylbenzene

KW - Heat/mass transfer

KW - Kinetic effects

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DO - 10.1016/j.ijheatmasstransfer.2015.10.039

M3 - Article

VL - 93

SP - 1206

EP - 1217

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

ER -