One-dimensional analytical approach to modelling evaporation and heating of deformed drops

Tonini, Simona; Cossali, Gianpietro

doi:10.1016/j.ijheatmasstransfer.2016.02.004

Cited by 34 publications

(15 citation statements)

References 38 publications

(50 reference statements)

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“…The different behaviour is due to a combination of the effects of boiling temperature and latent heat of vaporisation. These peculiarities should be considered when approximating the heat transfer coefficient from the analytic relation that can be deduced from the uniform surface temperature analysis [9,14]. The drop deformation has an effect on the deviation of the local Nusselt number from the values for the uniform temperature case, as reported in figure 5.…”

Section: Resultsmentioning

confidence: 99%

“…(see also [9] for further details). The evaporation model is coupled with the energy equation, which has the form: (see again [9] for further details).…”

Section: Mathematical Modellingmentioning

confidence: 99%

“…Tests were performed to choose a proper value of ζ max to make the solution practically independent of it. Grid refinement was performed in the drop surface vicinity introducing a proper stretching function, which was optimised by comparison to the analytical solution of the energy equation available for uniform surface temperature condition (see [9]). Grid independence tests were performed and a final grid of 2000 cells proved to be enough to assure a sufficient grid independence of the solution and particularly of the fluxes on the drop surface.…”

Section: Spherical and Spheroidal Dropsmentioning

confidence: 99%

“…Numerical investigations on oscillating drops [4,5] have shown that the vapour and heat fluxes on the drop surface are not uniform and they were empirically correlated to the local mean curvature of the surface [1,6]. Analytical modelling of the heating and evaporation of spheroidal drops have shown that the local vapour and heat flux scale with the fourth root of the Gaussian curvature [7,8] and later the same result was extended to a wider class of drop shapes [9]. When dynamical simulation of droplet heating and evaporation is necessary, uniform drop temperature is often assumed, on the basis of a commonly accepted belief that the internal recirculation would maintain uniform conditions.…”

Section: Introductionmentioning

confidence: 99%

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Modelling of spheroidal drop evaporation with non-uniform temperature conditions

Cossali¹,

Ravasio²,

Tonini³

2017

Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems

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The heating and evaporation of single component spherical and spheroidal drops in gaseous quiescent environment are predicted, accounting for the effect of a non-uniform distribution of the temperature at the drop surface. The analytical solution of the species conservation equations in the proper coordinate system (spherical/spheroidal) is implemented to numerically solve the energy equation in a rectangular domain. The effect of temperature non-uniformity on the local Nusselt number and global heat and evaporation rates is calculated for different species, drop deformation and gaseous temperature. KeywordsDrop evaporation, spheroidal coordinates, non-uniform Dirichlet Boundary conditions. IntroductionMost of the models predicting the drop heating and evaporation to be implemented in CFD codes for dispersed phase applications rely on the assumption that drops are spherical, thus allowing a simpler solution in spherical coordinates of the energy and species conservation equations. However, experimental investigation on liquid drops in multi-particle systems has revealed that they are subject to significant shape deformations while interacting with the carrier phase [1-3], due to the interaction of surface tension and fluid-dynamic stresses on the drop surface [3]. Numerical investigations on oscillating drops [4,5] have shown that the vapour and heat fluxes on the drop surface are not uniform and they were empirically correlated to the local mean curvature of the surface [1,6]. Analytical modelling of the heating and evaporation of spheroidal drops have shown that the local vapour and heat flux scale with the fourth root of the Gaussian curvature [7,8] and later the same result was extended to a wider class of drop shapes [9]. When dynamical simulation of droplet heating and evaporation is necessary, uniform drop temperature is often assumed, on the basis of a commonly accepted belief that the internal recirculation would maintain uniform conditions. However a more accurate simulation can be obtained by using the concept of effective conductivity, firstly introduced by [10], to account for the effect of recirculation (see also [11] and [12]) and, although this cannot properly describe the temperature field inside the droplet, it can give a better estimation of the droplet surface temperature [13] . Recent modelling of heating and evaporation of spheroidal droplets [14] revealed that the uneven distribution of fluxes on the drop surface causes a corresponding uneven distribution of temperature on the drop surface, during most of the drop lifetime. This non-uniform temperature distribution affects the heat and vapour flow fields in a non neglectful way. The motivation of the work reported here is to investigate, through a combined analytical-numerical solution of the species and energy conservation equations, the effect of non-uniform Dirichlet boundary conditions at the drop surface (for spheroidal liquid drops) on the local heat and mass transfer coefficients.

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Section: Resultsmentioning

confidence: 99%

“…(see also [9] for further details). The evaporation model is coupled with the energy equation, which has the form: (see again [9] for further details).…”

Section: Mathematical Modellingmentioning

confidence: 99%

Section: Spherical and Spheroidal Dropsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling of spheroidal drop evaporation with non-uniform temperature conditions

Cossali¹,

Ravasio²,

Tonini³

2017

Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems

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“…The solution to Equation (44) yields (as in [26], except for the value of c pv ) the non-dimensionalised heat…”

Section: Appendix 1 Energy Equation With Inter-diffusional Termsmentioning

confidence: 99%

Mathematical modelling of heating and evaporation of a spheroidal droplet

Zubkov

Cossali

Tonini

et al. 2017

International Journal of Heat and Mass Transfer

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Most of the currently used models for droplet heating and evaporation are based on the assumption that droplets are perfect spheres. At the same time the shapes of many observed droplets in engineering applications are far from spherical. We have studied the influence of droplet non-sphericity on their heating and evaporation, approximating droplet shapes as prolate and oblate spheroids. The previously developed exact solutions to the heat and mass transfer equations for the gas phase surrounding a spheroidal droplet have been used as boundary conditions for the solutions to these equations in the liquid phase. The temperature gradients inside and at the surface of the droplets, and the changes in their shape during the heating and evaporation process have been taken into account. The effects of surface tension and droplet motion on droplet heating and evaporation are ignored. The results are applied to the analysis of heating and evaporation of an n-dodecane fuel droplet in Diesel engine-like conditions. The effect of droplet nonsphericity is shown to be relatively small for the evaporation time of these droplets with initial eccentricities 2/3 ≤ ǫ ≤ 1.5.

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An Analytical Approach to Model the Effect of Evaporation on Oscillation Amplitude of Liquid Drops in Gaseous Environment

Kochanattu

Cossali

Tonini

2020

Fluid Mechanics and Its Applications

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One-dimensional analytical approach to modelling evaporation and heating of deformed drops

Cited by 34 publications

References 38 publications

Modelling of spheroidal drop evaporation with non-uniform temperature conditions

Modelling of spheroidal drop evaporation with non-uniform temperature conditions

Mathematical modelling of heating and evaporation of a spheroidal droplet

An Analytical Approach to Model the Effect of Evaporation on Oscillation Amplitude of Liquid Drops in Gaseous Environment

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