Multi-component Droplet Heating Research Articles

Evaporation of Suspended Nanofluid (SiO$$_{2}$$/Water) Droplets: Experimental Results and Modelling

The results of experimental studies and modelling of the evaporation of suspended water droplets containing silicon dioxide SiO $$_{2}$$ nanoparticles at mass fractions 0.02 and 0.07 are presented. The experimental results are analysed using the previously developed model for multicomponent droplet heating and evaporation. In this model droplets are assumed to be spherical and the analytical solutions to the heat transfer and species diffusion equations are incorporated into the numerical code. They are used at each timestep of the calculations. Silicon dioxide nanoparticles are considered to be a non-evaporating component. It is demonstrated that both experimental and predicted values of droplet diameters to the power 1.5 decrease almost linearly with time, except at the beginning and the final stages of the evaporation process, and are only weakly affected by the presence of nanoparticles. At the final point in this process, the effect of nanoparticles becomes dominant when their mass fraction at the droplet surface reaches about 40 % and a cenosphere-like structure is formed. Both predicted and observed droplet surface temperatures rapidly decrease during the initial stage of droplet evaporation. After about $$t=100$$ s the predicted surface temperature remains almost constant whilst its experimentally observed values increase with time. This might be related to a decrease in the temperature of ambient air in the vicinity of droplets, not taken into account in the model. Both observed and predicted values of the mass fraction of silicon dioxide at the droplet surfaces are shown to increase with time until they reach about 0.4.

A model for multi-component droplet heating and evaporation and its implementation into ANSYS Fluent

The main ideas of the model for multi-component droplet heating and evaporation, based on the analytical solutions to the heat conduction and species diffusion equations in the liquid phase, and its implementation into ANSYS Fluent CFD software are described. The model is implemented into this software via User-Defined Functions (UDF). The predictions of ANSYS Fluent with the newly implemented model are verified against the results predicted by the previously developed in-house research code for droplets comprising of a mixture of ethanol and acetone evaporating and cooled down in ambient air.

New Models for Droplet Heating and Evaporation

A brief summary of new models for droplet heating and evaporation, developed mainly at the Sir Harry Ricardo Laboratory of the University of Brighton during 2011-2012, is presented. These are hydrodynamic models for mono-component droplet heating and evaporation, taking into account the effects of the moving boundary due to evaporation, hydrodynamic models of multi-component droplet heating and evaporation, taking and not taking into account the effects of the moving boundary, new kinetic models of mono-component droplet heating and evaporation, and a model for mono-component droplet evaporation, based on molecular dynamics simulation. The results, predicted by the new models are compared with experimental data and the prehctions of the previously developed models where possible.

Gravitational Effects on Multi-component Droplet Evaporation

This paper focuses on the analysis of multi-component droplet heating and evaporation under microgravity and normal gravity conditions. This analysis is based on the conventional conservation equations of species and energy for the gas phase, and the energy balance equation at the liquid–gas interface. The species diffusion is based on the Hirschfelder law, rather than on the less general Fick’s equation. Moreover, the heat flux due to species diffusion is taken into account in addition to the classical conduction heat flux between the gas and the liquid droplets. The liquid phase analysis is based on the infinite thermal conductivity liquid phase model, which has been justified by a reasonably good agreement between the predicted and experimental results. Indeed, the developed evaporation model has been validated against experimental data reported by Chauveau et al. (2008), where the droplets evaporation has been observed in microgravity and normal gravity conditions. The effects of gravity have been taken into account by introducing the Grashof number in the expressions of the Sherwood and Nusselt numbers. This model has been implemented in the multidimensional IFP-C3D industrial software. The modeling and experimental results have been shown to be reasonably close and the gravitational effects have been revealed to be significant especially for multi-component liquids including heavy components.

DROPLET HEATING AND EVAPORATION−RECENT RESULTS AND UNSOLVED PROBLEMS

Recently developed approaches to the hydrodynamic, kinetic, and molecular dynamic modeling of fuel droplet heating and evaporation are reviewed. Two new solutions to the heat conduction equation, taking into account the effect of the moving boundary during transient heating of an evaporating droplet, are discussed. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient heat conduction equation to the solution of the Volterra integral equation of the second kind. The new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. An alternative approach to the same problem has been based on the assumption that the time evolution of a droplet's radius, Rd (t), is known. For sufficiently small time steps, the time evolutions of droplet surface temperatures and radii predicted by both approaches coincide. A simplified model for multi-component droplet heating and evaporation, based on the analytical solution to the species diffusion equation inside droplets, is discussed. Two new solutions to the equation, describing the diffusion of species during multi-component droplet evaporation taking into account the effects of the moving boundary, are presented. A quasi-discrete model for heating and evaporation of complex multi-component hydrocarbon fuel droplets is described. The predictions of the model, taking into account the effects of the moving boundary during the time steps on the solutions to the heat transfer and species diffusion equations, are discussed. A new algorithm, based on simple approximations of the kinetic results, suitable for engineering applications, is discussed. The results of kinetic modeling, taking into account the effects of inelastic collisions, and applications of molecular dynamics simulations to study the evaporation of n-dodecane droplets are briefly summarized. The most challenging and practically important unsolved problems with regard to the modeling of droplet heating and evaporation are summarized and discussed.

Multi-component droplet heating and evaporation: Numerical simulation versus experimental data

The earlier reported simplified model for multi-component droplet heating and evaporation is generalised to take into account the coupling between droplets and the ambient gas. The effects of interaction between droplets are also considered. The size of the gas volume, where the interaction between droplets and gas needs to be taken into account, is estimated based on the characteristic thermal and mass diffusion scales. The model is applied to the analysis of the experimentally observed heating and evaporation of monodispersed n-decane/3-pentanone mixture droplets at atmospheric pressure. It is pointed out that the effect of coupling leads to noticeably better agreement between the predictions of the model and the experimentally observed average droplet temperatures. In most cases, the observed droplet temperatures lie between the average and central temperatures, predicted by the coupled solution. For the cases reported in this study, the observed time evolution of droplet radii cannot be used for the validation of the model. It is pointed out that the number of terms in the series in the expressions for droplet temperature and species mass fraction can be reduced to just three, with possible errors less than about 0.5%. In this case, the model can be recommended for the implementation into computational fluid dynamics (CFD) codes and used for various engineering applications, including those in internal combustion engines.

Modelling of droplet heating and evaporation: recent results and unsolved problems

The most recent results referring to the hydrodynamic and kinetic modelling of droplet heating and evaporation are briefly summarised. Two new solutions to the heat conduction equation, taking into account the effect of the moving boundary during transient heating of an evaporating droplet, are discussed. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient heat conduction equation to the solution of the Volterra integral equation of the second kind. It has been pointed out that the new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. A simplified model for multi-component droplet heating and evaporation, based on the analytical solution of the species diffusion equation inside droplets, is reviewed. A new algorithm, based on simple approximations of the kinetic results for droplet radii and temperatures, suitable for engineering applications, is discussed.