Monodisperse droplet heating and evaporation: Experimental study and modelling

Results of experimental studies and the modelling of heating and evaporation of monodisperse ethanol and acetone droplets in two regimes are presented. Firstly, pure heating and evaporation of droplets in a flow of air of prescribed temperature are considered. Secondly, droplet heating and evaporation in a flame produced by previously injected combusting droplets are studied. The phase Doppler anemometry technique is used for droplet velocity and size measurements. Two-colour laser induced fluorescence thermometry is used to estimate droplet temperatures. The experiments have been performed for various distances between droplets and various initial droplet radii and velocities. The experimental data have been compared with the results of modelling, based on given gas temperatures, measured by coherent anti-stokes Raman spectroscopy, and Nusselt and Sherwood numbers calculated using measured values of droplet relative velocities. When estimating the latter numbers the finite distance between droplets was taken into account. The model is based on the assumption that droplets are spherically symmetrical, but takes into account the radial distribution of temperature inside droplets. It is pointed out that for relatively small droplets (initial radii about 65 μm) the experimentally measured droplet temperatures are close to the predicted average droplet temperatures, while for larger droplets (initial radii about 120 μm) the experimentally measured droplet temperatures are close to the temperatures predicted at the centre of the droplets.     

Advanced models of fuel droplet heating and evaporation

Recent developments in modelling the heating and evaporation of fuel droplets are reviewed, and unsolved problems are identified. It is noted that modelling transient droplet heating using steady-state correlations for the convective heat transfer coefficient can be misleading. At the initial stage of heating stationary droplets, the well known steady-state result Nu=2 leads to under prediction of the rate of heating, while at the final stage the same result leads to over prediction. The numerical analysis of droplet heating using the effective thermal conductivity model can be based on the analytical solution of the heat conduction equation inside the droplet. This approach was shown to have clear advantages compared with the approach based on the numerical solution of the same equation both from the point of view of accuracy and computer efficiency. When highly accurate calculations are not required, but CPU time economy is essential then the effect of finite thermal conductivity and re-circulation in droplets can be taken into account using the so called parabolic model. For practical applications in computation fluid dynamics (CFD) codes the simplified model for radiative heating, describing the average droplet absorption efficiency factor, appears to be the most useful both from the point of view of accuracy and CPU efficiency. Models describing the effects of multi-component droplets need to be considered when modelling realistic fuel droplet heating and evaporation. However, most of these models are still rather complicated, which limits their wide application in CFD codes. The Distillation Curve Model for multi-component droplets seems to be a reasonable compromise between accuracy and CPU efficiency. The systems of equations describing droplet heating and evaporation and autoignition of fuel vapour/air mixture in individual computational cells are stiff. Establishing hierarchy between these equations, and separate analysis of the equations for fast and slow variables may be a constructive way forward in analysing these systems.     

A simplified model for bi-component droplet heating and evaporation

A simplified model for bi-component droplet heating and evaporation is developed and applied for the analysis of the observed average droplet temperatures in a monodisperse spray. The model takes into account all key processes, which take place during this heating and evaporation, including the distribution of temperature and diffusion of liquid species inside the droplet and the effects of the non-unity activity coefficient (ideal and non-ideal models). The effects of recirculation in the moving droplets on heat and mass diffusion within them are taken into account using the effective thermal conductivity and the effective diffusivity models. The previously obtained analytical solution of the transient heat conduction equation inside droplets is incorporated in the numerical code alongside the original analytical solution of the species diffusion equation inside droplets. The predicted time evolution of the average temperatures is shown to be reasonably close to the measured one, especially in the case of pure acetone and acetone-rich mixture droplets. It is shown that the temperatures predicted by the simplified model and the earlier reported vortex model are reasonably close. Also, the temperatures predicted by the ideal and non-ideal models differ by not more than several degrees. This can justify the application of the simplified model with the activity coefficient equal to 1 for the interpretation of the time evolution of temperatures measured with errors more than several degrees.     

加热板液滴蒸发的理论分析及实验研究

液滴蒸发是由气-液浓度差驱动的一种常见而复杂的扩散现象.通过实验与理论相结合对去离子水在玻璃表面和有机硅油表面的蒸发特性进行研究,测量了液滴接触角和接触直径随时间的动态演变过程.结果 发现:玻璃表面的液滴蒸发为典型的定底半径模式和混合模式;而液滴在有机硅油表面较为特殊,除了定底半径模式和混合模式还有周期性的黏滑模式.出...     

On molar- and mass-based approaches to single component drop evaporation modelling

Different approaches to model evaporation from single-component spherical liquid drop floating in a gaseous environment are analysed. The species conservation equations in molar and mass form are solved to yield different drop evaporation models. Two of them rely on the widely used assumption of constant (molar or mass) density and yield an explicit formula for the evaporation rate, whereas the third model relieves the constant density hypothesis and yields the evaporation rate in implicit form. The comparison among the results predicted by the models is made for a relative wide range of temperature, pressure and Reynolds number operating conditions and for different liquids, like water, alcohols, ketones and hydrocarbons.     

Experimental and numerical investigation of droplet evaporation under diesel engine conditions

Evaporation of mono-disperse fuel droplets under high temperature and high pressure conditions is investigated. The time-dependent growth of the boundary layer of the droplets and the influence of neighboring droplets are examined analytically. A transient Nusselt number is calculated from numerical data and compared to the quasi-steady correlations available in literature. The analogy between heat and mass transfer is tested considering transient and quasi-steady calculations for the gas phase up to the critical point for a single droplet. The droplet evaporation in a droplet chain is examined numerically. Experimental investigations are performed to examine the influence of neighboring droplets on the drag coefficients. The results are compared with drag coefficient models for single droplets in a temperature range from T = 293–550 K and gas pressure p = 0.1–2 MPa. The experimental data provide basis for model validation in computational fluid dynamics.     

A numerical investigation of evaporation characteristics of a fuel droplet suspended from a thermocouple

Numerical simulations of combined natural convection–conduction in a droplet of n-dodecane suspended from a thermocouple were carried out, taking into consideration evaporation, and the effect of thermocouple diameter on the evaporation characteristics was investigated. The calculated temperature history of the droplet is in good agreement with experimental results; both show that the rate of heating decreases with increasing thermocouple diameter. The maximum error in temperature due to the thermocouple increases linearly with increasing thermocouple diameter. Thus, in investigations involving a droplet suspended from a thermocouple, it is preferable to use a thermocouple with the smallest possible diameter.     

Numerical study of Marangoni convection during transient evaporation of two-component droplet under forced convective environment

Numerical simulations of the evaporation of stationary, spherical, two-component liquid droplets in a laminar, atmospheric pressure, forced convective hot-air environment are presented. The transient two-phase numerical model includes multi-component diffusion, a comprehensive method to deal with the interface including the surface tension effects and variation of thermo-physical properties as a function of temperature and species concentration in both liquid- and vapor-phases. The model has been validated using the experimental data available in literature for suspended heptane–decane blended droplets evaporating under a forced convective air environment. The validated model is used to study the vaporization characteristics of heptane–decane droplets under different convective conditions. For an initial composition having 75% by volume of more volatile fuel component, the evaporation transients are presented in terms of variations in interface quantities. Flow, species and temperature fields are presented at several time instants to show the relative strengths of forced convection and Marangoni convection. Results show that at low initial Reynolds numbers, the solutal Marangoni effects induce a flow-field within the liquid droplet, which opposes the flow of the external convective field. The strength of this liquid-phase flow field increases with the consumption of the more volatile fuel component.     

Hydronic heating systems: transient modelling,validation and load matching control

A dynamic model of a hydronic heating system is developed. The system consists of a boiler, baseboard terminal units, domestic hot water (DHW) heat exchanger coil and an environmental zone. The model is described by a set of time varying nonlinear coupled differential equations. Predicted responses from the model are compared with the measured data gathered on an on–off controlled hydronic heating system installed in an apartment building. Results show that the model predictions compare well with the field data. Using this validated model, feedback controllers are designed to achieve better regulation of zone air temperature, boiler water temperature and DHW temperature. A load tracking setpoint control strategy is proposed to regulate boiler temperature as a function of outdoor air temperature. Results showing the simulated responses of the system with the designed controllers subject to step changes in space heating and DHW loads are given. © 1998 John Wiley & Sons, Ltd.     

Laser heating and surface evaporation

In the present study, laser heating of solid substrate and evaporation of the surface are considered. The numerical method is employed to predict the temperature field in the solid as well as in the vapor front. The absorption of incident laser beam by the evaporating front and by the solid is accommodated to account for the absorption process. It is found that temperature decays sharply across the solid–vapor interface due to the location of the laser power intensity, which moves with the interface towards the solid bulk as evaporation of the surface progresses. The recession velocity becomes high in the early evaporation stage and as the heating period progresses, recession velocity becomes almost steady. Consequently, the transient behavior of evaporation can be observed during the early evaporation period.     

A numerical investigation of the evaporation process of a liquid droplet impinging onto a hot substrate

A numerical investigation of the evaporation process of n-heptane and water liquid droplets impinging onto a hot substrate is presented. Three different temperatures are investigated, covering flow regimes below and above Leidenfrost temperature. The Navier–Stokes equations expressing the flow distribution of the liquid and gas phases, coupled with the Volume of Fluid Method (VOF) for tracking the liquid–gas interface, are solved numerically using the finite volume methodology. Both two-dimensional axisymmetric and fully three-dimensional domains are utilized. An evaporation model coupled with the VOF methodology predicts the vapor blanket height between the evaporating droplet and the substrate, for cases with substrate temperature above the Leidenfrost point, and the formation of vapor bubbles in the region of nucleate boiling regime. The results are compared with available experimental data indicating the outcome of the impingement and the droplet shape during the impingement process, while additional information for the droplet evaporation rate and the temperature and vapor concentration fields is provided by the computational model.     

Effects of nanoparticles on nanofluid droplet evaporation

Laponite, Fe₂O₃ and Ag nanoparticles were added to deionized water to study their effect of evaporation rates. The results show that these nanofluid droplets evaporate at different rates (as indicated by the evaporation rate constant K in the well known D²-law) from the base fluid. Different particles lead to different values of K. As the particle concentration increases due to evaporation, K values of various Ag and Fe₂O₃ nanofluids go through a transition from one value to another, further demonstrating the effect of increasing nanoparticle concentration. The implication for the heat of vaporization (h_fg) is discussed.     

A molecular dynamics simulation of droplet evaporation

A molecular dynamics (MD) simulation method is developed to study the evaporation of submicron droplets in a gaseous surrounding. A new methodology is proposed to specify initial conditions for the droplet and the ambient fluid, and to identify droplet shape during the vaporization process. The vaporization of xenon droplets in nitrogen ambient under subcritical and supercritical conditions is examined. Both spherical and non-spherical droplets are considered. The MD simulations are shown to be independent of the droplet and system sizes considered, although the observed vaporization behavior exhibits some scatter, as expected. The MD results are used to examine the effects of ambient and droplet properties on the vaporization characteristics of submicron droplets. For subcritical conditions, it is shown that a spherical droplet maintains its sphericity, while an initially non-spherical droplet attains the spherical shape very early in its lifetime, i.e., within 10% of the lifetime. For both spherical and non-spherical droplets, the subcritical vaporization, which is characterized by the migration of xenon particles that constitute the droplet to the ambient, exhibits characteristics that are analogous to those reported for “continuum-size” droplets. The vaporization process consists of an initial liquid-heating stage during which the vaporization rate is relatively low, followed by nearly constant liquid-temperature evaporation at a “pseudo wet-bulb temperature”. The rate of vaporization increases as the ambient temperature and/or the initial droplet temperature are increased. For the supercritical case, the droplet does not return to the spherical configuration, i.e., its sphericity deteriorates sharply, and its temperature increases continuously during the “vaporization” process.     

Experimental investigation and numerical modelling of transient two-phase flow in a geysering geothermal well

Measurements of the periodic transient flow in a vertical geysering geothermal well are presented. The 70-m deep, 0.1-m internal diameter well taps a hot (about 87 °C) water aquifer rich in dissolved carbon dioxide. Transient pressures measured at various depths show the various flow regimes that develop in the borehole and demonstrate that the periodic flow is caused by the degassing of the water flowing up the well. A one-dimensional numerical model of the flow has been developed. The computed results exhibit the main characteristics of the test measurements. This agreement between model and measurements is considered to support both the numerical model and the conceptual model of the system deduced from the measurements.     

Current status of droplet evaporation in turbulent flows

This article reviews the available literature results concerning the effects of turbulence on the transport (heat and mass transfer) rates from a droplet. The survey emphasizes recent findings related specifically to physical models and correlations for predicting turbulence effects on the vaporization rate of a droplet. In addition, several research challenges on the vaporization of fuel droplets in turbulent flow environments are outlined.     

Comparison of analytical and numerical modeling approaches for sizing of seasonal storage solar heating systems

Analytical and numerical approaches for the predesign of central solar heating plants with seasonal storage (CSHPSS) systems are compared. The results indicate that the analytical approach employed in SOLCHIPS predesign tool is significantly faster and more powerful than the traditional numerical methods for predesign of high solar fraction seasonal storage solar heating systems.     

A discrete multicomponent droplet evaporation model; effects of O2-enrichment,steam injection,and EGR on evaporation of diesel droplet

A discrete multicomponent (DMC) model for droplet evaporation in convective ambient is developed. Three different sets of correlations for Nusselt and Sherwood number are examined. The model is compared with experimental data for single and multicomponent droplet evaporation at different conditions and the most suitable set of correlations is selected. Having validated model, the diesel droplet evaporation under different ambient conditions and compositions is investigated. Increasing of oxygen mass fraction in N₂–O₂ mixture ambient from 0 to 1 first decreases and then increases the lifetime. Steam addition enhances the evaporation rate and it affects evaporation more significantly at higher temperatures. Exhaust gas recirculation (EGR) results in slight variations in droplet lifetime and its heating period.     

Numerical simulation of droplet impact and evaporation on a porous surface

Numerical simulation is performed for the evaporation of a droplet impacted on a porous surface. A level-set formulation for tracking the droplet deformation is extended to include the effects of evaporation coupled to heat and mass transfer, porosity and porous drag and capillary forces. The local volume averaged conservation equations of mass, momentum, energy and vapor fraction for the porous region are simultaneously solved with the conservation equations for the external fluid region. The computations demonstrate not only the evolution of the liquid-gas interface during the whole period of droplet penetration and evaporation in a porous medium, but also the associated flow, temperature and vapor fraction fields. The effects of impact velocity, porosity and particle size on the droplet deformation and evaporation are quantified.     

Effects of gravity and ambient pressure on liquid fuel droplet evaporation

An axisymmetric numerical model has been developed to conduct a study of single droplet evaporation over a wide range of ambient pressures both under normal and microgravity conditions. Results for droplet lifetime as a function of ambient pressure and initial droplet diameter are presented. The enhancement in the droplet evaporation rate due to natural convection is predicted. This enhancement becomes more dominant with increasing ambient pressure due to the increase in the Grashof number. The higher the ambient pressure, the closer the Grashof number remains to its initial value throughout most of the droplet lifetime because of the droplet swelling and the heat-up of the droplet interior. Results should be particularly of interest to researchers conducting experiments on droplet evaporation at elevated pressures within a normal gravity environment. The model developed is in good agreement with experimental data at low pressures. Explanations have been provided for its deviation at high pressures.