International Journal of Heat and Mass Transfer 100 (2016) 615–626

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier.com/locate/ijhmt

Evaporation of a bicomponent droplet during depressurization ⇑ Lu Liu a, , Yan Liu a, Menglong Mi a, Zhi Wang a, Lulin Jiang b a School of Power, Energy and Mechanical Engineering, North China Electric Power University, 071003 Baoding, China b Department of Mechanical Engineering, University of Louisiana at Lafayette, Lafayette, LA 70508, USA article info abstract

Article history: This paper reports an experimental and numerical study of evaporation process of a two-volatile Received 19 November 2015 bicomponent (ethanol/water and acetic acid/water) droplet during depressurization. The environmental Accepted 3 May 2016 pressure, the ambient temperature, and the droplet temperature are investigated during the experiments. Available online 14 May 2016 A mathematic model is then constructed to simulate the droplet evaporation process. The model solves one-dimensional heat conduction equation and species diffusion equation to acquire the temperature Keywords: distribution and the concentration distribution inside the droplet. The activity coefficient is introduced Evaporation to imitate the vapor partial pressure at the droplet surface. By numerical calculations, the variations of Species diffusion temperature distribution and concentration distribution within the ethanol/water droplet and the acetic Depressurization Bicomponent acid/water droplet are discussed. The effects of composition, final ambient pressure and initial droplet diameter on droplet evaporation are also analyzed in the current study. Results show that the model pre- dictions agree well with the measured temperature data, demonstrating the soundness of the present model and providing insight into the complex heat and mass transfer during the evaporation process of a bicomponent droplet under depressurization. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction mation and the dynamic characteristics of spray flash evaporation. The mean size and the temperature of spray droplets were exper- Droplet evaporation during depressurization is a coupled heat imentally obtained and numerically predicted. and mass transfer process accompanied with phase change, which Although rapid evaporation process of a water droplet during has been widely used in spray drying, flash distillation, and desali- depressurization has received considerable attention, few studies nation. Many studies have so far investigated water droplet evap- have been research on the evaporation process of a bicomponent oration under reduced pressure. For experimental studies, Owen droplet during depressurization. Luo et al. [11] experimentally and Jalil [1] recorded the transient pressure and the droplet tem- investigated the factors influencing the temperature variation of perature during flash evaporation through the droplet hanging a brine droplet under reduced pressure. Those parameters involve method. Satoh et al. [2], Liu et al. [3] and Du et al. [4] experimen- initial salt concentration, final ambient pressure, initial droplet tally investigated the shape change and the temperature variation temperature and initial droplet diameter. Zhang et al. [12,13] stud- of a water droplet during rapid evaporation. While for theoretical ied the steam carrying effect in static flash of both pure water and studies, Shin et al. [5] and Kim et al. [6] analyzed the heat and mass aqueous NaCl solution. Muthunayagam et al. [14] developed a transfer process of a water droplet during rapid evaporation by vapor diffusion model to estimate the variations of droplet temper- using diffusion control model. Zhang et al. [7] established a lumped ature and diameter during evaporation process of a saline water thermodynamic model to predict the droplet temperature varia- droplet at low temperatures and reduced pressures. Liu et al. tion during flash evaporation and freezing process. Cheng et al. [15] constructed a mathematical model to simulate the evapora- [8] developed a comprehensive mathematical model of vacuum tion process of a saline droplet during depressurization. The influ- flash evaporation cooling of a water droplet based on the film con- encing factors on saline droplet temperature were theoretically trolled evaporation model and numerical analysis of the droplet analyzed. Nešic´ et al. [16] presented a more detailed description temperature and diameter after evaporation. Besides, Aguilar of various stages of droplet evaporation and drying. Their investi- et al. [9] and Zhou et al. [10] experimentally investigated the for- gation was mainly focused on solid layer formation of a droplet containing colloidal mater. Gopireddy et al. [17] numerically stud- ied the evaporation and drying process of a droplet of polymer in ⇑ Corresponding author. water and mannitol in water. The effects of drying conditions such E-mail address: [email protected] (L. Liu). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.05.007 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved. 616 L. Liu et al. / International Journal of Heat and Mass Transfer 100 (2016) 615–626

Nomenclature

AC cross section area in Eq. (45) b the parameter in Eq. (35) BM Spalding mass transfer number c activity coefficient BT Spalding heat transfer number e the fraction of evaporation rate in Eq. (22);or 1 1 CP specific heat capacity (J kg K ) characteristic Lennard–Jones energies D diffusion coefficient (m2 s1) g dimensionless factor in computational coordinate L latent heat of vaporization (J kg1) k thermal conductivity (W m1 K1) Le Lewis number l dynamic viscosity (Pa s) M molecular weight (kg mol1) q density (kg m3) m mass (kg) r characteristic Lennard–Jones lengths m_ mass vaporization rate (kg s1) u parameter defined by Eqs. (41) and (42) Nu Nusselt number v Effective coefficient P pressure (Pa) Pe Peclet number Subscripts Pr Prandtl number a ambient air 2 q heat flux (W m ) c droplet center 1 1 R gas constant(J mol K )) eff effective Re Reynolds number h convection r radial distance (m) i index for species Sc Schmidt number l liquid Sh Sherwood number m evaporation T temperature (K) r reference t time (s) s droplet surface 1 ua air velocity (m s ) v vapor phase 1 us maximal liquid velocity at droplet surface (m s ) 0 initial state V volume of the test vessel X molar fraction Superscripts and overscore Y mass fraction – average value ⁄ modified value Greek symbols a the parameter in Eq. (35)

as gas velocity, temperature, and relative humidity on evaporation Up to now, the investigations on evaporation of a bicomponent and drying rate were analyzed. In all the previous work, only water droplet have covered the high pressure domain as well as the evaporates within the droplets. atmospheric environment, which can be applied to the combustion However, the evaporation process of a two-volatile component of liquid fuel. However, the evaporation characteristics of a bicom- (such as: water/ethanol) droplet, also called bicomponent droplet, ponent droplet during depressurization remain unknown. Also, the is more complex. The variation of species concentration during temperature and concentration distributions inside the droplet evaporation further increases the complexity of the problem. have not been investigated in detail. The present paper aims to Sazhin et al. [18,19] experimentally and theoretically studied heat- explore evaporation process of a bicomponent droplet during ing and evaporation process of a bicomponent droplet at atmo- depressurization, with the two components evaporating simulta- spheric pressure. The model considered the distribution of neously. An experimental work has been performed to measure temperature and diffusion of liquid species inside the droplet, the environmental pressure, the ambient temperature and the dro- the effect of recirculation in the moving droplets on heat and mass plet temperature during depressurization. A mathematical model diffusion, and the effect of the non-unity activity coefficient. The is developed to simulate the droplet temperature variation with time evolutions of droplet temperature were discussed by compar- the gradual decrease in ambient pressure. The proposed model also ing numerical results with experimental data. Maqua et al. [20] simulates the heat and mass transfers because of evaporation and experimentally measured temperature variation of a bicomponent convection at the droplet surface, accompanying the species diffu- droplet in hot air plume by applying the three color laser induced sion and the temperature gradient inside the droplet. The activity fluorescence technique. The influences of initial composition and coefficient is introduced to simulate the vapor partial pressure at droplet diameter were revealed. Yarin et al. [21] theoretically the droplet surface. The effects of droplet components and final and experimentally investigated the evaporation of acoustically environmental pressure on droplet evaporation are theoretically levitated droplets of binary liquid mixtures. The temporal evolu- analyzed for ethanol/water droplets and acetic acid/water droplets. tions of the droplets surface and the aspect ratio of the droplet con- The model calculations help to comprehensively understand the tour were explored. Raghuram et al. [22] numerical studied the heat and mass transfer process of evaporation of a bicomponent evaporation of stationary, spherical, two-component liquid dro- droplet during depressurization. plets exposed to forced convective hot air at atmosphere pressure. The relative strengths of forced convection and Marangoni convec- tion, the resultant flow, temperature and species fields within the 2. Experimental System droplet were mainly analyzed. Ebrahimian et al. [23] developed a predictive evaporation model for multi-component hydrocarbon The schematic drawing of the experimental apparatus is shown droplets at atmospheric and high pressures to investigate effects in Fig. 1. It consists of four subsystems including a test vessel, a of pressure and composition. vacuum system, a photography system and a data acquisition sys- Download English Version: https://daneshyari.com/en/article/656389

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