Flash Evaporation Process: Semi-Analytical Model Development for Droplets and Laminar Thin Film Flow

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Sharma, Manvendra
Chakraborty, Prodyut R.
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Indian Institute of Technology Jodhpur
With the advent of miniaturization technology of electronic components and development of high energy devices, the cooling requirements of electronic systems has changed drastically. The localised high heat flux on micro level components has also become of the order of kW/cm2. For such a high heat flux, the conventional methods are unviable, as they need large flow rate of coolant to achieve tough temperature control. Due to the aforementioned reasons, the research in the field of Thermal Management System (TMS) for electronic systems becomes need of present to identify new cooling technologies. Flash evaporation cooling method is one of the potential contestants among futuristic thermal management technologies. Typically, flash evaporation process involves sudden depressurization of liquids below the saturation pressure corresponding to the liquid temperature. Due to the sudden drop in pressure, the whole energy cannot be contained in the liquid as sensible heat, and the surplus heat gets converted into latent heat of vaporization followed by a violent transition of liquid to vapor phase. During flash evaporation process, the latent heat of evaporation is absorbed mostly from the liquid itself, and temperature of the liquid falls very quickly. The commonly adopted mechanisms in industries are pool flashing, spraying of fluid in the form of droplets, flashing of flowing fluid and flashing of jets etc. Albeit being a fundamental cooling mechanism with numerous day today applications, there exists many a rarely studied problem description that involves evaporation cooling mechanism requiring suitable analytical treatment. Therefore, the present work focuses on investigating the flashing phenomenon with varying flow conditions? as droplet evaporation, flashing of film on vertical plane and convective heat transfer of falling film with emphasis on development of analytical and numerical models. The first part of the study is attributed to the development of a semi analytical transient heat diffusion model of droplet evaporation. The model is developed considering the effect of change in droplet size due to evaporation from its surface? when the droplet is injected into vacuum. Hertz and Knudsen formulation based on kinetic theory to evaluate evaporation mass flux from the free surface is considered. The study addresses the discrepancy in the values of obtained evaporation coefficients reported for diffusion based mathematical model and lumped heat model, where evaporation coefficient is termed as the ratio of actual evaporating mass flux rate to the maximum possible evaporating mass flux rate. The model shows strong dependence of evaporation coefficient on microdroplet size. Moreover, when the droplet radius is less than that of mean free path of vapor molecules at the evaporating surface, the evaporation coefficient is found to approach theoretical limit of unity and reduces rapidly for larger radii. Water has been considered as working fluid for the saturation temperature range of 295273.16K in the present study. The next set of analysis involves the development of a semi analytical model that addresses the hydrodynamic behavior of fluid film, falling on an adiabatic wall, under the effect of gravity with smooth laminar flow conditions. Although many researchers have carried out the hydrodynamic study of gravity driven vertical falling film in the last five decades, Reynolds Transport Theorem (RTT) has never been employed prior to the present work. The adopted approach is validated with the help of published literature, by comparing obtained parametric relations with the reported set of equations. A good agreement of the experimental results with obtained data provided an adequate confidence to use RTT for further study of convective heat transfer and flash evaporation. Thereby, the analysis led the foundation for heat transfer studies made further. With the shown conformity of previous investigations, the study is extended to convective heat transfer from the free surface of gravity driven vertical falling film. Unlike falling film evaporators, where fluid film gets heated from the wall on which it travels, the heat transfer takes place from the free surface to the film's interior in the present analysis. Consequently, an entirely new phenomenon has been considered, where thermal boundary layer develops at free surface, and thickens in the downstream flow direction towards wall. Therefore, the effect of thermal boundary layer on heat transfer mechanism from the free surface has rigorously investigated with the help of 1D heat transfer model. The developed model is based on the RTT. The model has further been extended by exposing the falling film in the vacuum, where pressure is maintained lower than the saturation pressure of liquid, corresponding to liquid temperature. A semi analytical 1D model has been developed considering RTT and Hertz and Knudsen formulation based on kinetic theory to evaluate evaporation mass flux from the free surface. Oneway coupling ( i.e hydrodynamic parameters effect the thermal behavior but reverses not true) has been employed. The rigorous study of the model involves the numerous parametric variations that have been checked for the physical consistency. The required parameters for the flash evaporation based thermal management system design have been evaluated minutely and distinctly. The detailed examination of thermal parameters like? surface temperature, bulk temperature, mass flux rate along with hydrodynamic parameters has been culminated in the form of unique unprecedented correlations. The correlations determined for local Nusselt number, surface temperature, bulk mean temperature and film thickness are validated with the set of data distinct from the data set through which the correlations are developed. Excellent agreement between the data obtained through proposed semi analytical model and data calculated through determined correlations is observed. The proposed analytical and numerical models along with the correlations, contribute towards heat transfer mechanism from the free surface of smooth laminar film under low pressure environment. The models further help to identify design parameters for flash evaporation based cooling. Moreover, the presented analysis provides an underlying basis for the development of two way coupling for thermal behavior and hydrodynamic analysis. Waviness of surface, temperature dependency of fluid properties, surface tension of liquid, buoyancy effect and roughness of adiabatic wall, may further be added in the present model at the cost of increasing complexity.
Sharma, Manvendra. (2023).Flash Evaporation Process: Semi-Analytical Model Development for Droplets and Laminar Thin Film Flow (Doctor's thesis). Indian Institute of Technology Jodhpur, Jodhpur.