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Flash Evaporation Process: Semi-Analytical Model Development for Droplets and Laminar Thin Film Flow
(Indian Institute of Technology Jodhpur, 2022-12) Chakraborty, Prodyut R.
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.
On Some Important Reliability Aspects of General Coherent Systems
(Indian Institute of Technology Jodhpur, 2023-11) Hazra, Nil Kamal
In practice, we use di?erent kinds of systems that are structurally equivalent to various well-established systems available in the literature, namely, ordinary coherent systems, ordinary r-out-of-n systems, sequential r-out-of-n systems, fixed weighted coherent systems, fixed weighted r-out-of-n systems, random weighted coherent systems, random weighted r-out-of-n systems, etc. In this thesis, we study di?erent reliability aspects of these systems under various scenarios. In most real-life scenarios, the components of a system work in the same environment and share the same load. As a consequence, there may exist two di?erent types of dependencies between the components of a system, namely, interdependency and failure dependency. The interdependency structure between the components of a system is usually modeled by a copula. The family of Archimedean copulas is commonly used to serve this purpose as it describes a wide spectrum of dependence structures. On the other hand, the failure dependancy for a system means that the failure of one component has an e?ect on the lifetimes of the remaining components of the system. This failure dependency is often modeled by assuming distributional changes in the lifetimes of the remaining components, upon each failure, of the system. The sequential order statistics (SOS) and the developed sequential order statistics (DSOS) are two models that are commonly used to describe the failure dependency of a system. There is a one-to-one relationship between order statistics and the lifetimes of systems. For example, the lifetime of an ordinary r-out-of-n system is the same as the (n ? r + 1)-th order statistic of the lifetimes of the components of the system. Similar relationships exist for SOS and DSOS. Thus, the study of order statistics is the same as the study of the lifetimes of systems. In this thesis, we study various ordering and ageing properties of ordinary r-out-of-n systems formed by dependent and identically distributed components, where the dependence structure is described by an Archimedean copula. Further, we study the ordering properties of the developed sequential order statistics (DSOS) with the dependence structure described by the Archimedean copula. Similar to the DSOS model, we introduce the notion of developed generalized order statistics (DGOS) which is an extended generalized order statistics (GOS) model formed by dependent random variables. This model contains all existing models of ordered random variables. We study various univariate and multivariate ordering properties of the DGOS model governed by the Archimedean copula. Further, we consider the SOS model with non-identical components and study several univariate and multivariate stochastic comparison results. The basic structures of many real-life systems match with random weighted coherent systems. The performance of a random weighted coherent system is usually measured by its total capacity. However, the major drawback of this measure is that it does not take into account the structure of a system. To overcome this drawback, we introduce a new structure-based performance measure, namely, the survival capacity. Based on this measure, we define three survival mechanisms (namely, Types-I, II and III) for random weighted coherent systems. We develop a methodology to evaluate the reliability of a random weighted coherent system, and provide a signature-based reliability representation for this system. Further, we study di?erent reliability importance measures for the components of a random weighted coherent system. We study the optimal allocation strategy of active redundancies and the optimal assembly method of random weights in a random weighted coherent system. By developing the results for random weighted coherent systems, we generalize many well-established results available for ordinary coherent systems and weighted coherent systems in the literature.
Development of Green Multicomponent Reactions, Cascade Reactions and Direct Oxidation: Efficient Strategies for the Synthesis of Biologically Active Organic Scaffolds
(Indian Institute of Technology Jodhpur, 2023-11) Erande, Rohan D
The development of green multi-component reactions as an efficient synthetic methodology for the construction of biologically active molecules have received great attention in the last couple of decades. However, organic scaffolds such as 2,3-dihydrofurans and 2,3-dihydrofuro[3,2-c]coumarins (DHFC), despite possessing an extremely wide range of biological activities were yet to be succumb in greener way. Following the nature's footsteps, herein we reported an eco-friendly, inexpensive, and efficient one-pot green multicomponent approach to synthesize trans-2,3-dihydrofuro[3,2-c]coumarins (DHFC) catalyzed by imidazole in water under mild conditions. Applications of the developed catalytic process under a multicomponent strategy in a greener medium revealed the outstanding activity, productivity, and broad functional group tolerance, affording a series of newly designed DHFC in excellent yields. In addition, the biological study that was carried out by the collaborative group demonstrates the ability of the sthesized DHFC derivatives to bind to human serum albumin (HSA). Detailed in silico and in vitro structure-activity analysis has been performed, covering all the bases of this biological investigation. Furthermore, the developed strategy was implemented to synthesize bioactive heterocycles, namely dimedone fused 2,3-dihydrofuran derivatives, under mild conditions with excellent yields, using imidazole and water as green catalyst and solvent, respectively. The synthesized dimedone based 2,3-dihydrofuran derivatives have been found to inhibit SaTR in vitro at low to medium micromolar concentrations. On the other hand, the indole alkaloids are known as an epic family of natural products with structurally diverse architecture and a wide range of biological activities. In line, a BF3.OEt2 catalysed cascade strategy for the synthesis of highly substituted pyrrolo[1,2-a]indole core with high diastereoselectivity has been developed. Further, biological evaluation of synthesized derivatives was reflected in their excellent bioactivity. Further, oxidation of polycyclic aromatic hydrocarbons (PAHs) found to be an important area belongs to the biochemistry, astrochemistry, and chemical industries. In line, we have developed the one-pot oxidation of naphthalene, anthracene, pyrene and substituted PAHs in the presence of H2O2 and newly designed [CuIIL] complex derived from non-toxic transition metal and ligand based redox-active PLY backbone, that provided a route for their detoxification and conversion into industrially important compounds. Furthermore, transforming the alcohols and aldehyde groups to esters via oxidative coupling with alcohols has become an attractive target for organic chemists, due to the significance and omnipresence of ester group in chemistry. Thus, a new-designed V-catalyst [(L2)VIVO](ClO4) was synthesized and utilized for its potential catalytic activity towards direct oxidation of two different functionalities, alcohols and aldehydes to their corresponding esters in one-pot procedure using H2O2 and alcoholic medium. Moreover, cinnamate esters transformed to ester (via C=C bond breaking followed by oxidation of in-situ generated aldehyde) in single-step, which is found to be the first ever report to this end.
Towards More Realistic Shock Models with Applications in Optimal Maintenance
(Indian Institute of Technology Jodhpur, 2023-02) Hazra, Nil Kamal
In this thesis we study some generalized shock models with applications in optimal maintenance. Most of the systems used in reality are directly or indirectly a↵ected by some harmful “instantaneous” events (shocks of di↵erent nature), which either cause the system’s failure or decrease the system’s lifetime. Thus, the study of systems’ lifetimes subject to external shocks is one of the important problems in reliability theory. In a shock modeling, one has to answer two important questions, namely, “how the occurrences of shocks a↵ect or decrease the lifetime of a system” and “how one can model the occurrences of shocks on a system ”. In this thesis, we answer these questions in di↵erent setups. Existing shock models are usually classified into four broad classes, namely, extreme shock models, cumulative shock models, run shock models and !-shock models. The !-shock model, which is an object of our study, is di↵erent in nature from other aforementioned shock models. In all !-shock models developed so far in the literature, the recovery time ! was assumed to be constant. However, this assumption is too restrictive and unrealistic in describing many real-life scenarios. Indeed, ! can obviously depend on other parameters, namely, magnitude of shocks, arrival times of shocks, etc. This motivates us to introduce a new time-dependent !-shock model wherein the recovery time of a system is assumed to be an increasing function of arrival times of shocks. For this model, we assume that shocks occur according to the generalized P´olya process (GPP) that contains the homogeneous Poisson process (HPP), the non-homogeneous Poisson process (NHPP) and the P´olya process as particular cases. We further generalize this model to the general !-shock model by considering the recovery time ! as the function of both arrival times and magnitudes of shocks. We also consider a more general and flexible shock process, namely, the Poisson generalized gamma process (PGGP) that includes the HPP, the NHPP, the P´olya process and the GPP as the particular cases. With the same motivation, we study a history-dependent mixed shock model which is a combination of the history-dependent extreme shock model and the history-dependent !-shock model. As an application of the aforementioned new shock models, we study the optimal replacement policy. Although Poisson processes are widely used in various applications for modeling of recurrent point events, there exist obvious limitations. Several specific mixed Poisson processes (which are formally not Poisson processes any more) that were recently introduced in the literature overcome some of these limitations. We define a general mixed Poisson process with the phase-type (PH) distribution as the mixing one. As the PH distribution is dense in the set of lifetime distributions, the new process can be used to approximate any mixed Poisson process. We study some basic stochastic properties of this new process and discuss some relevant applications by considering the extreme shock model, the stochastic failure rate model and the !-shock model. We introduce and study a general class of shock models with dependent inter-arrival times of shocks that occur according to the homogeneous Poisson generalized gamma process (HPGGP). A lifetime of a system a↵ected by a shock process from this class is represented by the convolution of inter-arrival times of shocks. This class contains many popular shock models, namely, the extreme shock model, the generalized extreme shock model, the run shock model, the generalized run shock model, specific mixed shock models, etc. For systems operating under shocks, we derive and discuss the main reliability characteristics and illustrate our findings by the application that considers an optimal mission duration policy. Counting processes based on heavy-tailed distributions (namely, the fractional homogeneous Poisson process (FHPP), the renewal process of matrix Mittag-Leffler type (RPMML), etc.) have not yet been considered in the literature for modeling the occurrences of shocks. Thus, we study some general shock models under the assumption that shocks occur according to a renewal process with the matrix Mittag-Leffler (MML) distributed inter-arrival times. As the class of MML distributions is wide and well-suited for modeling the heavy tail phenomena, these shock models can be very useful for analysis of lifetimes of systems subject to random shocks with inter-arrival times having heavier tails. Some relevant stochastic properties of the introduced models are described. Moreover, two applications, namely, the optimal replacement policy and the optimal mission duration are discussed. Lastly, we consider coherent systems subject to random shocks that can damage a random number of components of a system. Based on the distribution of the number of failed components, we discuss three models, namely, (i) a shock can damage any number of components (including zero) with the same probability, (ii) each shock damages, at least, one component, and (iii) a shock can damage, at most, one component. Moreover, the arrivals of shocks are modeled using three important counting processes, namely, the PGPP, the Poisson phase-type process (PPHP) and the RPMML. For the defined shock models, we study some reliability properties of coherent systems. At the end, we discuss the optimal replacement policy as an application of the proposed models.
Islanding and Faults Detection in Utility Grid Integrated With Solar Renewable Energy Source Using Signal Processing and Machine Learning Algorithms
(Indian Institute of Technology Jodhpur, 2022-07) Yadav, Sandeep Kumar
The interfacing of renewable energy sources (RES) with the utility grid due to the growing demand for clean and cost-effective energy poses new challenges like power quality disturbances, unintentional islanding, change in fault levels, and fault current directions. These unpredictable events pose a significant threat to the continuous supply of loads, the safety of the equipment and personnel involved and also cause considerable economic losses. Hence, the proposed schemes must be able to tackle these challenges and to detect faults and islanding conditions at the earliest. In addition to fault detection and classification, fault location in the distribution system is also a challenging task due to short feeders, complex topology, various laterals, unbalanced operation, and time-varying load profile. Various signal processing techniques such as Wavelet Transform and S-transform, have been employed to extract time-frequency information to detect islanding and fault diagnosis. Empirical Mode Decomposition (EMD) is reported to be adaptive and overcomes the limitations of Wavelet transform (suitable wavelet selection) and S-Transform (non-adaptive selection of Gaussian windows). This thesis proposes high-speed protection algorithms based on Empirical Mode Decomposition of three-phase current signals collected at the substation of a distribution network for detecting islanding and discriminating the same from faults. Fault classification and location have also been accomplished, followed by detection. The three-phase current signals collected at a substation over a moving window are decomposed using the EMD method to extract residues at various levels. These residues are utilized to detect the faults and classify them as LG, LL/LLG, and LLLG (L: line, G: ground). The discrimination between LL and LLG faults is achieved with the help of a neutral current. The first algorithm utilizes the absolute mean (AM) value and Standard deviation (SD) of the first-level residue obtained from EMD to compute fault indices to detect and classify various faults and islanding by comparing with a threshold value within a half cycle. After fault detection and classification, the features of SD and AM from first-level residues are fed to a decision tree (DT) machine-learning algorithm to locate the fault. This algorithm has been successfully tested on IEEE 13 and 34 bus systems with DG penetration in the presence of noise with 20 dB signal to noise ratio (SNR). The second algorithm proposed is based on a combination of EMD and Hilbert Transform (HT), widely known as Hilbert-Huang Transform (HHT), which extracts instantaneous features like instantaneous frequency (IF), instantaneous amplitude (IA), Standard deviation of instantaneous frequency (SDIF), and standard deviation of instantaneous amplitude (SDIA) from the first level residue. A fault index computed based on SDIF is proposed to detect and classify the faults within a quarter cycle by comparing it with a predefined threshold without DG penetration. A machine learning algorithm is proposed to avoid multiple thresholds in the event of DG penetration that requires islanding detection. The instantaneous features are fed to DT to classify faults and islanding. Also, the faulty zone is located using various ML models to evaluate their performance with varying capacities of DG using quarter cycle post-fault data (PFD) in the presence of noise. In third algorithm, image-based fault diagnosis is accomplished by generating unique symmetrical dot patterns (SDP) with the help of monotonic residue after EMD. A novel protection algorithm based on SDP has been proposed with the alienation coefficient of SDPs after a fault and normal conditions as fault index to achieve fault detection and classification. These SDPs, when fed to Convolutional Neural Network (CNN), removed the feature extraction process involved in distribution system fault diagnosis. The proposed algorithms have been successfully tested by varying the type of fault, fault incidence angle, fault resistance, and fault location in the presence of noise. The selectivity of the proposed algorithms has been established by testing with non-faulty transients such as transformer excitation and de-excitation, feeder energization and de-energization, load switching, capacitor switching, and DG tripping in the presence of noise. Thus, the proposed algorithms using a combination of signal processing and machine learning methods can be implemented efficiently for the online monitoring of distribution systems.