Search results for: Clean Energy

Authors: Zahra Yazdani Paraii, Zohreh Yazdani Paraei

Abstract:

Many urban designers and planners have been involved in the design of environmentally friendly or nature adaptable urban development models due to increase in urban populations in the recent century, limitation on natural resources, climate change, and lack of enough water and food. Ecological city is one of the latest models proposed to accomplish the latter goal. In this work, the existing establishing indicators of the ecological city are used regarding energy, water, land use and transportation issues. The model is used to compare the function of traditional settlements of Iran. The result of investigation shows that the specifications and functions of the traditional settlements of Iran fit well into the ecological city model. It is found that the inhabitants of the old cities and villages in Iran had founded ecological cities based on their knowledge of the environment and its natural opportunities and limitations.

Keywords: Ecological city, traditional city, urban design, environment.

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Authors: Betül Özgenç Kaya, Soner Kuslu, Sabri Çolak, Turan Çalban

Abstract:

Ulexite (Na2O.2CaO.5B2O3.16H2O) is boron mineral that is found in large quantities in the Turkey and world. In this study, the dissolution of this mineral in the disodium hydrogen phosphate solutions has been studied. Temperature, concentration, stirring speed, solid liquid ratio and particle size were selected as parameters. The experimental results were successfully correlated by linear regression using Statistica program. Dissolution curves were evaluated shrinking core models for solid-fluid systems. It was observed that increase in the reaction temperature and decrease in the solid/liquid ratio causes an increase the dissolution rate of ulexite. The activation energy was found to be 63.4 kJ/mol. The leaching of ulexite was controlled by chemical reaction.

Keywords: Disodium hydrogen phosphate, Leaching kinetics, Ulexite.

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Authors: Gregor Radonjič, Aleksandra P. Korda, Damijan Krajnc

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The aim of the study was to investigate whether there is the promotion of product ecodesign measures as a result of adopting ISO 14001 certification in manufacturing companies in the Republic of Slovenia. Companies gave the most of their product development attention to waste and energy reduction during manufacturing process and reduction of material consumption per unit of product. Regarding the importance of different ecodesign criteria reduction of material consumption per unit of product was reported as the most important criterion. Less attention is paid to endof- life issues considering recycling or packaging. Most manufacturing enterprises considered ISO 14001 standard as a very useful tool or at least a useful tool helping them to accelerate and establish product ecodesign activities. Two most frequently considered ecodesign drivers are increased competitive advantage and legal requirements and two most important barriers are high development costs and insufficient market demand.

Keywords: ecodesign, environmental management system, ISO 14001, products

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Authors: Cafer Görkem Pınar, İlker Coşar, Serkan Uzun, Atahan Çelebi, Mehmet Ali Ersoy, Ali Pınarbaşı

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In this study, it was numerically investigated that a 1:1 scale model of the Renault Clio MK4 SW brand vehicle aerodynamic analysis was performed in the commercial computational fluid dynamics (CFD) package program of ANSYS CFX 2021 R1 under steady, subsonic, and 3-D conditions. The model of vehicle used for the analysis was made independent of the number of mesh elements and the k-epsilon turbulence model was applied during the analysis. Results were interpreted as streamlines, pressure gradient, and turbulent kinetic energy contours around the vehicle at 50 km/h and 100 km/h speeds. In addition, the validity of the analysis was decided by comparing the drag coefficient of the vehicle with the values in the literature. As a result, the pressure gradient contours of the taillight of the Renault Clio MK4 SW vehicle were examined and the behavior of the total force at speeds of 50 km/h and 100 km/h was interpreted.

Keywords: CFD, k-epsilon, aerodynamics, drag coefficient, taillight.

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Authors: Jyoti Narayan, S. Choudhary

Abstract:

Nanowire arrays of copper with uniform diameters have been synthesized by potentiostatic electrochemical metal deposition (EMD) of copper sulphate and potassium chloride solution within the nano-channels of porous Indium-Tin Oxide (ITO), also known as Tin doped Indium Oxide templates. The nanowires developed were fairly continuous with diameters ranging from 110-140 nm along the entire length. Single as well as poly-crystalline copper wires have been prepared by application of appropriate potential during the EMD process. Scanning electron microscopy (SEM), high resolution transmission electron microscopy (HRTEM), small angle electron diffraction (SAED) and atomic force microscopy (AFM) were used to characterize the synthesized nano wires at room temperature. The electrochemical response of synthesized products was evaluated by cyclic voltammetry while surface energy analysis was carried out using a Goniometer.

Keywords: Electro-deposition, Metallic nano-wires, Nanomaterials, Template synthesis

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Authors: Catherine K. Thubakgale, Richard K.K. Mbaya, Kaby Kabongo

Abstract:

The morphology, mineralogical and chemical composition of a low-grade nickel ore from Mpumalanga, South Africa, were studied by scanning electron microscope (SEM), X-ray diffraction (XRD) and X-ray fluorescence (XRF), respectively. The ore was subjected to atmospheric agitation leaching using sulphuric acid to investigate the effects of acid concentration, leaching temperature, leaching time and particle size on extraction of nickel and cobalt. Analyses results indicated the ore to be a saprolitic nickel laterite belonging to the serpentine group of minerals. Sulphuric acid was found to be able to extract nickel from the ore. Increased acid concentration and temperature only produced low amounts of nickel but improved cobalt extraction. As high as 77.44% Ni was achieved when leaching a -106+75μm fraction with 4.0M acid concentration at 25oC. The kinetics of nickel leaching from the saprolitic ore were studied and the activation energy was determined to be 18.16kJ/mol. This indicated that nickel leaching reaction was diffusion controlled.

Keywords: Laterite, sulphuric acid, atmospheric leaching, nickel.

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Authors: André Smith, Amr Abdel-Dayem

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The stereo matching problem, while having been present for several decades, continues to be an active area of research. The goal of this research is to find correspondences between elements found in a set of stereoscopic images. With these pairings, it is possible to infer the distance of objects within a scene, relative to the observer. Advancements in this field have led to experimentations with various techniques, from graph-cut energy minimization to artificial neural networks. At the basis of these techniques is a cost function, which is used to evaluate the likelihood of a particular match between points in each image. While at its core, the cost is based on comparing the image pixel data; there is a general lack of consistency as to what image data representation to use. This paper presents an experimental analysis to compare the effectiveness of more common image data representations. The goal is to determine the effectiveness of these data representations to reduce the cost for the correct correspondence relative to other possible matches.

Keywords: Colour data, local stereo matching, stereo correspondence, disparity map.

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Authors: M.R. Ebrahimi, M. Ehsan

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This paper presents a practical scheme that can be used for allocating the transmission loss to generators and loads. In this scheme first the share of a generator or load on the current through a branch is determined using Z-bus modified matrix. Then the current components are decomposed and the branch loss allocation is obtained. A motivation of proposed scheme is to improve the results of Z-bus method and to reach more fair allocation. The proposed scheme has been implemented and tested on several networks. To achieve practical and applicable results, the proposed scheme is simulated and compared on the transmission network (400kv) of Khorasan region in Iran and the 14-bus standard IEEE network. The results show that the proposed scheme is comprehensive and fair to allocating the energy losses of a power market to its participants.

Keywords: Transmission Loss, Loss Allocation, Z-bus modifiedmatrix, current Components Decomposition and Restructured PowerSystems

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Authors: Omar Qasaimeh

Abstract:

The effect of the number of quantum dot (QD) layers on the saturated gain of doped QD semiconductor optical amplifiers (SOAs) has been studied using multi-population coupled rate equations. The developed model takes into account the effect of carrier coupling between adjacent layers. It has been found that increasing the number of QD layers (K) increases the unsaturated optical gain for K<8 and approximately has no effect on the unsaturated gain for K ≥ 8. Our analysis shows that the optimum ptype concentration that maximizes the unsaturated optical gain of the ground state is NA Ôëê 0.75 ×1018cm-3 . On the other hand, it has been found that the saturated optical gain for both the ground state and the excited state are strong function of both the doping concentration and K where we find that it is required to dope the dots with n-type concentration for very large K at high photon energy.

Keywords: doping, multilayer, quantum dot optical amplifier, saturated gain.

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Authors: Seyedehzahra Mirrahimi, Nik Lukman Nik Ibrahim, M. Surat

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This paper investigated the impact of ceiling height and window head heights variation on daylighting inside architectural teaching studio with a full width window. In architectural education, using the studio is more than normal classroom in most credit hours. Therefore, window position, size and dimension of studio have direct influence on level of daylighting. Daylighting design is a critical factor that improves student learning, concentration and behavior, in addition to these, it also reduces energy consumption. The methodology of analysis involves using Radiance in IES software under overcast and cloudy sky in Malaysia. It has been established that presentation of daylighting of architecture studio can be enhanced by changing the ceiling heights and window level, because, different ceiling heights and window head heights can contribute to different range of daylight levels.

Keywords: Ceiling height, window head height, daylighting, studio architecture, simulation.

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Authors: C. F. Kumru, C. Kocatepe, O. Arikan

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In this study, electric field distribution analyses for three pylon models are carried out by a Finite Element Method (FEM) based software. Analyses are performed in both stationary and time domains to observe instantaneous values along with the effective ones. Considering the results of the study, different line geometries is considerably affecting the magnitude and distribution of electric field although the line voltages are the same. Furthermore, it is observed that maximum values of instantaneous electric field obtained in time domain analysis are quite higher than the effective ones in stationary mode. In consequence, electric field distribution analyses should be individually made for each different line model and the limit exposure values or distances to residential buildings should be defined according to the results obtained.

Keywords: Electric field, energy transmission line, finite element method, pylon.

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Authors: Anant Oonsivilai, Kenedy A. Greyson

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The growth and interconnection of power networks in many regions has invited complicated techniques for energy management services (EMS). State estimation techniques become a powerful tool in power system control centers, and that more information is required to achieve the objective of EMS. For the online state estimator, assuming the continuous time is equidistantly sampled with period Δt, processing events must be finished within this period. Advantage of Kalman Filtering (KF) algorithm in using system information to improve the estimation precision is utilized. Computational power is a major issue responsible for the achievement of the objective, i.e. estimators- solution at a small sampled period. This paper presents the optimum utilization of processors in a state estimator based on KF. The model used is presented using Petri net (PN) theory.

Keywords: Kalman filters, model, Petri Net, power system, sequential State estimator.

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Authors: Alexandre Marin, Alexandra Bac, Laurent Astart

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New numerical methods for PDE resolution (such as Finite Volumes (FV) or Virtual Element Method (VEM)) open new needs in terms of meshing of domains of interest, and in particular polyhedral meshes have many advantages. One way to build such meshes consists in constructing Restricted Voronoi Diagrams (RVDs) whose boundaries respect the domain of interest. By minimizing a function defined for RVDs, the shapes of cells can be controlled, i.e. elongated according to user-defined directions or adjusted to comply with given aspect ratios (anisotropy) and density variations. In this paper, our contribution is threefold: first, we present a gradient formula for the Voronoi tessellation energy under a continuous anisotropy field. Second, we describe a meshing algorithm based on the optimisation of this function that we validate against state-of-the-art approaches. Finally, we propose a hierarchical approach to speed up our meshing algorithm.

Keywords: Anisotropic Voronoi Diagrams, Meshes for Numerical Simulations, Optimisation, Volumic Polyhedral Meshing.

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Authors: Yasaman Zeinali, Farid Khosravikia

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This paper presents a multi-objective framework for sustainable urban development. The proposed framework aims to address different aspects of sustainability in urban development planning. These aspects include, but are not limited to education, health, job opportunities, architecture, culture, environment, mobility, energy, water, waste, and so on. Then, the proposed framework is applied to the Brackenridge Tract (an area in downtown Austin, Texas), to redevelop that area in a sustainable way. The detail of the implementation process is presented in this paper. The ultimate goal of this paper is to develop a sustainable area in downtown Austin with ensuring that it locally meets the needs of present and future generations with respect to economic, social, environmental, health as well as cultural aspects. Moreover, it helps the city with the population growth problem by accommodating more people in that area.

Keywords: Environmental impacts of human activities, sustainability, urban planning.

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Authors: Martha C. Orazulume, Jibril D. Jiya

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Flexible satellites are equipped with various appendages which vibrate under the influence of any excitation and make the attitude of the satellite to be unstable. Therefore, the system must be able to adjust to balance the effect of these appendages in order to point accurately and satisfactorily which is one of the most important problems in satellite design. Proportional Integral Derivative (PID) Controller is simple to design and computationally efficient to implement which is used to stabilize the effect of these flexible appendages. However, manual turning of the PID is time consuming, waste energy and money. Particle Swarm Optimization (PSO) is used to tune the parameters of PID Controller. Simulation results obtained show that PSO tuned PID Controller is able to re-orient the spacecraft attitude as well as dampen the effect of mechanical resonance and yields better performance when compared with manually tuned PID Controller.

Keywords: Attitude control, flexible satellite, particle swarm optimization, PID controller.

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Authors: N. A. Salim, M. M. Othman, I. Musirin, M. S. Serwan

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Over the past few decades, power system industry in many developing and developed countries has gone through a restructuring process of the industry where they are moving towards deregulated power industry. This situation will lead to competition among the generation and distribution companies to provide quality and efficient production of electric energy, which will reduce the price of electricity. Therefore it is important to obtain an accurate value of the available transfer capability (ATC) and transmission reliability margin (TRM) in order to ensure the effective power transfer between areas during the occurrence of uncertainties in the system. In this paper, the TRM and ATC is determined by taking into consideration the uncertainties of the system operating condition and system cascading collapse by applying the bootstrap technique. A case study of the IEEE RTS-79 is employed to verify the robustness of the technique proposed in the determination of TRM and ATC.

Keywords: Available transfer capability, bootstrap technique, cascading collapse, transmission reliability margin.

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Authors: D. G. Jung, J. B. Lim, J. H. Kim, J. J. Kim

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The international society focuses on the environment protection and natural energy sources control for the global cooperation against weather change and sustainable growth. The study presents the overview of the water shortage status and the necessity of wastewater reuse facility in military facilities and for the possibility of the introduction, compares the economics by means of cost-benefit analysis. The military features such as the number of users of military barracks and the water use were surveyed by the design principles by facility types, the application method of wastewater reuse facility was selected, the feed water, its application and the volume of reuse volume were defined and the expectation was estimated, confirming the possibility of introducing a wastewater reuse possibility by means of cost-benefit analysis.

Keywords: military barracks, wastewater reuse facility, cost-benefit analysis

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Authors: Emine Teke, Soner Kuşlu, Sabri Çolak, Turan Çalban

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The aim of the present study was to investigate the dissolution kinetics of ulexite in sodium dihydrogen phosphate in a mechanical agitation system and also to declare an alternative reactant to produce the boric acid. Reaction temperature, concentration of sodium dihydrogen phosphate, stirring speed, solid-liquid ratio, and ulexite particle size were selected as parameters. The experimental results were successfully correlated by using linear regression and a statistical program. Dissolution curves were evaluated in order to test the shrinking core models for solid-fluid systems. It was observed that increase in the reaction temperature and decrease in the solid/liquid ratio causes an increase in the dissolution rate of ulexite. The activation energy was found to be 36.4 kJ/mol. The leaching of ulexite was controlled by diffusion through the ash (or product) layer.

Keywords: Sodium dihydrogen phosphate, leaching kinetics, ulexite.

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Authors: Sam Rasoulzadeh, Atefeh Mousavi

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Fluidized bed reactors are known as highly exothermic and endothermic according to uniformity in temperature as a safe and effective mean for catalytic reactors. In these reactors, a wide range of catalyst particles can be used and by using a continuous operation proceed to produce in succession. Providing optimal conditions for the operation of these types of reactors will prevent the exorbitant costs necessary to carry out laboratory work. In this regard, a hydrodynamic analysis was carried out with heat transfer in the solid-gas fluidized bed reactor for solar thermal applications. The results showed that in the fluid flow the input of the reactor has a lower temperature than the outlet, and when the fluid is passing from the reactor, the heat transfer happens between cylinder and solar panel and fluid. It increases the fluid temperature in the outlet pump and also the kinetic energy of the fluid has been raised in the outlet areas.

Keywords: Heat transfer, solar reactor, fluidized bed reactor, CFD.

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Authors: A. Kardi, R. Zagrouba, M. Alqahtani

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The Internet of Everything (IoE) presents today a very attractive and motivating field of research. It is basically based on Wireless Sensor Networks (WSNs) in which the routing task is the major analysis topic. In fact, it directly affects the effectiveness and the lifetime of the network. This paper, developed from recent works and based on extensive researches, proposes a taxonomy of routing protocols in WSNs. Our main contribution is that we propose a classification model based on nine classes namely application type, delivery mode, initiator of communication, network architecture, path establishment (route discovery), network topology (structure), protocol operation, next hop selection and latency-awareness and energy-efficient routing protocols. In order to provide a total classification pattern to serve as reference for network designers, each class is subdivided into possible subclasses, presented, and discussed using different parameters such as purposes and characteristics.

Keywords: WSNs, sensor, routing protocols, survey.

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Authors: Labiba I. Hussein, Maher Z. Elsabee, Eid A. Ismail, Hala F. Naguib, Hilda A. Aziz, Moataz A. Elsawy

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Jojoba oil-wax is extracted from the seeds of the jojoba (Simmondsia chinensis Link Schneider), a perennial shrub that grows in semi desert areas in Egypt and in some parts of the world. The main uses of jojoba oil-wax are in the cosmetics and pharmaceutical industry, but new uses could arise related to the search of new energetic crops. This paper summarizes a process to convert the jojoba oil-wax to biodiesel by transesterification with ethanol and a series of aliphatic alcohols using a more economic and energy saving method in a domestic microwave. The effect of time and power of the microwave on the extent of the transesterification using ethanol and other aliphatic alcohols has been studied. The separation of the alkyl esters from the fatty alcohols rich fraction has been done in a single crystallization step at low temperature (−18°C) from low boiling point petroleum ether. Gas chromatography has been used to follow up the transesterification process. All products have been characterized by spectral analysis.

Keywords: Jojoba oil, transesterification, microwave, gas chromatography jojoba esters, Jojoba alcohol.

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Authors: Pawel P. Czapski, Andrzej Sluzek

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This paper presents preliminary results regarding system-level power awareness for FPGA implementations in wireless sensor networks. Re-configurability of field programmable gate arrays (FPGA) allows for significant flexibility in its applications to embedded systems. However, high power consumption in FPGA becomes a significant factor in design considerations. We present several ideas and their experimental verifications on how to optimize power consumption at high level of designing process while maintaining the same energy per operation (low-level methods can be used additionally). This paper demonstrates that it is possible to estimate feasible power consumption savings even at the high level of designing process. It is envisaged that our results can be also applied to other embedded systems applications, not limited to FPGA-based.

Keywords: Power optimization, FPGA, system-level designing, wireless sensor networks.

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Authors: Muhammad Y.K. Barozai, Ifthikhar A. Baloch, M. Din

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MicroRNAs (miRNAs) are small, non-coding and regulatory RNAs about 20 to 24 nucleotides long. Their conserved nature among the various organisms makes them a good source of new miRNAs discovery by comparative genomics approach. The study resulted in 21 miRNAs of 20 pre-miRNAs belonging to 16 families (miR156, 157, 158, 164, 165, 168, 169, 172, 319, 390, 393, 394, 395, 400, 472 and 861) in evergreen spruce tree (Picea). The miRNA families; miR 157, 158, 164, 165, 168, 169, 319, 390, 393, 394, 400, 472 and 861 are reported for the first time in the Picea. All 20 miRNA precursors form stable minimum free energy stem-loop structure as their orthologues form in Arabidopsis and the mature miRNA reside in the stem portion of the stem loop structure. Sixteen (16) miRNAs are from Picea glauca and five (5) belong to Picea sitchensis. Their targets consist of transcription factors, growth related, stressed related and hypothetical proteins.

Keywords: BLAST, Comparative Genomics, Micro-RNAs, Spruce

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Authors: Jin Myoung Kim, Tae Ho Cho

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Wireless Sensor networks have a wide spectrum of civil and military applications that call for secure communication such as the terrorist tracking, target surveillance in hostile environments. For the secure communication in these application areas, we propose a method for generating a hierarchical key structure for the efficient group key management. In this paper, we apply A* algorithm in generating a hierarchical key structure by considering the history data of the ratio of addition and eviction of sensor nodes in a location where sensor nodes are deployed. Thus generated key tree structure provides an efficient way of managing the group key in terms of energy consumption when addition and eviction event occurs. A* algorithm tries to minimize the number of messages needed for group key management by the history data. The experimentation with the tree shows efficiency of the proposed method.

Keywords: Heuristic search, key management, security, sensor network.

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Authors: M. Arockia Jaswin, D. Mohan Lal

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Cryogenic treatment is the process of cooling a material to extremely low temperatures to generate enhanced mechanical and physical properties. The purpose of this study is to examine the effect of cryogenic treatment on the impact behavior of En 52 and 21-4N valve steels. The valve steels are subjected to shallow (193 K) and deep cryogenic treatment (85 K), and the impact behavior is compared with the valve steel materials subjected to conventional heat treatment. The impact test is carried out in accordance with the ASTM E 23-02a standard. The results show an improvement of 23 % in the impact energy for the En 52 deep cryo-treated samples when compared to that of the conventionally heat treated samples. It is revealed that during cryogenic treatment fine platelets of martensite are formed from the retained austenite, and these platelets promote the precipitation of fine carbides by a diffusion mechanism during tempering.

Keywords: Cryogenic treatment, valve steel, Fractograph, carbides, impact strength.

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Authors: Thomas Paris, Vincent Bruyere, Patrick Namy

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A numerical model is developed to simulate gas blowdowns through a thin tube and a filter (porous media), separating a high pressure gas filled reservoir to low pressure ones. Based on a previous work, a one-dimensional approach is developed by using the finite element method to solve the transient compressible flow and to predict the pressure and temperature evolution in space and time. Mass, momentum, and energy conservation equations are solved in a fully coupled way in the reservoirs, the pipes and the porous media. Numerical results, such as pressure and temperature evolutions, are firstly compared with experimental data to validate the model for different configurations. Couplings between porous media and pipe flow are then validated by checking mass balance. The influence of the porous media and the nature of the gas is then studied for different initial high pressure values.

Keywords: Fluid mechanics, compressible flow, heat transfer, porous media.

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Authors: D. V. Sreekanth, M. Sreenivasa Rao

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Abrasive jet machining is one of the promising non-traditional machining processes which uses mechanical energy (pressure and velocity) for machining various materials. The process parameters that influence the metal removal rate are kerfs, surface finish, depth of cut, air pressure, and distance between nozzle and work piece, nozzle diameter, abrasive type, abrasive shape, and mass flow rate of abrasive particles. The abrasive particles coming out with high pressure not only hits work surface but also passes through the nozzle resulting in erosion. This paper focuses mainly on the effect of different parameters on the erosion of nozzle in Abrasive jet machining. Three different types of nozzles made of sapphire, tungsten carbide, and high carbon high chromium steel (HCHCS) are used for machining glass and the erosion of these nozzles are calculated. The results are shown in tabular form and graphical representation.

Keywords: AJM, nozzle, sapphire, tungsten carbide, chrome steel.

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Authors: Benjamin Anderson-Sackaney, Amr Abdel-Dayem

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This paper presents a comprehensive survey of recent source camera identification (SCI) systems. Then, the performance of various sensor pattern noise (SPN) estimators was experimentally assessed, under common photo response non-uniformity (PRNU) frameworks. The experiments used 1350 natural and 900 flat-field images, captured by 18 individual cameras. 12 different experiments, grouped into three sets, were conducted. The results were analyzed using the receiver operator characteristic (ROC) curves. The experimental results demonstrated that combining the basic SPN estimator with a wavelet-based filtering scheme provides promising results. However, the phase SPN estimator fits better with both patch-based (BM3D) and anisotropic diffusion (AD) filtering schemes.

Keywords: Sensor pattern noise, source camera identification, photo response non-uniformity, anisotropic diffusion, peak to correlation energy ratio.

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Authors: A. Elnady

Abstract:

This paper presents an improved Direct Power Control (DPC) scheme applied to the multilevel inverter that forms a Distributed Generation Unit (DGU). This paper demonstrates the performance of active and reactive power injected by the DGU to the smart grid. The DPC is traditionally operated by the hysteresis controller with the Space Vector Modulation (SVM) which is applied on the 2-level inverters or 3-level inverters. In this paper, the DPC is operated by the PI controller with the Phase-Disposition Pulse Width Modulation (PD-PWM) applied to the 5-level diode clamped inverter. The new combination of the DPC, PI controller, PD-PWM and multilevel inverter proves that its performance is much better than the conventional hysteresis-SVM based DPC. Simulations results have been presented to validate the performance of the suggested control scheme in the grid-connected mode.

Keywords: Direct power control, PI controller, PD-PWM, and power control.

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Authors: Nemat Abazari, Ilgin Sager

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In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

Keywords: Optimal control, Hamiltonian vector field, Darboux vector, maximum principle, lie group, Rigid body motion, Lorentz metric.

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