Search results for: non-linear thermal radiation

Authors: Mutabar Shah, Muhammad Hassan Sayyad, Khasan S. Karimov

Abstract:

Thin films of Nickel phthalocynine (NiPc) of different thicknesses (100, 150 and 200 nm) were deposited by thermal evaporator on glass substrates with preliminary deposited aluminum electrodes to form Al/NiPc/Al surface-type capacitive humidity sensors. The capacitance-humidity relationships of the sensors were investigated at humidity levels from 35 to 90% RH. It was observed that the capacitance value increases nonlinearly with increasing humidity level. All measurements were taken at room temperature.

Keywords: Capacitive sensor, Humidity, Nickel phthalocyanine, Organic semiconductor.

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Authors: Zainab Almukhtar, Adel Merabet

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In this paper, a method for maximum power point tracking of a photovoltaic energy conversion system is presented. This method is based on using the difference between the power from the solar panel and an estimated power value to control the DC-DC converter of the photovoltaic system. The difference is continuously compared with a preset error permitted value. If the power difference is more than the error, the estimated power is multiplied by a factor and the operation is repeated until the difference is less or equal to the threshold error. The difference in power will be used to trigger a DC-DC boost converter in order to raise the voltage to where the maximum power point is achieved. The proposed method was experimentally verified through a PV energy conversion system driven by the OPAL-RT real time controller. The method was tested on varying radiation conditions and load requirements, and the Photovoltaic Panel was operated at its maximum power in different conditions of irradiation.

Keywords: Control system, power error, solar panel, MPPT.

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Authors: Ibrahim S. Alnomay, Jihad Y. Alhammad

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Lately, an interest has grown greatly in the usages of RFID in an un-presidential applications. It is shown in the adaptation of major software companies such as Microsoft, IBM, and Oracle the RFID capabilities in their major software products. For example Microsoft SharePoints 2010 workflow is now fully compatible with RFID platform. In addition, Microsoft BizTalk server is also capable of all RFID sensors data acquisition. This will lead to applications that required high bit rate, long range and a multimedia content in nature. Higher frequencies of operation have been designated for RFID tags, among them are the 2.45 and 5.8 GHz. The higher the frequency means higher range, and higher bit rate, but the drawback is the greater cost. In this paper we present a single layer, low profile patch antenna operates at 5.8 GHz with pure resistive input impedance of 50 and close to directive radiation. Also, we propose a modification to the design in order to improve the operation band width from 8.7 to 13.8

Keywords: Microstrip Antenna, RFID, U-shaped, double layer, circular antenna.

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Authors: A.S. Kipcak, N. Baran Acarali, S. Kolemen, N. Tugrul, E. Moroydor Derun, S. Piskin

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Fly ash is one of the residues generated in combustion, and comprises the fine particles that rise with the flue gases. Ash which does not rise is termed bottom ash [1]. In our country, it is expected that will be occurred 50 million tons of waste ash per year until 2020. Released waste from the thermal power plants is caused very significant problems as known. The fly ashes can be evaluated by using as adsorbent material. The purpose of this study is to investigate the possibility of use of Tuncbilek fly ash like low-cost adsorbents for heavy metal adsorption. First of all, Tuncbilek fly ash was characterized. For this purpose; analysis such as sieve analysis, XRD, XRF, SEM and FT-IR were performed.

Keywords: Fly ash, heavy metal, sieve, adsorbent

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Authors: Kyung Hyun, Choi, Minh Ngoc, Nong, M. Asif Ali, Rehmani

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This present paper proposes the modified Elastic Strip method for mobile robot to avoid obstacles with a real time system in an uncertain environment. The method deals with the problem of robot in driving from an initial position to a target position based on elastic force and potential field force. To avoid the obstacles, the robot has to modify the trajectory based on signal received from the sensor system in the sampling times. It was evident that with the combination of Modification Elastic strip and Pseudomedian filter to process the nonlinear data from sensor uncertainties in the data received from the sensor system can be reduced. The simulations and experiments of these methods were carried out.

Keywords: Collision avoidance, Avoidance obstacle, Elastic Strip, Real time collision avoidance.

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Authors: O. Onal, O. Turan

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In this paper, some performance parameters of a selected turbofan engine (JT9D) are analyzed. The engine is a high bypass turbofan engine which powers a wide-body aircraft and it produces 206 kN thrust force (thrust/weight ratio is 5.4). The objective parameters for the engine include calculation of power, specific fuel consumption, specific thrust, engine propulsive, thermal and overall efficiencies according to the various definitions given in the literature. Furthermore, in the case study, wasted energy from the exhaust is calculated at the maximum power setting (i.e. take off phase) for the engine.

Keywords: Turbofan, power, efficiency, trust.

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Authors: Dimitrie Marinceu, Alan Murchison

Abstract:

The Canadian Used Fuel Container (UFC) is a mid-size hemispherical headed copper coated steel container measuring 2.5 meters in length and 0.5 meters in diameter containing 48 used fuel bundles. The contained used fuel produces significant gamma radiation requiring automated assembly processes to complete the assembly. The design throughput of 2,500 UFCs per year places constraints on equipment and hot cell design for repeatability, speed of processing, robustness and recovery from upset conditions. After UFC assembly, the UFC is inserted into a Buffer Box (BB). The BB is made from adequately pre-shaped blocks (lower and upper block) and Highly Compacted Bentonite (HCB) material. The blocks are practically ‘sandwiching’ the UFC between them after assembly. This paper identifies one possible approach for the BB automatic assembly cell and processes. Automation of the BB assembly will have a significant positive impact on nuclear safety, quality, productivity, and reliability.

Keywords: Used fuel packing plant, automatic assembly cell, used fuel container, buffer box, deep geological repository.

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Authors: M. Zamani, O. Kahar

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Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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Authors: Mingyu Xie, Mietek Brdys

Abstract:

The paper develops a Non-Linear Model Predictive Control (NMPC) of water quality in Drinking Water Distribution Systems (DWDS) based on the advanced non-linear quality dynamics model including disinfections by-products (DBPs). A special attention is paid to the analysis of an impact of the flow trajectories prescribed by an upper control level of the recently developed two-time scale architecture of an integrated quality and quantity control in DWDS. The new quality controller is to operate within this architecture in the fast time scale as the lower level quality controller. The controller performance is validated by a comprehensive simulation study based on an example case study DWDS.

Keywords: Model predictive control, hierarchical control structure, genetic algorithm, water quality with DBPs objectives.

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: Evapotranspiration, Hargreaves equation, FAOPenman method.

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Authors: William Anderson, Kyle Kobold, Oleg Yakimenko

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Green microgrids using mostly renewable energy (RE) for generation, are complex systems with inherent nonlinear dynamics. Among a variety of different optimization tools there are only a few ones that adequately consider this complexity. This paper evaluates applicability of two somewhat similar optimization tools tailored for standalone RE microgrids and also assesses a machine learning tool for performance prediction that can enhance the reliability of any chosen optimization tool. It shows that one of these microgrid optimization tools has certain advantages over another and presents a detailed routine of preparing input data to simulate RE microgrid behavior. The paper also shows how neural-network-based predictive modeling can be used to validate and forecast solar power generation based on weather time series data, which improves the overall quality of standalone RE microgrid analysis.

Keywords: Microgrid, renewable energy, complex systems, optimization, predictive modeling, neural networks.

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Authors: V. D. Thi, M. Li, M. Khelifa, M. El Ganaoui, Y. Rogaume

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This paper presents a two-dimensional model to study the heat and moisture transfer through porous building materials. Dynamic and static coupled models of heat and moisture transfer in porous material under low temperature are presented and the coupled models together with variable initial and boundary conditions have been considered in an analytical way and using the finite element method. The resulting coupled model is converted to two nonlinear partial differential equations, which is then numerically solved by an implicit iterative scheme. The numerical results of temperature and moisture potential changes are compared with the experimental measurements available in the literature. Predicted results demonstrate validation of the theoretical model and effectiveness of the developed numerical algorithms. It is expected to provide useful information for the porous building material design based on heat and moisture transfer model.

Keywords: Finite element method, heat transfer, moisture transfer, porous materials, wood.

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Authors: S. Niksarlioglu, F. Kulahci

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Earthquakes are natural phenomena that occur with influence of a lot of parameters such as seismic activity, changing in the ground waters' motion, changing in the water-s temperature, etc. On the other hand, the radon gas concentrations in soil vary as nonlinear generally with earthquakes. Continuous measurement of the soil radon gas is very important for determination of characteristic of the seismic activity. The radon gas changes as continuous with strain occurring within the Earth-s surface during an earthquake and effects from the physical and the chemical processes such as soil structure, soil permeability, soil temperature, the barometric pressure, etc. Therefore, at the modeling researches are notsufficient to knowthe concentration ofradon gas. In this research, we determined relationships between radon emissions based on the environmental parameters and earthquakes occurring along the East Anatolian Fault Zone (EAFZ), Turkiye and predicted magnitudes of some earthquakes with the artificial neural network (ANN) model.

Keywords: Earthquake, Modeling, Prediction, Radon.

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Authors: Nashwa Kamel Ibrahim

Abstract:

Kombucha Tea Ferment (KT), was given to male albino rats, (1ml/Kg of body weight), via gavages, during 2 weeks before intraperitoneal administration of 3.5 mg/Kg body weight CdCl2 and/or whole body γ-irradiation with 4Gy, and during 4 weeks after each treatment. Hepatic and nephritic pathological changes included significant increases of serum alanine transaminase (ALT), aspartate transaminase (AST), and alkaline phosphatase (ALP) activities, and creatinine and urea contents with significant decrease in serum total antioxidant capacity (TAC). Increase in oxidative stress markers in liver and kidney tissues expressed by significant increase in malondialdehyde (MDA) and nitric oxide (NO) contents associated to significant depletion in superoxide dismutase (SOD) and catalase (CAT) activities, and reduced glutathione (GSH) content were recorded. KT administration results in recovery of all the pathological changes. It could be concluded that KT might protect liver and kidney from oxidative damage induced by exposure to cadmium and/ or γ-irradiation.

Keywords: Cadmium, Kombucha, radiation, rats

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Authors: E. Karakulak, R. Yamanoğlu, M. Zeren

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In the current study, fly ash obtained from a thermal power plant was used as reinforcement in pure magnesium. The composite materials with different fly ash contents were produced with powder metallurgical methods. Powder mixtures were sintered at 540^oC under 30 MPa pressure for 15 minutes in a vacuum assisted hot press. Results showed that increasing ash content continuously increases hardness of the composite. On the other hand, minimum wear damage was obtained at 2 wt. % ash content. Addition of higher level of fly ash results with formation of cracks in the matrix and increases wear damage of the material.

Keywords: Mg composite, fly ash, wear, powder metallurgy.

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Authors: Amin Lotfi Eghlim, Mehran pourgholi

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Explosion occurs due to sudden release of energy. Common examples of explosion include chemical, atomic, heat, and pressure tank (due to ignition) explosions. Petroleum, gas, and petrochemical industries operations are threatened by natural risks and processes. Fires and explosions are the greatest process risks which cause financial damages. This study aims at designing a single-floor structure for the control room of a petroleum refinery to be resistant against gas explosion loads, and the information related to the structure specifications have been provided regarding the fact that the structure is made on the ground's surface. In this research, the lateral stiffness of single pile is calculated by SPPLN.FOR computer program, and its value for 13624 KN/m single pile has been assessed. The analysis used due to the loading conditions, is dynamic nonlinear analysis with direct integration method.

Keywords: Gas Explosion Load, Petroleum Refinery, Single-Floor Structure

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Authors: Anil Kumar Pandey

Abstract:

A compact planar monopole antenna with dual-band operation suitable for wireless local area network (WLAN) application is presented in this paper. The antenna occupies an overall area of 18 ×12 mm². The antenna is fed by a coplanar waveguide (CPW) transmission line and it combines two folded strips, which radiates at 2.4 and 5.2 GHz. In the proposed antenna, by optimally selecting the antenna dimensions, dual-band resonant modes with a much wider impedance matching at the higher band can be produced. Prototypes of the obtained optimized design have been simulated using EM solver. The simulated results explore good dual-band operation with -10 dB impedance bandwidths of 50 MHz and 2400 MHz at bands of 2.4 and 5.2 GHz, respectively, which cover the 2.4/5.2/5.8 GHz WLAN operating bands. Good antenna performances such as radiation patterns and antenna gains over the operating bands have also been observed. The antenna with a compact size of 18×12×1.6 mm³ is designed on an FR4 substrate with a dielectric constant of 4.4.

Keywords: CPW fed antenna, dual-band, electromagnetic simulation, wireless local area network, WLAN.

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Authors: Yul Y. Nazaruddin, Anas Y. Widiaribowo, Satriyo Nugroho

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Boiler is one of the critical unit in a petrochemical plant. Steam produced by the boiler is used for various processes in the plant such as urea and ammonia plant. An alternative method to optimize the boiler combustion system is presented in this paper. Adaptive Neuro-Fuzzy Inference System (ANFIS) approach is applied to model the boiler using real-time operational data collected from a boiler unit of the petrochemical plant. Nonlinear equation obtained is then used to optimize the air to fuel ratio using Genetic Algorithm, resulting an optimal ratio of 15.85. This optimal ratio is then maintained constant by ratio controller designed using inverse dynamics based on ANFIS. As a result, constant value of oxygen content in the flue gas is obtained which indicates more efficient combustion process.

Keywords: ANFIS, boiler, combustion process, genetic algorithm, optimization.

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Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

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Authors: Li Jie, Zhang Wei

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In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.

Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.

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Authors: Jin-Wei Liang, Hung-Yi Chen, Lung Lin

Abstract:

In this paper feedforward controller is designed to eliminate nonlinear hysteresis behaviors of a piezoelectric stack actuator (PSA) driven system. The control design is based on inverse Prandtl-Ishlinskii (P-I) hysteresis model identified using particle swarm optimization (PSO) technique. Based on the identified P-I model, both the inverse P-I hysteresis model and feedforward controller can be determined. Experimental results obtained using the inverse P-I feedforward control are compared with their counterparts using hysteresis estimates obtained from the identified Bouc-Wen model. Effectiveness of the proposed feedforward control scheme is demonstrated. To improve control performance feedback compensation using traditional PID scheme is adopted to integrate with the feedforward controller. 

Keywords: The Bouc-Wen hysteresis model, Particle swarm optimization, Prandtl-Ishlinskii model.

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Authors: Anil S. Khopkar, Kartik S. Pandya

Abstract:

Lightning overvoltage phenomenon in power systems cannot be avoided; however, it can be controlled to certain extent. To prevent system failure, power system equipment must be protected against overvoltage. Metal Oxide Surge Arrestors (MOSA) are connected in the system to provide protection against overvoltages. Under normal working conditions, MOSA function as, insulators, offering a conductive path during overvoltage events. MOSA consists of zinc oxide elements (ZnO Blocks) which has non-linear V-I characteristics. The ZnO blocks are connected in series and fitted in ceramic or polymer housing. Over time, these components degrade due to continuous operation. The degradation of zinc oxide elements increases the leakage current flowing through the surge arrestors. This increased leakage current results in elevated temperatures within the surge arrester, further decreasing the resistance of the zinc oxide elements. Consequently, the leakage current increases, leading to higher temperatures within the MOSA. This cycle creates thermal runaway conditions for the MOSA. Once a surge arrester reaches the thermal runaway condition, it cannot return to normal working conditions. This condition is a primary cause of premature failure of surge arrestors. Given that MOSA constitutes a core protective device for electrical power systems against transients, it contributes significantly to the reliable operation of power system networks. Therefore, periodic condition monitoring of surge arrestors is essential. Both online and offline condition monitoring techniques are available for surge arrestors. Offline condition monitoring techniques are not as popular because they require the removal of surge arrestors from the system, which requires system shutdown. Therefore, online condition monitoring techniques are more commonly used. This paper presents an evaluation technique for the surge arrester condition based on leakage current analysis. The maximum amplitudes of total leakage current (IT), fundamental resistive leakage current (IR), and third harmonic resistive leakage current (I3rd) are analyzed as indicators for surge arrester condition monitoring.

Keywords: Metal Oxide Surge Arrester, MOSA, Over voltage, total leakage current, resistive leakage current, third harmonic resistive leakage current, capacitive leakage current.

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Authors: Traian Chiulan, Brandusa Pantelimon

Abstract:

The paper analyzes the large power transformer unit regimes, indicating the criteria for the management of the voltage operating conditions, as well as the change in the operating conditions with the load connected to the secondary winding of the transformer unit. Further, the paper presents the software application for the evaluation of the transformer unit operation under different conditions. The software application was developed by means of virtual instrumentation.

Keywords: Operating regimes, power transformer, overload, lifetime, virtual instrumentation.

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Authors: Siliang Wang, Minghui Wang

Abstract:

This work proposes a novel market-based air traffic flow control model considering competitive airlines in air traffic network. In the flow model, an agent based framework for resources (link/time pair) pricing is described. Resource agent and auctioneer for groups of resources are also introduced to simulate the flow management in Air Traffic Control (ATC). Secondly, the distributed group pricing algorithm is introduced, which efficiently reflect the competitive nature of the airline industry. Resources in the system are grouped according to the degree of interaction, and each auctioneer adjust s the price of one group of resources respectively until the excess demand of resources becomes zero when the demand and supply of resources of the system changes. Numerical simulation results show the feasibility of solving the air traffic flow control problem using market mechanism and pricing algorithms on the air traffic network.

Keywords: Air traffic control, Nonlinear programming, Marketmechanism, Route policy.

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Authors: Fábio A. S. Mota, Mauro A. S. S. Ravagnani, E. P. Carvalho

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In the present paper the design of plate heat exchangers is formulated as an optimization problem considering two mathematical modelling. The number of plates is the objective function to be minimized, considering implicitly some parameters configuration. Screening is the optimization method used to solve the problem. Thermal and hydraulic constraints are verified, not viable solutions are discarded and the method searches for the convergence to the optimum, case it exists. A case study is presented to test the applicability of the developed algorithm. Results show coherency with the literature.

Keywords: Plate heat exchanger, optimization, modeling, simulation.

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Authors: Ramdan B. A. Koad, Ahmed. F. Zobaa

Abstract:

Since the output characteristics of photovoltaic (PV) system depends on the ambient temperature, solar radiation and load impedance, its maximum power point (MPP) is not constant. Under each condition PV module has a point at which it can produce its MPP. Therefore, a maximum power point tracking (MPPT) method is needed to uphold the PV panel operating at its MPP. This paper presents comparative study between the conventional MPPT methods used in (PV) system: Perturb and Observe (P&O), Incremental Conductance (IncCond), andParticle Swarm Optimization (PSO) algorithmfor (MPPT) of (PV) system. To evaluate the study, the proposed PSO MPPT is implemented on a DC-DC cuk converter and has been compared with P&O and INcond methods in terms of their tracking speed, accuracy and performance by using the Matlab tool Simulink. The simulation result shows that the proposed algorithm is simple, and is superior to the P&O and IncCond methods.

Keywords: Incremental Conductance (IncCond) Method, Perturb and Observe (P&O) Method, Photovoltaic Systems (PV) and Practical Swarm Optimization Algorithm (PSO).

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Authors: S. Distantina, Rochmadi, M. Fahrurrozi, Wiratni

Abstract:

Preparation of hydrogel based on carrageenan extracted from Kappaphycus alvarezii was conducted with film immersion in glutaraldehyde solution (GA 4%w/w) for 2min and then followed by thermal curing at 110°C for 25min. The method of carrageenan recovery strongly determines the properties of crosslinked carrageenan. Hydrogel obtained from alkali treated carrageenan showed higher swelling ability compared to hydrogel from nonalkali treated carrageenan. Hydrogel from alkali treated showed the ability of sensitive to pH media.

Keywords: Hydrogel, carrageenan, swelling, alkali treated.

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Authors: C. Kocatepe, E. Taslak, C. F. Kumru, O. Arıkan

Abstract:

While choosing insulating oil, characteristic features such as thermal cooling, endurance, efficiency and being environment-friendly should be considered. Mineral oils are referred as petroleum-based oil. In this study, vegetable oils investigated as an alternative insulating liquid to mineral oil. Dissipation factor, breakdown voltage, relative dielectric constant and resistivity changes with the frequency and voltage of mineral, rapeseed and nut oils were measured. Experimental studies were performed according to ASTM D924 and IEC 60156 standards.

Keywords: Breakdown voltage, dielectric dissipation factor, mineral oil, vegetable oils.

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Authors: Omid A. Zargar

Abstract:

Material damages dynamic analysis is difficult to deal with different material geometry and mechanism. In addition, it is difficult to measure the dynamic behavior of cracks, debond and delamination inside the material. Different simulation methods are developed in recent years for different physical features of mechanical systems like vibration and acoustic. Nonlinear fractures are analyzed and identified for different locations in this paper. The main idea of this work is to perform dynamic analysis on different types of materials (from normal homogeneous material to complex composite laminates). Technical factors like cracks, voids, interfaces and the damages’ locations are evaluated. In this project the modal analysis is performed on different types of materials. The results could be helpful in finding modal frequencies, natural frequencies, Time domain and fast Fourier transform (FFT) in industrial applications.

Keywords: Finite element method, dynamic analysis, vibration and acoustic, composite, crack, delamination.

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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