Search results for: Transient energy

Authors: Mamta Patel, R. N. Patel

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Transmission and distribution lines are vital links between the generating unit and consumers. They are exposed to atmosphere, hence chances of occurrence of fault in transmission line is very high which has to be immediately taken care of in order to minimize damage caused by it. In this paper Discrete wavelet transform of voltage signals at the two ends of transmission lines have been analyzed. The transient energy of the detail information of level five is calculated for different fault conditions. It is observed that the variation of transient energy of healthy and faulted line can give important information which can be very useful in classifying and locating the fault.

Keywords: Wavelet, Discrete wavelet transform, Multiresolution analysis, Transient energy

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Authors: Ashok K. Satapathy, Prerana Nashine

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Radiative heat transfer in participating medium was carried out using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab and by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient radiation equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: Participating media, finite volume method, radiation coupled with conduction, heat transfer.

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Authors: A. Kojah, A. Nacaroğlu

Abstract:

Single phase transmission lines are used to transfer data or energy between two users. Transient conditions such as switching operations and short circuit faults cause the generation of the fluctuation on the waveform to be transmitted. Spatial voltage distribution on the single phase transmission line may change owing to the position and duration of the short circuit fault in the system. In this paper, the state space representation of the single phase transmission line for short circuit fault and for various types of terminations is given. Since the transmission line is modeled in time domain using distributed parametric elements, the mathematical representation of the event is given in state space (time domain) differential equation form. It also makes easy to solve the problem because of the time and space dependent characteristics of the voltage variations on the distributed parametrically modeled transmission line.

Keywords: Energy transmission, transient effects, transmission line, transient voltage, RLC short circuit, single phase.

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Authors: Raoudha Chaabane, Faouzi Askri, Sassi Ben Nasrallah

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Simultaneous transient conduction and radiation heat transfer with heat generation is investigated. Analysis is carried out for both steady and unsteady situations. two-dimensional gray cylindrical enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperatures. The heat generation rate is considered uniform and constant throughout the medium. The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The control volume finite element method (CVFEM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the CVFEM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 2-D cylindrical geometries were considered. In order to establish the suitability of the LBM, the energy equation of the present problem was also solved using the the finite difference method (FDM) of the computational fluid dynamics. The CVFEM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FDM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the CVFEM for the radiative information, results were analyzed for the effects of various parameters such as the boundary emissivity. The results of the LBMCVFEM combination were found to be in excellent agreement with the FDM-CVFEM combination. The number of iterations and the steady state temperature in both of the combinations were found comparable. Results are found for situations with and without heat generation. Heat generation is found to have significant bearing on temperature distribution.

Keywords: heat generation, cylindrical coordinates; RTE;transient; coupled conduction radiation; heat transfer; CVFEM; LBM

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Authors: D. He, Y. Pang, G. Lodewijks

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Belt conveyors play an important role in continuous dry bulk material transport, especially at the mining industry. Speed control is expected to reduce the energy consumption of belt conveyors. Transient operation is the operation of increasing or decreasing conveyor speed for speed control. According to literature review, current research rarely takes the conveyor dynamics in transient operation into account. However, in belt conveyor speed control, the conveyor dynamic behaviors are significantly important since the poor dynamics might result in risks. In this paper, the potential risks in transient operation will be analyzed. An existing finite element model will be applied to build a conveyor model, and simulations will be carried out to analyze the conveyor dynamics. In order to realize the soft speed regulation, Harrison’s sinusoid acceleration profile will be applied, and Lodewijks estimator will be built to approximate the required acceleration time. A long inclined belt conveyor will be studied with two major simulations. The conveyor dynamics will be given.

Keywords: Belt conveyor, speed control, transient operation, dynamics

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Authors: T Panigrahi, G Panda, Mulgrew

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This paper introduces a new approach for the performance analysis of adaptive filter with error saturation nonlinearity in the presence of impulsive noise. The performance analysis of adaptive filters includes both transient analysis which shows that how fast a filter learns and the steady-state analysis gives how well a filter learns. The recursive expressions for mean-square deviation(MSD) and excess mean-square error(EMSE) are derived based on weighted energy conservation arguments which provide the transient behavior of the adaptive algorithm. The steady-state analysis for co-related input regressor data is analyzed, so this approach leads to a new performance results without restricting the input regression data to be white.

Keywords: Error saturation nonlinearity, transient analysis, impulsive noise.

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Authors: Tadashi Watanabe

Abstract:

Transient shape variation of a rotating liquid dropletis simulated numerically. The three dimensional Navier-Stokes equations were solved by using the level set method. The shape variation from the sphere to the rotating ellipsoid, and to the two-robed shapeare simulated, and the elongation of the two-robed droplet is discussed. The two-robed shape after the initial transient is found to be stable and the elongation is almost the same for the cases with different initial rotation rate. The relationship between the elongation and the rotation rate is obtained by averaging the transient shape variation. It is shown that the elongation of two-robed shape is in good agreement with the existing experimental data. It is found that the transient numerical simulation is necessary for analyzing the largely elongated two-robed shape of rotating droplet.

Keywords: Droplet, rotation, two-robed shape, transient simulation.

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Authors: Muhammad Ali, Awais Adnan

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Network on a chip (NoC) has been proposed as a viable solution to counter the inefficiency of buses in the current VLSI on-chip interconnects. However, as the silicon chip accommodates more transistors, the probability of transient faults is increasing, making fault tolerance a key concern in scaling chips. In packet based communication on a chip, transient failures can corrupt the data packet and hence, undermine the accuracy of data communication. In this paper, we present a comparative analysis of transient fault tolerant techniques including end-to-end, node-by-node, and stochastic communication based on flooding principle.

Keywords: NoC, fault-tolerance, transient faults.

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Authors: M. Cañada-Soriano, C. Aparicio-Fernández, P. Sebastián Ferrer Gisbert, M. Val Field, J.-L. Vivancos-Bono

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The lack of insulation along with the existence of air leakages constitute a meaningful impact on the energy performance of buildings. Both of them lead to increases in the energy demand through additional heating and/or cooling loads. Additionally, they cause thermal discomfort. In order to quantify these uncontrolled air currents, the Blower Door test can be used. It is a standardized procedure that determines the airtightness of a space by characterizing the rate of air leakages through the envelope surface. In this sense, the low-energy buildings complying with the Passive House design criteria are required to achieve high levels of airtightness. Due to the invisible nature of air leakages, additional tools are often considered to identify where the infiltrations take place such as the infrared thermography. The aim of this study is to assess the airtightness of a typical Mediterranean dwelling house, refurbished under the Passive House standard, using the Blower Door test. Moreover, the building energy performance modelling tools TRNSYS (TRaNsient System Simulation program) and TRNFlow (TRaNsient Flow) have been used to estimate the energy demand in different scenarios. In this sense, a sequential implementation of three different energy improvement measures (insulation thickness, glazing type and infiltrations) have been analyzed.

Keywords: Airtightness, blower door, TRNSYS, infrared thermography, energy demand.

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Authors: Omid Borazjani, Alireza Rajabi, Mojtaba Saeedimoghadam, Khodakhast Isapour

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High Voltage Direct Current (HVDC) power transmission is employed to move large amounts of electric power. There are several possibilities to enhance the transient stability in a power system. One adequate option is by using the high controllability of the HVDC if HVDC is available in the system. This paper presents a control technique for HVDC to enhance the transient stability. The strategy controls the power through the HVDC to help make the system more transient stable during disturbances. Loss of synchronism is prevented by quickly producing sufficient decelerating energy to counteract accelerating energy gained during. In this study, the power flow in the HVDC link is modulated with the addition of an auxiliary signal to the current reference of the rectifier firing angle controller. This modulation control signal is derived from speed deviation signal of the generator utilizing a PD controller; the utilization of a PD controller is suitable because it has the property of fast response. The effectiveness of the proposed controller is demonstrated with a SMIB test system.

Keywords: HVDC, SMIB, Stability, Power System.

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Authors: Sen-Yung Lee, Li-Kuo Chou, Chao-Kuang Chen

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In this study, the problem of temperature transient response of a spiral fin, with its end insulated, is analyzed with base end subjected to a variation of fluid temperature. The hybrid method of Laplace transforms/Adomian decomposed method-Padé, is applied to the temperature transient response of the fin, the result of the temperature distribution and the heat flux at the base of the spiral fin are obtained, show a good agreement in the physical phenomenon.

Keywords: Laplace transforms/Adomian decomposed method- Padé, transient response, heat transfer.

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Authors: I. Abuiziah, A. Oulhaj, K. Sebari, D. Ouazar

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The primary objectives of transient analysis are to determine the values of transient pressures that can result from flow control operations and to establish the design criteria for system equipment and devices (such as control devices and pipe wall thickness) so as to provide an acceptable level of protection against system failure due to pipe collapse or bursting. Because of the complexity of the equations needed to describe transients, numerical computer models are used to analyze transient flow hydraulics. An effective numerical model allows the hydraulic engineer to analyze potential transient events and to identify and evaluate alternative solutions for controlling hydraulic transients, thereby protecting the integrity of the hydraulic system. This paper presents the influence of using the protection devices to control the adverse effects due to excessive and low pressure occurs in the transient.

Keywords: Flow Transient, Water hammer, Pipeline System, Surge Tank, Simulation Model, Protection Devices.

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Authors: D. Zabala, N. Sánchez, J. Pinto

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A transient heat transfer mathematical model for the prediction of temperature distribution in the car body during primer baking has been developed by considering the thermal radiation and convection in the furnace chamber and transient heat conduction governing equations in the car framework. The car cockpit is considered like a structure with six flat plates, four vertical plates representing the car doors and the rear and front panels. The other two flat plates are the car roof and floor. The transient heat conduction in each flat plate is modeled by the lumped capacitance method. Comparison with the experimental data shows that the heat transfer model works well for the prediction of thermal behavior of the car body in the curing furnace, with deviations below 5%.

Keywords: Transient heat transfer, car body, lumpedcapacitance, primer baking.

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Authors: Arunrungrusmi S, Chaokamnerd W, Tanitteerapan T, Mungkung N., Yuji T.

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The purpose of this research was to analyze and compare the instability of a contact surface between Copper and Nickel an alloy cathode in vacuum, the different ratio of Copper and Copper were conducted at 1%, 2% and 4% by using the cathode spot model. The transient recovery voltage is predicted. The cathode spot region is recognized as the collisionless space charge sheath connected with singly ionized collisional plasma. It was found that the transient voltage is decreased with increasing the percentage of an amount of Nickel in cathode materials.

Keywords: Vacuum arc, Instability, Low current, Cathode spot, copper, Nickel, Transient Recovery Voltage.

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Authors: Ramesh Rajagopalan, Adam Dahlstrom

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Noise removal techniques play a vital role in the performance of electrocardiographic (ECG) signal processing systems. ECG signals can be corrupted by various kinds of noise such as baseline wander noise, electromyographic interference, and powerline interference. One of the significant challenges in ECG signal processing is the degradation caused by additive 50 or 60 Hz powerline interference. This work investigates the removal of power line interference and suppression of transient response for filtering noise corrupted ECG signals. We demonstrate the effectiveness of infinite impulse response (IIR) notch filter with time varying pole radius for improving the transient behavior. The temporary change in the pole radius of the filter diminishes the transient behavior. Simulation results show that the proposed IIR filter with time varying pole radius outperforms traditional IIR notch filters in terms of mean square error and transient suppression.

Keywords: Notch filter, ECG, transient, pole radius.

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Authors: Vitalice K. Oduol

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The paper considers a single-server queue with fixedsize batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values.

Keywords: batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis.

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Authors: Muhammad Sheikh Sadi, D. G. Myers, Cesar Ortega Sanchez

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This paper proposes the use of metrics in design space exploration that highlight where in the structure of the model and at what point in the behaviour, prevention is needed against transient faults. Previous approaches to tackle transient faults focused on recovery after detection. Almost no research has been directed towards preventive measures. But in real-time systems, hard deadlines are performance requirements that absolutely must be met and a missed deadline constitutes an erroneous action and a possible system failure. This paper proposes the use of metrics to assess the system design to flag where transient faults may have significant impact. These tools then allow the design to be changed to minimize that impact, and they also flag where particular design techniques – such as coding of communications or memories – need to be applied in later stages of design.

Keywords: Criticality, Metrics, Real-Time Systems, Transient Faults.

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Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

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This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: Power system, Transient stability, Critical trajectory method, Energy function method.

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Authors: Jun Sung Go, Jong Kang Park, Jong Tae Kim

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As semi-conductor manufacturing technology evolves; the single event transient problem becomes more significant issue. Single event transient has a critical impact on both combinational and sequential logic circuits, so it is important to evaluate the soft error tolerance of the circuits at the design stage. In this paper, we present a soft error detecting simulation using scan chain. The simulation model generates a single event transient randomly in the circuit, and detects the soft error during the execution of the test patterns. We verified this model by inserting a scan chain in an 8051 microprocessor using 65 nm CMOS technology. While the test patterns generated by ATPG program are passing through the scan chain, we insert a single event transient and detect the number of soft errors per sub-module. The experiments show that the soft error rates per cell area of the SFR module is 277% larger than other modules.

Keywords: Scan chain, single event transient, soft error, 8051 processor.

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Authors: S. Padma, Dr. R. Lakshmipathi, K. Ramash Kumar, P. Nandagopal

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The power system network is becoming more complex nowadays and it is very difficult to maintain the stability of the system. Today-s enhancement of technology makes it possible to include new energy storage devices in the electric power system. In addition, with the aid of power electronic devices, it is possible to independently exchange active and reactive power flow with the utility grid. The main purpose of this paper proposes a Proportional – Integral (PI) control based 48 – pulse Inverter based Static Synchronous Series Compensator (SSSC) with and without Superconducting Magnetic Energy Storage (SMES) used for enhancing the transient stability and regulating power flow in automatic mode. Using a test power system through the dynamic simulation in Matlab/Simulink platform validates the performance of the proposed SSSC with and without SMES system.

Keywords: Flexible AC transmission system (FACTS), PIControl, Superconducting Magnetic Energy Storage (SMES), Static Synchronous Series Compensator (SSSC).

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Authors: A. Ashok, K.Satapathy, B. Prerana Nashine

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The objective of this research work is to investigate for one dimensional transient radiative transfer equations with conduction using finite volume method. Within the infrastructure of finite-volume, we obtain the conservative discretization of the terms in order to preserve the overall conservative property of finitevolume schemes. Coupling of conductive and radiative equation resulting in fluxes is governed by the magnitude of emissivity, extinction coefficient, and temperature of the medium as well as geometry of the problem. The problem under consideration has been solved, for a slab dominating radiation coupled with transient conduction based on finite volume method. The boundary conditions are also chosen so as to give a good model of the discretized form of radiation transfer equation. The important feature of the present method is flexibility in specifying the control angles in the FVM, while keeping the simplicity in the solution procedure. Effects of various model parameters are examined on the distributions of temperature, radiative and conductive heat fluxes and incident radiation energy etc. The finite volume method is considered to effectively evaluate the propagation of radiation intensity through a participating medium.

Keywords: Radiative transfer equation, finite volume method, conduction, transient radiation.

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Authors: Khoshnaw Khalid Hama Saleh, Ergun Ercelebi

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Increasingly complex modern power systems require stability, especially for transient and small disturbances. Transient stability plays a major role in stability during fault and large disturbance. This paper compares a power system stabilizer (PSS) and static Var compensator (SVC) to improve damping oscillation and enhance transient stability. The effectiveness of a PSS connected to the exciter and/or governor in damping electromechanical oscillations of isolated synchronous generator was tested. The SVC device is a member of the shunt FACTS (flexible alternating current transmission system) family, utilized in power transmission systems. The designed model was tested with a multi-machine system consisting of four machines six bus, using MATLAB/SIMULINK software. The results obtained indicate that SVC solutions are better than PSS.

Keywords: FACTS, MATLAB/SIMULINK, multi-machine system, PSS, SVC, transient stability.

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Authors: Vinod Tejwani, Bhavik Suthar

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The paper presents and energy management strategy for a Fuel Cell, Ultracapacitor, Battery hybrid energy storage. The fuel cell hybrid power system is devised basically for emergency power requirements and transient load applications. The power density of an Ultracapacitor is extremely high and for a battery, it is subtle. For a fuel cell, the value of power density is medium. The energy density of these three stockpiling gadgets is contrarily about the power density, i.e. for the batteries it is most noteworthy and for the Ultracapacitor, it is least. Again the fuel cell has medium energy density. The proposed Energy Management System (EMS) is trying to rationalize these parameters viz. the energy density and power density. The working of the fuel cell, Ultracapacitor and batteries are controlled in a coordinated environment in a way to optimize the energy usage and at the same time to get benefits of power and energy density from their inherent characteristics. MATLAB/ Simulink® based test bench is created by using different DC-DC converters for all energy storage devices and an inverter is modeled to supply the time varying load. The results provided by the EMS are highly satisfactory that proves its adaptability.

Keywords: Energy Management System (EMS) Fuel Cell, Ultracapacitor, Battery, Hybrid Energy Storage.

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Authors: U. Ramesh Babu, V. Vijay Kumar Reddy, S. Tara Kalyani

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The growth in the demand of electrical energy is leading to load on the Power system which increases the occurrence of frequent oscillations in the system. The reason for the oscillations is due to the lack of damping torque which is required to dominate the disturbances of Power system. By using FACT devices, such as Unified Power Flow Controller (UPFC) can control power flow, reduce sub-synchronous resonances and increase transient stability. Hence, UPFC is used to damp the oscillations occurred in Power system. This research focuses on adapting the neuro fuzzy controller for the UPFC design by connecting the infinite bus (SMIB - Single machine Infinite Bus) to a linearized model of synchronous machine (Heffron-Phillips) in the power system. This model gains the capability to improve the transient stability and to damp the oscillations of the system.

Keywords: Power System, UPFC, (ANFIS) Adaptive Neuro Fuzzy Inference System, transient, Low frequency oscillations.

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Authors: H. Bhowmik, A. Faisal, Ahmed Al Yaarubi, Nabil Al Alawi

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Experiments are conducted to analyze the steady-state and the power-on transient natural convection heat transfer from a horizontal cylinder mounted in a vertical up flow circular duct. The heat flux ranges from 177 W/m² to 2426 W/m² and the Rayleigh number ranges from 1×10⁴ to 4.35×10⁴. For natural air flow and constant heat flux condition, the effects of heat transfer around the cylinder under steady-state condition are investigated. The steady-state results compare favorably with that of the available data. The effects of transient heat transfer data on different angular position of the thermocouple (0^o, 90^o, 180^o) are also reported. It is observed that the transient heat transfer around the cylinder is strongly affected by the position of thermocouples. In the transient region, the rate of heat transfer obtained at 90^o and 180^o are higher than that of stagnation point (0^o). Finally, the dependence of the average Nusselt number on Rayleigh number for steady and transient natural convection heat transfer are analyzed, and a correlation equation is presented.

Keywords: Steady-state, transient, natural convection, Rayleigh number, Nusselt number, Fourier Number.

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Authors: Horng-Yuan Wu, Chin-Yuan Hsu, Tsair-Fwu Lee

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A novel three-phase active power filter (APF) circuit with photovoltaic (PV) system to improve the quality of service and to reduce the capacity of energy storage capacitor is presented. The energy balance concept and sampling technique were used to simplify the calculation algorithm for the required utility source current and to control the voltage of the energy storage capacitor. The feasibility was verified by using the Pspice simulations and experiments. When the APF mode was used during non-operational period, not only the utilization rate, power factor and power quality could be improved, but also the capacity of energy storage capacitor could sparing. As the results, the advantages of the APF circuit are simplicity of control circuits, low cost, and good transient response.

Keywords: active power filter, sampling, energy-storagecapacitor, harmonic current, energy balance.

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Authors: G. Tamulevičius, A. Serackis, T. Sledevič, D. Navakauskas

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We consider the biggest challenge in speech recognition – noise reduction. Traditionally detected transient noise pulses are removed with the corrupted speech using pulse models. In this paper we propose to cope with the problem directly in Dynamic Time Warping domain. Bidirectional Dynamic Time Warping algorithm for the recognition of isolated words impacted by transient noise pulses is proposed. It uses simple transient noise pulse detector, employs bidirectional computation of dynamic time warping and directly manipulates with warping results. Experimental investigation with several alternative solutions confirms effectiveness of the proposed algorithm in the reduction of impact of noise on recognition process – 3.9% increase of the noisy speech recognition is achieved.

Keywords: Transient noise pulses, noise reduction, dynamic time warping, speech recognition.

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Authors: Ernst D. Schmitter

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Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automation of the analysis and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for this task and serve as input into a radial basis function network that is trained to discriminate transient shapes from pulse like to wave like. We concentrate on signals in the Very Low Frequency (VLF, 3 -30 kHz) range in this paper, but the developed methods are independent of this specific choice.

Keywords: Transient signals, statistics, wavelets, neural networks

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Authors: I. Abuiziah, A. Oulhaj, K. Sebari, D. Ouazar, A. A. Saber

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Fluid transient analysis is one of the more challenging and complicated flow problems in the design and the operation of water pipeline systems (wps). When transient conditions "water hammer" exists, the life expectancy of the wps can be adversely impacted, resulting in pump and valve failures and catastrophic pipe ruptures. Transient control has become an essential requirement for ensuring safe operation of wps. An accurate analysis and suitable protection devices should be used to protect wps. This paper presents the problem of modeling and simulation of transient phenomena in wps based on the characteristics method. Also, it provides the influence of using the protection devices to control the adverse effects due to excessive and low pressure occur in the transient. The developed model applied for main wps: pump combined with closed surge tank connected to a reservoir. The results obtained provide that the model is an efficient tool for water hammer analysis. Moreover; using the closed surge tank reduces the unfavorable effects of transients.

Keywords: Flow Transient, Water hammer, Pipeline System, Closed Surge Tank, Simulation Model, Protection Devices, Characteristics Method.

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Authors: M. Behbahani-Nejad, Y. Shekari

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A reduced order modeling approach for natural gas transient flow in pipelines is presented. The Euler equations are considered as the governing equations and solved numerically using the implicit Steger-Warming flux vector splitting method. Next, the linearized form of the equations is derived and the corresponding eigensystem is obtained. Then, a few dominant flow eigenmodes are used to construct an efficient reduced-order model. A well-known test case is presented to demonstrate the accuracy and the computational efficiency of the proposed method. The results obtained are in good agreement with those of the direct numerical method and field data. Moreover, it is shown that the present reduced-order model is more efficient than the conventional numerical techniques for transient flow analysis of natural gas in pipelines.

Keywords: Eigenmode, Natural Gas, Reduced Order Modeling, Transient Flow.

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