Search results for: wave propagation equations.

Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Maria Neagu

Abstract:

This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parameters. These results are verified using the finite differences method applied to the conservation equations.

Keywords: Finite difference method, natural convection, porous medium, scale analysis, thermal stratification.

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Authors: Jevgenijs Carkovs

Abstract:

The paper is devoted to stochastic analysis of finite dimensional difference equation with dependent on ergodic Markov chain increments, which are proportional to small parameter ". A point-form solution of this difference equation may be represented as vertexes of a time-dependent continuous broken line given on the segment [0,1] with "-dependent scaling of intervals between vertexes. Tending " to zero one may apply stochastic averaging and diffusion approximation procedures and construct continuous approximation of the initial stochastic iterations as an ordinary or stochastic Ito differential equation. The paper proves that for sufficiently small " these equations may be successfully applied not only to approximate finite number of iterations but also for asymptotic analysis of iterations, when number of iterations tends to infinity.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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Authors: Foad Nazari, Seyed Mahmood Hosseini, Mohammad Hossein Abolbashari, Mohammad Hassan Abolbashari

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The present study is concerned with the optimal design of functionally graded plates using particle swarm optimization (PSO) algorithm. In this study, meshless local Petrov-Galerkin (MLPG) method is employed to obtain the functionally graded (FG) plate’s natural frequencies. Effects of two parameters including thickness to height ratio and volume fraction index on the natural frequencies and total mass of plate are studied by using the MLPG results. Then the first natural frequency of the plate, for different conditions where MLPG data are not available, is predicted by an artificial neural network (ANN) approach which is trained by back-error propagation (BEP) technique. The ANN results show that the predicted data are in good agreement with the actual one. To maximize the first natural frequency and minimize the mass of FG plate simultaneously, the weighted sum optimization approach and PSO algorithm are used. However, the proposed optimization process of this study can provide the designers of FG plates with useful data.

Keywords: Optimal design, natural frequency, FG plate, hybrid meshless method, MLPG method, ANN approach, particle swarm optimization.

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Authors: Prem Singh, Jagdeep Singh

Abstract:

In an attempt to investigate the performance of single basin solar still for climate conditions of Ludhiana a single basin solar still was designed, fabricated and tested. The energy balance equations for various parts of the still are solved by Gauss-Seidel iteration method. Computer model was made and experimentally validated. The validated computer model was used to estimate the annual distillation yield and performance ratio of the still for Ludhiana. The Theoretical and experimental distillation yield were 4318.79 ml and 3850 ml respectively for the typical day. The predicted distillation yield was 12.5% higher than the experimental yield. The annual distillation yield per square metre aperture area and annual performance ratio for single basin solar still is 1095 litres and 0.43 respectively. The payback period for micro-stepped solar still is 2.5 years.

Keywords: Solar distillation, solar still, single basin, still.

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Authors: Adamu Mudi, Fawole Wahab Ibrahim, Abubakar Abba Kolo

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In this paper, we present a microcontroller-based liquid level controller which identifies the various levels of a liquid, carries out certain actions and is capable of communicating with the human being and other devices through the GSM network. This project is useful in ensuring that a liquid is not wasted. It also contributes to the internet of things paradigm, which is the future of the internet. The method used in this work includes designing the circuit and simulating it. The circuit is then implemented on a solderless breadboard after which it is implemented on a strip board. A C++ computer program is developed and uploaded into the microcontroller. This program instructs the microcontroller on how to carry out its actions. In other to determine levels of the liquid, an ultrasonic wave is sent to the surface of the liquid similar to radar or the method for detecting the level of sea bed. Message is sent to the phone of the user similar to the way computers send messages to phones of GSM users. It is concluded that the routine of observing the levels of a liquid in a tank, refilling the tank when the liquid level is too low can be entirely handled by a programmable device without wastage of the liquid or bothering a human being with such tasks.

Keywords: Arduino Uno, HC-SR04 ultrasonic sensor, Internet of Things, IoT, SIM900 GSM Module.

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Authors: Yongkun Li, Meng Hu

Abstract:

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.

Keywords: Predator-prey system, stage structure, time delay, HOPF bifurcation, periodic solution, stability.

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Authors: Amal Ezzidani, Abdelghani Ben Tahar, Mohamed Hanini

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A sequence of finite tandem queue is considered for this study. Each one has a single server, which operates under the egalitarian processor sharing discipline. External customers arrive at each queue according to a renewal input process and having a general service times distribution. Upon completing service, customers leave the current queue and enter to the next. Under mild assumptions, including critical data, we prove the existence and the uniqueness of the fluid solution. For asymptotic behavior, we provide necessary and sufficient conditions for the invariant state and the convergence to this invariant state. In the end, we establish the convergence of a correctly normalized state process to a fluid limit characterized by a system of algebraic and integral equations.

Keywords: Fluid Limit, fluid model, measure valued process, processor sharing, tandem queue.

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Authors: S. S. Mishra, D. K. Yadav

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This paper focuses on cost and profit analysis of single-server Markovian queuing system with two priority classes. In this paper, functions of total expected cost, revenue and profit of the system are constructed and subjected to optimization with respect to its service rates of lower and higher priority classes. A computing algorithm has been developed on the basis of fast converging numerical method to solve the system of non linear equations formed out of the mathematical analysis. A novel performance measure of cost and profit analysis in view of its economic interpretation for the system with priority classes is attempted to discuss in this paper. On the basis of computed tables observations are also drawn to enlighten the variational-effect of the model on the parameters involved therein.

Keywords: Cost and Profit, Computing, Expected Revenue, Priority classes

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Authors: Pradyumna Kumar Sahoo, Prasanta Kumar Satpathy

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This paper aims at finding a suitable neural network for monitoring congestion level in electrical power systems. In this paper, the input data has been framed properly to meet the target objective through supervised learning mechanism by defining normal and abnormal operating conditions for the system under study. The congestion level, expressed as line congestion index (LCI), is evaluated for each operating condition and is presented to the NN along with the bus voltages to represent the input and target data. Once, the training goes successful, the NN learns how to deal with a set of newly presented data through validation and testing mechanism. The crux of the results presented in this paper rests on performance comparison of a multi-layered feed forward neural network with eleven types of back propagation techniques so as to evolve the best training criteria. The proposed methodology has been tested on the standard IEEE-14 bus test system with the support of MATLAB based NN toolbox. The results presented in this paper signify that the Levenberg-Marquardt backpropagation algorithm gives best training performance of all the eleven cases considered in this paper, thus validating the proposed methodology.

Keywords: Line congestion index, critical bus, contingency, neural network.

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Authors: Lari Kela

Abstract:

An adaptive Helmholtz resonator was designed and adapted to hydraulics. The resonator was controlled by open- and closed-loop controls so that 20 dB attenuation of the peak-to-peak value of the pulsating pressure was maintained. The closed-loop control was noted to be better, albeit it was slower because of its low pressure and temperature variation, which caused variation in the effective bulk modulus of the hydraulic system. Low-pressure hydraulics contains air, which affects the stiffness of the hydraulics, and temperature variation changes the viscosity of the oil. Thus, an open-loop control loses its efficiency if a condition such as temperature or the amount of air changes after calibration. The instability of the low-pressure hydraulic system reduced the operational frequency range of the Helmholtz resonator when compared with the results of an analytical model. Different dampers for hydraulics are presented. Then analytical models of a hydraulic pipe and a hydraulic pipe with a Helmholtz resonator are presented. The analytical models are based on the wave equation of sound pressure. Finally, control methods and the results of experiments are presented.

Keywords: adaptive, damper, hydraulics, pressure, pulsating

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Authors: Sanchita Chauhan, V.K. Srivastava

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Catalytic converters are used for minimizing the release of pollutants to the atmosphere. It is during the warm-up period that hydrocarbons are seen to be released in appreciable quantities from these converters. In this paper the conversion of a fast oxidizing hydrocarbon propylene is analysed using two numerical methods. The quasi steady state method assumes the accumulation terms to be negligible in the gas phase mass and energy balance equations, however this term is present in the solid phase energy balance. The unsteady state model accounts for the accumulation term to be present in the gas phase mass and energy balance and in the solid phase energy balance. The results derived from the two models for gas concentration, gas temperature and solid temperature are compared.

Keywords: Propylene, catalyst, quasi steady state, unsteady state.

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Authors: Axay J Mehta, Hema A Mehta, T.C.Manjunath, C. Ardil

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In this paper, the modelling and design of artificial neural network architecture for load forecasting purposes is investigated. The primary pre-requisite for power system planning is to arrive at realistic estimates of future demand of power, which is known as Load Forecasting. Short Term Load Forecasting (STLF) helps in determining the economic, reliable and secure operating strategies for power system. The dependence of load on several factors makes the load forecasting a very challenging job. An over estimation of the load may cause premature investment and unnecessary blocking of the capital where as under estimation of load may result in shortage of equipment and circuits. It is always better to plan the system for the load slightly higher than expected one so that no exigency may arise. In this paper, a load-forecasting model is proposed using a multilayer neural network with an appropriately modified back propagation learning algorithm. Once the neural network model is designed and trained, it can forecast the load of the power system 24 hours ahead on daily basis and can also forecast the cumulative load on daily basis. The real load data that is used for the Artificial Neural Network training was taken from LDC, Gujarat Electricity Board, Jambuva, Gujarat, India. The results show that the load forecasting of the ANN model follows the actual load pattern more accurately throughout the forecasted period.

Keywords: Power system, Load forecasting, Neural Network, Neuron, Stabilization, Network structure, Load.

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Authors: V.V. Lyahov, V.M. Neshchadim

Abstract:

The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.

Keywords: Distribution function, electromagnetic field, magnetoactive plasma, nonelectroneutral current sheath, structural instability, bifurcational current sheath.

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Authors: Muhammad Naeem, Abdus Salam, Muhammad Asghar Bashir, Abir Ishtiaq, Qurat-ul-Ane Gillani and Asma Salam

Abstract:

In the present study, 49 Hybrid (Catla catla ♂ x Labeo rohita ♀) were sampled from Al-Raheem Fish Hatchery, Village Ali Pure Shamali, Jhang Road, 18 Km from Muzaffar Garh using a cast net and Live fishes were transported to research laboratory. Mean percentage for water found 79.13 %, ash 6.58 %, fat 2.22 % and protein content 12.06 % in whole wet body weight. It was observed that body constituents were found increasing in the same proportion with an increase in body weight while significant proportional increase was observed with total length. However, condition factor remained insignificant (P>0.05) with body constituents.

Keywords: Hybrid fish, Body composition, Condition factor, Predictive equations

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Authors: Caihong Su

Abstract:

Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.

Keywords: Boundary layer, e-N method, PSE, Transition

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Authors: A. Uchaipichat

Abstract:

The hydro-mechanical model for unsaturated soils has been presented based on the effective stress principle taking into account effects of drying-wetting process. The elasto-plastic constitutive equations for stress-strain relations of the soil skeleton have been established. A plasticity model is modified from modified Cam-Clay model. The hardening rule has been established by considering the isotropic consolidation paths. The effect of dryingwetting process is introduced through the ¤ç parameter. All model coefficients are identified in terms of measurable parameters. The simulations from the proposed model are compared with the experimental results. The model calibration was performed to extract the model parameter from the experimental results. Good agreement between the results predicted using proposed model and the experimental results was obtained.

Keywords: Drying-wetting process, Effective stress, Elastoplasticmodel, Unsaturated soils

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Authors: Chang Su Woo, Hyun Sung Park

Abstract:

Useful lifetime evaluation of chevron rubber spring was very important in design procedure to assure the safety and reliability. It is, therefore, necessary to establish a suitable criterion for the replacement period of chevron rubber spring. In this study, we performed characteristic analysis and useful lifetime prediction of chevron rubber spring. Rubber material coefficient was obtained by curve fittings of uniaxial tension equibiaxial tension and pure shear test. Computer simulation was executed to predict and evaluate the load capacity and stiffness for chevron rubber spring. In order to useful lifetime prediction of rubber material, we carried out the compression set with heat aging test in an oven at the temperature ranging from 50°C to 100°C during a period 180 days. By using the Arrhenius plot, several useful lifetime prediction equations for rubber material was proposed.

Keywords: Chevron rubber spring, material coefficient, finite element analysis, useful lifetime prediction.

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Authors: Weihao Chung, Iau-Teh Wang, Yu-Hsi Hu

Abstract:

This is the second part of the paper. It, aside from the core subroutine test reported previously, focuses on the simulation of turbulence governed by the full STF Navier-Stokes equations on a large scale. Law of the wall is found plausible in this study as a model of the boundary layer dynamics. Model validations proceed to include velocity profiles of a stationary turbulent Couette flow, pure sloshing flow simulations, and the identification of water-surface inclination due to fluid accelerations. Errors resulting from the irrotational and hydrostatic assumptions are explored when studying a wind-driven water circulation with no shakings. Illustrative examples show that this numerical strategy works for the simulation of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.

Keywords: potential flow theory, sloshing flow, space-timefiltering, order of accuracy.

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Authors: Z. Jovanovic, Z. Masonicic, S. Dragutinovic, Z. Sakota

Abstract:

In this paper, a methodology for noise reduction of motor vehicles in use is presented. The methodology relies on synergic model of noise generation as a function of time. The arbitrary number of motor vehicle noise sources act in concert yielding the generation of the overall noise level of motor vehicle thereafter. The number of noise sources participating in the overall noise level of motor vehicle is subjected to the constraint of the calculation of the acoustic potential of each noise source under consideration. It is the prerequisite condition for the calculation of the acoustic potential of the whole vehicle. The recast form of pertinent set of equations describing the synergic model is laid down and solved by dint of Gauss method. The bunch of results emerged and some of them i.e. those ensuing from model application to MDD FAP Priboj motor vehicle in use are particularly elucidated.

Keywords: Noise abatement, MV noise sources, noise source identification, muffler.

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Authors: R. Mirabdollah Yani, E. Darabi

Abstract:

Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.

Keywords: variational iteration method (VIM), cable vibration, closed-form solution

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Authors: Hamed Jamshidi, Pooya Djamshidi

Abstract:

In this paper the complete rotor system including elastic shaft with distributed mass, allowing for the effects of oil film in bearings. Also, flexibility of foundation is modeled. As a whole this article is a relatively complete research in modeling and vibration analysis of rotor considering gyroscopic effect, damping, dependency of stiffness and damping coefficients on frequency and solving the vibration equations including these parameters. On the basis of finite element method and utilizing four element types including element of shaft, disk, bearing and foundation and using MATLAB, a computer program is written. So the responses in several cases and considering different effects are obtained. Then the results are compared with each other, with exact solutions and results of other papers.

Keywords: Damping coefficients , Finite element method, Modeling , Rotor vibration

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Authors: Phu-Cuong Nguyen, Seung-Eock Kim

Abstract:

This paper presents nonlinear elastic dynamic analysis of 3-D semi-rigid steel frames including geometric and connection nonlinearities. The geometric nonlinearity is considered by using stability functions and updating geometric stiffness matrix. The nonlinear behavior of the steel beam-to-column connection is considered by using a zero-length independent connection element comprising of six translational and rotational springs. The nonlinear dynamic equilibrium equations are solved by the Newmark numerical integration method. The nonlinear time-history analysis results are compared with those of previous studies and commercial SAP2000 software to verify the accuracy and efficiency of the proposed procedure.

Keywords: Geometric nonlinearity, nonlinear time-historyanalysis, semi-rigid connection, stability functions.

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Authors: S. Selvaperumal, M. S. Sivagamasundari

Abstract:

In this paper, selective harmonic elimination pulse width modulation technique is employed to eliminate lower order harmonics like third by determination of solving non-linear equations. The cascaded H-bridge five level inverter is driven by the Peripheral Interface Controlled (PIC) Microcontroller 16F877A. The performance of single phase cascaded H-bridge five level inverter with relevant to harmonics and a variety of switches with solar cell as its input source is simulated by employing MATLAB/Simulink. A hardware model is developed to verify the performance of the developed system.

Keywords: Multilevel inverter, cascaded H-Bridge multilevel inverter, total harmonic distortion, selective harmonic elimination pulse width modulation, MATLAB.

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Authors: A. Schirru, A. Irimescu, S. Merola, A. d’Adamo, S. Fontanesi

Abstract:

One of the aspects that are usually neglected during the design phase of an engine is the effect of the spark plug on the flow field inside the combustion chamber. Because of the difficulties in the experimental investigation of the mutual interaction between flow alteration and early flame kernel convection effect inside the engine combustion chamber, CFD-3D simulation is usually exploited in such cases. Experimentally speaking, a particular type of engine has to be used in order to directly observe the flame propagation process. In this study, a double electrode spark plug was fitted into an optically accessible engine and a high-speed camera was used to capture the initial stages of the combustion process. Both the arc and the kernel phases were observed. Then, a morphologic analysis was carried out and the position of the center of mass of the flame, relative to the spark plug position, was calculated. The crossflow orientation was chosen for the spark plug and the kernel growth process was observed for different air-fuel ratios. It was observed that during a normal cycle the flow field between the electrodes tends to transport the arc deforming it. Because of that, the kernel growth phase takes place away from the electrodes and the flame propagates with a preferential direction dictated by the flow field.

Keywords: Combustion, Kernel growth, optically accessible engine, spark-ignition engine, spark plug orientation.

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Authors: Balgaisha G. Mukanova, Yelbek B. Utepov, Aida G. Nazarova, Alisher Z. Imanov

Abstract:

The problem of identifying local noise sources on a construction site using a sensor system is considered. Mathematical modeling of detected signals on sensors was carried out, considering signal decay and signal delay time between the source and detector. Recordings of noises produced by construction tools were used as a dependence of noise on time. Synthetic sensor data was constructed based on these data, and a model of the propagation of acoustic waves from a point source in the three-dimensional space was applied. All sensors and sources are assumed to be located in the same plane. A source localization method is checked based on the signal time delay between two adjacent detectors and plotting the direction of the source. Based on the two direct lines' crossline, the noise source's position is determined. Cases of one dominant source and the case of two sources in the presence of several other sources of lower intensity are considered. The number of detectors varies from three to eight detectors. The intensity of the noise field in the assessed area is plotted. The signal of a two-second duration is considered. The source is located for subsequent parts of the signal with a duration above 0.04 sec; the final result is obtained by computing the average value.

Keywords: Acoustic model, direction of arrival, inverse source problem, sound localization, urban noises.

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Authors: J. H. Kim, J. H. Kwon, J. S. Park, K. J. Lim

Abstract:

This paper has been investigated a technique that predicts the performance of a bar-type unimorph piezoelectric vibration actuator depending on the frequency. This paper has been proposed an equivalent circuit that can be easily analyzed for the bar-type unimorph piezoelectric vibration actuator. In the dynamic analysis, rigidity and resonance frequency, which are important mechanical elements, were derived using the basic beam theory. In the equivalent circuit analysis, the displacement and bandwidth of the piezoelectric vibration actuator depending on the frequency were predicted. Also, for the reliability of the derived equations, the predicted performance depending on the shape change was compared with the result of a finite element analysis program.

Keywords: Actuator, performance, piezoelectric, unimorph.Actuator, performance, piezoelectric, unimorph.

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Authors: N. K. Singh, S. Sarkar

Abstract:

Direct numerical simulation (DNS) is used to study the evolution of a boundary layer that was laminar initially followed by separation and then reattachment owing to generation of turbulence. This creates a closed region of recirculation, known as the laminar-separation bubble. The present simulation emulates the flow environment encountered in a modern LP turbine blade, where a laminar separation bubble may occur on the suction surface. The unsteady, incompressible three-dimensional (3-D) Navier-Stokes (NS) equations have been solved over a flat plate in the Cartesian coordinates. The adverse pressure gradient, which causes the flow to separate, is created by a boundary condition. The separated shear layer undergoes transition through appearance of ╬ø vortices, stretching of these create longitudinal streaks. Breakdown of the streaks into small and irregular structures makes the flow turbulent downstream.

Keywords: Adverse pressure gradient, direct numerical simulation, laminar separation bubble.

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Authors: M. Ouagued, A. Khellaf

Abstract:

The objectif of the present work is to determinate the potential of the solar parabolic trough collector (PTC) for use in the design of a solar thermal power plant in Algeria. The study is based on a mathematical modeling of the PTC. Heat balance has been established respectively on the heat transfer fluid (HTF), the absorber tube and the glass envelop using the principle of energy conservation at each surface of the HCE cross-sectionn. The modified Euler method is used to solve the obtained differential equations. At first the results for typical days of two seasons the thermal behavior of the HTF, the absorber and the envelope are obtained. Then to determine the thermal performances of the heat transfer fluid, different oils are considered and their temperature and heat gain evolutions compared.

Keywords: Direct solar irradiance, solar radiation in Algeria, solar parabolic trough collector, heat balance, thermal oil performance

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Authors: A. M. Tahsini

Abstract:

The Spalart and Allmaras turbulence model has been implemented in a numerical code to study the compressible turbulent flows, which the system of governing equations is solved with a finite volume approach using a structured grid. The AUSM+ scheme is used to calculate the inviscid fluxes. Different benchmark problems have been computed to validate the implementation and numerical results are shown. A special Attention is paid to wall jet applications. In this study, the jet is submitted to various wall boundary conditions (adiabatic or uniform heat flux) in forced convection regime and both two-dimensional and axisymmetric wall jets are considered. The comparison between the numerical results and experimental data has given the validity of this turbulence model to study the turbulent wall jets especially in engineering applications.

Keywords: Wall Jet, Heat transfer, Numerical Simulation, Spalart-Allmaras Turbulence model.

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