Search results for: flow function

Authors: Hoyoung Lee, Dong-Kyu Kim, Seung-Young Kho, R. Eddie Wilson

Abstract:

This study quantifies a decrement in freeway capacity during rainfall. Traffic and rainfall data were gathered from Highway Agencies and Wunderground weather service. Three inter-urban freeway sections and its nearest weather stations were selected as experimental sites. Capacity analysis found reductions of maximum and mean pre-breakdown flow rates due to rainfall. The Kruskal-Wallis test also provided some evidence to suggest that the variance in the pre-breakdown flow rate is statistically insignificant. Potential application of this study lies in the operation of real time traffic management schemes such as Variable Speed Limits (VSL), Hard Shoulder Running (HSR), and Ramp Metering System (RMS), where speed or flow limits could be set based on a number of factors, including rainfall events and their intensities.

Keywords: Capacity randomness, flow breakdown, freeway capacity, rainfall.

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Authors: Nasser Ghassembaglou, Abdullah Bolek, Oktay Yilmaz, Ertan Oznergiz, Hikmet Kocabas, Safak Yilmaz

Abstract:

Different designs of attenuator systems have been studied in this research; new analysis have been done on existed designs considering fibers effect on air flow; it was comprehended that, at fibers presence, there is an air flow which agglomerates fibers as a negative effect. So some new representations have been designed and CFD analysis has been done on them. Afterwards, one of these representations selected as the most optimum and effective design which is brought in this paper.

Keywords: Attenuator, CFD, nanofiber, spun-bond.

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Authors: Lütfü Saribulut, Mehmet Tümay, İlyas Eker

Abstract:

FACTS devices are used to control the power flow, to increase the transmission capacity and to optimize the stability of the power system. One of the most widely used FACTS devices is Unified Power Flow Controller (UPFC). The controller used in the control mechanism has a significantly effects on controlling of the power flow and enhancing the system stability of UPFC. According to this, the capability of UPFC is observed by using different control mechanisms based on P, PI, PID and fuzzy logic controllers (FLC) in this study. FLC was developed by taking consideration of Takagi- Sugeno inference system in the decision process and Sugeno-s weighted average method in the defuzzification process. Case studies with different operating conditions are applied to prove the ability of UPFC on controlling the power flow and the effectiveness of controllers on the performance of UPFC. PSCAD/EMTDC program is used to create the FLC and to simulate UPFC model.

Keywords: FACTS, Fuzzy Logic Controller, UPFC.

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Authors: Ali Jahanfar, Brajesh Dubey, Bahram Gharabaghi, Saber Bayat Movahed

Abstract:

Ever increasing population growth of major urban centers and environmental challenges in siting new landfills have resulted in a growing trend in design of mega-landfills some with extraordinary heights and dangerously steep slopes. Landfill failure mobility risk analysis is one of the most uncertain types of dynamic rheology models due to very large inherent variabilities in the heterogeneous solid waste material shear strength properties. The waste flow of three historic dumpsite and two landfill failures were back-analyzed using run-out modeling with DAN-W model. The travel distances of the waste flow during landfill failures were calculated approach by taking into account variability in material shear strength properties. The probability distribution function for shear strength properties of the waste material were grouped into four major classed based on waste material compaction (landfills versus dumpsites) and composition (high versus low quantity) of high shear strength waste materials such as wood, metal, plastic, paper and cardboard in the waste. This paper presents a probabilistic method for estimation of the spatial extent of waste avalanches, after a potential landfill failure, to create maps of vulnerability scores to inform property owners and residents of the level of the risk.

Keywords: Landfill failure, waste flow, Voellmy rheology, friction coefficient, waste compaction and type.

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Authors: Azli Abd. Razak, Yusli Yaakob, Mohd Nazir Ramli

Abstract:

This study comprehensively simulate the use of k-ε model for predicting flow and heat transfer with measured flow field data in a stationary duct with elucidates on the detailed physics encountered in the fully developed flow region, and the sharp 180° bend region. Among the major flow features predicted with accuracy are flow transition at the entrance of the duct, the distribution of mean and turbulent quantities in the developing, fully developed, and sharp 180° bend, the development of secondary flows in the duct cross-section and the sharp 180° bend, and heat transfer augmentation. Turbulence intensities in the sharp 180° bend are found to reach high values and local heat transfer comparisons show that the heat transfer augmentation shifts towards the wall and along the duct. Therefore, understanding of the unsteady heat transfer in sharp 180° bends is important. The design and simulation are related to concept of fluid mechanics, heat transfer and thermodynamics. Simulation study has been conducted on the response of turbulent flow in a rectangular duct in order to evaluate the heat transfer rate along the small scale multiple rectangular duct

Keywords: Heat transfer, turbulence, rectangular duct, simulation.

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Authors: Karam Y. Maalawi, Hanan E.M EL-Sayed

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This paper presents an exact analytical model for optimizing stability of thin-walled, composite, functionally graded pipes conveying fluid. The critical flow velocity at which divergence occurs is maximized for a specified total structural mass in order to ensure the economic feasibility of the attained optimum designs. The composition of the material of construction is optimized by defining the spatial distribution of volume fractions of the material constituents using piecewise variations along the pipe length. The major aim is to tailor the material distribution in the axial direction so as to avoid the occurrence of divergence instability without the penalty of increasing structural mass. Three types of boundary conditions have been examined; namely, Hinged-Hinged, Clamped- Hinged and Clamped-Clamped pipelines. The resulting optimization problem has been formulated as a nonlinear mathematical programming problem solved by invoking the MatLab optimization toolbox routines, which implement constrained function minimization routine named “fmincon" interacting with the associated eigenvalue problem routines. In fact, the proposed mathematical models have succeeded in maximizing the critical flow velocity without mass penalty and producing efficient and economic designs having enhanced stability characteristics as compared with the baseline designs.

Keywords: Functionally graded materials, pipe flow, optimumdesign, fluid- structure interaction

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Authors: Ezad Hafidz Hafidzuddin, Roslinda Nazar, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: Boundary Layer, Exponentially Stretching/Shrinking Sheet, Generalized Slip, Heat Transfer, Numerical Solutions.

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Authors: Hironori Kakuta, Kajiro Watanabe, Yosuke Kurihara

Abstract:

Water leakage is a serious problem in the maintenance of a waterworks facility. Monitoring the water flow rate is one way to locate leakage. However, conventional flowmeters such as the wet-type flowmeter and the clamp-on type ultrasonic flowmeter require additional construction for their installation and are therefore quite expensive. This paper proposes a novel estimation system for the flow rate in a water pipeline, which employs a vibration sensor. This assembly can be attached to any water pipeline without the need for additional high-cost construction. The vibration sensor is designed based on a condenser microphone. This sensor detects vibration caused by water flowing through a pipeline. It is possible to estimate the water flow rate by measuring the amplitude of the output signal from the vibration sensor. We confirmed the validity of the proposed sensing system experimentally.

Keywords: Condenser microphone, Flow rate estimation, Piping vibration, Water pipe.

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Authors: Hsuan-Chu Li

Abstract:

We demonstrate a way to count the number of Young tableau u of shape λ = (k, k,L, k) with | λ |= lk by expanding Schur function. This result gives an answer to the question that was put out by Jenny Buontempo and Brian Hopkins.

Keywords: Young tableau, Schur function.

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Authors: Maysam Saidi, Reza Maddahian, Bijan Farhanieh

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In this research a comparison between k-epsilon and LES model for a deoiling hydrocyclone is conducted. Flow field of hydrocyclone is obtained by three-dimensional simulations with OpenFOAM code. Potential of prediction for both methods of this complex swirl flow is discussed. Large eddy simulation method results have more similarity to experiment and its results are presented in figures from different hydrocyclone cross sections.

Keywords: Deoiling hydrocyclones, k-epsilon model, Largeeddy simulation, OpenFOAM

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Authors: Rana Khalid Naeem, Asif Mansoor

Abstract:

The hydrologic time series data display periodic structure and periodic autoregressive process receives considerable attention in modeling of such series. In this communication long term record of monthly waste flow of Lyari river is utilized to quantify by using PAR modeling technique. The parameters of model are estimated by using Frances & Paap methodology. This study shows that periodic autoregressive model of order 2 is the most parsimonious model for assessing periodicity in waste flow of the river. A careful statistical analysis of residuals of PAR (2) model is used for establishing goodness of fit. The forecast by using proposed model confirms significance and effectiveness of the model.

Keywords: Diagnostic checks, Lyari river, Model selection, Monthly waste flow, Periodicity, Periodic autoregressive model.

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Authors: A. Guellati, F-M Lounis, N. Guemras, K. Daoud

Abstract:

Micro droplet formation is considered as a growing emerging area of research due to its wide-range application in chemistry as well as biology. The mechanism of micro droplet formation using two immiscible liquids running through a T-junction has been widely studied. We believe that the flow of these two immiscible phases can be of greater important factor that could have an impact on out-flow hydrodynamic behavior, the droplets generated and the size of the droplets. In this study, the type of the capillary tubes used also represents another important factor that can have an impact on the generation of micro droplets. The tygon capillary tubing with hydrophilic inner surface doesn't allow regular out-flows due to the fact that the continuous phase doesn't adhere to the wall of the capillary inner surface. Teflon capillary tubing, presents better wettability than tygon tubing, and allows to obtain steady and regular regimes of out-flow, and the micro droplets are homogeneoussize. The size of the droplets is directly dependent on the flows of the continuous and dispersed phases. Thus, as increasing the flow of the continuous phase, to flow of the dispersed phase stationary, the size of the drops decreases. Inversely, while increasing the flow of the dispersed phase, to flow of the continuous phase stationary, the size of the droplet increases.

Keywords: Microfluidic system, micro droplets generation, T-junction.

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Authors: Hadi Taghvafard

Abstract:

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Omer F. Can, Nevin Celik

Abstract:

In this study, a semi-cylinder obstacle placed in a channel is handled to determine the effect of flow and heat transfer around the obstacle. Both faces of the semi-cylinder are used in the numerical analysis. First, the front face of the semi-cylinder is stated perpendicular to flow, than the rear face is placed. The study is carried out numerically, by using commercial software ANSYS 11.0. The well-known κ-ε model is applied as the turbulence model. Reynolds number is in the range of 104 to 105 and air is assumed as the flowing fluid. The results showed that, heat transfer increased approximately 15 % in the front faze case, while it enhanced up to 28 % in the rear face case.

Keywords: External flow, semi-cylinder obstacle, heat transfer, friction.

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Authors: P.G. Jayathilake, B.C. Khoo, Zhijun Tan

Abstract:

A two-dimensional thin-walled capsule of a flexible semi-permeable membrane is adhered onto a rigid planar substrate under adhesive forces (derived from a potential function) in the presence of osmosis across the membrane. The capsule is immersed in a hypotonic and diluted binary solution of a non-electrolyte solute. The Stokes flow problem is solved by the immersed interface method (IIM) with equal viscosities for the enclosed and surrounding fluid of the capsule. The numerical results obtained are verified against two simplified theoretical solutions and the agreements are good. The osmotic inflation of the adhered capsule is studied as a function of the solute concentration field, hydraulic conductivity, and the initial capsule shape. Our findings indicate that the contact length shrinks in dimension as capsule inflates in the hypotonic medium, and the equilibrium contact length does not depend on the hydraulic conductivity of the membrane and the initial shape of the capsule.

Keywords: Capsule-substrate adhesion, Fluid mechanics, Immersed interface method, Osmosis, Mass transfer.

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Authors: T. J. Jamaleddine

Abstract:

Purge columns or degasser vessels are widely used in the polyolefin process for removing trapped hydrocarbons and in-excess catalyst residues from the polymer particles. A uniform distribution of purged gases coupled with a plug-flow characteristic inside the column system is desirable to obtain optimum desorption characteristics of trapped hydrocarbon and catalyst residues. Computational Fluid Dynamics (CFD) approach is a promising tool for design optimization of these vessels. The success of this approach is profoundly dependent on the solution strategy and the choice of geometrical layout at the vessel outlet. Filling the column with solids and initially solving for the solids flow minimized numerical diffusion substantially. Adopting a cylindrical configuration at the vessel outlet resulted in less numerical instability and resembled the hydrodynamics flow of solids in the hopper segment reasonably well.

Keywords: CFD, gas-solids flow, gas purging, species transport, purge column, degasser vessel.

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Authors: Jayendra Krishna, Laxmi Srivastava

Abstract:

Power flow (PF) study, which is performed to determine the power system static states (voltage magnitudes and voltage angles) at each bus to find the steady state operating condition of a system, is very important and is the most frequently carried out study by power utilities for power system planning, operation and control. In this paper, a counterpropagation neural network (CPNN) is proposed to solve power flow problem under different loading/contingency conditions for computing bus voltage magnitudes and angles of the power system. The counterpropagation network uses a different mapping strategy namely counterpropagation and provides a practical approach for implementing a pattern mapping task, since learning is fast in this network. The composition of the input variables for the proposed neural network has been selected to emulate the solution process of a conventional power flow program. The effectiveness of the proposed CPNN based approach for solving power flow is demonstrated by computation of bus voltage magnitudes and voltage angles for different loading conditions and single line-outage contingencies in IEEE 14-bus system.

Keywords: Admittance matrix, counterpropagation neural network, line outage contingency, power flow

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Authors: Kentaro Miyoko, Yoshihiko Mori, Yugo Ikeda, Yoshihiro Nishino, Yong-Bok Choi, Hiromi Okada

Abstract:

Optical burst switching (OBS) has been proposed to realize the next generation Internet based on the wavelength division multiplexing (WDM) network technologies. In the OBS, the burst contention is one of the major problems. The deflection routing has been designed for resolving the problem. However, the deflection routing becomes difficult to prevent from the burst contentions as the network load becomes high. In this paper, we introduce a flow rate control methods to reduce burst contentions. We propose new flow rate control methods based on the leaky bucket algorithm and deflection routing, i.e. separate leaky bucket deflection method, and dynamic leaky bucket deflection method. In proposed methods, edge nodes which generate data bursts carry out the flow rate control protocols. In order to verify the effectiveness of the flow rate control in OBS networks, we show that the proposed methods improve the network utilization and reduce the burst loss probability through computer simulations.

Keywords: Optical burst switching, OBS, flow rate control.

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Authors: Yiping Wang, Zhengqi Gu, Weiping Li, Xiaohui Lin

Abstract:

The aerodynamic noise radiation from a side view mirror (SVM) in the high-speed airflow is calculated by the combination of unsteady incompressible fluid flow analysis and acoustic analysis. The transient flow past the generic SVM is simulated with variable turbulence model, namely DES Detached Eddy Simulation and LES (Large Eddy Simulation). Detailed velocity vectors and contour plots of the time-varying velocity and pressure fields are presented along cut planes in the flow-field. Mean and transient pressure are also monitored at several points in the flow field and compared to corresponding experimentally data published in literature. The acoustic predictions made using the Ffowcs-Williams-Hawkins acoustic analogy (FW-H) and the boundary element (BEM).

Keywords: Aerodynamic noise, BEM, DES, FW-H acousticanalogy, LES

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Authors: Marko A. Rodriguez

Abstract:

There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a topological feature of the directed network. Also, there exists an injective function that maps a directed network to an undirected network (i.e. an undirected unlabeled network). The edge directionality in the directed network is represented as a topological feature of the undirected network. Through function composition, there exists an injective function that maps a semantic network to an undirected network. Thus, aside from space constraints, the semantic network construct does not have any modeling functionality that is not possible with either a directed or undirected network representation. Two proofs of this idea will be presented. The first is a proof of the aforementioned function composition concept. The second is a simpler proof involving an undirected binary encoding of a semantic network.

Keywords: general-modeling, multi-relational networks, semantic networks

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Authors: Ke Wang, Zhi-Qiang Zhang, Z. Chen

Abstract:

A submerged horizontal plate type breakwater is pointed out as an efficient wave protection device for cage culture in marine fishery. In order to reveal the wave elimination principle of this type breakwater, boundary element method is utilized to investigate this problem. The flow field and the trajectory of water particles are studied carefully. The flow field analysis shows that: the interaction of incident wave and adverse current above the plate disturbs the water domain drastically. This can slow down the horizontal velocity and vertical velocity of the water particles.

Keywords: boundary element method, plate type breakwater, flow field analysis

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Authors: Shuguo Yang, Xiaoyan Yang

Abstract:

It is practically significant to research the traffic flow of intersection because the capacity of intersection affects the efficiency of highway network directly. This paper analyzes the traffic conditions of an intersection in certain urban by the methods of queuing theory and statistical experiment, sets up a corresponding mathematical model and compares it with the actual values. The result shows that queuing theory is applied in the study of intersection traffic flow and it can provide references for the other similar designs.

Keywords: Intersection, Queuing theory, Statistical experiment, System metrics.

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Authors: Yu-Kai Ting, Jia-Ying Tu, Chung-Chun Hsiao

Abstract:

New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work.

Keywords: Galerkin method, Lorenz equations, Navier-Stokes equations.

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Authors: Moataz M. Naguib, Hatem Khater, A. Baith Mohamed

Abstract:

MARS is a shared-key (symmetric) block cipher algorithm supporting 128-bit block size and a variable key size of between 128 and 448 bits. MARS has a several rounds of cryptographic core that is designed to take advantage of the powerful results for improving security/performance tradeoff over existing ciphers. In this work, a new function added to improve the ciphering process it is called, Meta-Morphic function. This function use XOR, Rotating, Inverting and No-Operation logical operations before and after encryption process. The aim of these operations is to improve MARS cipher process and makes a high confusion criterion for the Ciphertext.

Keywords: AES, MARS, Metamorphic, Cryptography, Block Cipher.

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Authors: Mashitah Mohd Hussain, Salleh Serwan, Zuhaina Hj Zakaria

Abstract:

This paper presents a method to estimate load profile in a multiple power flow solutions for every minutes in 24 hours per day. A method to calculate multiple solutions of non linear profile is introduced. The Power System Simulation/Engineering (PSS®E) and python has been used to solve the load power flow. The result of this power flow solutions has been used to estimate the load profiles for each load at buses using Independent Component Analysis (ICA) without any knowledge of parameter and network topology of the systems. The proposed algorithm is tested with IEEE 69 test bus system represents for distribution part and the method of ICA has been programmed in MATLAB R2012b version. Simulation results and errors of estimations are discussed in this paper.

Keywords: Electrical Distribution System, Power Flow Solution, Distribution Network, Independent Component Analysis, Newton Raphson, Power System Simulation for Engineering.

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Authors: B. Lakghomi, E. Kolahchian, A. Jalali, F. Farhadi

Abstract:

Different approaches for heating\cooling of stirred tanks, coils and jackets, are investigated using computational fluid dynamics (CFD).A time-dependant sliding mesh approach is applied to simulate the flow in both conditions. The investigations are carried out under the turbulent flow conditions for a Rushton impeller and heating elements are considered isothermal. The flow behavior and temperature distribution are studied for each case and heat transfer coefficient is calculated. Results show different velocity profiles for each case. Unsteady temperature distribution is not similar for different cases .In the case of the coiled stirred vessel more uniform temperature and higher heat transfer coefficient is resulted.

Keywords: CFD, coil and jacket, heat transfer, stirred tank.

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Authors: Carmen D. Pricinâ, E. Corina Cipu, Victor Ţigoiu

Abstract:

The flow of a third grade fluid in an orthogonal rheometer is studied. We employ the admissible velocity field proposed in [5]. We solve the problem and obtain the velocity field as well as the components for the Cauchy tensor. We compare the results with those from [9]. Some diagrams concerning the velocity and Cauchy stress components profiles are presented for different values of material constants and compared with the corresponding values for a linear viscous fluid.

Keywords: Non newtonian fluid flow, orthogonal rheometer, third grade fluid.

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Authors: Naimi Abdelhamid, Othmane Abdelkhalek

Abstract:

With the current rise in the demand of electrical energy, present-day power systems which are large and complex, will continue to grow in both size and complexity. Flexible AC Transmission System (FACTS) controllers provide new facilities, both in steady state power flow control and dynamic stability control. Thyristor Controlled Series Capacitor (TCSC) is one of FACTS equipment, which is used for power flow control of active power in electric power system and for increase of capacities of transmission lines. In this paper, a Backstepping Power Flow Controller (BPFC) for TCSC in multimachine power system is developed and tested. The simulation results show that the TCSC proposed controller is capable of controlling the transmitted active power and improving the transient stability when compared with conventional PI Power Flow Controller (PIPFC).

Keywords: FACTS, Thyristor Controlled Series Capacitor (TCSC), Backstepping, BPFC, PIPFC.

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Authors: D. R. Delgado Sobrino, P. Košťál, J. Oravcová

Abstract:

Lately, significant work in the area of Intelligent Manufacturing has become public and mainly applied within the frame of industrial purposes. Special efforts have been made in the implementation of new technologies, management and control systems, among many others which have all evolved the field. Aware of all this and due to the scope of new projects and the need of turning the existing flexible ideas into more autonomous and intelligent ones, i.e.: Intelligent Manufacturing, the present paper emerges with the main aim of contributing to the design and analysis of the material flow in either systems, cells or work stations under this new “intelligent" denomination. For this, besides offering a conceptual basis in some of the key points to be taken into account and some general principles to consider in the design and analysis of the material flow, also some tips on how to define other possible alternative material flow scenarios and a classification of the states a system, cell or workstation are offered as well. All this is done with the intentions of relating it with the use of simulation tools, for which these have been briefly addressed with a special focus on the Witness simulation package. For a better comprehension, the previous elements are supported by a detailed layout, other figures and a few expressions which could help obtaining necessary data. Such data and others will be used in the future, when simulating the scenarios in the search of the best material flow configurations.

Keywords: Flexible/Intelligent Manufacturing System/Cell (F/IMS/C), material flow/design/configuration (MF/D/C), workstation.

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Authors: M. Ezkurra, J. A. Esnaola, M. Martinez-Agirre, U. Etxeberria, U. Lertxundi, L. Colomo, M. Begiristain, I. Zurutuza

Abstract:

Butterfly valves are widely used industrial piping components as on-off and flow controlling devices. The main challenge in the design process of this type of valves is the correct dimensioning to ensure proper mechanical performance as well as to minimise flow losses that affect the efficiency of the system. Butterfly valves are typically dimensioned in a closed position based on mechanical approaches considering uniform hydrostatic pressure, whereas the flow losses are analysed by means of CFD simulations. The main limitation of these approaches is that they do not consider either the influence of the dynamics of the manoeuvring stage or coupled phenomena. Recent works have included the influence of the flow on the mechanical behaviour for different opening angles by means of one-way FSI approach. However, these works consider steady-state flow for the selected angles, not capturing the effect of the transient flow evolution during the manoeuvring stage. Two-way FSI modelling approach could allow overcoming such limitations providing more accurate results. Nevertheless, the use of this technique is limited due to the increase in the computational cost. In the present work, the applicability of FSI one-way and two-way approaches is evaluated for the analysis of butterfly valves, showing that not considering fluid-structure coupling involves not capturing the most critical situation for the valve disc.

Keywords: Butterfly valves, fluid-structure interaction, one-way approach, two-way approach.

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