Search results for: Meshes for Numerical Simulations

Authors: M. Goodarzi, P. Lashgari

Abstract:

A major part of the flow field involves no complicated turbulent behavior in many turbulent flows. In this research work, in order to reduce required memory and CPU time, the flow field was decomposed into several blocks, each block including its special turbulence. A two dimensional backward facing step was considered here. Four combinations of the Prandtl mixing length and standard k- E models were implemented as well. Computer memory and CPU time consumption in addition to numerical convergence and accuracy of the obtained results were mainly investigated. Observations showed that, a suitable combination of turbulence models in different blocks led to the results with the same accuracy as the high order turbulence model for all of the blocks, in addition to the reductions in memory and CPU time consumption.

Keywords: Computer memory, CPU time, Multi-block method, Turbulence modeling.

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Authors: A. Chaudhuri, C. Guha, T. K. Dutta

Abstract:

Pressure driven microscale gas flow-separation has been investigated by solving the compressible Navier-Stokes (NS) system of equations. A two dimensional explicit finite volume (FV) compressible flow solver has been developed using modified advection upwind splitting methods (AUSM+) with no-slip/first order Maxwell-s velocity slip conditions to predict the flowseparation behavior in microdimensions. The effects of scale-factor of the flow geometry and gas species on the microscale gas flowseparation have been studied in this work. The intensity of flowseparation gets reduced with the decrease in scale of the flow geometry. In reduced dimension, flow-separation may not at all be present under similar flow conditions compared to the larger flow geometry. The flow-separation patterns greatly depend on the properties of the medium under similar flow conditions.

Keywords: AUSM+, FVM, Flow-separation, Microflow.

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Authors: Tan K. B., Norhashidah Hj. M. Ali

Abstract:

In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Lee P. Leon, Raymond Charles

Abstract:

This paper presents a method of evaluating the effect of aggregate angularity on hot mix asphalt (HMA) properties and its relationship to the Permanent Deformation resistance. The research concluded that aggregate particle angularity had a significant effect on the Permanent Deformation performance, and also that with an increase in coarse aggregate angularity there was an increase in the resistance of mixes to Permanent Deformation. A comparison between the measured data and predictive data of permanent deformation predictive models showed the limits of existing prediction models. The numerical analysis described the permanent deformation zones and concluded that angularity has an effect of the onset of these zones. Prediction of permanent deformation help road agencies and by extension economists and engineers determine the best approach for maintenance, rehabilitation, and new construction works of the road infrastructure.

Keywords: Aggregate angularity, asphalt concrete, permanent deformation, rutting prediction.

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Authors: S. N. Deepa, G. Sugumaran

Abstract:

This paper proposes the novel model order formulation scheme to design a discrete PID controller for higher order linear time invariant discrete systems. Modified PSO (MPSO) based model order formulation technique has used to obtain the successful formulated second order system. PID controller is tuned to meet the desired performance specification by using pole-zero cancellation and proposed design procedures. Proposed PID controller is attached with both higher order system and formulated second order system. System specifications are tabulated and closed loop response is observed for stabilization process. The proposed method is illustrated through numerical examples from literature.

Keywords: Discrete PID controller, Model Order Formulation, Modified Particle Swarm Optimization, Pole-Zero Cancellation

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

Abstract:

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: Keunhong Chae, Seokho Yoon

Abstract:

In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: Frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol.

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Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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Authors: E. Keramaris, V. Kanakoudis

Abstract:

In this study the water flow in an open channel over a sharp-crested weir is investigated experimentally. For this reason a series of laboratory experiments were performed in an open channel with a sharp-crested weir. The maximum head expected over the weir, the total upstream water height and the downstream water height of the impact in the constant bed of the open channel were measured. The discharge was measured using a tank put right after the open channel. In addition, the discharge and the upstream velocity were also calculated using already known equations. The main finding is that the relative error percentage for the majority of the experimental measurements is ± 4%, meaning that the calculation of the discharge with a sharp-crested weir gives very good results compared to the numerical results from known equations.

Keywords: Sharp-crested weir, weir height, flow measurement, open channel flow.

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Authors: Dangjun Zhao, Yongji Wang, Lei Liu

Abstract:

Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.

Keywords: GPI observer, sliding mode control, master-slave synchronization, chaotic systems.

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Authors: Mohammad Hasan Raouf, Ebrahim Rasooli Anarmarzi, Hamid Lesani, Javad Olamaei

Abstract:

This paper proposes the application of a hierarchical fuzzy system (HFS) based on multi-input power system stabilizer (MPSS) and also Static Var Compensator (SVC) in multi-machine environment.The number of rules grows exponentially with the number of variables in a conventional fuzzy logic system. The proposed HFS method is developed to solve this problem. To reduce the number of rules the HFS consists of a number of low-dimensional fuzzy systems in a hierarchical structure. In fact, by using HFS the total number of involved rules increases only linearly with the number of input variables. In the MPSS, to have better efficiency an auxiliary signal of reactive power deviation (ΔQ) is added with ΔP+ Δω input type Power system stabilizer (PSS). Phasor model of SVC is described and used in this paper. The performances of MPSS, Conventional power system stabilizer (CPSS), hierarchical Fuzzy Multi-input Power System Stabilizer (HFMPSS) and the proposed method in damping inter-area mode of oscillation are examined in response to disturbances. By using digital simulations the comparative study is illustrated. It can be seen that the proposed PSS is performing satisfactorily within the whole range of disturbances.

Keywords: Power system stabilizer (PSS), hierarchical fuzzysystem (HFS), Static VAR compensator (SVC)

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Authors: Yu Chen, Weiwei Ren, Xiaojing Mu, Feng Zhang, Yi Xu

Abstract:

The superhydrophobic surface is widely used to reduce friction for the flow inside micro-channel and can be used to control/manipulate fluid, cells and even proteins in lab-on-chip. Fabricating micro grooves on hydrophobic surfaces is a common method to obtain such superhydrophobic surface. This study utilized the numerical method to investigate the effect of eccentric micro-grooves on the friction of flow inside micro-channel. A detailed parametric study was conducted to reveal how the eccentricity of micro-grooves affects the micro-channel flow under different grooves sizes, channel heights, Reynolds number. The results showed that the superhydrophobic surface with eccentric micro-grooves induces less friction than the counter part with aligning micro-grooves, which means requiring less power for pumps.

Keywords: Superhydrophobic, transverse grooves, heat transfer, slip length, microfluidics.

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Authors: Sedrak Vardanyan

Abstract:

The investigation of the vibrational character of magnetic cylindrical shells placed in an axial magnetic field has important practical applications. In this work, we study the vibrational behaviour of such a cylindrical shell by making use of the so-called exact space treatment, which does not assume any hypothesis. We discuss the effects of several practically important boundary conditions on the vibrations of the described setup. We find that, for some cases of boundary conditions, e.g. clamped, simply supported or peripherally earthed, as well as for some values of the wave numbers, the vibrational frequencies of the shell are approximately zero. The theoretical and numerical exploration of this fact confirms that the vibrations are absent or attenuate very rapidly. For all the considered cases, the imaginary part of the frequencies is negative, which implies stability for the vibrational process.

Keywords: Free vibrations, magnetic cylindrical shells, exact space treatment, bending vibrational frequencies.

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Authors: M. A. Nozari, R. Ziaie Moayed

Abstract:

Electro-osmosis in clayey soils and sediments, for purposes of clay consolidation, dewatering, or cleanup, and electro injection in porous media is widespread recent decades. It is experimentally found that the chemical properties of porous media especially PH change the characteristics of media. Electro-osmotic conductivity is a function of soil and grout material chemistry, altering with time. Many numerical approaches exist to simulate the of electro kinetic flow rate considering chemical changes. This paper presents a simplified analytical solution for constant flow rate based on varying electro osmotic conductivity and time dependent viscosity for injection of colloidal silica.

Keywords: Colloidal silica, electro-osmosis, pH, viscosity, zeta potential.

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Authors: Tsung-Chia Chen

Abstract:

The orthogonal processes to shape the triangle steel plate into a equilateral vertical steel are examined by an incremental elasto-plastic finite-element method based on an updated Lagrangian formulation. The highly non-linear problems due to the geometric changes, the inelastic constitutive behavior and the boundary conditions varied with deformation are taken into account in an incremental manner. On the contact boundary, a modified Coulomb friction mode is specially considered. A weighting factor r-minimum is employed to limit the step size of loading increment to linear relation. In particular, selective reduced integration was adopted to formulate the stiffness matrix. The simulated geometries of verticality could clearly demonstrate the vertical processes until unloading. A series of experiments and simulations were performed to validate the formulation in the theory, leading to the development of the computer codes. The whole deformation history and the distribution of stress, strain and thickness during the forming process were obtained by carefully considering the moving boundary condition in the finite-element method. Therefore, this modeling can be used for judging whether a equilateral vertical steel can be shaped successfully. The present work may be expected to improve the understanding of the formation of the equilateral vertical steel.

Keywords: Elasto-plastic, finite element, orthogonal pressing process, vertical steel.

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Authors: Anatoli Torokhti, Phil Howlett

Abstract:

We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: stochastic signals, optimization problems in signal processing.

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Authors: Hamed Vahdat Nejad, Hameed Reza Pourreza, Hasan Ebrahimi

Abstract:

A new fuzzy filter is presented for noise reduction of images corrupted with additive noise. The filter consists of two stages. In the first stage, all the pixels of image are processed for determining noisy pixels. For this, a fuzzy rule based system associates a degree to each pixel. The degree of a pixel is a real number in the range [0,1], which denotes a probability that the pixel is not considered as a noisy pixel. In the second stage, another fuzzy rule based system is employed. It uses the output of the previous fuzzy system to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Experimental results are obtained to show the feasibility of the proposed filter. These results are also compared to other filters by numerical measure and visual inspection.

Keywords: Additive noise, Fuzzy logic, Image processing, Noise reduction.

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Authors: Quy Dang Nguyen, Reza Nakhaie Jazar

Abstract:

The paper investigates vibration dynamics of tire-road separation for a quarter-car model; this separation model is developed to be close to the real situation considering the tire is able to separate from the ground plane. A set of piecewise linear mathematical models is developed and matches the in-contact and no-contact states to be considered as mother models for further investigations. The bound dynamics are numerically simulated in the time response and phase portraits. The separation analysis may determine which values of suspension parameters can delay and avoid the no-contact phenomenon, which results in improving ride comfort and eliminating the potentially dangerous oscillation. Finally, model verification is carried out in the MSC-ADAMS environment.

Keywords: Quarter-car vibrations, tire-road separation, separation analysis, separation dynamics, ride comfort, ADAMS validation.

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: Anatoli Torokhti, Phil Howlett

Abstract:

A theory for optimal filtering of infinite sets of random signals is presented. There are several new distinctive features of the proposed approach. First, a single optimal filter for processing any signal from a given infinite signal set is provided. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the scheme concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: Optimal filtering, data compression, stochastic signals.

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Authors: Mahdi Hamzehei

Abstract:

In this research, heat transfer of a poly Ethylene fluidized bed reactor without reaction were studied experimentally and computationally at different superficial gas velocities. A multifluid Eulerian computational model incorporating the kinetic theory for solid particles was developed and used to simulate the heat conducting gas–solid flows in a fluidized bed configuration. Momentum exchange coefficients were evaluated using the Syamlal– O-Brien drag functions. Temperature distributions of different phases in the reactor were also computed. Good agreement was found between the model predictions and the experimentally obtained data for the bed expansion ratio as well as the qualitative gas–solid flow patterns. The simulation and experimental results showed that the gas temperature decreases as it moves upward in the reactor, while the solid particle temperature increases. Pressure drop and temperature distribution predicted by the simulations were in good agreement with the experimental measurements at superficial gas velocities higher than the minimum fluidization velocity. Also, the predicted time-average local voidage profiles were in reasonable agreement with the experimental results. The study showed that the computational model was capable of predicting the heat transfer and the hydrodynamic behavior of gas-solid fluidized bed flows with reasonable accuracy.

Keywords: Gas-solid flows, fluidized bed, Hydrodynamics, Heat transfer, Turbulence model, CFD

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Authors: M. Morri, A. Soualmia, P. Belleudy

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Vegetation affects the mean and turbulent flow structure. It may increase flood risks and sediment transport. Therefore, it is important to develop analytical approaches for the bed shear stress on vegetated bed, to predict resistance caused by vegetation. In the recent years, experimental and numerical models have both been developed to model the effects of submerged vegetation on open-channel flow. In this paper, different analytic models are compared and tested using the criteria of deviation, to explore their capacity for predicting the mean velocity and select the suitable one that will be applied in real case of rivers. The comparison between the measured data in vegetated flume and simulated mean velocities indicated, a good performance, in the case of rigid vegetation, whereas, Huthoff model shows the best agreement with a high coefficient of determination (R2=80%) and the smallest error in the prediction of the average velocities.

Keywords: Analytic Models, Comparison, Mean Velocity, Vegetation.

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Authors: Celso A. G. Santos, Paula K. M. M. Freire

Abstract:

The urban centers within northeastern Brazil are mainly influenced by the intense rainfalls, which can occur after long periods of drought, when flood events can be observed during such events. Thus, this paper aims to study the rainfall frequencies in such region through the wavelet transform. An application of wavelet analysis is done with long time series of the total monthly rainfall amount at the capital cities of northeastern Brazil. The main frequency components in the time series are studied by the global wavelet spectrum and the modulation in separated periodicity bands were done in order to extract additional information, e.g., the 8 and 16 months band was examined by an average of all scales, giving a measure of the average annual variance versus time, where the periods with low or high variance could be identified. The important increases were identified in the average variance for some periods, e.g. 1947 to 1952 at Teresina city, which can be considered as high wet periods. Although, the precipitation in those sites showed similar global wavelet spectra, the wavelet spectra revealed particular features. This study can be considered an important tool for time series analysis, which can help the studies concerning flood control, mainly when they are applied together with rainfall-runoff simulations.

Keywords: rainfall data, urban center, wavelet transform.

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Authors: S. A. Eftekhari

Abstract:

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

Keywords: Dam-reservoir system, Differential quadrature method, Fluid-structure interaction, Galerkin method, Integral quadrature method.

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Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe

Abstract:

We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: Indentation, contact problem, stress distribution, coating materials, layer-substrate body.

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Authors: Abdelouahab Bouttout, Mohamed Amara

Abstract:

The present paper examines the impact noise transmission through some floor building assemblies. The Acoubat software numerical simulation has been used to simulate the impact noise transmission through different floor configurations used in Algerian construction mode. The results are compared with the available measurements. We have developed two experimental methods, i) field method, and ii) laboratory method using Brüel and Kjær equipments. The results show that the different cases of floor configurations need some improvement to ensure the acoustic comfort in the receiving apartment. The recommended value of the impact sound level in the receiving room should not exceed 58 dB. The important results obtained in this paper can be used as platform to improve the Algerian building acoustic regulation aimed at the construction of the multi-storey residential building.

Keywords: Impact noise, building acoustic, floor insulation, resilient material.

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Authors: W. Du, X. Wang, Jun Cao, H. F. Wang

Abstract:

Due to the randomness and uncertainty of wind energy, modern power systems integrating large-scale wind generation will be significantly impacted in terms of system performance and technical challenges. System inertia with high wind penetration is decreasing when conventional thermal generators are gradually replaced by wind turbines, which do not naturally contribute to inertia response. The power imbalance caused by wind power or demand fluctuations leads to the instability of system frequency. Accordingly, the need to attach the supplementary virtual inertia control to wind farms (WFs) strongly arises. When multi-wind farms are connected to the grid simultaneously, the selection of which critical WFs to install the virtual inertia control is greatly important to enhance the stability of system frequency. By building the small signal model of wind power systems considering frequency regulation, the installation locations are identified by the geometric measures of the mode observability of WFs. In addition, this paper takes the impacts of grid topology and selection of feedback control signals into consideration. Finally, simulations are conducted on a multi-wind farms power system and the results demonstrate that the designed virtual inertia control method can effectively assist the frequency regulation.

Keywords: Frequency regulation, virtual inertia control, installation locations, observability, wind farms.

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Authors: Mohana Sundaram Muthuvalu, Jumat Sulaiman

Abstract:

In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

Keywords: Complexity reduction approach, Composite trapezoidal scheme, Jacobi method, Linear Fredholm integral equations

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Authors: Roslinda Nazar, Anuar Ishak, Ioan Pop

Abstract:

Unsteady boundary layer flow of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane is studied in this paper. The stretching velocity is assumed to vary linearly with the distance along the sheet. Two equal and opposite forces are impulsively applied along the x-axis so that the sheet is stretched, keeping the origin fixed in a micropolar fluid. The transformed unsteady boundary layer equations are solved numerically using the Keller-box method for the whole transient from the initial state to final steady-state flow. Numerical results are obtained for the velocity and microrotation distributions as well as the skin friction coefficient for various values of the material parameter K. It is found that there is a smooth transition from the small-time solution to the large-time solution.

Keywords: Boundary layer, micropolar fluid, stretching surface, unsteady flow.

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Authors: M’hamed Outanoute, Mohamed Baslam, Belaid Bouikhalene

Abstract:

The customers use the best compromise criterion between price and quality of service (QoS) to select or change their Service Provider (SP). The SPs share the same market and are competing to attract more customers to gain more profit. Due to the divergence of SPs interests, we believe that this situation is a non-cooperative game of price and QoS. The game converges to an equilibrium position known Nash Equilibrium (NE). In this work, we formulate a game theoretic framework for the dynamical behaviors of SPs. We use Genetic Algorithms (GAs) to find the price and QoS strategies that maximize the profit for each SP and illustrate the corresponding strategy in NE. In order to quantify how this NE point is performant, we perform a detailed analysis of the price of anarchy induced by the NE solution. Finally, we provide an extensive numerical study to point out the importance of considering price and QoS as a joint decision parameter.

Keywords: Pricing, QoS, Market share game, Genetic algorithms, Nash equilibrium, Learning, Price of anarchy.

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