Search results for: simplified torque equation

Authors: H. T. Le Luong, C. Hénaux, F. Messine, G. Bueno-Mariani, S. Mollov, N. Voyer

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This paper presents a comparative study of different modular brushless wound rotor synchronous machine (MB-WRSM). The goal of the study is to highlight the structure which offers the best fault tolerant capability and the highest output performances. The fundamental winding factor is calculated by using the method based on EMF phasors as a significant criterion to select the preferred number of phases, stator slots, and poles. With the limited number of poles for a small machine (3.67kW/7000rpm), 15 different machines for preferred phase/slot/pole combinations are analyzed using two-dimensional (2-D) finite element method and compared according to three criteria: torque density, torque ripple and efficiency. The 7phase/7slot/6pole machine is chosen with the best compromise of high torque density, small torque ripple (3.89%) and high nominal efficiency (95%). This machine is then compared with a reference design surface permanent magnet synchronous machine (SPMSM). In conclusion, this paper provides an electromagnetic analysis of a new brushless wound-rotor synchronous machine using multiphase non-overlapping fractional slot double layer winding. The simulation results are discussed and demonstrate that the MB-WRSM presents interesting performance features, with overall performance closely matching that of an equivalent SPMSM.

Keywords: finite element method (FEM), machine performance, modular wound rotor synchronous machine, non-overlapping concentrated winding

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Authors: Kamand Bagherian, Nariman Niknejad

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A vibration isolation technology for precise position control of a rotary system powered by two permanent magnet DC (PMDC) motors is proposed, where this system is mounted on an oscillatory frame. To achieve vibration isolation for this system, active damping and disturbance rejection (ADDR) technology is presented which introduces a cooperation of a main and an auxiliary PMDC, controlled by discrete-time sliding mode control (DTSMC) based schemes. The controller of the main actuator tracks a desired position and the auxiliary actuator simultaneously isolates the induced vibration, as its controller follows a torque trend. To determine this torque trend, a combination of two algorithms is introduced by the ADDR technology. The first torque-trend producing algorithm rejects the disturbance by counteracting the perturbation, estimated using a model-based observer. The second torque trend applies active variable damping to minimize the oscillation of the output shaft. In this practice, the presented technology is implemented on a rotary system with a pendulum attached, mounted on a linear actuator simulating an oscillation-transmitting structure. In addition, the obtained results illustrate the functionality of the proposed technology.

Keywords: active damping, discrete-time nonlinear controller, disturbance tracking algorithm, oscillation transmitting support, position control, stability robustness, vibration isolation

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Authors: A. Majczak, G. Baranski, K. Pietrykowski

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Due to the growing popularity of light aircraft, it has become necessary to develop aircraft engines for this type of construction. One of engine system, designed to increase efficiency and reduce weight, is the engine with opposed pistons. In such an engine, the combustion chamber is formed by two pistons moving in one cylinder. Therefore, this type of engines run in a two-stroke cycle, so they have many advantages such as high power and torque, high efficiency, or a favorable power-to-weight ratio. Tests of one of the available aircraft engines with opposing piston system fueled with diesel oil were carried out on an engine dynamometer equipped with an eddy current brake and the necessary measuring and testing equipment. In order to get to know the basic parameters of the engine, the tests were carried out under partial load conditions for the following torque values: 40, 60, 80, 100 Nm. The rotational speed was changed from 1600 to 2500 rpm. Measurements were also taken for designated points of propeller characteristics. During the tests, the engine torque, engine power, fuel consumption, intake manifold pressure, and oil pressure were recorded. On the basis of the measurements carried out for particular loads, the power curve, hourly and specific fuel consumption curves were determined. Characteristics of charge pressure as a function of rotational speed as well as power, torque, hourly and specific fuel consumption curves for propeller characteristics were also prepared. The obtained characteristics make it possible to select the optimal points of engine operation.

Keywords: aircraft, diesel, engine testing, opposed piston

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation

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Authors: Kouzi Katia

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This paper proposes a Direct Torque Control (DTC) algorithm of dual Stator Induction Motor (DSIM) drive using two approach intelligent techniques: Artificial Neural Network (ANN) approach replaces the switching table selector block of conventional DTC and Mamdani Fuzzy Logic controller (FLC) is used for stator resistance estimation. The fuzzy estimation method is based on an online stator resistance correction through the variations of stator current estimation error and its variation. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of suggested algorithm control is to reduce the hardware complexity of conventional selectors, to avoid the drive instability that may occur in certain situation and ensure the tracking of the actual of the stator resistance. The effectiveness of the technique and the improvement of the whole system performance are proved by results.

Keywords: artificial neural network, direct torque control, dual stator induction motor, fuzzy logic estimator, switching table

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Authors: Narumol Chintaganun

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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

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Authors: Hossein Ramezani Ali-Akbari

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This paper presents an innovative method to control the rotational speed of a satellite solar panel during its deployment phase. A brushed DC motor has been utilized in the passive spring driven deployment mechanism to reduce the deployment speed. In order to use the DC motor as a damper, its connector terminals have been connected with an external resistance in a closed circuit. It means that, in this approach, there is no external power supply in the circuit. The working principle of this method is based on the back electromotive force (or back EMF) of the DC motor when an external torque (here the torque produced by the torsional springs) is coupled to the DC motor’s shaft. In fact, the DC motor converts to an electric generator and the current flows into the circuit and then produces the back EMF. Based on Lenz’s law, the generated current produced a torque which acts opposite to the applied external torque, and as a result, the deployment speed of the solar panel decreases. The main advantage of this method is to set an intended damping coefficient to the system via changing the external resistance. To produce the sufficient current, a gearbox has been assembled to the DC motor which magnifies the number of turns experienced by the DC motor. The coupled electro-mechanical equations of the system have been derived and solved, then, the obtained results have been presented. A full-scale prototype of the deployment mechanism has been built and tested. The potential application of brushed DC motors as a rotational speed damper has been successfully demonstrated.

Keywords: back electromotive force, brushed DC motor, rotational speed damper, satellite solar panel deployment mechanism

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Authors: H. Ozbasaran

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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: cantilever, IPN, IPE, lateral torsional buckling

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Authors: Geochul Jeong, In-Gun Kim, Hyun-Seok Hong, Dong-Woo Kang, Ju Lee

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This study is about IPMSM design for obtaining the maximum traction force of Tram-Train. Tram-Train is a Tram and Train-combined railway vehicles, which operates at a maximum speed of 70km/h in the city section (Tram section) and at a maximum speed of 150km/h in the out-of-city section (Train section). For this reason, tram-train was designed to be an IPMSM (Interior Permanent Synchronous Motor) with a wide range of speed variation. IPMSM’s magnetic path varies depending on the shape of rotor and in this case, the power characteristics are different in the constant torque area and the flux weakening area. Therefore, this study suggests a method to improve Tram-Train’s traction force, based on the relationship between magnetic torque and reluctance torque. The suggested method was applied through IPMSM rotor shape design and electromagnetic field finite element method was conducted to verify the validity of the suggested method.

Keywords: tram-train, traction motor, IPMSM, synchronous motor, railway vehicles

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Mohsin Raza, Rizwan Latif, Syed Adnan Qasim, Imran Shafi

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High torque low-speed diesel engine has a wide range of industrial and commercial applications. In literature, it’s found that lot of work has been done for the high-speed diesel engine and research on High Torque low-speed is rare. The fuel injection plays a key role in the efficiency of engine and reduction in exhaust emission. The fuel breakup plays a critical role in air-fuel mixture and spray combustion. The current study explains numerically an important phenomenon in spray combustion which is deformation and breakup of liquid drops in compression ignition internal combustion engine. The secondary breakup and its influence on spray and characteristics of compressed gas in-cylinder have been calculated by using simulation software in the backdrop of high torque low-speed diesel like conditions. The secondary spray breakup is modeled with KH - RT instabilities. The continuous field is described by turbulence model and dynamics of the dispersed droplet is modeled by Lagrangian tracking scheme. The results by using KH - RT model are compared against other default methods in OpenFOAM and published experimental data from research and implemented in CFD (Computational Fluid Dynamics). These numerical simulation, done in OpenFoam and Matlab, results are analyzed for the complete 720- degree 4 stroke engine cycle at a low engine speed, for favorable agreement to be achieved. Results thus obtained will be analyzed for better evaporation in near nozzle region. The proposed analyses will further help in better engine efficiency, low emission and improved fuel economy.

Keywords: diesel fuel, KH-RT, Lagrangian , Open FOAM, secondary breakup

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Authors: Kendouci Khedidja, Mazari Benyounes, Benhadria Mohamed Rachid, Dadi Rachida

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In recent years, direct torque control (DTC) has become an alternative to the well-known vector control especially for permanent magnet synchronous motor (PMSM). However, it presents a problem of field linkage and torque ripple. In order to solve this problem, the conventional DTC is combined with space vector pulse width modulation (SVPWM). This control theory has achieved great success in the control of PMSM. That has become a hotspot for resolving. The main objective of this paper gives us an introduction of the DTC and SVPWM-DTC control theory of PMSM which has been simulating on each part of the system via Matlab/Simulink based on the mathematical modeling. Moreover, the outcome of the simulation proved that the improved SVPWM- DTC of PMSM has a good dynamic and static performance.

Keywords: PMSM, DTC, SVM, speed control

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Authors: B. Ladghem Chikouche

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The influence of slot wedges permeability on the electromagnetic performance of three-phase permanent magnet synchronous machine is investigated in this paper. It is shown that the back-EMF waveform, electromagnetic torque and electromagnetic torque ripple are all significantly affected by slot wedges permeability. The paper presents an accurate analytical subdomain model and confirmed by finite-element analyses.

Keywords: exact analytical calculation, finite-element method, magnetic field distribution, permanent magnet machines performance, stator slot wedges permeability

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: Shinji Kajiwara, Tadamasa Fukuoka

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The formula project of Kinki University has been involved in the student Formula SAE of Japan (JSAE) since the second year the competition was held. The vehicle developed in the project uses a ZX-6R engine, which has been manufactured by Kawasaki Heavy Industries for the JSAE competition for the eighth time. The limited performance of the concept vehicle was improved through the development of a power train. The supercharger loading, engine dry sump, and engine cooling management of the vehicle were also enhanced. The supercharger loading enabled the vehicle to achieve a maximum output of 59.6 kW (80.6 PS)/9000 rpm and a maximum torque of 70.6 Nm (7.2 kgf m)/8000 rpm. We successfully achieved 90% of the engine’s torque band (4000–10000 rpm) with 50% of the revolutions in regular engine use (2000–12000 rpm). Using a dry sump system, we periodically managed hydraulic pressure during engine operation. A system that controls engine stoppage when hydraulic pressure falls was also constructed. Using the dry sump system at 80 mm reduced the required engine load and the vehicle’s center of gravity. Even when engine motion was suspended by the electromotive force exerted by the water pump, the circulation of cooling water was still possible. These findings enabled us to create a cooling system in accordance with the requirements of the competition.

Keywords: engine, combustion, cooling system, numerical simulation, power, torque, mechanical super charger

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Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

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Authors: Chih-Wei Cheng, Wei-Jen Chan, Yu-Han Huang, Yi-Tsung Lin, Yen-Wei Huang, Min-Cheng Chen, Shou-Zen Chang, G. Chern, Yuan-Chieh Tseng

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How to develop spin-orbit-torque (SOT) devices with the virtues of field-free, perpendicular magnetic anisotropy (PMA), and low switching current is one of the many challenges in spintronics today. We propose a CoFeB/Ta/CoFeB tri-layer antiferromagnetic SOT device that could meet the above requirements. The device’s PMA was developed by adopting CoFeB–MgO interface. The key to the success of this structure is to ensure that (i)changes of the inter-layer coupling(IEC) and CoFeB anisotropy can occur simultaneously; (ii) one of the CoFeB needs to have a slightly tilted moment in the beginning. When sufficient current is given, the SHEreverses the already-tiltedCoFeB, and the other CoFeB can be reversed simultaneously by the IEC with the field-free nature. Adjusting the thickness of Ta can modify the coupling state to reduce the switching current while the field-free nature was preserved. Micromagnetic simulation suggests that the Néel orange peel effect (NOPE) is non-negligible due to interface roughness and coupling effect in the presence of perpendicular anisotropy. Fortunately, the Néel field induced by the NOPE appears to favor the field-free reversal.

Keywords: CoFeB, spin-orbit torque, antiferromagnetic, MRAM, trilayer

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Authors: L. Benaaouinate, M. Khafallah, A. Martinez, A. Mesbahi, T. Bouragba

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This paper concerns with the modeling, simulation, and emulation of a wind turbine emulator for standalone wind energy conversion systems. By using emulation system, we aim to reproduce the dynamic behavior of the wind turbine torque on the generator shaft: it provides the testing facilities to optimize generator control strategies in a controlled environment, without reliance on natural resources. The aerodynamic, mechanical, electrical models have been detailed as well as the control of pitch angle using Fuzzy Logic for horizontal axis wind turbines. The wind turbine emulator consists mainly of an induction motor with AC power drive with torque control. The control of the induction motor and the mathematical models of the wind turbine are designed with MATLAB/Simulink environment. The simulation results confirm the effectiveness of the induction motor control system and the functionality of the wind turbine emulator for providing all necessary parameters of the wind turbine system such as wind speed, output torque, power coefficient and tip speed ratio. The findings are of direct practical relevance.

Keywords: electrical generator, induction motor drive, modeling, pitch angle control, real time control, renewable energy, wind turbine, wind turbine emulator

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Authors: Ilija Plecas, Dalibor Arbutina

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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Aziz Sezgin

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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Xiao-Dong Wang, Wei-Mon Yan

Abstract:

The flow field design in the bipolar plates affects the performance of the proton exchange membrane (PEM) fuel cell. This work adopted a combined optimization procedure, including a simplified conjugate-gradient method and a completely three-dimensional, two-phase, non-isothermal fuel cell model, to look for optimal flow field design for a single serpentine fuel cell of size 9×9 mm with five channels. For the direct solution, the two-fluid method was adopted to incorporate the heat effects using energy equations for entire cells. The model assumes that the system is steady; the inlet reactants are ideal gases; the flow is laminar; and the porous layers such as the diffusion layer, catalyst layer and PEM are isotropic. The model includes continuity, momentum and species equations for gaseous species, liquid water transport equations in the channels, gas diffusion layers, and catalyst layers, water transport equation in the membrane, electron and proton transport equations. The Bulter-Volumer equation was used to describe electrochemical reactions in the catalyst layers. The cell output power density Pcell is maximized subjected to an optimal set of channel heights, H1-H5, and channel widths, W2-W5. The basic case with all channel heights and widths set at 1 mm yields a Pcell=7260 Wm-2. The optimal design displays a tapered characteristic for channels 1, 3 and 4, and a diverging characteristic in height for channels 2 and 5, producing a Pcell=8894 Wm-2, about 22.5% increment. The reduced channel heights of channels 2-4 significantly increase the sub-rib convection and widths for effectively removing liquid water and oxygen transport in gas diffusion layer. The final diverging channel minimizes the leakage of fuel to outlet via sub-rib convection from channel 4 to channel 5. Near-optimal design without huge loss in cell performance but is easily manufactured is tested. The use of a straight, final channel of 0.1 mm height has led to 7.37% power loss, while the design with all channel widths to be 1 mm with optimal channel heights obtained above yields only 1.68% loss of current density. The presence of a final, diverging channel has greater impact on cell performance than the fine adjustment of channel width at the simulation conditions set herein studied.

Keywords: optimization, flow field design, simplified conjugate-gradient method, serpentine flow field, sub-rib convection

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Adewoyin O. Olusegun, Emmanuel O. Joshua, Marvel L. Akinyemi

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The heterogeneous nature of the subsurface requires the use of factual information to deal with rather than assumptions or generalized equations. Therefore, there is need to determine the actual rate of settlement possible in the soil before structures are built on it. This information will help in determining the type of foundation design and the kind of reinforcement that will be necessary in constructions. This paper presents a simplified and a faster approach for determining foundation settlement in any type of soil using real field data acquired from seismic refraction techniques and cone penetration tests. This approach was also able to determine the depth of settlement of each strata of soil. The results obtained revealed the different settlement time and depth of settlement possible.

Keywords: heterogeneous, settlement, foundation, seismic, technique

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