Search results for: numerical stability

Authors: Xinhua Zhang, Kelin Li

Abstract:

In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.

Keywords: Exponential stability, stochastic fuzzy cellular neural networks, time-varying delays, impulses, reaction-diffusion terms.

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Authors: Abdelhakam A. Noreldien, Sakhr B. Abudarag, Muslim S. Eltoum, Salih O. Osman

Abstract:

This paper presents an analytical study of Small Unmanned Aerial Vehicle (SUAV) dynamic stability derivatives. Simulating SUAV dynamics and analyzing its behavior at the earliest design stages is too important and more efficient design aspect. The approach suggested in this paper is using the wind tunnel experiment to collect the aerodynamic data and get the dynamic stability derivatives. AutoCAD Software was used to draw the case study (wildlife surveillance SUAV). The SUAV is scaled down to be 0.25% of the real SUAV dimensions and converted to a wind tunnel model. The model was tested in three different speeds for three different attitudes which are; pitch, roll and yaw. The wind tunnel results were then used to determine the case study stability derivative values, and hence it used to calculate the roots of the characteristic equation for both longitudinal and lateral motions. Finally, the characteristic equation roots were found and discussed in all possible cases.

Keywords: Model, simulating, SUAV, wind tunnel.

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Authors: M. Sallam, A. Ramadan, M. Fanni, M. Abdellatif

Abstract:

Time delay in bilateral teleoperation system was introduced as a sufficient reason to make the system unstable or certainly degrade the system performance. In this paper, simulations and experimental results of implementing p-like control scheme, under different ranges of variable time delay, will be presented to verify a certain criteria, which guarantee the system stability and position tracking. The system consists of two Phantom premium 1.5A devices. One of them acts as a master and the other acts as a slave. The study includes deriving the Phantom kinematic and dynamic model, establishing the link between the two Phantoms over Simulink in Matlab, and verifying the stability criteria with simulations and real experiments.

Keywords: bilateral teleoperation, Phantom premium 1.5, varying time delay

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Authors: Cătălin Mărculescu, Andrei Avram, Cătălin Pârvulescu, Marioara Avram, Cătălin Mihai Bălan

Abstract:

The present microfluidic study is emphasizing the flow behavior within a Y shape micro-bifurcation in two similar flow configurations. We report here a numerical and experimental investigation on the velocity profiles evolution and secondary flows, manifested at different Reynolds numbers (Re) and for two different boundary conditions. The experiments are performed using special designed setup based on optical microscopic devices. With this setup, direct visualizations and quantitative measurements of the path-lines are obtained. A Micro-PIV measurement system is used to obtain velocity profiles distributions in a spatial evolution in the main flows domains. The experimental data is compared with numerical simulations performed with commercial computational code FLUENT in a 3D geometry with the same dimensions as the experimental one. The numerical flow patterns are found to be in good agreement with the experimental manifestations.

Keywords: Micro-PIV, numerical investigations, secondary flows, velocity profiles.

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Authors: Mustapha Kamel Mihoubi, Hocine Dahmani

Abstract:

Over recent years much progress has been achieved in the fields of numerical modeling shoreline processes: waves, currents, waves and current. However, there are still some problems in the existing models to link the on the first, the hydrodynamics of waves and currents and secondly, the sediment transport processes and due to the variability in time, space and interaction and the simultaneous action of wave-current near the shore. This paper is the establishment of a numerical modeling to forecast the sediment transport from development scenarios of harbor structure. It is established on the basis of a numerical simulation of a water-sediment model via a 2D model using a set of codes calculation MIKE 21-DHI software. This is to examine the effect of the sediment transport drivers following the dominant incident wave in the direction to pass input harbor work under different variants planning studies to find the technical and economic limitations to the sediment transport and protection of the harbor structure optimum solution.

Keywords: Swell, current, radiation, stress, mesh, MIKE21, sediment.

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Authors: Mohammed A. Aziz, Ibrahim A. M. Gad, El Shahat F. A. Mohammed, Ramy H. Mohammed

Abstract:

This paper investigates experimental and numerical study of the airflow characteristics for vortex, round and square ceiling diffusers and its effect on the thermal comfort in a ventilated room. Three different thermal comfort criteria namely; Mean Age of the Air (MAA), ventilation effectiveness (E), and Effective Draft Temperature (EDT) have been used to predict the thermal comfort zone inside the room. In experimental work, a sub-scale room is set-up to measure the temperature field in the room. In numerical analysis, unstructured grids have been used to discretize the numerical domain. Conservation equations are solved using FLUENT commercial flow solver. The code is validated by comparing the numerical results obtained from three different turbulence models with the available experimental data. The comparison between the various numerical models shows that the standard k-ε turbulence model can be used to simulate these cases successfully. After validation of the code, effect of supply air velocity on the flow and thermal field could be investigated and hence the thermal comfort. The results show that the pressure coefficient created by the square diffuser is 1.5 times greater than that created by the vortex diffuser. The velocity decay coefficient is nearly the same for square and round diffusers and is 2.6 times greater than that for the vortex diffuser.

Keywords: Ceiling diffuser, Thermal Comfort, MAA, EDT, Fluent, Turbulence model.

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Authors: M. Raciti Castelli, S. Toniato, E. Benini

Abstract:

The flow filed around a flatted-roof compound has been investigated by means of 2D and 3D numerical simulations. A constant wind velocity profile, based both on the maximum reference wind speed in the building site (peak gust speed worked out for a 50- year return period) and on the local roughness coefficient, has been simulated in order to determine the wind-induced loads on top of the roof. After determining the influence of the incoming wind directions on the induced roof loads, a 2D analysis of the most severe load condition has been performed, achieving a numerical quantification of the expected wind-induced forces on the PV panels on top of the roof.

Keywords: CFD, wind-induced loads, flow around buildings, photovoltaic system

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Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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Authors: Rihab Gam, Anis Sakly, Faouzi M'sahli

Abstract:

A new strategy of control is formulated for chaos synchronization of non-identical chaotic systems with different orders using the Borne and Gentina practical criterion associated with the Benrejeb canonical arrow form matrix, to drift the stability property of dynamic complex systems. The designed controller ensures that the state variables of controlled chaotic slave systems globally synchronize with the state variables of the master systems, respectively. Numerical simulations are performed to illustrate the efficiency of the proposed method.

Keywords: Synchronization, Non-identical chaotic systems, Different orders, Arrow form matrix.

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Authors: R. Kongnuy, P. Pongsumpun

Abstract:

Dengue, a disease found in most tropical and subtropical areas of the world. It has become the most common arboviral disease of humans. This disease is caused by any of four serotypes of dengue virus (DEN1-DEN4). In many endemic countries, the average age of getting dengue infection is shifting upwards, dengue in pregnancy and infancy are likely to be encountered more frequently. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the pregnant, infant human and the vector populations. The stability of each equilibrium point is given. The epidemic dynamic is discussed. Moreover, the numerical results are shown for difference values of dengue antibody.

Keywords: Dengue antibody, infant, pregnant human, mathematical model.

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Authors: Mahmoud Zarrini, R.N. Pralhad

Abstract:

In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.

Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

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Authors: Nor Hayati Ibrahim, Shamini Nair Achudan

Abstract:

This study was conducted in order to determine the physical properties and stability of mayonnaise-like emulsions as affected by modified yam starches. Native yam starch was modified via pre-gelatinization and cross-linking phosphorylation procedures. The emulsions (50% oil dispersed phase) were prepared with 0.3% native potato, native yam, pre-gelatinized yam and cross-linking phosphorylation yam starches. The droplet size of surface weighted mean diameter was found to be significantly (p < 0.05) lower in the sample with cross-linking phosphorylation yam starch as compared to other samples. Moreover, the viscosity of the sample with pregelatinized yam starch was observed to be higher than that of other samples. The phase separation stability was low in the freshly prepared and stored (45 days, 5°C) emulsions containing native yam starch. This study thus generally suggested that modified yam starches were more suitable (i.e. better physical properties and stability) to be used as stabilizers in a similar system i.e. light mayonnaises, rather than a native yam starch.

Keywords: Oil-in-water emulsions, low-fat mayonnaises, modified yam starches, droplet size distribution, viscosity.

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Authors: Huaizhi Han, Bingxi Li, Yurong He, Rushan Bie, Zhao Wu

Abstract:

The flow and heat transfer mechanism in convex corrugated tubes have been investigated through numerical simulations in this paper. Two kinds of tube types named as symmetric corrugated tube (SCT) and asymmetric corrugated tube (ACT) are modeled and studied numerically based on the RST model. The predictive capability of RST model is examined in the corrugation wall in order to check the reliability of RST model under the corrugation wall condition. We propose a comparison between the RST modelling the corrugation wall with existing direct numerical simulation of Maaß C and Schumann U [14]. The numerical results pressure coefficient at different profiles between RST and DNS are well matched. The influences of large corrugation tough radii to heat transfer and flow characteristic had been considered. Flow and heat transfer comparison between SCT and ACT had been discussed. The numerical results show that ACT exhibits higher overall heat transfer performance than SCT.

Keywords: Asymmetric corrugated tube, RST, DNS, flow and heat transfer mechanism.

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Authors: Razieh Jalalabadi, Norouz Mohammad Nouri

Abstract:

Cavitation, usually known as a destructive phenomenon, involves turbulent unsteady two-phase flow. Having such features, cavitating flows have been turned to a challenging topic in numerical studies and many researches are being done for better understanding of bubbly flows and proposing solutions to reduce its consequent destructive effects. Aeration may be regarded as an effective protection against cavitation erosion in many hydraulic structures, like gated tunnels. The paper concerns numerical simulation of flow in discharge gated tunnel of a dam using ing RNG k -ε model coupled with the volume of fluid (VOF) method and the zone which is susceptible of cavitation inception in the tunnel is predicted. In the second step, a vent is considered in the mentioned zone for aeration and the numerical simulation is done again to study the effects of aeration. The results show that aeration is an impressively useful method to exclude cavitation in mentioned tunnels.

Keywords: Aeration, Cavitation, Two-phase flow, TurbulentFlow, Volume of Fluid (VOF) method.

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Authors: Agung Budi Muljono, I Made Ginarsa, I Made Ari Nrartha

Abstract:

A large-scale power system (LSPS) consists of two or more sub-systems connected by inter-connecting transmission. Loading pattern on an LSPS always changes from time to time and varies depend on consumer need. The serious instability problem is appeared in an LSPS due to load fluctuation in all of the bus. Adaptive neuro-fuzzy inference system (ANFIS)-based power system stabilizer (PSS) is presented to cover the stability problem and to enhance the stability of an LSPS. The ANFIS control is presented because the ANFIS control is more effective than Mamdani fuzzy control in the computation aspect. Simulation results show that the presented PSS is able to maintain the stability by decreasing peak overshoot to the value of −2.56 × 10−5 pu for rotor speed deviation Δω2−3. The presented PSS also makes the settling time to achieve at 3.78 s on local mode oscillation. Furthermore, the presented PSS is able to improve the peak overshoot and settling time of Δω3−9 to the value of −0.868 × 10−5 pu and at the time of 3.50 s for inter-area oscillation.

Keywords: ANFIS, large-scale, power system, PSS, stability enhancement.

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Authors: S.Asadi, H.Panahi

Abstract:

The Navier–Stokes equations for unsteady, incompressible, viscous fluids in the axisymmetric coordinate system are solved using a control volume method. The volume-of-fluid (VOF) technique is used to track the free-surface of the liquid. Model predictions are in good agreement with experimental measurements. It is found that the dynamic processes after impact are sensitive to the initial droplet velocity and the liquid pool depth. The time evolution of the crown height and diameter are obtained by numerical simulation. The critical We number for splashing (Wecr) is studied for Oh (Ohnesorge) numbers in the range of 0.01~0.1; the results compares well with those of the experiments.

Keywords: Droplet impingement, free surface flows, liquid crown, numerical simulation, thin liquid film.

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Authors: K. Sandjak, B. Tiliouine

Abstract:

This article presents the main results of three-dimensional (3-D) numerical investigation of asphalt pavement structures behaviour using a coupled Finite Element-Mapped Infinite Element (FE-MIE) model. The validation and numerical performance of this model are assessed by confronting critical pavement responses with Burmister’s solution and FEM simulation results for multi-layered elastic structures. The coupled model is then efficiently utilised to perform 3-D simulations of a typical asphalt pavement structure in order to investigate the impact of two tire configurations (conventional dual and new generation wide-base tires) on critical pavement response parameters. The numerical results obtained show the effectiveness and the accuracy of the coupled (FE-MIE) model. In addition, the simulation results indicate that, compared with conventional dual tire assembly, single wide base tire caused slightly greater fatigue asphalt cracking and subgrade rutting potentials and can thus be utilised in view of its potential to provide numerous mechanical, economic, and environmental benefits.

Keywords: Infinite elements, 3-D numerical investigation, asphalt pavements, dual and wide base tires.

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Authors: Yih-Ferng Peng

Abstract:

In this paper, the local grid refinement is focused by using a nested grid technique. The Cartesian grid numerical method is developed for simulating unsteady, viscous, incompressible flows with complex immersed boundaries. A finite volume method is used in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a nested grid solver are imposition of interface conditions on the inter-block and accurate discretization of the governing equation in cells that are with the inter-block as a control surface. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the spatial accuracy of the underlying solver. The present nested grid method has been tested by two numerical examples to examine its performance in the two dimensional problems. The numerical examples include flow past a circular cylinder symmetrically installed in a Channel and flow past two circular cylinders with different diameters. From the numerical experiments, the ability of the solver to simulate flows with complicated immersed boundaries is demonstrated and the nested grid approach can efficiently speed up the numerical solutions.

Keywords: local grid refinement, Cartesian grid, nested grid, fractional-step method.

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Authors: Changjin Xu, Yusen Wu

Abstract:

In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.

Keywords: Web-site system, stability, Nyquist criterion, Hopf bifurcation, frequency domain.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Stability, Functionally graded beam, First order shear deformation theory, Piezoelectric layer.

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Authors: A. R. Salimi, M. Esmaeili, B. Salehi

Abstract:

The development and extension of large cities induced a need for shallow tunnel in soft ground of building areas. Estimation of ground settlement caused by the tunnel excavation is important engineering point. In this paper, prediction of surface subsidence caused by tunneling in one section of seventh line of Tehran subway is considered. On the basis of studied geotechnical conditions of the region, tunnel with the length of 26.9km has been excavated applying a mechanized method using an EPB-TBM with a diameter of 9.14m. In this regard, settlement is estimated utilizing both analytical and numerical finite element method. The numerical method shows that the value of settlement in this section is 5cm. Besides, the analytical consequences (Bobet and Loganathan-Polous) are 5.29 and 12.36cm, respectively. According to results of this study, due tosaturation of this section, there are good agreement between Bobet and numerical methods. Therefore, tunneling processes in this section needs a special consolidation measurement and support system before the passage of tunnel boring machine.

Keywords: TBM, Subsidence, Numerical Method, Analytical Method.

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Authors: Man Young Kim

Abstract:

Catalytic combustion is generally accepted as an environmentally preferred alternative for the generation of heat and power from fossil fuels mainly due to its advantages related to the stable combustion under very lean conditions with low emissions of NOx, CO, and UHC at temperatures lower than those occurred in conventional flame combustion. Despite these advantages, the commercial application of catalytic combustion has been delayed because of complicated reaction processes and the difficulty in developing appropriate catalysts with the required stability and durability. To develop the catalytic combustors, detailed studies on the combustion characteristics of catalytic combustion should be conducted. To the end, in current research, quantitative studies on the combustion characteristics of the catalytic combustors, with a Pd-based catalyst for MCFC power generation systems, relying on numerical simulations have been conducted. In addition, data from experimental studies of variations in outlet temperatures and fuel conversion, taken after operating conditions have been used to validate the present numerical approach. After introducing the governing equations for mass, momentum, and energy equations as well as a description of catalytic combustion kinetics, the effects of the excess air ratio, space velocity, and inlet gas temperature on the catalytic combustion characteristics are extensively investigated. Quantitative comparisons are also conducted with previous experimental data. Finally, some concluding remarks are presented.

Keywords: Catalytic combustion, Methane, BOP, MCFC power generation system, Inlet temperature, Excess air ratio, Space velocity.

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: Wenjuan Du, Jingtian Bi, Tong Wang, Haifeng Wang

Abstract:

Grid connection of a large-scale wind farm affects power system small-signal angular stability in two aspects. Firstly, connection of the wind farm brings about the change of load flow and configuration of a power system. Secondly, the dynamic interaction is introduced by the wind farm with the synchronous generators (SGs) in the power system. This paper proposes a method to assess the two aspects of the effect of the wind farm on power system small-signal angular stability. The effect of the change of load flow/system configuration brought about by the wind farm can be examined separately by displacing wind farms with constant power sources, then the effect of the dynamic interaction of the wind farm with the SGs can be also computed individually. Thus, a clearer picture and better understanding on the power system small-signal angular stability as affected by grid connection of the large-scale wind farm are provided. In the paper, an example power system with grid connection of a wind farm is presented to demonstrate the proposed approach.

Keywords: power system small-signal angular stability, power system low-frequency oscillations, electromechanical oscillation modes, wind farms, double fed induction generator (DFIG)

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Authors: Nizar Bouguerra, Ahmed Khabou, Sébastien Poncet, Saïd Elkoun

Abstract:

The present work focuses on the preparation and the stabilization of Al₂O₃-water based nanofluids. Though they have been widely considered in the past, to the best of our knowledge, there is no clear consensus about a proper way to prepare and stabilize them by the appropriate surfactant. In this paper, a careful experimental investigation is performed to quantify the combined influence of pH and the surfactant on the stability of Al₂O₃-water based nanofluids. Two volume concentrations of nanoparticles and three nanoparticle sizes have been considered. The good preparation and stability of these nanofluids are evaluated through thermal conductivity measurements. The results show that the optimum value for the thermal conductivity is obtained mainly by controlling the pH of the mixture and surfactants are not necessary to stabilize the solution.

Keywords: Nanofluid, thermal conductivity, pH, transient hot wire, surfactant, Al2O3, stability, dispersion, preparation.

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Authors: Michal Spilacek, Martin Lisy, Marek Balas, Zdenek Skala

Abstract:

This article is trying to determine the status of flue gas that is entering the KWH heat exchanger from combustion chamber in order to calculate the heat transfer ratio of the heat exchanger. Combination of measurement, calculation and computer simulation was used to create a useful way to approximate the heat transfer rate. The measurements were taken by a number of sensors that are mounted on the experimental device and by a thermal imaging camera. The results of the numerical calculation are in a good correspondence with the real power output of the experimental device. That result shows that the research has a good direction and can be used to propose changes in the construction of the heat exchanger, but still needs enhancements.

Keywords: Heat exchanger, heat transfer rate, numerical calculation, thermal images.

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Authors: A. Darvizeh, H. Rajabi, S. Fatahtooei Nejad, A. Khaheshi, P. Haghdoust

Abstract:

In this article, biomechanical aspects of hen-s eggshell as a natural ceramic structure are studied. The images, taken by a scanning electron microscope (SEM), are used to investigate the microscopic aspects of the egg. It is observed that eggshell has a three-layered microstructure with different morphological and structural characteristics. Studies on the eggshell membrane (ESM) as a prosperous tissue suggest that it is placed to prevent the penetration of microorganisms into the egg. Finally, numerical models of the egg are presented to study the stress distribution and its deformation under different loading conditions. The effects of two different types of loading (hydrostatic and point loadings) on two different shell models (with constant and variable thicknesses) are investigated in detail.

Keywords: Eggshell, biomechanical properties, Scanning electron microscope, Numerical Modeling.

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Authors: M. Raciti Castelli, G. Grandi, E. Benini

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This paper presents a study of laminar to turbulent transition on a profile specifically designed for wind turbine blades, the DU91-W2-250, which belongs to a class of wind turbine dedicated airfoils, developed by Delft University of Technology. A comparison between the experimental behavior of the airfoil studied at Delft wind tunnel and the numerical predictions of the commercial CFD solver ANSYS FLUENT® has been performed. The prediction capabilities of the Spalart-Allmaras turbulence model and of the γ-θ Transitional model have been tested. A sensitivity analysis of the numerical results to the spatial domain discretization has also been performed using four different computational grids, which have been created using the mesher GAMBIT®. The comparison between experimental measurements and CFD results have allowed to determine the importance of the numerical prediction of the laminar to turbulent transition, in order not to overestimate airfoil friction drag due to a fully turbulent-regime flow computation.

Keywords: CFD, wind turbine, DU91-W2-250, laminar to turbulent transition.

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Authors: N. A. Samat, D. F. Percy

Abstract:

The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease. 

Keywords: Dengue disease, disease mapping, numerical analysis, SIR-SI differential equations.

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