Search results for: moving boundary

Authors: Ch. Ramreddy, P. Naveen, D. Srinivasacharya

Abstract:

The objective of the present study is to investigate the effect of nonlinear temperature and concentration on the mixed convective flow of micropolar fluid over an inclined flat plate in a non-Darcy porous medium in the presence of convective boundary condition. In order to analyze all the essential features, the transformed nonlinear conservation equations are worked out numerically by spectral method. By insisting the comparison between vertical, horizontal and inclined plates, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters. An increase in the coupling number and inclination of angle tend to decrease the skin friction, mass transfer rate and the reverse change is there in wall couple stress and heat transfer rate. The nominal effect on the wall couple stress and skin friction is encountered whereas the significant effect on the local heat and mass transfer rates are found for high enough values of Biot number.

Keywords: convective boundary condition, micropolar fluid, non-darcy porous medium, non-linear convection, spectral method

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Authors: H. Niranjan, S. Sivasankaran

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Heat and mass transfer near a steady stagnation point boundary layer flow of viscous incompressible fluid through porous media investigates along a vertical plate is thoroughly studied under the presence of magneto hydrodynamic (MHD) effects. The fluid flow is steady, laminar, incompressible and in two-dimensional. The nonlinear differential coupled parabolic partial differential equations of continuity, momentum, energy and specie diffusion are converted into the non-similar boundary layer equations using similarity transformation, which are then solved numerically using the Runge-Kutta method along with shooting method. The effects of the conjugate heat transfer parameter, the porous medium parameter, the permeability parameter, the mixed convection parameter, the magnetic parameter, and the thermal radiation on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are presented and analyzed. The validity of the methodology and analysis is checked by comparing the results obtained for some specific cases with those available in the literature. The various parameters on local skin friction, heat and mass transfer rates are presented in tabular form.

Keywords: MHD, porous medium, slip, convective boundary condition, stagnation point

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Authors: Samuel Ahamefula

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Turbulent motion is a highly nonlinear and complex phenomenon, and its modelling is still very challenging. In this study, we developed a hybrid computational approach to accurately simulate fluid turbulence phenomenon. The focus is coupling and transitioning between Direct Numerical Simulation (DNS) and Large Eddy Simulating Wall Models (LES-WM) regions. In the framework, high-order fidelity fluid dynamical methods are utilized to simulate the unsteady compressible Navier-Stokes equations in the Eulerian format on the unstructured moving grids. The coupling and transitioning of DNS and LES-WM are conducted through the linearly staggered Dirichlet-Neumann coupling scheme. The high-fidelity framework is verified and validated based on namely, DNS ability for capture full range of turbulent scales, giving accurate results and LES-WM efficiency in simulating near-wall turbulent boundary layer by using wall models.

Keywords: computational methods, turbulence modelling, turbulence entropy, navier-stokes equations

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Authors: Mourad Hrizi

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In this paper, we study the inverse problem of reconstructing an interior interface D appearing in the elliptic partial differential equation: Δu+χ(D)u=0 from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown subdomain D is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

Keywords: inverse problem, topological optimization, topological gradient, Kohn-Vogelius formulation

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Authors: Gyo Woo Lee, Man Young Kim

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A mathematical heat transfer model for the prediction of transient heating of the slab in a direct-fired walking beam type reheating furnace has been developed by considering the nongray thermal radiation with given furnace environments. The furnace is modeled as radiating nongray medium with carbon dioxide and water with five-zoned gas temperature and the furnace wall is considered as a constant temperature lower than furnace gas one. The slabs are moving with constant velocity depending on the residence time through the non-firing, charging, preheating, heating, and final soaking zones. Radiative heat flux obtained by considering the radiative heat exchange inside the furnace as well as convective one from the surrounding hot gases are introduced as boundary condition of the transient heat conduction within the slab. After validating thermal radiation model adopted in this work, thermal fields in both model and real reheating furnace are investigated in terms of radiative heat flux in the furnace and temperature inside the slab. The results show that the slab in the furnace can be more heated with higher slab emissivity and residence time.

Keywords: reheating furnace, steel slab, radiative heat transfer, WSGGM, emissivity, residence time

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Yang Geng, Anqi Zhao

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The misreading theory of Harold Bloom provides a new diachronic perspective as an approach to the consistency between rhetoric of digital technology, dynamic movement of digital images and uncertain meaning of text. Reinterpreting the diachroneity of 'intertextuality' in the context of misreading theory extended the range of the 'intermediality' of transmedia to the intense tension between digital images and symbolic images throughout history of images. With the analogy between six categories of revisionary ratios and six steps of digital transformation, digital rhetoric might be illustrated as a linear process reflecting dynamic, intensive relations between digital moving images and original static images. Finally, it was concluded that two-way framework of the rhetoric of transformation of digital images and reversed served as a renarrative structure to revive static images by reconnecting them with digital moving images.

Keywords: rhetoric, digital art, intermediality, misreading theory

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Authors: Rehan Ali Shah, A. M. Siddiqui, T. Haroon

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Slip boundary value problem in wire coating analysis with heat transfer is examined. The fluid is assumed to be viscoelastic PTT (Phan-Thien and Tanner). The rheological constitutive equation of PTT fluid model simulates various polymer melts. Therefore, the current consequences are valuable in a number of realistic situations. Effects of slip parameter γ as well as εDec^2 (viscoelastic index) on the axial velocity, shear stress, normal stress, average velocity, volume flux, thickness of coated wire, shear stress, force on the total wire and temperature distribution profiles have been investigated. A new direction is explored to analyze the flow with the slip parameter. The slippage at the boundaries plays an important role in thickness of coated wire. It is noted that as the slip parameter increases the flow rate and thickness of coated wire increases while, temperature distribution decreases. The results reduce to no slip when the slip parameter is vanished. Furthermore, we can obtain the results for Maxwell and viscous model by setting ε and λ equal to zero respectively.

Keywords: wire coating, straight annular die, PTT fluid, heat transfer, slip boundary conditions

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Authors: Yuan-Hsiang Chang, Pin-Chi Lin, Li-Der Jeng

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Advance in techniques of image and video processing has enabled the development of intelligent video surveillance systems. This study was aimed to automatically detect moving human objects and to analyze events of dual human interaction in a surveillance scene. Our system was developed in four major steps: image preprocessing, human object detection, human object tracking, and motion trajectory analysis. The adaptive background subtraction and image processing techniques were used to detect and track moving human objects. To solve the occlusion problem during the interaction, the Kalman filter was used to retain a complete trajectory for each human object. Finally, the motion trajectory analysis was developed to distinguish between the interaction and non-interaction events based on derivatives of trajectories related to the speed of the moving objects. Using a database of 60 video sequences, our system could achieve the classification accuracy of 80% in interaction events and 95% in non-interaction events, respectively. In summary, we have explored the idea to investigate a system for the automatic classification of events for interaction and non-interaction events using surveillance cameras. Ultimately, this system could be incorporated in an intelligent surveillance system for the detection and/or classification of abnormal or criminal events (e.g., theft, snatch, fighting, etc.).

Keywords: motion detection, motion tracking, trajectory analysis, video surveillance

Procedia PDF Downloads 519

Authors: Spandan Sahu, Amiya Kumar Pati, Kishanjit Kumar Khatua

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River is our main source of water which is a form of open channel flow and the flow in open channel provides with many complex phenomenon of sciences that needs to be tackled such as the critical flow conditions, boundary shear stress and depth averaged velocity. During floods, part of a river is carried by the simple main channel and rest is carried by flood plains. For such compound asymmetric channels, the flow structure becomes complicated due to momentum exchange between main channel and adjoining flood plains. Distribution of boundary shear in subsections provides us with the concept of momentum transfer between the interface of main channel and the flood plains. Experimentally, to get better data with accurate results are very complex because of the complexity of the problem. Hence, CES software has been used to tackle the complex processes to determine the shear stresses at different sections of an open channel having asymmetric flood plains on both sides of the main channel and the results is compared with the symmetric flood plains for various geometrical shapes and flow conditions. Error analysis is also performed to know the degree of accuracy of the model implemented.

Keywords: depth average velocity, non prismatic compound channel, relative flow depth, velocity distribution

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Authors: Svea Missfeldt, Rainer Höger

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A number of studies show that aircraft noise around airports negatively affects the reading comprehension of children attending schools in the neighbourhood. Yet little is known about the underlying mechanisms. Explanatory approaches discuss the attention capturing effect of noise sources which occupy mental capacity. Research suggests that attentional capacities are especially demanded when different modalities are involved at the same time. To explore whether aircraft noise affects reading processes in specific manners, students read texts in variable sound conditions while their eye movements were recorded. Besides noise caused by aircraft flyovers, which represent moving sound sources, saccades were also recorded under the condition of white noise, a natural sound setting and silence for comparison. Data showed an increase in regressive saccades when the sound of moving sources was presented. Interestingly, this effect was significantly high when the aircrafts moved in the opposite of the reading direction. Especially the latter result is not compatible with the hypothesis of a general impairment of cognitive processes by noise where the direction of movement should not have an influence. Reading is assumed to be based on two different attentional mechanisms: overt and covert attention, where the latter supports control and pre-planning of eye movements during reading. We believe that covert attention is affected by moving sound sources, resulting in an enhanced number of backwardly directed saccades.

Keywords: aircraft noise, attentional processes, cognition, eye movements, reading saccades

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Authors: Jyh Jyh Chen, Fu H. Yang, Chen W. Wang, Yu M. Lin

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In this work, a reaction chamber is reciprocated among three temperature regions by using an oscillatory thermal cycling machine. Three cartridge heaters are collocated to heat three aluminum blocks in order to achieve PCR requirements in the reaction chamber. The effects of various chamber moving speeds among different temperature regions on the chamber temperature profiles are presented. To solve the evaporation effect of the sample in the PCR experiment, the mineral oil and the cover lid are used. The influences of various extension times on DNA amplification are also demonstrated. The target fragments of the amplification are 385-bp and 420-bp. The results show when the forward speed is set at 6 mm/s and the backward speed is 2.4 mm/s, the temperature required for the experiment can be achieved. It is successful to perform the amplification of DNA fragments in our device.

Keywords: oscillatory, polymerase chain reaction, reaction chamber, thermal cycling machine

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Authors: Saowanit Sukparungsee

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Generally, the traditional Shewhart p chart has been developed by for charting the binomial data. This chart has been developed using the normal approximation with condition as low defect level and the small to moderate sample size. In real applications, however, are away from these assumptions due to skewness in the exact distribution. In this paper, a modified Exponentially Weighted Moving Average (EWMA) control chat for detecting a change in binomial data by improving square root transformations, namely ISRT p EWMA control chart. The numerical results show that ISRT p EWMA chart is superior to ISRT p chart for small to moderate shifts, otherwise, the latter is better for large shifts.

Keywords: number of defects, exponentially weighted moving average, average run length, square root transformations

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Authors: Sowntharya L.

Abstract:

Aerodynamics is the most important factor when it comes to resistive forces such as lift, drag and side forces acting on the vehicle. In passenger vehicles, reducing the drag will not only unlock the door for higher achievable speed but will also reduce the fuel consumption of the vehicle. Generally, tyre contributes significantly to the overall aerodynamics of the vehicle. Hence, understanding the air-flow behaviour around the tyre is vital to optimize the aerodynamic performance in the early stage of design process. Nowadays, aerodynamic simulation employing Computational Fluid Dynamics (CFD) is gaining more importance as it reduces the number of physical wind-tunnel experiments during vehicle development process. This research develops a methodology to predict aerodynamic drag of a standalone tyre using Numerical CFD Solver and to validate the same using a wind tunnel experiment. A parametric study was carried out on different tread pattern tyres such as slick, circumferential groove & patterned tyre in stationary and rotating boundary conditions. In order to represent wheel rotation contact with the ground, moving reference frame (MRF) approach was used in this study. Aerodynamic parameters such as drag lift & air flow behaviour around the tire were simulated and compared with experimental results.

Keywords: aerodynamics, CFD, drag, MRF, wind-tunnel

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Authors: Te Wen Tu, Sen Yung Lee

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An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition

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Authors: Judith Stein, Elfriede Friedmann

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The injection of a drug into the vitreous body for the treatment of retinal diseases like wet aged-related macular degeneration (AMD) is the most common medical intervention worldwide. We develop mathematical models for drug transport in the vitreous body of a human eye to analyse the impact of different rheological models of the vitreous on drug distribution. In addition to the convection diffusion equation characterizing the drug spreading, we use porous media modeling for the healthy vitreous with a dense collagen network and include the steady permeating flow of the aqueous humor described by Darcy's law driven by a pressure drop. Additionally, the vitreous body in a healthy human eye behaves like a viscoelastic gel through the collagen fibers suspended in the network of hyaluronic acid and acts as a drug depot for the treatment of retinal diseases. In a completely liquefied vitreous, we couple the drug diffusion with the classical Navier-Stokes flow equations. We prove the global existence and uniqueness of the weak solution of the developed initial-boundary value problem describing the drug distribution in the healthy vitreous considering the permeating aqueous humor flow in the realistic three-dimensional setting. In particular, for the drug diffusion equation, results from the literature are extended from homogeneous Dirichlet boundary conditions to our mixed boundary conditions that describe the eye with the Galerkin's method using Cauchy-Schwarz inequality and trace theorem. Because there is only a small effective drug concentration range and higher concentrations may be toxic, the ability to model the drug transport could improve the therapy by considering patient individual differences and give a better understanding of the physiological and pathological processes in the vitreous.

Keywords: coupled PDE systems, drug diffusion, mixed boundary conditions, vitreous body

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Authors: R. Resmi, M. R. Baiju

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The thermal damping of a dynamic vibrating micromirror is an important factor affecting the design of MEMS based actuator systems. In the development process of new micromirror systems, assessing the extent of energy loss due to thermal damping accurately and predicting the performance of the system is very essential. In this paper, the depth of the thermal penetration layer at different eigenfrequencies and the temperature variation distributions surrounding a vibrating micromirror is analyzed. The thermal penetration depth corresponds to the thermal boundary layer in which energy is lost which is a measure of the thermal damping is found out. The energy is mainly dissipated in the thermal boundary layer and thickness of the layer is an important parameter. The detailed thermoacoustics is used to model the air domain surrounding the micromirror. The thickness of the boundary layer, temperature variations and thermal power dissipation are analyzed for a Si based torsional mode micromirror. It is found that thermal penetration depth decreases with eigenfrequency and hence operating the micromirror at higher frequencies is essential for reducing thermal damping. The temperature variations and thermal power dissipations at different eigenfrequencies are also analyzed. Both frequency-response and eigenfrequency analyses are done using COMSOL Multiphysics software.

Keywords: Eigen frequency analysis, micromirrors, thermal damping, thermoacoustic interactions

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Authors: D. S. Naumann, B. J. Evans, O. Hassan

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This paper outlines the development of an automated aerodynamic optimisation algorithm using a novel method of parameterising a computational mesh by employing user–defined control nodes. The shape boundary movement is coupled to the movement of the novel concept of the control nodes via a quasi-1D-linear deformation. Additionally, a second order smoothing step has been integrated to act on the boundary during the mesh movement based on the change in its second derivative. This allows for both linear and non-linear shape transformations dependent on the preference of the user. The domain mesh movement is then coupled to the shape boundary movement via a Delaunay graph mapping. A Modified Cuckoo Search (MCS) algorithm is used for optimisation within the prescribed design space defined by the allowed range of control node displacement. A finite volume compressible NavierStokes solver is used for aerodynamic modelling to predict aerodynamic design fitness. The resulting coupled algorithm is applied to a range of test cases in two dimensions including the design of a subsonic, transonic and supersonic intake and the optimisation approach is compared with more conventional optimisation strategies. Ultimately, the algorithm is tested on a three dimensional wing optimisation case.

Keywords: mesh movement, aerodynamic shape optimization, cuckoo search, shape parameterisation

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Authors: Anuar Ishak

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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

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Authors: Sadia Siddiqa, Z. Khan, M. A. Hossain

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In this article, the effect of thermal radiation on mixed convection boundary layer flow of a viscous fluid along a highly heated vertical flat plate is considered with varying density and volumetric expansion coefficient. The density of the fluid is assumed to vary exponentially with temperature, however; volumetric expansion coefficient depends linearly on temperature. Boundary layer equations are transformed into convenient form by introducing primitive variable formulations. Solutions of transformed system of equations are obtained numerically through implicit finite difference method along with Gaussian elimination technique. Results are discussed in view of various parameters, like thermal radiation parameter, volumetric expansion parameter and density variation parameter on the wall shear stress and heat transfer rate. It is concluded from the present investigation that increase in volumetric expansion parameter decreases wall shear stress and enhances heat transfer rate.

Keywords: thermal radiation, mixed convection, variable density, variable volumetric expansion coefficient

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Authors: András Szekrényes

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Delamination is one of the major failure modes in laminated composite structures. Delamination tips are mostly captured by spatial numerical models in order to predict crack growth. This paper presents some mechanical models of delaminated composite shells based on shallow shell theories. The mechanical fields are based on a third-order displacement field in terms of the through-thickness coordinate of the laminated shell. The undelaminated and delaminated parts are captured by separate models and the continuity and boundary conditions are also formulated in a general way providing a large size boundary value problem. The system of differential equations is solved by the state space method for an elliptic delaminated shell having simply supported edges. The comparison of the proposed and a numerical model indicates that the primary indicator of the model is the deflection, the secondary is the widthwise distribution of the energy release rate. The model is promising and suitable to determine accurately the J-integral distribution along the delamination front. Based on the proposed model it is also possible to develop finite elements which are able to replace the computationally expensive spatial models of delaminated structures.

Keywords: J-integral, levy method, third-order shell theory, state space solution

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Authors: Pradeepa Teegala, Ramreddy Chitteti

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This article analyzes the mixed convection flow of chemically reacting micropolar fluid over a truncated cone embedded in non-Darcy porous medium with convective boundary condition. In addition, heat generation/absorption and Joule heating effects are taken into consideration. The similarity solution does not exist for this complex fluid flow problem, and hence non-similarity transformations are used to convert the governing fluid flow equations along with related boundary conditions into a set of nondimensional partial differential equations. Many authors have been applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The effect of pertinent parameters namely, Biot number, mixed convection parameter, heat generation/absorption, Joule heating, Forchheimer number, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, mixed convection, spectral quasi-linearization method

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: El Harraj Abdeslam, Raissouni Naoufal

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The detection of moving objects from a video image sequences is very important for object tracking, activity recognition, and behavior understanding in video surveillance. The most used approach for moving objects detection / tracking is background subtraction algorithms. Many approaches have been suggested for background subtraction. But, these are illumination change sensitive and the solutions proposed to bypass this problem are time consuming. In this paper, we propose a robust yet computationally efficient background subtraction approach and, mainly, focus on the ability to detect moving objects on dynamic scenes, for possible applications in complex and restricted access areas monitoring, where moving and motionless persons must be reliably detected. It consists of three main phases, establishing illumination changes in variance, background/foreground modeling and morphological analysis for noise removing. We handle illumination changes using Contrast Limited Histogram Equalization (CLAHE), which limits the intensity of each pixel to user determined maximum. Thus, it mitigates the degradation due to scene illumination changes and improves the visibility of the video signal. Initially, the background and foreground images are extracted from the video sequence. Then, the background and foreground images are separately enhanced by applying CLAHE. In order to form multi-modal backgrounds we model each channel of a pixel as a mixture of K Gaussians (K=5) using Gaussian Mixture Model (GMM). Finally, we post process the resulting binary foreground mask using morphological erosion and dilation transformations to remove possible noise. For experimental test, we used a standard dataset to challenge the efficiency and accuracy of the proposed method on a diverse set of dynamic scenes.

Keywords: video surveillance, background subtraction, contrast limited histogram equalization, illumination invariance, object tracking, object detection, behavior understanding, dynamic scenes

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Authors: Reda Mankbadi

Abstract:

The current work explores the use of Synthetic Jet Actuators (SJAs) for control of the acoustic radiation of a low-speed transitioning airfoil in a uniform stream. In the adopted numerical procedure, the actuator is modeled without its resonator cavity through imposing a simple fluctuating-velocity boundary condition at the bottom of the actuator's orifice. The orifice cavity, with the properly defined boundary condition, is then embedded into the airfoil surface. High-accuracy viscous simulations are then conducted to study the effects of the actuation on sound radiated by the airfoil. Results show that SJA can considerably suppress the radiated sound of the airfoil in uniform incoming stream.

Keywords: simulations, aeroacoustics, wind turbine noise, synthetic jet actuators (SJAs)

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

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In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

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Authors: Bakur Gulua

Abstract:

In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Pezhman Taghipour Birgani, Mehdi Shekarzadeh

Abstract:

In this paper, the propagation of lamb waves in three-layer joints is investigated using global matrix method. Theoretical boundary value problem in three-layer adhesive joints with perfect bond and traction free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with the lowest attenuation. The characteristic equation is derived by applying continuity and boundary conditions in three-layer joints using global matrix method. Attenuation and phase velocity dispersion curves are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results of the characteristic equation, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. The purpose of present paper is to find a combination of frequencies and modes with minimum attenuation in high and low frequencies. These frequencies and modes are recognizable by transducers in inspections with Lamb waves because of low attenuation level.

Keywords: three-layer adhesive joints, viscoelastic, lamb waves, global matrix method

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Authors: Nitin Dewangan, Nitin Kattula, Megha Anawat

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Hydraulic reservoir is the key component in the mobile construction vehicles; most of the off-road earth moving construction machinery requires bigger side hydraulic reservoirs. Their reservoir construction is very much non-uniform and designers used such design to utilize the space available under the vehicle. There is no way to find out the space utilization of the reservoir by oil and validity of design except virtual simulation. Computational fluid dynamics (CFD) helps to predict the reservoir space utilization by vortex mapping, path line plots and dwell time prediction to make sure the design is valid and efficient for the vehicle. The dwell time acceptance criteria for effective reservoir design is 15 seconds. The paper will describe the hydraulic reservoir simulation which is carried out using CFD tool acuSolve using automated mesh strategy. The free surface flow and moving reference mesh is used to define the oil flow level inside the reservoir. The first baseline design is not able to meet the acceptance criteria, i.e., dwell time below 15 seconds because the oil entry and exit ports were very close. CFD is used to redefine the port locations for the reservoir so that oil dwell time increases in the reservoir. CFD also proposed baffle design the effective space utilization. The final design proposed through CFD analysis is used for physical validation on the machine.

Keywords: reservoir, turbulence model, transient model, level set, free-surface flow, moving frame of reference

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