Search results for: dimensional splitting

Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: M. Karamifard, M. Kazeminejad, A. Maghsoodloo

Abstract:

Electromagnetic flow meter by measuring the varying of magnetic flux, which is related to the velocity of conductive flow, can measure the rate of fluids very carefully and precisely. Electromagnetic flow meter operation is based on famous Faraday's second Law. In these equipments, the constant magnetostatic field is produced by electromagnet (winding around the tube) outside of pipe and inducting voltage that is due to conductive liquid flow is measured by electrodes located on two end side of the pipe wall. In this research, we consider to 2-dimensional mathematical model that can be solved by numerical finite difference (FD) solution approach to calculate induction potential between electrodes. The fundamental concept to design the electromagnetic flow meter, exciting winding and simulations are come out by using MATLAB and PDE-Tool software. In the last stage, simulations results will be shown for improvement and accuracy of technical provision.

Keywords: Electromagnetic Flow Meter, Induction Voltage, Finite Difference

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Authors: Subrata Das, Sisir Kumar Guha

Abstract:

The objective of the present paper is to theoretically investigate the steady-state performance characteristics of journal bearing of finite width, operating with micropolar lubricant in a turbulent regime. In this analysis, the turbulent shear stress coefficients are used based on the Constantinescu’s turbulent model suggested by Taylor and Dowson with the assumption of parallel and inertia-less flow. The numerical solution of the modified Reynolds equation has yielded the distribution of film pressure which determines the static performance characteristics in terms of load capacity, attitude angle, end flow rate and frictional parameter at various values of eccentricity ratio, non-dimensional characteristics length, coupling number and Reynolds number.

Keywords: Hydrodynamic lubrication, steady-state, micropolar lubricant, turbulent.

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Authors: Majid Forghani, Michael Khachay

Abstract:

In genetics, the impact of neighboring amino acids on a target site is referred as the nearest-neighbor effect or simply neighbor effect. In this paper, a new method called wavelet particle decomposition representing the one-dimensional neighbor effect using wavelet packet decomposition is proposed. The main idea lies in known dependence of wavelet packet sub-bands on location and order of neighboring samples. The method decomposes the value of a signal sample into small values called particles that represent a part of the neighbor effect information. The results have shown that the information obtained from the particle decomposition can be used to create better model variables or features. As an example, the approach has been applied to improve the correlation of test and reference sequence distance with titer in the hemagglutination inhibition assay.

Keywords: Antigenic variants, neighbor effect, wavelet packet, wavelet particle decomposition.

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Authors: R. O. Rominu, C. Sinescu, D.M. Pop, M. Hughes, A. Bradu, M. Rominu, A. Gh. Podoleanu

Abstract:

Bonding has become a routine procedure in several dental specialties – from prosthodontics to conservative dentistry and even orthodontics. In many of these fields it is important to be able to investigate the bonded interfaces to assess their quality. All currently employed investigative methods are invasive, meaning that samples are destroyed in the testing procedure and cannot be used again. We have investigated the interface between human enamel and bonded ceramic brackets non-invasively, introducing a combination of new investigative methods – optical coherence tomography (OCT), fluorescence OCT and confocal microscopy (CM). Brackets were conventionally bonded on conditioned buccal surfaces of teeth. The bonding was assessed using these methods. Three dimensional reconstructions of the detected material defects were developed using manual and semi-automatic segmentation. The results clearly prove that OCT, fluorescence OCT and CM are useful in orthodontic bonding investigations.

Keywords: Optical coherence tomography, Confocal Microscopy, Orthodontic Bonding.

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Authors: Pavel Y. Tabakov, Kevin Duffy

Abstract:

The present study presents a new approach to automatic data clustering and classification problems in large and complex databases and, at the same time, derives specific types of explicit rules describing each cluster. The method works well in both sparse and dense multidimensional data spaces. The members of the data space can be of the same nature or represent different classes. A number of N-dimensional ellipsoids are used for enclosing the data clouds. Due to the geometry of an ellipsoid and its free rotation in space the detection of clusters becomes very efficient. The method is based on genetic algorithms that are used for the optimization of location, orientation and geometric characteristics of the hyper-ellipsoids. The proposed approach can serve as a basis for the development of general knowledge systems for discovering hidden knowledge and unexpected patterns and rules in various large databases.

Keywords: Classification, clustering, data minig, genetic algorithms.

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Authors: Mohamed Othmani, Yassine Khlifi

Abstract:

This paper presents a technique for compact three dimensional (3D) object model reconstruction using wavelet networks. It consists to transform an input surface vertices into signals,and uses wavelet network parameters for signal approximations. To prove this, we use a wavelet network architecture founded on several mother wavelet families. POLYnomials WindOwed with Gaussians (POLYWOG) wavelet families are used to maximize the probability to select the best wavelets which ensure the good generalization of the network. To achieve a better reconstruction, the network is trained several iterations to optimize the wavelet network parameters until the error criterion is small enough. Experimental results will shown that our proposed technique can effectively reconstruct an irregular 3D object models when using the optimized wavelet network parameters. We will prove that an accurateness reconstruction depends on the best choice of the mother wavelets.

Keywords: 3D object, optimization, parametrization, Polywog wavelets, reconstruction, wavelet networks.

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Authors: Dušan Kravec, Ondrej Staš, Marián Tolnay, Michal Bachratý

Abstract:

This article gives a short preview of the new software created especially for palletizing process in automated production systems. Each chapter of this article is about problem solving in development of modules in Java programming language. First part describes structure of the software, its modules and data flow between them. Second part describes all deployment methods, which are implemented in the software. Next chapter is about twodimensional editor created for manipulation with objects in each layer of the load and gives calculations for collision control. Module of virtual reality used for three-dimensional preview and creation of the load is described in the fifth chapter. The last part of this article describes communication and data flow between control system of the robot, vision system and software.

Keywords: Palletizing, deployment methods, palletizing software, virtual reality in palletizing.

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

Abstract:

This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, Decomposition Method, Generalized Thermoelasticity, algorithm, empirical parameter, lattice design.

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Authors: A.-C. Bennis, F. Dumas, F. Ardhuin, B. Blanke

Abstract:

The mechanics of rip currents are complex, involving interactions between waves, currents, water levels and the bathymetry, that present particular challenges for numerical models. Here, the effects of a grid-spacing dependent horizontal mixing on the wave-current interactions are studied. Near the shore, wave rays diverge from channels towards bar crests because of refraction by topography and currents, in a way that depends on the rip current intensity which is itself modulated by the horizontal mixing. At low resolution with the grid-spacing dependent horizontal mixing, the wave motion is the same for both coupling modes because the wave deviation by the currents is weak. In high resolution case, however, classical results are found with the stabilizing effect of the flow by feedback of waves on currents. Lastly, wave-current interactions and the horizontal mixing strongly affect the intensity of the three-dimensional rip velocity.

Keywords: Numerical modeling, Rip currents, Turbulence modeling, Wave-current interactions.

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Authors: Maidul Islam, Dibakar Roy Chowdhury, Gagan Kumar

Abstract:

We investigate sensing capabilities of a planar plasmonic THz waveguide. The waveguide is comprised of one dimensional array of periodically arranged sub wavelength scale corrugations in the form of rectangular dimples in order to ensure the plasmonic response. The THz waveguide transmission is observed for polyimide (as thin film) substance filling the dimples. The refractive index of the polyimide film is varied to examine various sensing parameters such as frequency shift, sensitivity and Figure of Merit (FoM) of the fundamental plasmonic resonance supported by the waveguide. In efforts to improve sensing characteristics, we also examine sensing capabilities of a plasmonic waveguide having V shaped corrugations and compare results with that of rectangular dimples. The proposed study could be significant in developing new terahertz sensors with improved sensitivity utilizing the plasmonic waveguides.

Keywords: Terahertz, plasmonic, sensor, sub-wavelength structures.

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Authors: T. S. Chou, K. K. Yen, J. Luo

Abstract:

The network traffic data provided for the design of intrusion detection always are large with ineffective information and enclose limited and ambiguous information about users- activities. We study the problems and propose a two phases approach in our intrusion detection design. In the first phase, we develop a correlation-based feature selection algorithm to remove the worthless information from the original high dimensional database. Next, we design an intrusion detection method to solve the problems of uncertainty caused by limited and ambiguous information. In the experiments, we choose six UCI databases and DARPA KDD99 intrusion detection data set as our evaluation tools. Empirical studies indicate that our feature selection algorithm is capable of reducing the size of data set. Our intrusion detection method achieves a better performance than those of participating intrusion detectors.

Keywords: Intrusion detection, feature selection, k-nearest neighbors, fuzzy clustering, Dempster-Shafer theory

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Authors: Han-Taw Chen, Chung-Hou Lai, Tzu-Hsiang Lin, Ge-Jang He

Abstract:

This study applies the inverse method and three- dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a closed rectangular enclosure for various values of fin height. The inverse method with the finite difference method and the experimental temperature data is applied to determine the heat transfer coefficient. The k-ε turbulence model is used to obtain the heat transfer and fluid flow characteristics within the fins. To validate the accuracy of the results obtained, the comparison of the average heat transfer coefficient is made. The calculated temperature at selected measurement locations on the plate-fin is also compared with experimental data.

Keywords: Inverse method, FLUENT, k-ε model, Heat transfer characteristics, Plate-fin heat sink.

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Authors: Muhammad Amjad Sohail, Rizwan Ullah

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This research paper presents the CFD analysis of oscillating airfoil during pitch cycle. Unsteady subsonic flow is simulated for pitching airfoil at Mach number 0.283 and Reynolds number 3.45 millions. Turbulent effects are also considered for this study by using K-ω SST turbulent model. Two-dimensional unsteady compressible Navier-Stokes code including two-equation turbulence model and PISO pressure velocity coupling is used. Pressure based implicit solver with first order implicit unsteady formulation is used. The simulated pitch cycle results are compared with the available experimental data. The results have a good agreement with the experimental data. Aerodynamic characteristics during pitch cycles have been studied and validated.

Keywords: Angle of attack, Centre of pressure, subsonic flow, pitching moment coefficient, turbulence mode

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Authors: Farhad Hadinejad, Hasan Saberi, Saeed Kazem

Abstract:

Support vector clustering (SVC) is an important kernelbased clustering algorithm in multi applications. It has got two main bottle necks, the high computation price and labeling piece. In this paper, we presented a modified SVC method, named Grid–SVC, to improve the original algorithm computationally. First we normalized and then we parted the interval, where the SVC is processing, using a novel Grid–based clustering algorithm. The algorithm parts the intervals, based on the density function of the data set and then applying the cartesian multiply makes multi-dimensional grids. Eliminating many outliers and noise in the preprocess, we apply an improved SVC method to each parted grid in a parallel way. The experimental results show both improvement in time complexity order and the accuracy.

Keywords: Grid–based clustering, SVC, Density function, Radial basis function.

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Authors: Maryam Meftahi, Yashar Hamidzadeh

Abstract:

In recent decades, the amount of solid waste production has been rising. In the meantime, plastic waste is one of the major parts of urban solid waste, so, recycling plastic waste from water bottles has become a serious challenge in the whole world. The experimental program includes the study of the effect of waste plastic fibers on maximum dry density (MDD), optimum moisture content (OMC) with different sizes and contents. Also, one dimensional consolidation tests were carried out to evaluate the benefit of utilizing randomly distributed waste plastics fiber to improve the engineering behavior of a tested soils. Silty soil specimens were prepared and tested at five different percentages of plastic waste content (i.e. 0.25%, 0.50%, 0.75%, 1% and 1.25% by weight of the parent soil). The size of plastic chips used, are 4 mm, 8 mm and 12 mm long and 4 mm in width. The results show that with the addition of waste plastic fibers, the MDD and OMC and also the compressibility of soil decrease significantly.

Keywords: Silty soil, waste plastic, compaction, consolidation, reinforcement.

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Authors: Helen Zhang

Abstract:

Accurate segmentation of the airways from CT scans is crucial for early diagnosis of lung cancer. However, the existing airway segmentation algorithms often rely on thin-slice CT scans, which can be inconvenient and costly. This paper presents a set of machine learning-based 3D super-resolution algorithms along heterogenous dimensions to improve the resolution of thicker CT scans to reduce the reliance on thin-slice scans. To evaluate the efficacy of the super-resolution algorithms, quantitative assessments using PSNR (Peak Signal to Noise Ratio) and SSIM (Structural SIMilarity index) were performed. The impact of super-resolution on airway segmentation accuracy is also studied. The proposed approach has the potential to make airway segmentation more accessible and affordable, thereby facilitating early diagnosis and treatment of lung cancer.

Keywords: 3D super-resolution, airway segmentation, thin-slice CT scans, machine learning.

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Authors: Zulfadhli Hasan Adli, Mohd Hafiz Musa, M. N. Khairul Arifin

Abstract:

The objective of this paper is to study the electrical resistivity complexity between field and laboratory measurement, in order to improve the effectiveness of data interpretation for geophysical ground resistivity survey. The geological outcrop in Penang, Malaysia with an obvious layering contact was chosen as the study site. Two dimensional geoelectrical resistivity imaging were used in this study to maps the resistivity distribution of subsurface, whereas few subsurface sample were obtained for laboratory advance. In this study, resistivity of samples in original conditions is measured in laboratory by using time domain low-voltage technique, particularly for granite core sample and soil resistivity measuring set for soil sample. The experimentation results from both schemes are studied, analyzed, calibrated and verified, including basis and correlation, degree of tolerance and characteristics of substance. Consequently, the significant different between both schemes is explained comprehensively within this paper.

Keywords: Electrical Resistivity, Granite, Soil.

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Authors: V. Azadeh Ranjbar

Abstract:

Rarefied gas flows are often occurred in micro electro mechanical systems and classical CFD could not precisely anticipate the flow and thermal behavior due to the high Knudsen number. Therefore, the heat transfer and the fluid dynamics characteristics of rarefied gas flows in both a two-dimensional simple microchannel and geometry similar to single Knudsen compressor have been investigated with a goal of increasing performance of a actual Knudsen compressor by using a particle simulation method. Thermal transpiration and thermal creep, which are rarefied gas dynamic phenomena, that cause movement of the flow from less to higher temperature is generated by using two different longitude temperature gradients (Linear, Step) along the walls of the flow microchannel. In this study the influence of amount of temperature gradient and governing pressure in various Knudsen numbers and length-to-height ratios have been examined.

Keywords: DSMC, Thermal transpiration, Thermal creep, MEMS, Knudsen Compressor.

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Authors: S.C. Chin, N. Shafiq, M.F. Nuruddin

Abstract:

To date, theoretical studies concerning the Carbon Fiber Reinforced Polymer (CFRP) strengthening of RC beams with openings have been rather limited. In addition, various numerical analyses presented so far have effectively simulated the behaviour of solid beam strengthened by FRP material. In this paper, a two dimensional nonlinear finite element analysis is presented to validate against the laboratory test results of six RC beams. All beams had the same rectangular cross-section geometry and were loaded under four point bending. The crack pattern results of the finite element model show good agreement with the crack pattern of the experimental beams. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption used between the concrete and steel reinforcement.

Keywords: CFRP, large opening, RC beam, strengthening

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Authors: Achouri Ryma, Hatem Dhaouadi, Hatem Mhiri, Philippe Bournot

Abstract:

Stirred tanks are widely used in all industrial sectors. The need for further studies of the mixing operation and its different aspects comes from the diversity of agitation tools and implemented geometries in addition to the specific characteristics of each application. Viscous fluids are often encountered in industry and they represent the majority of treated cases, as in the polymer sector, food processing, pharmaceuticals and cosmetics. That's why in this paper, we will present a three-dimensional numerical study using the software Fluent, to study the effect of varying the fluid viscosity in a stirred tank with a Rushton turbine. This viscosity variation was performed by adding carboxymethylcellulose (CMC) to the fluid (water) in the vessel. In this work, we studied first the flow generated in the tank with a Rushton turbine. Second, we studied the effect of the fluid viscosity variation on the thermodynamic quantities defining the flow. For this, three viscosities (0.9% CMC, 1.1% CMC and 1.7% CMC) were considered.

Keywords: CFD, CMC, Mixing, Viscosity, Rushton turbine.

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Authors: Su Su Yi Mon, Fang Jiancheng

Abstract:

Synthetic Aperture Radar (SAR) is an imaging radar form by taking full advantage of the relative movement of the antenna with respect to the target. Through the simultaneous processing of the radar reflections over the movement of the antenna via the Range Doppler Algorithm (RDA), the superior resolution of a theoretical wider antenna, termed synthetic aperture, is obtained. Therefore, SAR can achieve high resolution two dimensional imagery of the ground surface. In addition, two filtering steps in range and azimuth direction provide accurate enough result. This paper develops a simulation in which realistic SAR images can be generated. Also, the effect of velocity errors in the resulting image has also been investigated. Taking some velocity errors into account, the simulation results on the image resolution would be presented. Most of the times, algorithms need to be adjusted for particular datasets, or particular applications.

Keywords: Synthetic Aperture Radar (SAR), Range Doppler Algorithm (RDA), Image Resolution.

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Authors: S. Fawzia, T. Fatima

Abstract:

The design of high-rise building is more often dictated by its serviceability rather than strength. Structural Engineers are always striving to overcome challenge of controlling lateral deflection and storey drifts as well as self weight of structure imposed on foundation. One of the most effective techniques is the use of outrigger and belt truss system in Composite structures that can astutely solve the above two issues in High-rise constructions. This paper investigates deflection control by effective utilisation of belt truss and outrigger system on a 60-storey composite building subjected to wind loads. A three dimensional Finite Element Analysis is performed with one, two and three outrigger levels. The reductions in lateral deflection are 34%, 42% and 51% respectively as compared to a model without any outrigger system. There is an appreciable decline in the storey drifts with the introduction of these stiffer arrangements.

Keywords: Composite building, belt truss, deflection, FE model, outrigger truss, 3D analysis.

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Authors: Pil Un Kim, Yunjung Lee, Gihyoun Lee, Jin Ho Cho, Myoung Nam Kim

Abstract:

In this paper, the vessel inscribed trigonometry (VITM) for the vessel progression orientation (VPO) is proposed in the two-dimensional fundus image. The VPO is a major factor in the optic disc (OD) detection which is a basic process in the retina analysis. To measure the VPO, skeletons of vessel are used. First, the vessels are classified into three classes as vessel end, vessel branch and vessel stem. And the chain code maps of VS are generated. Next, two farthest neighborhoods of each point on VS are searched by the proposed angle restriction. Lastly, a gradient of the straight line between two farthest neighborhoods is estimated to measure the VPO. VITM is validated by comparing with manual results and 2D Gaussian templates. It is confirmed that VPO of the proposed mensuration is correct enough to detect OD from the results of experiment which applied VITM to detect OD in fundus images.

Keywords: Angle measurement, Optic disc, Retina vessel, Vessel progression orientation.

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Authors: Igor Nedelkovski, Ilios Vilos, Tale Geramitcioski

Abstract:

Computational simulation of steam flow and heat transfer in power plant condensers on the basis of the threedimensional mathematical model for the flow through porous media is presented. In order to solve the mathematical model of steam flow and heat transfer in power plant condensers, the Streamline Upwind Petrov-Galerkin finite element method is applied. By comparison of the results of simulation with experimental results about an experimental condenser, it is confirmed that SUPG finite element method can be successfully applied for solving the three-dimensional mathematical model of steam flow and heat transfer in power plant condensers.

Keywords: Navier-Stokes, FEM, condensers, steam.

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Authors: Gurjit Kaur, Neena Gupta

Abstract:

In this paper, we have analyzed and compared the performance of various coding schemes. The basic ID prime sequence codes are unique in only dimension, i.e. time slots, whereas 2D coding techniques are not unique by their time slots but with their wavelengths also. In this research, we have evaluated and compared the performance of 1D and 2D coding techniques constructed using prime sequence coding pattern for Optical Code Division Multiple Access (OCDMA) system on a single platform. Analysis shows that 2D prime code supports lesser number of active users than 1D codes, but they are having large code family and are the most secure codes compared to other codes. The performance of all these codes is analyzed on basis of number of active users supported at a Bit Error Rate (BER) of 10-9.

Keywords: CDMA, OCDMA, BER, OOC, PC, EPC, MPC, 2-D PC/PC, λc, λa.

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Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability of wake-shear layers in two-phase shallow flows is analyzed in the present paper. Stability analysis is based on two-dimensional shallow water equations. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. Linear stability curves are obtained for different values of the particle loading parameter, the velocity ratio and the velocity deficit. It is shown that the increase in the velocity ratio destabilizes the flow. The particle loading parameter has a stabilizing effect on the flow. The role of the velocity deficit is also destabilizing: the increase of the velocity deficit leads to less stable flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Jackeline Kafie-Martinez, Peter B. Keating

Abstract:

A three-dimensional finite element model is developed to capture the stress field generated in connected plates during the installation of hot-driven rivets. Clamping stress is generated when a steel rivet heated to approximately 1000 °C comes in contact with the material to be fastened at ambient temperature. As the rivet cools, thermal contraction subjects the rivet into tensile stress, while the material being fastened is subjected to compressive stress. Model characteristics and assumptions, as well as steel properties variation with respect to temperature are discussed. The thermal stresses developed around the rivet hole are assessed and reported. Results from the analysis are utilized to detect possible regions for fatigue crack propagation under cyclic loads.

Keywords: Jackeline Kafie-Martinez, Peter B. Keating.

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