Search results for: MATLAB numerical quadrature
3660 Numerical Investigation of the Electromagnetic Common Rail Injector Characteristics
Authors: Rafal Sochaczewski, Ksenia Siadkowska, Tytus Tulwin
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The paper describes the modeling of a fuel injector for common rail systems. A one-dimensional model of a solenoid-valve-controlled injector with Valve Closes Orifice (VCO) spray was modelled in the AVL Hydsim. This model shows the dynamic phenomena that occur in the injector. The accuracy of the calibration, based on a regulation of the parameters of the control valve and the nozzle needle lift, was verified by comparing the numerical results of injector flow rate. Our model is capable of a precise simulation of injector operating parameters in relation to injection time and fuel pressure in a fuel rail. As a result, there were made characteristics of the injector flow rate and backflow.Keywords: common rail, diesel engine, fuel injector, modeling
Procedia PDF Downloads 4123659 Numerical Modeling of Various Support Systems to Stabilize Deep Excavations
Authors: M. Abdallah
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Urban development requires deep excavations near buildings and other structures. Deep excavation has become more a necessity for better utilization of space as the population of the world has dramatically increased. In Lebanon, some urban areas are very crowded and lack spaces for new buildings and underground projects, which makes the usage of underground space indispensable. In this paper, a numerical modeling is performed using the finite element method to study the deep excavation-diaphragm wall soil-structure interaction in the case of nonlinear soil behavior. The study is focused on a comparison of the results obtained using different support systems. Furthermore, a parametric study is performed according to the remoteness of the structure.Keywords: deep excavation, ground anchors, interaction soil-structure, struts
Procedia PDF Downloads 4143658 Experimental Validation of Computational Fluid Dynamics Used for Pharyngeal Flow Patterns during Obstructive Sleep Apnea
Authors: Pragathi Gurumurthy, Christina Hagen, Patricia Ulloa, Martin A. Koch, Thorsten M. Buzug
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Obstructive sleep apnea (OSA) is a sleep disorder where the patient suffers a disturbed airflow during sleep due to partial or complete occlusion of the pharyngeal airway. Recently, numerical simulations have been used to better understand the mechanism of pharyngeal collapse. However, to gain confidence in the solutions so obtained, an experimental validation is required. Therefore, in this study an experimental validation of computational fluid dynamics (CFD) used for the study of human pharyngeal flow patterns during OSA is performed. A stationary incompressible Navier-Stokes equation solved using the finite element method was used to numerically study the flow patterns in a computed tomography-based human pharynx model. The inlet flow rate was set to 250 ml/s and such that a flat profile was maintained at the inlet. The outlet pressure was set to 0 Pa. The experimental technique used for the validation of CFD of fluid flow patterns is phase contrast-MRI (PC-MRI). Using the same computed tomography data of the human pharynx as in the simulations, a phantom for the experiment was 3 D printed. Glycerol (55.27% weight) in water was used as a test fluid at 25°C. Inflow conditions similar to the CFD study were simulated using an MRI compatible flow pump (CardioFlow-5000MR, Shelley Medical Imaging Technologies). The entire experiment was done on a 3 T MR system (Ingenia, Philips) with 108 channel body coil using an RF-spoiled, gradient echo sequence. A comparison of the axial velocity obtained in the pharynx from the numerical simulations and PC-MRI shows good agreement. The region of jet impingement and recirculation also coincide, therefore validating the numerical simulations. Hence, the experimental validation proves the reliability and correctness of the numerical simulations.Keywords: computational fluid dynamics, experimental validation, phase contrast-MRI, obstructive sleep apnea
Procedia PDF Downloads 3113657 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory
Authors: Reza Mohammadi, Mahdieh Sahebi
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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points
Procedia PDF Downloads 3523656 Implementation of Fuzzy Version of Block Backward Differentiation Formulas for Solving Fuzzy Differential Equations
Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman
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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.Keywords: block, backward differentiation formulas, first order, fuzzy differential equations
Procedia PDF Downloads 3193655 Explicit Numerical Approximations for a Pricing Weather Derivatives Model
Authors: Clarinda V. Nhangumbe, Ercília Sousa
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Weather Derivatives are financial instruments used to cover non-catastrophic weather events and can be expressed in the form of standard or plain vanilla products, structured or exotics products. The underlying asset, in this case, is the weather index, such as temperature, rainfall, humidity, wind, and snowfall. The complexity of the Weather Derivatives structure shows the weakness of the Black Scholes framework. Therefore, under the risk-neutral probability measure, the option price of a weather contract can be given as a unique solution of a two-dimensional partial differential equation (parabolic in one direction and hyperbolic in other directions), with an initial condition and subjected to adequate boundary conditions. To calculate the price of the option, one can use numerical methods such as the Monte Carlo simulations and implicit finite difference schemes conjugated with Semi-Lagrangian methods. This paper is proposed two explicit methods, namely, first-order upwind in the hyperbolic direction combined with Lax-Wendroff in the parabolic direction and first-order upwind in the hyperbolic direction combined with second-order upwind in the parabolic direction. One of the advantages of these methods is the fact that they take into consideration the boundary conditions obtained from the financial interpretation and deal efficiently with the different choices of the convection coefficients.Keywords: incomplete markets, numerical methods, partial differential equations, stochastic process, weather derivatives
Procedia PDF Downloads 853654 Heat and Mass Transfer in a Saturated Porous Medium Confined in Cylindrical Annular Geometry
Authors: A. Ja, J. Belabid, A. Cheddadi
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This paper reports the numerical simulation of double diffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.Keywords: natural convection, double-diffusion, porous medium, annular geometry, finite differences
Procedia PDF Downloads 3423653 Numerical Study of Fire Propagation in Confined and Open Area
Authors: Hadj Miloua, Abbes Azzi
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The objective of the present paper is to understand, predict and modeled the fire behavior in confined and open area in different conditions and diverse fuels such as liquid pool fire and the vegetative materials. The distinctive problems are a ventilated road tunnel used for urban transport, by the characterization installations of ventilation and his influence in the mode of smoke dispersion and the flame shape. A general investigation is relatively traditional, based on the modeling and simulation the scenario of the pool fire interacted with wind ventilation by the use of numerical software fire dynamic simulator FDS ver.5 to simulate the fire in ventilated tunnel. The second simulation by WFDS.5 is Wildland fire which is always occurs in forest and rangeland fire environments and will thus have an impact on people, property and resources.Keywords: fire, road tunnel, simulation, vegetation, wildland
Procedia PDF Downloads 5143652 Investigation of Failure Mechanisms of Composite Laminates with Delamination and Repaired with Bolts
Authors: Shuxin Li, Peihao Song, Haixiao Hu, Dongfeng Cao
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The interactive deformation and failure mechanisms, including local bucking/delamination propagation and global bucking, are investigated in this paper with numerical simulation and validation with experimental results. Three dimensional numerical models using ABAQUS brick elements combined with cohesive elements and contact elements are developed to simulate the deformation and failure characteristics of composite laminates with and without delamination under compressive loading. The zero-thickness cohesive elements are inserted on the possible path of delamination propagation, and the inter-laminate behavior is characterized by the mixed-mode traction-separation law. The numerical simulations identified the complex feature of interaction among local buckling and/or delamination propagation and final global bucking for composite laminates with delamination under compressive loading. Firstly there is an interaction between the local buckling and delamination propagation, i.e., local buckling induces delamination propagation, and then delamination growth further enhances the local buckling. Secondly, the interaction between the out-plan deformation caused by local buckling and the global bucking deformation results in final failure of the composite laminates. The simulation results are validated by the good agreement with the experimental results published in the literature. The numerical simulation validated with experimental results revealed that the degradation of the load capacity, in particular of the compressive strength of composite structures with delamination, is mainly attributed to the combined local buckling/delamination propagation effects. Consequently, a simple field-bolt repair approach that can hinder the local buckling and prevent delamination growth is explored. The analysis and simulation results demonstrated field-bolt repair could effectively restore compressive strength of composite laminates with delamination.Keywords: cohesive elements, composite laminates, delamination, local and global bucking, field-bolt repair
Procedia PDF Downloads 1203651 Thermal Network Model for a Large Scale AC Induction Motor
Authors: Sushil Kumar, M. Dakshina Murty
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Thermal network modelling has proven to be important tool for thermal analysis of electrical machine. This article investigates numerical thermal network model and experimental performance of a large-scale AC motor. Experimental temperatures were measured using RTD in the stator which have been compared with the numerical data. Thermal network modelling fairly predicts the temperature of various components inside the large-scale AC motor. Results of stator winding temperature is compared with experimental results which are in close agreement with accuracy of 6-10%. This method of predicting hot spots within AC motors can be readily used by the motor designers for estimating the thermal hot spots of the machine.Keywords: AC motor, thermal network, heat transfer, modelling
Procedia PDF Downloads 3263650 3D Numerical Studies and Design Optimization of a Swallowtail Butterfly with Twin Tail
Authors: Arunkumar Balamurugan, G. Soundharya Lakshmi, V. Thenmozhi, M. Jegannath, V. R. Sanal Kumar
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Aerodynamics of insects is of topical interest in aeronautical industries due to its wide applications on various types of Micro Air Vehicles (MAVs). Note that the MAVs are having smaller geometric dimensions operate at significantly lower speeds on the order of 10 m/s and their Reynolds numbers range is approximately 1,50,000 or lower. In this paper, numerical study has been carried out to capture the flow physics of a biological inspired Swallowtail Butterfly with fixed wing having twin tail at a flight speed of 10 m/s. Comprehensive numerical simulations have been carried out on swallow butterfly with twin tail flying at a speed of 10 m/s with uniform upper and lower angles of attack in both lateral and longitudinal position for identifying the best wing orientation with better aerodynamic efficiency. Grid system in the computational domain is selected after a detailed grid refinement exercises. Parametric analytical studies have been carried out with different lateral and longitudinal angles of attack for finding the better aerodynamic efficiency at the same flight speed. The results reveal that lift coefficient significantly increases with marginal changes in the longitudinal angle and vice versa. But in the case of drag coefficient the conventional changes have been noticed, viz., drag increases at high longitudinal angles. We observed that the change of twin tail section has a significant impact on the formation of vortices and aerodynamic efficiency of the MAV’s. We concluded that for every lateral angle there is an exact longitudinal orientation for the existence of an aerodynamically efficient flying condition of any MAV. This numerical study is a pointer towards for the design optimization of Twin tail MAVs with flapping wings.Keywords: aerodynamics of insects, MAV, swallowtail butterfly, twin tail MAV design
Procedia PDF Downloads 3953649 A Case Study on the Numerical-Probability Approach for Deep Excavation Analysis
Authors: Komeil Valipourian
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Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.Keywords: numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method (FDM)
Procedia PDF Downloads 1273648 Evaluating the Capability of the Flux-Limiter Schemes in Capturing the Turbulence Structures in a Fully Developed Channel Flow
Authors: Mohamed Elghorab, Vendra C. Madhav Rao, Jennifer X. Wen
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Turbulence modelling is still evolving, and efforts are on to improve and develop numerical methods to simulate the real turbulence structures by using the empirical and experimental information. The monotonically integrated large eddy simulation (MILES) is an attractive approach for modelling turbulence in high Re flows, which is based on the solving of the unfiltered flow equations with no explicit sub-grid scale (SGS) model. In the current work, this approach has been used, and the action of the SGS model has been included implicitly by intrinsic nonlinear high-frequency filters built into the convection discretization schemes. The MILES solver is developed using the opensource CFD OpenFOAM libraries. The role of flux limiters schemes namely, Gamma, superBee, van-Albada and van-Leer, is studied in predicting turbulent statistical quantities for a fully developed channel flow with a friction Reynolds number, ReT = 180, and compared the numerical predictions with the well-established Direct Numerical Simulation (DNS) results for studying the wall generated turbulence. It is inferred from the numerical predictions that Gamma, van-Leer and van-Albada limiters produced more diffusion and overpredicted the velocity profiles, while superBee scheme reproduced velocity profiles and turbulence statistical quantities in good agreement with the reference DNS data in the streamwise direction although it deviated slightly in the spanwise and normal to the wall directions. The simulation results are further discussed in terms of the turbulence intensities and Reynolds stresses averaged in time and space to draw conclusion on the flux limiter schemes performance in OpenFOAM context.Keywords: flux limiters, implicit SGS, MILES, OpenFOAM, turbulence statistics
Procedia PDF Downloads 1903647 Design of Rigid L-Shaped Retaining Walls
Authors: Ahmed Rouili
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Cantilever L-shaped walls are known to be relatively economical as retaining solution. The design starts by proportioning the wall dimensions for which the stability is checked for. A ratio between the lengths of the base and the stem, falling between 0,5 to 0,7, ensure the stability requirements in most cases. However, the displacement pattern of the wall in terms of rotations and translations, and the lateral pressure profile, do not have the same figure for all wall’s proportioning, as it is usually assumed. In the present work, the results of a numerical analysis are presented, different wall geometries were considered. The results show that the proportioning governs the equilibrium between the instantaneous rotation and the translation of the wall-toe, also, the lateral pressure estimation based on the average value between the at-rest and the active pressure, recommended by most design standards, is found to be not applicable for all walls.Keywords: cantilever wall, proportioning, numerical analysis, lateral pressure estimation
Procedia PDF Downloads 3233646 Fast Algorithm to Determine Initial Tsunami Wave Shape at Source
Authors: Alexander P. Vazhenin, Mikhail M. Lavrentiev, Alexey A. Romanenko, Pavel V. Tatarintsev
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One of the problems obstructing effective tsunami modelling is the lack of information about initial wave shape at source. The existing methods; geological, sea radars, satellite images, contain an important part of uncertainty. Therefore, direct measurement of tsunami waves obtained at the deep water bottom peruse recorders is also used. In this paper we propose a new method to reconstruct the initial sea surface displacement at tsunami source by the measured signal (marigram) approximation with the help of linear combination of synthetic marigrams from the selected set of unit sources, calculated in advance. This method has demonstrated good precision and very high performance. The mathematical model and results of numerical tests are here described.Keywords: numerical tests, orthogonal decomposition, Tsunami Initial Sea Surface Displacement
Procedia PDF Downloads 4693645 Stress Field Induced By an Interfacial Edge Dislocation in a Multi-Layered Medium
Authors: Aditya Khanna, Andrei Kotousov
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A novel method is presented for obtaining the stress field induced by an edge dislocation in a multilayered composite. To demonstrate the applications of the obtained solution, we consider the problem of an interfacial crack in a periodically layered bimaterial medium. The crack is modeled as a continuous distribution of edge dislocations and the Distributed Dislocation Technique (DDT) is utilized to obtain numerical results for the energy release rate (ERR). The numerical results correspond well with previously published results and the comparison serves as a validation of the obtained dislocation solution.Keywords: distributed dislocation technique, edge dislocation, elastic field, interfacial crack, multi-layered composite
Procedia PDF Downloads 4453644 Vibration Control of a Horizontally Supported Rotor System by Using a Radial Active Magnetic Bearing
Authors: Vishnu A., Ashesh Saha
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The operation of high-speed rotating machinery in industries is accompanied by rotor vibrations due to many factors. One of the primary instability mechanisms in a rotor system is the centrifugal force induced due to the eccentricity of the center of mass away from the center of rotation. These unwanted vibrations may lead to catastrophic fatigue failure. So, there is a need to control these rotor vibrations. In this work, control of rotor vibrations by using a 4-pole Radial Active Magnetic Bearing (RAMB) as an actuator is analysed. A continuous rotor system model is considered for the analysis. Several important factors, like the gyroscopic effect and rotary inertia of the shaft and disc, are incorporated into this model. The large deflection of the shaft and the restriction to axial motion of the shaft at the bearings result in nonlinearities in the system governing equation. The rotor system is modeled in such a way that the system dynamics can be related to the geometric and material properties of the shaft and disc. The mathematical model of the rotor system is developed by incorporating the control forces generated by the RAMB. A simple PD controller is used for the attenuation of system vibrations. An analytical expression for the amplitude and phase equations is derived using the Method of Multiple Scales (MMS). Analytical results are verified with the numerical results obtained using an ‘ode’ solver in-built into MATLAB Software. The control force is found to be effective in attenuating the system vibrations. The multi-valued solutions leading to the jump phenomenon are also eliminated with a proper choice of control gains. Most interestingly, the shape of the backbone curves can also be altered for certain values of control parameters.Keywords: rotor dynamics, continuous rotor system model, active magnetic bearing, PD controller, method of multiple scales, backbone curve
Procedia PDF Downloads 793643 Numerical Study of Natural Convection of a Localized Heat Source at the up of a Nanofluid-Filled Enclosure
Authors: Marziyeh Heydari, Hossein Shokouhmand
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This article presents a numerical study of natural convection of a heat source embedded on the up wall of an enclosure filled with nanofluid. The bottom and vertical walls of the enclosure are maintained at a relatively low temperature. The type of nanofluid and solid volume fraction of nanoparticle on the heat transfer performance is studied. The results indicated that adding nanoparticle into pure paraffin improves heat transfer. The results are presented over a wide range of Rayleigh numbers(Ra=〖10〗^3 〖-10〗^5), the volume fraction of nanoparticles (0≤ɸ≤0.4%). For an enclosure, the Nusselt number of a cu-paraffin nanofluid was reduced by increasing the volume fraction of nanoparticles above 0.2%.Keywords: nanofluid, heat transfer, heat source, enclosure
Procedia PDF Downloads 3103642 Numerical Study of Wettability on the Triangular Micro-pillared Surfaces Using Lattice Boltzmann Method
Authors: Ganesh Meshram, Gloria Biswal
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In this study, we present the numerical investigation of surface wettability on triangular micropillar surfaces by using a two-dimensional (2D) pseudo-potential multiphase lattice Boltzmann method with a D2Q9 model for various interaction parameters of the range varies from -1.40 to -2.50. Initially, simulation of the equilibrium state of a water droplet on a flat surface is considered for various interaction parameters to examine the accuracy of the present numerical model. We then imposed the microscale pillars on the bottom wall of the surface with different heights of the pillars to form the hydrophobic and superhydrophobic surfaces which enable the higher contact angle. The wettability of surfaces is simulated with water droplets of radius 100 lattice units in the domain of 800x800 lattice units. The present study shows that increasing the interaction parameter of the pillared hydrophobic surfaces dramatically reduces the contact area between water droplets and solid walls due to the momentum redirection phenomenon. Contact angles for different values of interaction strength have been validated qualitatively with the analytical results.Keywords: contact angle, lattice boltzmann method, d2q9 model, pseudo-potential multiphase method, hydrophobic surfaces, wenzel state, cassie-baxter state, wettability
Procedia PDF Downloads 693641 Dynamical and Thermal Study of Twin Impinging Jets a Vertical Plate with Various Jet Velocities and Impinging Distance
Authors: Louaifi Hamaili Samira, Mataoui Amina, Cheraitia Tadjeddine
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This investigation proposes a numerical analysis of two turbulent parallel jets impinging a heated plate. The heat transfer enhancement is carried out according of the main parameters of the jet-wall interaction. The numerical solution of the stationary equations (RANS) is performed by the finite volume method using the k - ε model. A parametric study is performed to evaluate simultaneously the effect of nozzle-plate distance and velocity ratios in the range 0≤λ≤1. It is found that good local cooling is obtained for λ= 0.25 when the impinging distance is between 4w and 8w than for velocity ratios λ=1 and λ= 0.75. On the other hand, for impinging distances exceeding 8w, the velocity ratio λ =0.75 is more appropriate for good local cooling of the plate.Keywords: two unequal jets, turbulence, mixing, heat transfer, CFD
Procedia PDF Downloads 323640 Dynamic Response Analysis of Structure with Random Parameters
Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire
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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters
Procedia PDF Downloads 1903639 Numerical Verification of a Backfill-Rectangular Tank-Fluid System
Authors: Ramazan Livaoğlu, Tufan Çakır
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The performance of rectangular tanks during earthquakes has been observed to depend significantly on the existence of water in the container and the presence of the backfill acting on tank wall. Therefore, in design of rectangular tanks, the topics of fluid-structure-backfill interactions and determination of modal characteristics of the interaction system have traditionally been one of the great theoretical and practical controversy. Although finite element method has been and will continue to be used to a significant extent in treating the response of the system, experimental verification of numerical models remains prerequisite for their adoption and reliable application in practice. Thus, in this study, the numerical and experimental investigations were performed on the backfill-exterior wall-fluid interaction system. Firstly, three dimensional finite element model (3D-FEM) was developed to acquire modal frequencies and mode shapes of the system by means of ANSYS. Secondly, a series of in-situ tests were fulfilled to define modal characteristics of same system to determine the applicability of the FEM to a real physical situation under field conditions. Finally, comparing the theoretical predictions from the model to results from experimental measurement, a close agreement was found between theory and experiment. Thus, it can be easily stated that experimental verification provides strong support for the use of proposed model in further investigations.Keywords: fluid-structure interaction, modal analysis, rectangular tank, soil structure interaction
Procedia PDF Downloads 3933638 A Hybrid Block Multistep Method for Direct Numerical Integration of Fourth Order Initial Value Problems
Authors: Adamu S. Salawu, Ibrahim O. Isah
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Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation
Procedia PDF Downloads 1233637 High Sensitivity Crack Detection and Locating with Optimized Spatial Wavelet Analysis
Authors: A. Ghanbari Mardasi, N. Wu, C. Wu
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In this study, a spatial wavelet-based crack localization technique for a thick beam is presented. Wavelet scale in spatial wavelet transformation is optimized to enhance crack detection sensitivity. A windowing function is also employed to erase the edge effect of the wavelet transformation, which enables the method to detect and localize cracks near the beam/measurement boundaries. Theoretical model and vibration analysis considering the crack effect are first proposed and performed in MATLAB based on the Timoshenko beam model. Gabor wavelet family is applied to the beam vibration mode shapes derived from the theoretical beam model to magnify the crack effect so as to locate the crack. Relative wavelet coefficient is obtained for sensitivity analysis by comparing the coefficient values at different positions of the beam with the lowest value in the intact area of the beam. Afterward, the optimal wavelet scale corresponding to the highest relative wavelet coefficient at the crack position is obtained for each vibration mode, through numerical simulations. The same procedure is performed for cracks with different sizes and positions in order to find the optimal scale range for the Gabor wavelet family. Finally, Hanning window is applied to different vibration mode shapes in order to overcome the edge effect problem of wavelet transformation and its effect on the localization of crack close to the measurement boundaries. Comparison of the wavelet coefficients distribution of windowed and initial mode shapes demonstrates that window function eases the identification of the cracks close to the boundaries.Keywords: edge effect, scale optimization, small crack locating, spatial wavelet
Procedia PDF Downloads 3573636 Study of Wake Dynamics for a Rim-Driven Thruster Based on Numerical Method
Authors: Bao Liu, Maarten Vanierschot, Frank Buysschaert
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The present work examines the wake dynamics of a rim-driven thruster (RDT) with Computational Fluid Dynamics (CFD). Unsteady Reynolds-averaged Navier-Stokes (URANS) equations were solved in the commercial solver ANSYS Fluent in combination with the SST k-ω turbulence model. The application of the moving reference frame (MRF) and sliding mesh (SM) approach to handling the rotational movement of the propeller were compared in the transient simulations. Validation and verification of the numerical model was performed to ensure numerical accuracy. Two representative scenarios were considered, i.e., the bollard condition (J=0) and a very light loading condition(J=0.7), respectively. From the results, it’s confirmed that compared to the SM method, the MRF method is not suitable for resolving the unsteady flow features as it only gives the general mean flow but smooths out lots of characteristic details in the flow field. By evaluating the simulation results with the SM technique, the instantaneous wake flow field under both conditions is presented and analyzed, most notably the helical vortex structure. It’s observed from the results that the tip vortices, blade shed vortices, and hub vortices are present in the wake flow field and convect downstream in a highly non-linear way. The shear layer vortices shedding from the duct displayed a strong interaction with the distorted tip vortices in an irregularmanner.Keywords: computational fluid dynamics, rim-driven thruster, sliding mesh, wake dynamics
Procedia PDF Downloads 2603635 Numerical Investigation of the Flow Characteristics inside the Scrubber Unit
Authors: Kumaresh Selvakumar, Man Young Kim
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Wet scrubbers have found widespread use in cleaning contaminated gas streams because of their ability to remove particulates and based on the applications of scrubbing of marine engine exhaust gases by spraying sea-water. In order to examine the flow characteristics inside the scrubber, the model is designated with flow properties of hot air and water sprayer. The flow dynamics of evaporation of hot air by the injection of water droplets is the key factor considered in this paper. The flow behavior inside the scrubber was investigated from the previous works and to sum up the evaporation rate with respect to the concentration of water droplets are predicted to bring out the competent modelling. The numerical analysis using CFD facilitates in understanding the problem better and empathies the behavior of the model over its entire operating envelope.Keywords: concentration of water droplets, evaporation rate, scrubber, water sprayer
Procedia PDF Downloads 2183634 Estimation of Residual Stresses in Thick Walled Cylinder by Radial Basis Artificial Neural
Authors: Mohammad Heidari
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In this paper a method for high strength steel is proposed of residual stresses in autofrettaged tubes by combination of artificial neural networks is presented. Many different thick walled cylinders that were subjected to different conditions were studied. At first, the residual stress is calculated by analytical solution. Then by changing of the parameters that influenced in residual stresses such as percentage of autofrettage, internal pressure, wall ratio of cylinder, material property of cylinder, bauschinger and hardening effect factor, a neural network is created. These parameters are the input of network. The output of network is residual stress. Numerical data, employed for training the network and capabilities of the model in predicting the residual stress has been verified. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 2.75% in predicting residual stress of thick wall cylinder. Further analysis of residual stress of thick wall cylinder under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach.Keywords: thick walled cylinder, residual stress, radial basis, artificial neural network
Procedia PDF Downloads 4163633 Analysis of Interpolation Factor in Pulse Shaping Filter on MRC for CDMA 2000 Systems
Authors: Pankaj Verma, Gagandeep Singh Walia, Padma Devi, H. P. Singh
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Code Division Multiple Access 2000 operates on various RF channel bandwidths 1.2288 or 3.6864 Mcps. CDMA offers high bandwidth and wireless broadband services but the efficiency gets decreased because of many interfering factors like fading, interference, scattering, diffraction, refraction, reflection etc. To reduce the spectral bandwidth is one of the major concerns in modern day technology and this is achieved by pulse shaping filter. This paper investigates the effect of diversity (MRC), interpolation factor in Root Raised Cosine (RRC) filter for the QPSK and BPSK modulation schemes. It is made possible to send information with minimum inter symbol interference and within limited bandwidth with proper pulse shaping technique. Bit error rate (BER) performance is analyzed by applying diversity technique by varying the interpolation factor for Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK). Interpolation factor increases the original sampling rate of a sequence to a higher rate and reduces the interference and diversity reduces the fading.Keywords: CDMA2000, root raised cosine, roll off factor, ISI, diversity, interference, fading
Procedia PDF Downloads 4753632 The Experimental and Numerical Analysis of TRIP Steel Wire Drawing Processes Drawn with Different Partial Reductions
Authors: Sylwia Wiewiorowska, Zbigniew Muskalski
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The strain intensity and redundant strains, dependent in multistage TRIP wire drawing processes from values used single partial reductions, should influence on the intensity of transformation the retained austenite into martensite and thereby on mechanical properties of drawn wires. The numerical analysis of drawing processes with use of Drawing 2D programme, for steel wires made from TRIP steel with 0,29 % has been shown in the work. The change of strain intensity Ԑc and the values of redundant strain Ԑxy, has been determined for particular draws in dependence of used single partial reductions.Keywords: steel wire, TRIP steel, drawing processes, fem modelling
Procedia PDF Downloads 5973631 Static and Dynamical Analysis on Clutch Discs on Different Material and Geometries
Authors: Jairo Aparecido Martins, Estaner Claro Romão
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This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOLTM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.Keywords: aluminum, industrial clutch, static and dynamic loading, numerical simulation
Procedia PDF Downloads 188