Search results for: coefficient inverse problem

Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

Abstract:

A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: Hyung Jong Ko, Kyoung Hoon Kim

Abstract:

In this study thermodynamic performance analysis of a combined organic Rankine cycle and ejector refrigeration cycle is carried out for use of low-grade heat source in the form of sensible energy. Special attention is paid to the effects of system parameters including the turbine inlet temperature and turbine inlet pressure on the characteristics of the system such as ratios of mass flow rate, net work production, and refrigeration capacity as well as the coefficient of performance and exergy efficiency of the system. Results show that for a given source the coefficient of performance increases with increasing of the turbine inlet pressure. However, the exergy efficiency has an optimal condition with respect to the turbine inlet pressure.

Keywords: Coefficient of performance, ejector refrigeration cycle, exergy efficiency, low-grade energy, organic rankine cycle.

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Authors: S. Nasri, H. Bouziri

Abstract:

Disasters are quite experienced in our days. They are caused by floods, landslides, and building fires that is the main objective of this study. To cope with these unexpected events, precautions must be taken to protect human lives. The emphasis on disposal work focuses on the resolution of the evacuation problem in case of no-notice disaster. The problem of evacuation is listed as a dynamic network flow problem. Particularly, we model the evacuation problem as an earliest arrival flow problem with load dependent transit time. This problem is classified as NP-Hard. Our challenge here is to propose a metaheuristic solution for solving the evacuation problem. We define our objective as the maximization of evacuees during earliest periods of a time horizon T. The objective provides the evacuation of persons as soon as possible. We performed an experimental study on emergency evacuation from the tunisian children’s hospital. This work prompts us to look for evacuation plans corresponding to several situations where the network dynamically changes.

Keywords: Dynamic network flow, Load dependent transit time, Evacuation strategy, Earliest arrival flow problem.

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Authors: M. Dinakaran, P. Balasubramanie

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With the demand of mobility by users, wireless technologies have become the hotspot developing arena. Internet Engineering Task Force (IETF) working group has developed Mobile IP to support node mobility. The concept of node mobility indicates that in spite of the movement of the node, it is still connected to the internet and all the data transactions are preserved. It provides location-independent access to Internet. After the incorporation of host mobility, network mobility has undergone intense research. There are several intricacies faced in the real world implementation of network mobility significantly the problem of nested networks and their consequences. This article is concerned regarding a problem of nested network called pinball route problem and proposes a solution to eliminate the above problem. The proposed mechanism is implemented using NS2 simulation tool and it is found that the proposed mechanism efficiently reduces the overload caused by the pinball route problem.

Keywords: Mobile IP, Pinball routing problem, NEMO

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Authors: Brajesh Kumar Jha, Neeru Adlakha, M. N. Mehta

Abstract:

Mathematical and computational modeling of calcium signalling in nerve cells has produced considerable insights into how the cells contracts with other cells under the variation of biophysical and physiological parameters. The modeling of calcium signaling in astrocytes has become more sophisticated. The modeling effort has provided insight to understand the cell contraction. Main objective of this work is to study the effect of voltage gated (Operated) calcium channel (VOC) on calcium profile in the form of advection diffusion equation. A mathematical model is developed in the form of advection diffusion equation for the calcium profile. The model incorporates the important physiological parameter like diffusion coefficient etc. Appropriate boundary conditions have been framed. Finite volume method is employed to solve the problem. A program has been developed using in MATLAB 7.5 for the entire problem and simulated on an AMD-Turion 32-bite machine to compute the numerical results.

Keywords: Ca2+ Profile, Advection Diffusion, VOC, FVM.

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Authors: N. Rugthaicharoencheep, S. Auchariyamet

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Optimal capacitor allocation in distribution systems has been studied for a long times. It is an optimization problem which has an objective to define the optimal sizes and locations of capacitors to be installed. In this works, an overview of capacitor placement problem in distribution systems is briefly introduced. The objective functions and constraints of the problem are listed and the methodologies for solving the problem are summarized.

Keywords: Capacitor Placement, Distribution Systems, Optimization Techniques

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Authors: Nageeb A. H. Haroun, Sabyasachi Mondal, Precious Sibanda

Abstract:

The effects of thermal radiation, Soret and Dufour parameters on mixed convection and nanofluid flow over a stretching sheet in the presence of a magnetic field are investigated. The flow is subject to temperature dependent viscosity and a chemical reaction parameter. It is assumed that the nanoparticle volume fraction at the wall may be actively controlled. The physical problem is modelled using systems of nonlinear differential equations which have been solved numerically using a spectral relaxation method. In addition to the discussion on heat and mass transfer processes, the velocity, nanoparticles volume fraction profiles as well as the skin friction coefficient are determined for different important physical parameters. A comparison of current findings with previously published results for some special cases of the problem shows an excellent agreement.

Keywords: Non-isothermal wedge, thermal radiation, nanofluid, magnetic field, Soret and Dufour effects.

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Authors: S. Deswal, M. Pal

Abstract:

The paper aims to compare the performance of vertical and inclined multiple plunging jets and to model and predict their mass transfer capacity by multi-linear regression based approach. The multiple vertical plunging jets have jet impact angle of θ = 90^O; whereas, multiple inclined plunging jets have jet impact angle of θ = 60^O. The results of the study suggests that mass transfer is higher for multiple jets, and inclined multiple plunging jets have up to 1.6 times higher mass transfer than vertical multiple plunging jets under similar conditions. The derived relationship, based on multi-linear regression approach, has successfully predicted the volumetric mass transfer coefficient (K_La) from operational parameters of multiple plunging jets with a correlation coefficient of 0.973, root mean square error of 0.002 and coefficient of determination of 0.946. The results suggests that predicted overall mass transfer coefficient is in good agreement with actual experimental values; thereby, suggesting the utility of derived relationship based on multi-linear regression based approach and can be successfully employed in modeling mass transfer by multiple plunging jets.

Keywords: Mass transfer, multiple plunging jets, multi-linear regression.

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Authors: R. Hosseini, A. Gholaminejad, H. Jahandar

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The present paper is an experimental investigation of roughness effects on nucleate pool boiling of refrigerant R113 on horizontal circular copper surfaces. The copper samples were treated by different sand paper grit sizes to achieve different surface roughness. The average surface roughness of the four samples was 0.901, 0.735, 0.65, and 0.09, respectively. The experiments were performed in the heat flux range of 8 to 200kW/m2. The heat transfer coefficient was calculated by measuring wall superheat of the samples and the input heat flux. The results show significant improvement of heat transfer coefficient as the surface roughness is increased. It is found that the heat transfer coefficient of the sample with Ra=0.901 is 3.4, 10.5, and 38.5% higher in comparison with surfaces with Ra of 0.735, 0.65, and 0.09 at heat flux of 170 kW/m2. Moreover, the results are compared with literature data and the well known Cooper correlation.

Keywords: Nucleate Boiling, Pool Boiling, R113, SurfaceRoughness

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Authors: S. H. Nasseri, M. Sohrabi, E. Ardil

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In this paper, we give a certain decomposition of the coefficient matrix of the fully fuzzy linear system (FFLS) to obtain a simple algorithm for solving these systems. The new algorithm can solve FFLS in a smaller computing process. We will illustrate our method by solving some examples.

Keywords: Fully fuzzy linear system, Fuzzy number, LUdecomposition.

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Authors: A. U. Haque, W. Asrar, A. A. Omar, E. Sulaeman, J. S. Mohamed Ali

Abstract:

Due to the interference effects, the intrinsic aerodynamic parameters obtained from the individual component testing are always fundamentally different than those obtained for complete model testing. Consideration and limitation for such testing need to be taken into account in any design work related to the component buildup method. In this paper, the scaled model of a straight rectangular canard of a hybrid buoyant aircraft is tested at 50 m/s in IIUM-LSWT (Low Speed Wind Tunnel). Model and its attachment with the balance are kept rigid to have results free from the aeroelastic distortion. Based on the velocity profile of the test section’s floor; the height of the model is kept equal to the corresponding boundary layer displacement. Balance measurements provide valuable but limited information of overall aerodynamic behavior of the model. Zero lift coefficient is obtained at -2.2o and the corresponding drag coefficient was found to be less than that at zero angle of attack. As a part of the validation of low fidelity tool, plot of lift coefficient plot was verified by the experimental data and except the value of zero lift coefficients, the overall trend has under predicted the lift coefficient. Based on this comparative study, a correction factor of 1.36 is proposed for lift curve slope obtained from the panel method.

Keywords: Wind tunnel testing, boundary layer displacement, lift curve slope, canard, aerodynamics.

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Authors: Divyesh Patel, Tanuja Srivastava

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This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: Discrete Tomography, exactly-1-4-adjacency, simulated annealing.

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Authors: M. Akbari, S. Sadodin

Abstract:

In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

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Authors: Chao Yuan, Bao Guang Tian

Abstract:

A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.

Keywords: Generalized linear model, generalized relative coefficient, least eigenvalue, relative efficiency.

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Authors: Khalifa AlShaqsi

Abstract:

The author introduced the integral operator , by using this operator a new subclasses of analytic functions are introduced. For these classes, several Fekete-Szeg¨ type coefficient inequalities are obtained.

Keywords: Integral operator, Fekete-Szeg¨ inequalities, Analytic functions.

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Authors: E. Moroydor Derun, A. S. Kipcak, A. Kaplan, S. Piskin

Abstract:

Magnesium wastes are produced by many industrial activities. This waste problem is becoming a future problem for the world. Magnesium borates have many advantages such as; high corrosion resistance, heat resistance, high coefficient of elasticity and can also be used in the production of material against radiation. Addition, magnesium borates have great potential in sectors including ceramic and detergents industry and superconducting materials. In this study, using the starting materials of waste magnesium and H3BO3 the hydrothermal method was applied at a moderate temperature of 70oC. Several mole ratios of waste magnesium to H3BO3 are selected as; 1:2, 1:4, 1:6, 1:8, 1:10. Reaction time was determined as 1 hour. After the synthesis, X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR) techniques are applied to products. As a result the forms of mcallisterite “Mg2(B6O7(OH)6)2.9(H2O)”, admontite “MgO(B2O3)3.7(H2O)” and magnesium boron hydrate (MgO(B2O3)3.6(H2O)” are obtained. 

Keywords: Hydrothermal synthesis, magnesium borates, waste magnesium.

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

Abstract:

In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: Binary cat swarm optimization, set covering problem, metaheuristic, binarization methods.

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Authors: Habtu Alemayehu, G. Radhakrishnamacharya

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The paper presents an analytical solution for dispersion of a solute in the peristaltic motion of a couple stress fluid through a porous medium with slip condition in the presence of both homogeneous and heterogeneous chemical reactions. The average effective dispersion coefficient has been found using Taylor-s limiting condition and long wavelength approximation. The effects of various relevant parameters on the average coefficient of dispersion have been studied. The average effective dispersion coefficient tends to increase with permeability parameter but tends to decrease with homogeneous chemical reaction rate parameter, couple stress parameter, slip parameter and heterogeneous reaction rate parameter.

Keywords: Dispersion, Peristalsis, Couple stress fluid, Porousmedium, Chemical reaction, Slip condition.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

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Authors: Halizah Awang, Ishak Ramly

Abstract:

Problem-based learning (PBL) is one of the student centered approaches and has been considered by a number of higher educational institutions in many parts of the world as a method of delivery. This paper presents a creative thinking approach for implementing Problem-based Learning in Mechanics of Structure within a Malaysian Polytechnics environment. In the learning process, students learn how to analyze the problem given among the students and sharing classroom knowledge into practice. Further, through this course-s emphasis on problem-based learning, students acquire creative thinking skills and professional skills as they tackle complex, interdisciplinary and real-situation problems. Once the creative ideas are generated, there are useful additional techniques for tender ideas that will grow into a productive concept or solution. The combination of creative skills and technical abilities will enable the students to be ready to “hit-the-ground-running" and produce in industry when they graduate.

Keywords: Creative Thinking Skills, Problem-based Learning, Problem Solving.

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Authors: Marina Franulovic, Robert Basan, Bozidar Krizan

Abstract:

Constitutive modeling of material behavior is becoming increasingly important in prediction of possible failures in highly loaded engineering components, and consequently, optimization of their design. In order to account for large number of phenomena that occur in the material during operation, such as kinematic hardening effect in low cycle fatigue behavior of steels, complex nonlinear material models are used ever more frequently, despite of the complexity of determination of their parameters. As a method for the determination of these parameters, genetic algorithm is good choice because of its capability to provide very good approximation of the solution in systems with large number of unknown variables. For the application of genetic algorithm to parameter identification, inverse analysis must be primarily defined. It is used as a tool to fine-tune calculated stress-strain values with experimental ones. In order to choose proper objective function for inverse analysis among already existent and newly developed functions, the research is performed to investigate its influence on material behavior modeling.

Keywords: Genetic algorithm, kinematic hardening, material model, objective function

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s problem solves the problem of fitting three circles into a right triangle such that these three 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; it is called the 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 the 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 the 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 as in Tri(Tn) problems. We call these problems the Carc(Tn) problems. The algorithm is a mO(Tn) algorithm, where m is the number of iterations in the loop. It takes less than 1000 iterations and less than 1 second for the Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties. This algorithm gives a solution for circle packing problem inside convex circular triangle with arbitrarily-sized circles. Many applications concerning circle packing may come from the result of the algorithm, such as logo design, architecture design, etc.

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

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Authors: Ruiheng Li, Amir Parsa Anvar, Amir M. Anvar, Tien-Fu Lu

Abstract:

High redundancy and strong uncertainty are two main characteristics for underwater robotic manipulators with unlimited workspace and mobility, but they also make the motion planning and control difficult and complex. In order to setup the groundwork for the research on control schemes, the mathematical representation is built by using the Denavit-Hartenberg (D-H) method [9]&[12]; in addition to the geometry of the manipulator which was studied for establishing the direct and inverse kinematics. Then, the dynamic model is developed and used by employing the Lagrange theorem. Furthermore, derivation and computer simulation is accomplished using the MATLAB environment. The result obtained is compared with mechanical system dynamics analysis software, ADAMS. In addition, the creation of intelligent artificial skin using Interlink Force Sensing ResistorTM technology is presented as groundwork for future work

Keywords: Manipulator System, Robot, AUV, Denavit- Hartenberg method Lagrange theorem, MALTAB, ADAMS, Direct and Inverse Kinematics, Dynamics, PD Control-law, Interlink Force Sensing ResistorTM, intelligent artificial skin system.

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Authors: Fatma A. Karkory, Ali A. Abudalmola

Abstract:

The travelling salesman problem (TSP) is a combinatorial optimization problem in which the goal is to find the shortest path between different cities that the salesman takes. In other words, the problem deals with finding a route covering all cities so that total distance and execution time is minimized. This paper adopts the nearest neighbor and minimum spanning tree algorithm to solve the well-known travelling salesman problem. The algorithms were implemented using java programming language. The approach is tested on three graphs that making a TSP tour instance of 5-city, 10 –city, and 229–city. The computation results validate the performance of the proposed algorithm.

Keywords: Heuristics, minimum spanning tree algorithm, Nearest Neighbor, Travelling Salesman Problem (TSP).

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Authors: Young S. Bang, Dong H. Yoon, Seung H. Yoo

Abstract:

Emergency Core Coolant Bypass (ECC Bypass) has been regarded as an important phenomenon to peak cladding temperature of large-break loss-of-coolant-accidents (LBLOCA) in nuclear power plants (NPP). A modeling scheme to address the ECC Bypass phenomena and the calculation of LBLOCA using that scheme are discussed in the present paper. A hydraulic form loss coefficient (HFLC) from the reactor vessel downcomer to the broken cold leg is predicted by the computational fluid dynamics (CFD) code with a variation of the void fraction incoming from the downcomer. The maximum, mean, and minimum values of FLC are derived from the CFD results and are incorporated into the LBLOCA calculation using a system thermal-hydraulic code, MARS-KS. As a relevant parameter addressing the ECC Bypass phenomena, the FLC to the break and its range are proposed.

Keywords: CFD analysis, ECC Bypass, hydraulic form loss coefficient, system thermal-hydraulic code.

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Authors: Francisco Miranda

Abstract:

The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here.

Keywords: Lagrange multipliers, mathematical programming, optimization problem, time scales.

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Authors: S. Babaie-Kafaki, R. Ghanbari, S.H. Nasseri, E. Ardil

Abstract:

Bus networks design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved. The genetic algorithm (GA) is a search and optimization technique which works based on evolutionary principle of natural chromosomes. Specifically, the evolution of chromosomes due to the action of crossover, mutation and natural selection of chromosomes based on Darwin's survival-of-the-fittest principle, are all artificially simulated to constitute a robust search and optimization procedure. In this paper, we first state the problem as a mixed integer programming (MIP) problem. Then we design a new crossover and mutation for bus terminal location problem (BTLP). We tested the different parameters of genetic algorithm (for a sample problem) and obtained the optimal parameters for solving BTLP with numerical try and error.

Keywords: Bus networks, Genetic algorithm (GA), Locationproblem, Mixed integer programming (MIP).

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Authors: Latha Parameswaran, K. Anbumani

Abstract:

Multimedia security is an incredibly significant area of concern. The paper aims to discuss a robust image watermarking scheme, which can withstand geometric attacks. The source image is initially moment normalized in order to make it withstand geometric attacks. The moment normalized image is wavelet transformed. The first level wavelet transformed image is segmented into blocks if size 8x8. The product of mean and standard and standard deviation of each block is computed. The second level wavelet transformed image is divided into 8x8 blocks. The product of block mean and the standard deviation are computed. The difference between products in the two levels forms the watermark. The watermark is inserted by modulating the coefficients of the mid frequencies. The modulated image is inverse wavelet transformed and inverse moment normalized to generate the watermarked image. The watermarked image is now ready for transmission. The proposed scheme can be used to validate identification cards and financial instruments. The performance of this scheme has been evaluated using a set of parameters. Experimental results show the effectiveness of this scheme.

Keywords: Image moments, wavelets, content-based watermarking, moment normalization, geometric attacks.

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Authors: Hyu Sang Jo, Gyo Woo Lee

Abstract:

In this study, the evaluation of thermal stability of the micrometer-sized silica particle reinforced epoxy composite was carried out through the measurement of thermal expansion coefficient and Young’s modulus of the specimens. For all the specimens in this study from the baseline to those containing 50 wt% silica filler, the thermal expansion coefficients and the Young’s moduli were gradually decreased down to 20% and increased up to 41%, respectively. The experimental results were compared with fillervolume- based simple empirical relations. The experimental results of thermal expansion coefficients correspond with those of Thomas’s model which is modified from the rule of mixture. However, the measured result for Young’s modulus tends to be increased slightly. The differences in increments of the moduli between experimental and numerical model data are quite large.

Keywords: Thermal Stability, Silica-Reinforced, Epoxy Composite, Coefficient of Thermal Expansion, Empirical Model.

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Authors: Zhipeng Feng, Huanhuan Qi, Pingchuan Shen, Fenggang Zang, Yixiong Zhang

Abstract:

Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×10⁴. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.

Keywords: Vortex induced vibration, limit cycle, CFD, FEM.

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