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Table of Content
25 May 2011, Volume 43 Issue 3
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Research paper
Numerical investigation of selfaligning spiked bodies at hypersonic speeds
Geng Yunfei Chao Yan
2011, 43(3): 441446. DOI:
10.6052/0459187920113lxxb2010732
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The conventional fixed spike method, in which the spike is mounted with an alignment along the bodyaxis, always failed at relatively high angles of attack; therefore, a new selfaligning spike method is investigated in the present paper. This method is applied to 3D axisymmetrical blunt cone and compressed wedge configurations at hypersonic speeds. Numerical simulations are carried out to verify this new concept. Spiked geometries with different L/D parameters at angle of attack ranged from 0 to 12 degrees are investigated. Numerical results reveal that the selfaligning spike method has great capability in drag and heat reduction as compared with the conventional fixed spikes. It can still effectively work even at relatively large angles of attack. This new method can resolve the problem that encountered by the conventional spike method.
The study on microscale particle coagulation due to turbulent shear mechanism using TEMOM model
Yu Mingzhou Jiang Ying Zhang Kai
2011, 43(3): 447453. DOI:
10.6052/0459187920113lxxb2010115
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The coagulation due to turbulent shear is the main mechanism leading to the instability of micro and nanoparticleladen multiphase flows. The Smoluchowski meanfiled theory is considered to be a good selection for solving this problem since it can be coupled to some turbulent models. In this study, the Taylorexpansion method of moments (TEMOM) is first applied in micro and nanoparticle coagulation due to turbulent shear mechanism in which the closure of Smoluchowski equation as well as the relationship between the numerical accuracy and the order of Taylor series expansion are emphatically investigated. The result show the partial 4order Taylor expansion method of moments can be applied to analyze the problem involving micro and nanoparticle turbulent shear coagulation with high accuracy, and the pseudo selfpreserving size distribution is found in micro and nanoparticleladen multiphase systems dominated by turbulent shear mechanism.
Numerical research on the interaction between ionized gas and magnetic field under high hall parameter
Hu Haiyang Yang Yunjun Zhou Weijiang
2011, 43(3): 453460. DOI:
10.6052/0459187920113lxxb2010287
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By coupling Poisson's equation for the electric potential field with flowfield NS equations through Lorentz force and the joule heat, numerical simulation of magnetofluid with low magnetic Reynolds number was carried out. The influence of the Hall effect and the external circuit was considered. The Poisson's equation illconditioned matrix caused by high Hall parameter was overcomed by LUSGS pretreatment BICGSTAB algorithm without pseudo time step. Numerical simulations of two kind of phenomenon, hypersonic magnetofluid flow around a circular cylinder when Hall parameter reaching about 10$^2$ and the energy deposition in scramjet isolator, indicate that external circuit, electrode cooling measures and plasma uniformity have great influence on the electromagnetic force.
Breakdown of locally heated and subcooled laminar films with interfacial shear
Ye Xuemin Li Chunxi Yan Weiping
2011, 43(3): 461467. DOI:
10.6052/0459187920113lxxb2009673
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The theoretical models of critical film thickness and minimum wetting rate were established for locally heated and subcooled laminar films under different flow directions of gas and liquid, and the effects of the contact angle, film temperature, interfacial shear and heat flux were discussed driving by gravity or/and interfacial shear. The investigation shows that the critical film thickness and minimum wetting rate increase with increasing heat flux. The effect of contact angle is clearly different in different range of heat flux under gravity driving, and the film temperature has a contrary influence on minimum wetting rate driving by gravity and interfacial shear. The critical film thickness and minimum wetting rate decrease with cocurrent shear. Under the combination of gravity and interfacial shear, the effect of cocurrent shear on minimum wetting rate is closely related with the ratio of gravity to shear, and the increasing countercurrent shear leads the critical film thickness and minimum wetting rate to decrease.
Numerical simulation of the severe slug flow between waterair phases in a declination piperiser
Gao Song You Yunxiaing Li Wei Hu Tianqun Yu Zhong
2011, 43(3): 468475. DOI:
10.6052/0459187920113lxxb2009675
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In the present paper, a numerical method for simulating the characteristics of twophase flows in a declination piperiser system with the gas and fluid was developed. The Brackbill model was applied to simulate surface tension between two phases and the VOF method was used to capture the moving interfaces between gasliquid phases. At low superfical velocity of gas and liquid superficial velocities, severe slug flows in such a piperiser system were simulated and the variety characteristics for flow parameters were analyzed. The results show that the flow parameter characteristics due to such a severe slug flow have remarkably periodic characteristics, including the flow pattern, pressure, slug velocity, average phase velocity at the riser outlet and gas volume fraction, and severe slug flow in a period consists of four evolvement stages where the characteristics of such flow parameters in each evolvement stage were further given. The numerical results are good agreements with experimental results reported in the references, showing that the proposed method is effective.
A study of sediment transport modele in onedimensional numerical channel network model
Han Dong Fang Hongwei Chen Minghong He Jianguo Bai Jing
2011, 43(3): 476481. DOI:
10.6052/0459187920113lxxb2010384
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Hydrodynamics and sediment transport model are generally used to simulate the evolution of natural alluvial rivers. In this paper, an explicit recursive method for sediment transport in channel network is presented. Based on hydrodynamic calculation, the method can be used to directly calculate nonequilibrium sediment transport process, involving suspended load and bedload gradation adjustments one by one node in each river. This method avoids solving the matrix of the relationship between first and last sections, which is popular in traditional methods. A onedimensional mathematical model with the sediment transport method is applied to the Jingjiang RiverDongting Lake region in the Three Gorges Project. Results are greatly in accord with the actual measurement. Computation cost is reduced and high accuracy is obtained in the new method. Moreover, the differences among different models of suspended load diversion in the node are discussed in the paper.
Research on the deposition efficiency of nanoparticle in human nasal cavity
Zhao Xiaodong Zhang Kai Tian Fuzhen
2011, 43(3): 482487. DOI:
10.6052/0459187920113lxxb2010512
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The Eulerian and Lagrangian method are used to numerically simulate the transport and deposition of nanoparticle in human nasal cavity with finite volume method. The kw turbulence model is used to get the flow field, and oneway coupling Lagrangian method is used to track the trajectory of nanoparticle with Stokes, Brownian and thermophoretic force considered in this model. It's found that Deposition in the nasal cavity is high for very small nanoparticles. The particle diameter range in which the deposition drops from 80% to 18% is between 1,nm and 10,nm. From 10,nm to 150,nm however, there is only a small change in the deposition curve from 18% to 5%. These results are helpful to develop the medicine the disease of human nasal cavity.
Parametric variational principle and numerical algorithm for LQ optimal control with constrained control input
Peng Haijun Gao Qiang Zhang HongWu Wu Zhigang Zhong Wanxie
2011, 43(3): 488495. DOI:
10.6052/0459187920113lxxb2010465
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Based on the theory of analogy, the parametric variational principle derived from plastic mechanics and contact mechanics is developed and applied to the theory of optimal control. New coupled equations of Hamilton canonical equation and linear complementarity equation are established for the problem of LQ optimal control with constrained control input. By dividing the continuous time into a series of equidistant intervals, a new numerical algorithm based on the parametric quadratic programming method for solving the coupledequations is proposed in the discrete time domain. Numerical simulations show that the algorithm given in this paper is effective for the problem of LQ optimal control with constrained control input and the convergence speed and accuracy of the algorithm is satisfactory.
Collocation interval finite element method
Qiu Zhiping Qi Wuchao
2011, 43(3): 496504. DOI:
10.6052/0459187920113lxxb2010382
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Based on shortcoming analysis of `point approximation' interval finite element method with Taylor expansion, collocation interval finite element method based on the first Chebyshev polynomials which can approach objective function in global domain is proposed in this paper. The method does not require the sensitivities of the objective function with respect to uncertain variables and the assumption of narrow interval is also not needed. The method is suitable for solving the case that the objective function is strongly nonlinear with respect to the uncertain variables. The orthogonal expansion coefficients of the objective function are obtained from GaussChebyshev quadrature formula. So Gauss integration points are collocated in the intervals of uncertain variables. The main computational effort is to calculate the values of objective function at Gaussian integration points. When the number of the uncertain variables is $m$ and the tenpoint Gauss integral method is introduced, it is needed to analyze the system with 12m times. Examples show that the collocation interval finite element method can still obtain almost exact interval bounds in the case that other interval finite element methods are invalid.
Stochastic harmonic function and spectral representations
Chen Jianbin Li Jie
2011, 43(3): 505513. DOI:
10.6052/0459187920113lxxb2010375
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Stochastic harmonic function representations and their properties are studied. In the paper, it is firstly proved that as the distributions of the random frequencies are consistent with the target power spectral density function, the power spectral density of the stochastic harmonic process is identical to the target power spectral density. Further, it is proved that the stochastic harmonic process is asymptotically normally distributed. The rate of approaching normal distribution is discussed by adopting Pearson distribution to describe the onedimensional distribution of the stochastic harmonic process. Compared to existing representations of stochastic process, very few stochastic harmonic components can capture the exact target power spectral density. This greatly reduces the number of the random variables and thus eases the difficulty of stochastic dynamics. Finally, linear and nonlinear responses of a multidegreeoffreedom system subjected to random ground motions are carried out to exemplify the effectiveness and advantages of the stochastic harmonic representations. Keywords: Stochastic harmonic function, power spectral density function, covariance function, stationary process, nonlinearity
Analysis of equivalent elastic modulus of a honeycomb sandwich
Chen Daiheng Yang Lu
2011, 43(3): 514522. DOI:
10.6052/0459187920113lxxb2010113
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In this paper, inplane equivalent elastic modulus of a honeycomb sandwich, consisting of hexagonal cell core and face sheet, is studied by using a theoretical analysis. It is shown that the equivalent elastic modulus can not been analyzed with high precision by treating the honeycomb as a composite of two materials: the core and the face sheet, because the core consists of portions of the slanting cell walls and the vertical cell walls, whose rigidities differ greatly. Dividing the core into the slanting cell wall portion and the vertical cell wall portion, and regarding the honeycomb as a composite of three materials, a method to calculate elastic modulus is proposed based on the principle of the minimum potential energy, and its validity is verified by numerical results of FEM.
Ratcheting study of pressurized lateral nozzle of cylinder
Yang Lidong Dong Junhua Gao Bingjun
2011, 43(3): 523532. DOI:
10.6052/0459187920113lxxb2009698
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Lateral nozzle of cylinder or lateral tee piping is widely used in nuclear, electric, petroleum and chemical industries. The cylinder or the piping may suffer plastic accumulation, namely ratcheting, due to fluid pressure together with seismic load and thermal expansion. Extensive and quantitative ratcheting investigation is necessary to detemine the ratcheting boundary for the safety of the structure. As the phenomenological cyclic plastic constitutive models have made a great progress in the last two decades, some investigators have taken advantage of the advanced model to evaluate the ratcheting of simple structure of pressure vessels and piping. However, few literature studied ratcheting and ratcheting boundary of complicated strctures such as lateral nozzle of cylinder or lateral tee piping. In this paper, ratcheting of pressurized lateral nozzle of cylinder made of 20$^{\#}$ carbon steel was experimentally studied with a multiaxial fatigue testing system and a selfdesigned inplane bending apparatus for lateral nozzle structure. The specimen, pressurized by a pumping station with adjustable pressure, was simply supported on a stiff beam, and pulled in a pulsatile way by the servohydraulic testing machine to simulate the inplane cyclic bending. Ratcheting strains were acquired by multichannel strain processors with strain gauges. The cyclic loading and the strain acquirement were controlled and processed simutaneously by a computer. Ratcheting strains were detected around the acute angle region of the structure. It was found that ratcheting mainly occured in the direction of the first principle strain, which is directed to the intersecting weld. The maximum ratcheting strain occured at the nozzle side of the acute angle region in the symmetrical plane for the structue. Ratcheting boundaries of gauged points were experimentally determined by step pressure loading. Numerical ratcheting analysis of structure was accomplished by secondary development of ANSYS with four typical kinematic hardening models, in which OhnoWang model and its modified models improved the prediction of ratcheting strain. Ratcheting boundaries of gauged points were numerically determined by the equivalent plastic strain increment control method with MJS model(Modifed JiangSehitoglu model) and validated to be in good agreement with that experimental results. Finally, the ratcheting boundary of the structure was determined according to the values of maximum ratcheting strain point, which may be used to evaluate the shakedown of the structure.
The Green's function solution of Lamb's problem for a saturated porous medium
Ding Boyang Chen Jun Pan Xiaodong
2011, 43(3): 533541. DOI:
10.6052/0459187920113lxxb2010090
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At the beginning of last century, Lamb obtained the displacement solutions of a wave field on the semiinfinite space subjected to a concentrated force. These solutions are widely applied in soil dynamics, seismic engineering and geophysics. Lamb's achievements are still being regarded as an important tool to solve the response and vibration problems in current research and engineering. However, it should be noted that Lamb's solutions only satisfy a homogeneous single medium. There are many dynamic problems of the multiphase or saturated porous medium in practice. Thus, scientists and technicians have been concerned with the displacement solutions to a semiinfinite space of a saturated porous medium subjected to a concentrated force. Philippacopoulos obtained the solutions on the semiinfinite space of a saturated porous medium subjected to a concentrated force in 1987. This step occurred for 73 years after Lamb finished the abovementioned work, then 25 years after that Biot put forward a dynamics equation of a saturated porous medium. It is the mathematical difficulty that inhibits the development, and the most distinct difficulty is the coupling of fast and slow dilational waves in the dynamic equation of a saturated porous medium. Philippacopoulos have not solved the coupling problem. His solutions are gained with a corresponding determinant of Eigen equations, which equals to zero, so that the solutions are complex and the deduction is complicated. The loads applied to a saturated porous medium have been varied such as the moving, the torsions, the swing and so on. At this stage we should decouple the fast and slow dilational waves for regularization of solving the dynamics problem of a saturate porous medium. Based on the Homholtz's solution for the Biot dynamics equation of a saturated porous medium with complexcoefficient and Fourier transformation, especially, according to the reverse of the fast and slow dilational waves on vibration phase, the authors solved the coupling of the fast and slow dilational waves and obtained Green's function to the dynamics equation of a saturated porous medium in 1999. These results are consistent with Chen's results (1994) which were obtained by referring to the continuity of the solution to the dynamics equation with an inhomogeneous term $\delta $ function and the discontinuity of its first order derivative. Utilizing the Green functions and its transformation form in axisymmetric cylindrical coordinates, using Sommerfeld's integral and the influence of a free surface field, the authors obtained the dynamic displacement solutions of a saturated porous medium subjected to a concentrated force in the semiinfinite space. Naturally, the solutions are consistent with the Philippacopoulos's solutions. When a saturated porous medium decays a singlephase medium, the results are consistent with Lamb's results. The whole process of deduction is common with a clear physical meaning. Hence, it not only justifies the method of solving (by means of) a coupling of fast and slow dilational waves of a saturated porous medium in this paper, it also provides reference to regularization and generalization for solving the dynamics problem in the semiinfinite space of a saturated porous medium.
Simulation and comparison of different dynamical models of space webs
Li Jingyang Yu Yang Hexi Baoyin Junfeng Li
2011, 43(3): 542550. DOI:
10.6052/0459187920113lxxb2010390
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Space webs which have great potential applications in orbit Service, recovery of spacecraft, orbit cleaning, space interceptor, woven from lightweight and pliable rope, are webs of unstable configuration formed by throwing and spreading. This paper adopts the finite element software ABAQUS in order to model the system of elastic webs and the system of flexible webs, compares the projecting of two finite element models, proposes metrics on the deployable of webs' system and focuses on traction mass, projectile point, projectile velocity of webs and equivalent damping effect of ropes on webs' deployable under a variety of different conditions. The results of simulation indicate that the unfolding effect of flexible webs is better than that of the elastic webs; traction mass, projectile velocity of webs and equivalent damping effect of ropes are the key factors in effectively webs' unfolding, and projectile point is the main factor to decide the unfolding area to the predetermined location.
On the moment lyapunov exponent of a viscoelastic plate subjected to the excitation of wide band noises
Huang Yong Li Shenghong Liu Xianbin
2011, 43(3): 551560. DOI:
10.6052/0459187920113lxxb2009776
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In the present paper, the moment Lyapunov exponent of a viscoelastic plate in a supersonic gas flow subjected to the excitation of wide band noises is investigated. A aeroelastic model for two coupled degreesoffreedom panel is established by using the Von Karman plates theory, the quasifirstorder piston theory and Galerkin approximation. Via the stochastic averaging method, the fourdimensional system is reduced to a twodimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and FeynmannKac formula, the backward differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained and matched by the Monte Carle simulation results. Finally, the influences of the system parameters, gas dynamical parameters and the spectral density of noises on the stochastic stability of viscoelastic plate is studied.
Vibration analysis of cylindrical helical springs considering warping deformation effect
Hao Ying Yu Aimin
2011, 43(3): 561569. DOI:
10.6052/0459187920113lxxb2010101
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The free vibrational behavior of cylindrical helical springs with rectangular cross sections is analytically investigated in this paper based on spatial curved beam theory. In the differential equations of motion of the springs, all displacement functions and a generalized warping coordinate are defined at the centroid principal axes and the warping effect upon the natural frequencies is also considered in present study. Explicit analytical expressions which give the vibrating mode shapes are derived by rigorous application of the symbolic computing package MATHEMATICA and a process of searching is used to determine the exact natural frequencies. Numerical examples are provided for the springs with the rectangular crosssection and clampedclamped and clampedfree boundary conditions. The free vibrational parameters are chosen as the ratio of the width to height (a / b = 0.6  1.7) for a rectangular cross section, the number of active turns (n = 6  12), the helix pitch angle (\bar {\alpha } = 5  12.5^ \circ ) and the radial of cylinder (R = 4  10mm) in a wide range. Validation of the proposed model has been achieved through comparison with a finite element model using threedimensional solid elements (Solid 45) and the available literature, showing a good agreement among them.
Frictional contact analysis of spatial prismatic joints in multibody systems
Qi Zhaohui Luo Xiaoming Huang Zhihao
2011, 43(3): 570578. DOI:
10.6052/0459187920113lxxb2009669
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In traditional methods, the details of relative motion between two bodies is necessary to locate contact points. When they are applied to analyze the contact in a joint, the bodies linked by the joint must be taken as free, no matter how small the clearance of the joint is. As a result, such drawback makes numerical solution inefficient and inaccurate in some cases. It is found that, the system of contact forces in a joint and the system of constraint reaction forces of the joint are equivalent, and the motion of possible contact points in joint relate each other inherently. Based on these facts, this paper present a method for frictional contact analysis of spatial prismatic joints, by which the positions and forces of contacts can be obtained while the kinematic constraints of prismatic joints are kept. Numerical examples prove the validity of the method.
The iterative digraph cell mapping method of nonsmooth dynamical systems
Li Shuang He Qun
2011, 43(3): 579585. DOI:
10.6052/0459187920113lxxb2010042
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Digraph cell mapping method (DCMM) is an effective technique to analyze the global behavior of dynamical systems. Recently, it has been applied to the study of crises and stochastic bifurcation, which achieved a series of good results. However, many researches by DCMM are based on smooth dynamical systems, and it is unknown whether this method can be applied to nonsmooth systems. In this paper, the key problem named expansion of cell flow is discussed in detail when the digraph cell mapping method is applied to analyze nonsmooth dynamical systems. It is found that because of nonsmooth boundary the expansion of cell flow is usually serious, which may result in analysis distortion of DCMM. For the above problem, the notion of the artificial node set is introduced to record which state cells may cause the expansion of cell flow. Taking the artificial node set as the redivided object, an iterative version of DCMM together with its effective algorithm is designed to decrease the expansion of cell flow and improve the computing accuracy. Furthermore some remarks are suggested for readers to analyze complex nonsmooth systems. In the iterative processes, the present method can not only keep the integrality of all computing results but also significantly enhance the computing efficiency. As an illustrative example, the Duffingvan der Pol vibroimpact system with complex nonlinear structures is taken to demonstrate the validity of the proposed method.
Research of the dynamic experimental modeling for viscoelastic composite beam
Wu Jian Ye Min Li Xing Dou Suguang
2011, 43(3): 586597. DOI:
10.6052/0459187920113lxxb2010326
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The viscoelastic materials are used widely with the development of new materials, and the nonlinear dynamic behavior in viscoelastic composite structure is becoming increasingly outstanding and important. The main purpose of this paper is a study of some nonlinear dynamic problems of viscoelastic composite structure under parametric excitation by using the experimental modeling method. The dynamic modeling method based on the theory analysis increases the difficulty on account of the complexity of the constitutive relation of viscoelastic materials. So it is one of the important means in the construction of dynamic model to combine theory with experiment. The establishment of the experimental model corresponding to the theoretical model and the related identification theory of nonlinearity system must be considered in the experimental modeling. A series of composite material samples are synthesized by using ABS (acrylonitrilebu tadinestyrene copolymer) resin as basic material and adding rutile nanoscaled titania from 1% to 10% as reinforced material. The experiment platform of the nonlinear parametric excitation vibration system is set up. The vibration is investigated for the nanocomposites beam with one end pinned and the other movable support, when axial excitation and controlled Drpfrictional forces are applied. By taking the experimental modeling method and applying to the Incremental Harmonic Balance Nonlinearity Identification, the dynamical equation of the viscoelastic composite beam is then built. Based on numerical simulation, comparisons between theoretical model and experimental system show good agreement in qualitative and quantitative analysis. The theoretical model is applicable for a class of composite materials with different weight ratios of reinforced material and matrix.
Moving mass identification of vehiclebridge coupled system based on virtual distortion method
Zhang Qingxia Duan Zhongzheng Jankowski Lukasz
2011, 43(3): 598610. DOI:
10.6052/0459187920113lxxb2009481
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In the inverse analysis of vehiclebridge coupled system, moving vehicle (load) identification is a crucial problem. Traditionally moving vehicles are identified by identifying the equivalent moving forces, which is a wellknown illconditioning problem, and hence is sensitive to noise. Moreover identification of moving forces require the number of sensors equal to or bigger than the number of unknown forces to obtain the unique solution. In order to avoid these drawbacks, this paper presents an effective method to identify moving vehicles. Vehicle parameters are chosen as the variables, which are optimized by minimizing the square distance between the measured structural responses and estimated responses. During the optimization, the computational work is reduced a lot by the proposed concepts of dynamic moving influence matrix based on Virtual Distortion Method (VDM), which consists of impulse response matrix with respect to the changing positions of the moving masses and is independent of mass values, and only needs to be computed once in advance. In this way, the repeatedly construction of the variant system matrix is avoided, and hence the optimization efficiency is improved. In this method, a massspring damping model with two degree of freedoms (Dofs) is used to simulate moving vehicle and its dynamic behavior. Moving vehicles and the bridge are analyzed as different substructures. In addition the equivalent moving loads are reconstructed simultaneously, such that the wellconditioning of the identification is ensured and makes the method be accurate and robust to noise. Moreover the number of the necessary sensors is decreased. The numerical costs are considerably reduced further by using the concepts of VDM, which belongs to fast reanalysis method, that is, the response of the modified structure equals to the response of an intact structure subjected to the same external load and to certain virtual distortions which model the changes of the actual structure. In this way, during the optimization, the structural response under given optimization variables are estimated quickly without the whole analysis of the global structure. Numerical experiment of a frame beam with 5{\%} Gaussian measurement error is used to verify the proposed method, where the effectiveness of different simplified vehicle models is compared. It demonstrates that masses of multiple moving vehicles can be identified using fewer sensors. When the roughness of road surface is neglected, under normal speed, the structural response is mainly caused by the weight of vehicles, and the coupling between the vehicle and bridge is rather low, therefore the influence of the vehicle spring stiffness and damping is very weak on the mass identification. For the identification of multiple vehicles, masses of the massspring damping model with two Dofs can be identified satisfactorily with the stiffness and damping as the estimated initial values. The identification considering the road roughness or high speed using the proposed method in this paper is undergoing.
Multi objective optimization methodology for airfoil robust design under geometry uncertainty
Li Jiaozan Gao Zhenghong
2011, 43(3): 611615. DOI:
10.6052/0459187920113lxxb2010066
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Traditionally, aerodynamic shape optimization has focused on obtaining the best design given the requirements and flow conditions. However, the manufacturing accuracy of the optimal shape is depends on the available manufacturing technology and other factors, such as manufacturing cost. It is imperative that the performance of the optimal design is retained when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. Here we demonstrate how both multiobjective evolutionary algorithm and surrogate model can be used to achieve robust optimal designs. Test cases include the deterministic optimization and robust design of airfoils, and the results were compared. It was shown that the present robust aerodynamic shape optimization method is a useful tool to design the more practical airfoil for air vehicles.
Movingparticle semiimplicit method research based on large eddy simulation
Pan Xujie Zhang Huaixin Sun Xueyao
2011, 43(3): 616620. DOI:
10.6052/0459187920113lxxb2010403
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The movingparticle semiimplicit method (MPS), coupled with a large eddy simulation (LES), is presented to free surface problem for turbulent flow. The control equation for LES is derived though the filtering operation of the NavierStokers equation. In the control equation, additional Reynolds stress terms are only different between LES and MPS. Therefore MPS is extended to LES by coupled with a subparticlescale (SPS) turbulence model and the Smagorinsky model which is able to describe the Reynolds stress terms. The MPSLES method is used in the case of simulation of resonance sloshing, and the simulation result is very close to that of experiment or other numerical simulation.
Highorder discontinuous galerkin solution of linearized Euler equations
Lu Hongqiang Zhu Guoxiang Song Jiangyong Wu Yizhao
2011, 43(3): 621624. DOI:
10.6052/0459187920113lxxb2010077
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In this paper, the linearized Euler equations (LEE) for aeroacoustics are solved using highorder Discontinuous Galerkin (DG) on unstructured grid for complex geometries. The background field, calculated using Finite Volume Method on structured grid, is first transferred into the LEE grid with a highly accurate method . A straightforward quadraturefree implementation method and parallel computing are used to accelerate the computation. Numerical tests indicate that very detailed features can be resolved even though high order DG was used on very coarse grids.
The structure analysis about the cavitation flow around the cascade hydrofoil by numerical and experimental study
Shi Suguo Wang Guoyu Huang Biao
2011, 43(3): 625629. DOI:
10.6052/0459187920113lxxb2010427
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The unsteady dynamics of cavitating flows around a hydrofoil and in a cascade hydrofoil are investigated by numerical and experimental methods. Experiments around a hydrofoil and on a cascade hydrofoil are carried out in a rectangular test section of a cavitation tunnel，and the lift and drag force are conducted and the frequency characteristics of lift signals are analyzed. The cavitation model in calculation is Kubota model which can describe the unsteady vortex cavitation accurately; the filterbased turbulence model can capture the unsteady characteristics in the flow more exactly; the reliability of the numerical model is validated by the experiment of the cavitation tunnel. The results show that a good agreement is obtained between the experimental data and the numerical simulation results. Compared the results around a hydrofoil, the cavitation thickness about the cascade hydrofoil is thinner; the adverse pressure gradient near the wall of the cascade hydrofoil is smaller; the intensity of the reentrant jet and the velocity gradient in the mixing field are smaller and the shedding time is longer.
Thermoelastic behavior of interface of composite plate under thermal shock
Xiong Qilin Xiaogeng Tian Shen Yapeng Xia Ronghou
2011, 43(3): 630634. DOI:
10.6052/0459187920113lxxb2010284
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Based on the generalized thermoelasticity with two thermal relaxation times (GL theory), the mechanical parameters through the zeroimpedance interface in a laminated plate under transient thermal shock, such as the displacement, stress and temperature, are studied by using the finite element method. The displacement, stress and temperature near the interface of the composite plate are obtained. With the influence of specific heat capacities, heat conduction coefficients, thermal relaxation time and densities of two materials, it is found that the displacement and stress through the interface of composite plate has a sudden change. The results are useful to obtain the deflection of composite plate caused by heat.
Dynamic characteristics of spinning Rayleigh beams
Qian Xin Du Xingwen
2011, 43(3): 635640. DOI:
10.6052/0459187920113lxxb2009712
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This paper derives the motion equations of the spinning Rayleigh beam under gravitation using the extended Hamilton principle and investigates the dynamic characteristics of spinning Rayleigh beam under a hingedhinged boundary condition. The present equations show that an important gyroscopic term induced by centrifugal force is missing in similar equations in the literature, but this term is indispensable in the modeling and analysis of spinning beams. The influences of rotary inertia, spinning speed, gyroscopic effects, slenderness ratio on whirling frequencies, whirling modes and critical speeds are investigated in detail using analytical and numerical methods. The results show that the forward whirling speed increases up to the critical speed, and then decreases with the spinning speed; the corresponding backward whirling speed decreases the spinning speed. Each forward whirling speed is higher than the corresponding backward whirling speed. For a spinning Rayleigh beam, there are infinitedimensional forward and backward critical speeds.