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2009 Vol. 41, No. 6

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Inertia particle preferential dispersion in dilute two-phase turbulent flows
Bing Wang, Huiqiang Zhang, Xilin Wang
Preferential dispersion of the particles was numericallystudied in three types of turbulent flows, namely, the flow over abackward-facing step, the fully developed channel flow and the round jetflow. Gas-phase was simulated by means of large eddy simulation andparticle-phase was tracked by particle trajectory model. It's shown thatinertia particles have preferential dispersion in the three turbulent flows,and the property of preferential motion of the particles is related to theparticle following property. The particle preferential dispersions aredetermined both by particle inertia and by large eddy structures. Particleswith Stokes number in the order of magnitude 1 (based on the macrotime-scale of fluid flow) have the strongest preferential distribution inlarge scale structures and they tend to accumulate in the turbulent regionswith low vorticity or low fluctuating velocity.
2009, 41(6): 821-827. doi: 10.6052/0459-1879-2009-6-2008-409
Lattice boltzmann simulation of gas micro-flows in transitional regime
Zhiwei Tian, Chuguang Zheng, Xiaoming Wang
In this paper, gas micro-flows in transition regime havebeen investigated by lattice Boltzmann method (LBM). On the basis ofexisting LBM models for micro-flows simulation, the velocity correctionfunction for Knudsen layer was introduced into the model. And theappropriate expression of velocity correction was chosen with the suitableparameter according to the kinetic theory. In the treatment of boundarycondition, to avoid the difficulties posed by computing the higher-orderderivatives of the velocity, we took a substitute approach of higher-orderslip scheme to capture the slip velocity in transitional regime. The presentresults of two types of micro-flows agree well with the numerical solutions,and are evidently better than those with the former LBM simulations,especially in the case of Kn>0.5.
2009, 41(6): 828-834. doi: 10.6052/0459-1879-2009-6-2008-472
Numerical calculation of 3-D flow outside multi-tube pulse detonation engine
Jie Wang, Chunsheng Weng
To investigate the characteristics of 3-D viscous flowoutside multi-tube Pulse Detonation Engine (PDE), the 3-D viscous space-timeConservation Element and Solution Element(CE/SE) method was deduced tosimulate the flow-flied inside and outside Pulse Detonation Engine withseven tubes. In the multi-tube model, one tube is in the midst and the othersix tubes are around it with a circle. One-dimensional model was used forthe flow inside PDE, and three -dimensional model was adopted for the flowoutside PDE to obtain the varieties of the flow outside the multi-tube PDE.The results indicate that there are vortexes, shocks and expansion wavesoutside the multi-tube PDE. In addition, the results might be referrible toresearch the characteristics of the flow-field outside multi-tube PulseDetonation Engine.
2009, 41(6): 835-841. doi: 10.6052/0459-1879-2009-6-2008-032
Evolutions of flame around a cylinder suspended in a chamber
Zhanfeng Ying, Baochun Fan, Zhihua ChenJ, ingfang Ye
An experimental study has been carried out to investigateinteraction between flame and circular cylinder suspended in the middle ofchamber to observe flame and flow structures. The simulation of thisexperiment by high accuracy PPM scheme is presented. In the scheme, theturbulent model is used with Large Eddy Simulation (LES) and the reactionrate model with eddy-break-up (EBU) model. The immersed boundary method(IBM) was used to solve boundary condition of circular cylinder. Thesimulation results were in good agreement with the experimental results. Itcan reveal the characteristics of acceleration and distortion of flamefront. Furthermore, this paper discussed 3D shape of flame front, vortex andturbulent kinetic energy in the chamber, the interaction between flame andflow, the flame front location.
2009, 41(6): 842-849. doi: 10.6052/0459-1879-2009-6-2008-433
Design and research for a new type buoyancy-lifting row flying-wings
Feng Li, Zhengyin Ye
It has important sciencfic and engineering applicationsfor aircrafts of low speed to design the buoyancy-lifting aircraft with bothbigger volume and higher aerodynamic efficiency. Based on the aerofoilNACA0030, some aerodynamic configurations of row flying-wings with thehigher volume efficiency (volume/surface) were constructed. Differentarrayed row flying-wings were calculated and investigated minutely. Anaerodynamic configuration of row sweptback flying-wings with the bettermaneuverability and stability was educed. The numerical simulation resultsindicate that the lift-drag ratios of row straight flying-wings and rowsweptback flying-wings increase by up to 40% and 20%, respectively,and the aerodynamic efficiency of aircrafts are improved obviously from theblock of airflow under the anterior flying-wing by the posteriorflying-wing. Meanwhile, the chordwise size of buoyancy-lifting rowflying-wings is comparatively small so that the surface tension of skinmaterial can be reduced availably. This characteristic provides the widerscope on the skin flexible material selection for high altitude aircrafts.
2009, 41(6): 850-858. doi: 10.6052/0459-1879-2009-6-2009-033
Effect of randomly removing cell walls on the dynamic crushing behaviour of honeycomb structures
Dongpeng Kou, Jilin Yu, Zhijun Zheng
Finite element simulations are performed to study the effect of randomly removing cell wallson the dynamic crushing behaviour of honeycomb structures. The influences of the imperfection andimpact velocity on the deformation mode and plateau stress are investigated. Simulation results revealthat both imperfection and impact velocity affect the deformation modes as well as the criticalvelocities of mode transition. It is found that the plateau stress is proportional to the square of theimpact velocity when the imperfect honeycombs are deformed at transitional mode or dynamic mode.When the impact velocity is near the critical velocity between transitional mode and dynamic mode,honeycombs with small fraction of imperfection exhibit higher plateau stress, comparing to those ofregular honeycombs having the same relative density. However, when the imperfection furtherincreases, the plateau stress decreases obviously near the critical velocity between quasi-static modeand transitional mode.
2009, 41(6): 859-868. doi: 10.6052/0459-1879-2009-6-2008-232
A second-order cone linear complementarity approach for three-dimensional frictional contact problems
Jianyu Li, Shaohua Pan, Hongwu Zhang
Frictional contact problems frequently arise in variousengineering applications, but their solutions, especially the solutions ofthree dimensional (3D) frictional contact problems, are challenging sincethe conditions for contact and friction are highly nonlinear and non-smooth.The 3D frictional contact problem is nonlinear and non-differentiable atleast in three aspects: 1) The unilateral contact law, combining a geometriccondition of impenetrability, a static condition of no-tension and an energycondition of complementarity, is represented by a multi-valuedforce-displacement relation. 2) The friction law, governed by a relationbetween reaction force and local relative velocity, is also multi-valued. 3)The Coulomb friction law in 3D space is expressed as a nonlinear inequalitythat is non-differentiable in the ordinary sense. In this paper, we proposea new linear second-order cone complementarity formulation for the numericalfinite element analysis of 3D frictional contact problem by using theparametric variational principle. Specifically, we develop a regularizationtechnique to resolve the multi-valued difficulty involved in the unilateralcontact law, and utilize a second-order cone complementarity condition tohandle the regularized Coulomb friction law in contact analysis. Wereformulate the governing equations of the 3D frictional contact problem asa linear second-order cone complementarity problem (SOCCP) via theparametric variational principle and the finite element method. Comparedwith the linear complementarity formulation of 3D frictional contactproblems, the proposal SOCCP formulation avoids the polyhedral approximationto the Coulomb friction cone so that the problem to be solved has muchsmaller size and the solution has better accuracy. A semismooth Newtonmethod is used to solve the obtained linear SOCCP. Numerical examples arecomputed and the results confirm the effectiveness and robustness of theSOCCP formulation developed.
2009, 41(6): 869-877. doi: 10.6052/0459-1879-2009-6-2008-475
Topology optimal design of thermo-elastic structures
Shiping Sun, Weihong Zhang
This paper investigates the topology optimization of thermo-elastic structure for maximizing thestructure stiffness with the volume constraint and the uniform temperature distribution. Firstly, theinfluence of both the thermal loading and the mechanical loading on optimal design is studied.Secondly, Comparison of the effect of eliminating the intermediate density between power lawSIMP (Solid Isotropic Material with Penalization) and RAMP (Rational Approximation ofMaterial Properties) is made. The difficulties of the non-monotonous behavior of the complianceand the intermediate density of optimal solution arise from the same penalization to both thetemperature loadings and the force loadings. To resolve these problems, the new approach with thedifferent penalization to the different loading is developed to eliminate the intermediate density.Numerical results show that the proposed method is valid for the design of thermo-elasticstructure.
2009, 41(6): 878-887. doi: 10.6052/0459-1879-2009-6-2007-439
A mesh-free method based on linear complementary model for gradient plasticity continuum
Junbo Zhang, Xikui Li
A numerical method attributed to a solution procedure oflinear complementary problem (LCP) for gradient plasticity continuum isproposed. With the mesh-free method based on moving least-squareapproximation (MLS) procedure, the displacements and plastic multipliertaken as primary field variables are interpolated in terms of theirdiscretized counterparts defined at the nodal points and the integrationpoints, respectively. The weak form of the equilibrium equation along withthe non-local constitutive equation and the non-local yield criterionlocally enforced at each integration point are combined to mathematicallyeduce a normal form of LCP solved by means of Lexico-Lemke algorithm. Aniterative procedure based on the Newton-Raphson method is developed with noneed of consistent tangent elasto-plastic modulus matrix to be derived whilestill retaining the second convergence rate for the solution of the boundaryproblem of gradient plasticity continuum. The numerical results for one andtwo dimensional examples demonstrate the validity of the proposed method indealing with the numerical solution of the strain localization problem dueto strain softening.
2009, 41(6): 888-897. doi: 10.6052/0459-1879-2009-6-2008-376
Reproducing kernel particle boundary element-free method for potential problems
Yixiao Qin, Yumin Cheng
Reproducing kernel particle method (RKPM) is one of theimportant methods to obtain the shape functions in meshless (or mesh-free)methods. In this paper, combining the reproducing kernel particle method andboundary integral equations for two-dimensional potential problems, thereproducing kernel particle boundary element-free (RKP-BEF) method fortwo-dimensional potential problems is presented. The formulae of the RKP-BEFmethod for two-dimensional potential problems based on Poisson's equationare obtained. The discrete boundary integral equations of the RKP-BEF methodare formed, and the corresponding numerical integral methods are discussed.The boundary integral equations of the RKP-BEF method for the potentials atinterior points are obtained. The smoothness of the shape function of theRKPM is the same as that of the reproducing kernel function, and the valuesof polynomials at interpolating points can be exactly reconstructed, thenthe RKP-BEF method has higher precision. In comparison with other existingmeshless boundary integral equation methods, such as boundary node method(BNM) and local boundary integral equation (LBIE) method, the RKP-BEF methodis a direct numerical method, in which the basic unknown quantity is thereal solution of the nodal variables, of meshless boundary integral equationmethods. And the boundary conditions can be implemented directly. Thenumerical examples of 2-D potential problems are given for verifying theeffectiveness and correctness of the method in this paper.
2009, 41(6): 898-905. doi: 10.6052/0459-1879-2009-6-2008-009
The effects of age on viscoelasticity and deformation recovery of articular chondrocytes
Quanyou Zhang, Weiyi Chen, Xiaochun Wei, Chunjiang Li, Linlin Liu
The aim of this study was to characterize the age-relatedchanges of viscoelastic properties and deformation recovery of rabbitchondrocytes in natural development of articular cartilage. The micropipetteaspiration combined with a standard linear viscoelastic solid model was usedto quantify all parameters of chondrocytes from different age groups.Results indicate that the viscoelastic properties of chondrocytes in oldgroup exhibited a significantly lower instantaneous modulus (E_0),equilibrium modulus (E_\infty ), and apparent viscosity (\mu )compared withthose of young group (p<0.005) and adult group (p<0.005). But no differenceswere found between young and adult group (p>0.1). The process of creep anddeformation recovery of chondrocytes has changed significantly duringnatural development. The time t_E that old chondrocytes need to reach equilibrium is significantlyless than young and adult ones (p<0.05), but no differences were foundbetween young and adult ones (p>0.05). At the same time, maximal creep displacementL_M in old group dramatically higher than young and adult group(p<0.005), however, there were no differences between young and adult group(p>0.05).Comparisons of the deformation recovery ratio ofdifferent age groups before 8 seconds have shown that the ratio value ofyoung group is significantly higher than those of adult and old ones(p<0.005), and there were no significant difference between adult and oldones (p>0.05). Additionally, there were no significant correlation betweenthe viscoelastic parameters and the ratio of the cell to micropipette diameter.These results may be helpful for chondrocyte-based cartilage tissueengineering.
2009, 41(6): 906-912. doi: 10.6052/0459-1879-2009-6-2008-401
The nonlinear viscoelastic constitutive model of cardiac myocyte in simulation of micropipette aspiration experiment
Tao Tang, Shiqi Wang, Jun Qiu, Zhuo Zhuang
Numerical modeling with experimental analysis isincreasingly being used to evaluate the mechanical properties of livingcells in single cell mechanics. In the present study, through the continuummechanics process, a new constitutive model for cardiac myocyte isdeveloped, and together with the micropipette aspiration experiment, themechanical property of cardiac myocyte is investigated. The commonly usedstandard linear solid model is extended into a nonlinear viscoelasticconstitutive model in which was introduced the hyperelasticity to describethe large deformation of myocytes in response to micropipette aspiration.Based on the constitutive model and experiment data, the experiment processis simulated, and the computational results are compared with the experimentresults and classic theoretical solutions. The results show that the newconstitutive model suits the computation of large deformation of cells.
2009, 41(6): 913-919. doi: 10.6052/0459-1879-2009-6-2008-344
Dynamics research on the multibody system with fractional-derivative-damper
Qiang Tian
Based on the absolute nodal coordinate (ANC) framework, the dynamics modeling and solutionstrategy for the multibody system with fractional derivative damper is investigated. The flexibleparts are discretized by the ANC-based locking-free shear deformable beam element. The systemequations of motion with constant mass matrix are also obtained and solved by the numericaldissipation controllable generalized-a method. The effects of the algorithm parameter and thefractional index on the dynamics responses are also studied by solving the numerical examples.The presented procedures can also be used to solve many other practical engineering problems.
2009, 41(6): 920-928. doi: 10.6052/0459-1879-2009-6-2008-534
The quasi-periodic behavior in the chaotic movement of the generalized Chau's circuit with periodic excitation
xiaofang zhang, zhangyao chen, Ying Ji, Qinsheng Bi
Chaotic circuits can be established conveniently, whichcan be used for chaotic synchronization and chaotic control as well as theimitation of secret communication. The dynamics behavior of chaotic circuitshas been one of the key topics. Up to now, most of the results obtainedfocus on the nonlinear autonomous circuits. However, a lot of nonautonomousfactors such as the electric power source with alternation property mayexist in many real circuits, while few works for such systems can be found.To reveal the dynamics details, it is necessary to investigate the influenceof the nonautonomous terms on the behavior of the dynamics evolution of thecircuits. Based on a fourth-order Chua's circuit, dynamics of the model withperiod-exciting has been explored. Since the coexistence of two symmetricstable equilibrium points in the generalized Chua's circuit, periodicexcitation may lead to two coexisted bifurcation patterns corresponding ofdifferent initial conditions. Chaos can be observed via the break-up of thetorus corresponding quasi-periodic solution, which may evolve fromnon-synchronized state of phase to synchronization. With the variation ofparameters, the chaotic attractor may split into two chaotic attractorssymmetric to each other, which still keep the phase synchronization. Anenlarged chaotic attractor can be observed after the interaction between thetwo symmetric chaotic attractors, which visits the original two chaoticattractors in turn with obvious rhythm. Meanwhile, for every certain timeinterval, the trajectory of the chaos oscillates quasi-periodically forrelatively long time, called as quasi-periodic behavior in chaos. This typeof phenomenon may weaken gradually and finally disappear.
2009, 41(6): 929-935. doi: 10.6052/0459-1879-2009-6-2008-603
Liquid sloshing damping computation in cylindrical container based on vof method
Wei Yang, Shuhong Liu, Yulin Wu
For small-amplitude liquid sloshing, the viscous dampingnear the free surface is an important part of the whole damping in partlyfilled liquid container. The damping is affected by many factors and isdifficult to calculate with a reasonable accuracy. In order to compute thedamping in partly filled rigid circular cylinder more reliably, a volume offluid method based on finite volume method is used. It is difficult tocompute damping precisely through numerical computation based on Stokesequations, in which the adhesion wall boundary condition can not besimultaneously satisfied at both the bottom wall and side wall. The dampingcomputation discrepancy of this method based on Stokes equations depends onthe liquid height ratio, h/R, where h is the liquid height and R is the radiusof the cylindrical container. The present method maintains all the wallboundary conditions, both side wall and bottom wall, with no slip conditionsand can give an exact damping value instead of an estimation range. Thesimulation damping results show a better agreement with the publishedexperimental data, especially for liquid height ratio h/R < 1.
2009, 41(6): 936-940. doi: 10.6052/0459-1879-2009-6-2008-218
Steady characteristics of micro gas journal bearings based on rarefaction effect
The reference Knudsen number is defined for micro gasjournal bearings and its value range is obtained according to the viscositydata of air at different temperatures. With gas rarefaction effect, modifiedReynolds equation for micro gas journal bearings is presented based onBurgdorfer's first order slip boundary condition. The finite differencemethod is used to solve the modified Reynolds equation, and pressure, loadcapacity and journal attitude angle of the bearing are obtained at differentreference Knudsen numbers, bearing numbers and journal eccentricityratios.Numerical results show that with the increase of gas rarefaction, bearingpressure and non-dimensional load capacity decrease obviously, and journalattitude angle increase. When the journal eccentricity ratio is less than0.6, journal attitude angle changes insignificantly and the influence on itfrom the reference Knudsen number is unobvious. Moreover, when the bearingnumber is small, the influence of gas rarefaction on non-dimensional loadcapacity and journal attitude angle is also insignificant.
2009, 41(6): 941-946. doi: 10.6052/0459-1879-2009-6-2008-341
Some qualitative properties of frequency spectrum and modes of difference discrete system of multibearing beam
Qishen Wang, Lei Wu, Jun Wang
The qualitative properties of the frequency spectrum andmodes were studied extensively for the nonhomogeneous single spanbeams, in which the discrete and continuous systems were included. However,the qualitative properties about the multispan beams were studied and onlyshown in the book ``Oscillation Matrices and Kernels and Small Vibrations ofMechanical Systems'' published by Gantmakher, F. P. and Krein, M. G. Thediscrete model given in this book was formed by adding several masses tomassless continuous system of the multispan beam, and the adopted method wasbased on the influence function of the beam, related to the positivesystems. Nevertheless, the conditions about the positive systems were notdiscussed in the above-mentioned book. In this paper the difference discretemodels of the multispan beam with arbitrary supports at two ends areestablished. According to the above book, the flexibility coefficient of theabove models corresponding to the positive single span beam systems isgiven. The oscillating property of the flexibility matrix of the multispanbeam is determined based on that of the positive single span beam systems byintroducing an auxiliary system. A series of qualitative properties of thefrequency spectrum and modes of the multispan beams are obtained.
2009, 41(6): 947-952. doi: 10.6052/0459-1879-2009-6-2008-129
Exact finite element solutions of buckling analysis of frame structures
Taicong Chen, Haitao Ma
Based on general solution for the homogeneous governingequation for the linear buckling analysis of Euler beam, new shape functionsare constructed and a new finite element is formulated. With the derivedelement stiffness matrix and geometric stiffness matrix, an iterativealgorithm based on conventional eigenvalue calculation procedure is proposedfor linear buckling analysis of frame structures. The conventional finiteelement is proved to be an approximation of the proposed element. By theapplication of the proposed element and algorithm, exact buckling solutionsof frame structures can be obtained even with coarse meshes. Illustrativenumerical examples are presented to show the effectiveness of the newelement and algorithm.
2009, 41(6): 953-960. doi: 10.6052/0459-1879-2009-6-2008-100
Adaptive selection of parameters for precise computation of matrix exponential based on padé approximation
Shujun Tan, Zhigang Wu, Wanxie Zhong
Adaptive selection is discussed for scaling parametersN and expanded series q in precise integration method (PIM) of matrixexponential based on Pad\'{e} approximation. In general, scaling parametersN and expanded series q play important roles in the numerical accuracyand computational efficiency of matrix exponential. Using theapproximation theory of matrix functions, influences of parameters N andq on the computational accuracy and efficiency are firstly studied, andthen the iterative adaptive selection algorithm for optimal combination ofparameters (N,q) is presented. Appropriate parameters (N,q) can beselected automatically depending on the characteristics of the matrix, andthe computation amount of adaptive selection can be neglected compared withthat of matrix exponential. So it is very important for enhancing theadaptations and increasing the computation efficiencies of matrixexponential. In addition, computational examples are carried out to testifythe correctness and validity of the present method.
2009, 41(6): 961-966. doi: 10.6052/0459-1879-2009-6-2008-370
Vibration restrain of disordered weak coupling antenna structure in satellite by applying predictive control method
Xiangqiu Liu, Cong Wang, Zhenzhu Zou
In order to research the vibration control ofweak-coupling antenna structures in satellite, a simplified dynamicsstructure model is established in the present study. The vibration modeslocalization in the structures is investigated. Active vibration control ofthe structures is studied by applying predictive control method and LinearQuadratic Regulator (LQR) control method, respectively. The simulationresults show that small disorder of the weak-coupling antenna structures caninduce remarkable localization of vibration modes. The vibration controleffects predicted with the present method are superior to those with LQRmethod. The results also show that the predictive control method has perfectperformance in vibration control analysis while the models are mismatcheddue to the structure disorder. Therefore, the disorder must be consideredseriously in active vibration control of weak coupling antenna structures.
2009, 41(6): 967-973. doi: 10.6052/0459-1879-2009-6-2008-683
2009, 41(6): 974-980. doi: 10.6052/0459-1879-2009-6-2009-745