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2006 Vol. 38, No. 3

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Rayleigh-Taylor Instability of A Liquid Drop at High Bond Numbers
In this paper, an analytical solution is presented for the Rayleigh-Taylorinstability of a viscous liquid drop at high Bond numbers. The instabilityplays an important role in the early stage of the aerodynamic breakup ofliquid drops in a supersonic flow. Based on the analytical solution, themaximum size of a liquid drop stable with respect to Rayleigh-Taylor instability and theinitiation time of drop breakup can be predicted. The predictions show goodagreement with relevant experimental and analytical results from literature.
2006, 38(3): 289-295. doi: 10.6052/0459-1879-2006-3-2004-079
Numerical investigations on propagation of spherically imploding gas
This paper reports numerical simulations of the propagation of sphericallyimploding detonations in H$_{2}$/O$_{2}$ mixture. One-dimensional Eulerequations in spherical coordinates were solved with the dispersioncontrolled dissipative (DCD) scheme, coupled to an elementary chemicalreaction model. The pressure and temperature behind the detonation wave weretraced to show their change tendency. Its dependency on the geometrical sizeand initial conditions were also numerically examined. It is found that thevariation of front pressure is representable in terms of approximatefunctions of $r/R$ only outside the central zone. Linear relations existbetween the front and initial pressure. The front temperature increases muchslower than the pressure during implosion.
2006, 38(3): 296-301. doi: 10.6052/0459-1879-2006-3-2004-390
An algorithm in piv measurement of wind-sand two-phase flow
On the basis of characteristics of wind-sand two-phase flow CCDimages, an auto generated Digital Mask algorithm based on $K$-mean valuealgorithm of pattern recognition's dynamic clustering method is proposed tosolve the wind-sand two-phase flow. This algorithm simplifies the manualsetting operation of parameters in the process of the traditional generation ofDigital Mask, reduces the man-made error, and provides a safe and fastmethod to process two-phase PIV images in batch. Finally, this algorithm isapplied to real measurements of wind-sand two-phase flow. After computation,the flow fields of the phase of the wind, the phase of the sand and thetwo-phase of the wind-sand of different flow types are obtained.
2006, 38(3): 302-308. doi: 10.6052/0459-1879-2006-3-2004-425
Flow behavior of periodical electroosmosis in microchannel for biochips
This paper presents an analytical solution for periodical electroosmoticflows in a two-dimensional uniform microchannel based on Poisson-Boltzmannequations for electric double layer (EDL) and Navier-Stokes equation forincompressible viscous fluid. Analytical results indicate that thevelocities of periodical electroosmosis strongly depend on Reynoldsnumber $Re = \omega h^2 / \nu $, as well as on EDL properties and the appliedelectric field. The slip velocity of EDL decreases as the Reynolds numberincreases. The electroosmosis velocity outside the EDL rapidly decreases,and the lag phase angle of the velocity increases as the distance away from thechannel wall increases. A wave-like velocity profile across the microchannelis found. An asymptotic solution for low Reynolds number is also given inthis paper. Periodical electroosmosis with low Reynolds has the samevelocity amplitude and a plug-like velocity profile as that of the steadyelectroosmosis. Debye-H\"{u}ckel approximate solution of the periodicalelectroosmosis in cases of small $\kappa h$, the ratio of the microchannelwidth to EDL thickness, is obtained and compared with the analyticalsolution.
2006, 38(3): 309-315. doi: 10.6052/0459-1879-2006-3-2005-086
Experimental investigation of microscale premixed combustion of hydrogen
, Jinliang Xu
This paper describes the hydrogen and air premixedcombustion in a stainless steel tube of 1.66 millimeter in diameter.Temperature fields of combustor wall are measured with infrared thermometerand operating ranges of different combustors are obtained at differentthermal powers. With the help of recirculation zone in the facingback step,premixed combustion can be stabilized in the micro-combustor with a5\,mm-length facingback step and the maximum air excess coefficientis up to 1.415. But the premixed combustion can not be stabilized in thestainless steel tube without facingback step because of higher flow rate andgreat heat loss. It is proved that facingback step can steady the flame andenlarge the operating range for microscale combustion. The relation betweentemperature fields of combustor wall and air excess coefficient isreasonably interpreted by observing the shape and structure of the flame andanalyzing flow fields of combustor with facingback step. The resultscan be used in designs of the microscale combustor.
2006, 38(3): 316-322. doi: 10.6052/0459-1879-2006-3-2005-184
Estimate of effective properties of metal particle tape based on micromechanics
The magnetic interaction of the particles has significant effects on theeffective properties of high-density recording tape. The interaction direct derivation (IDD)estimate based on the single particle's Stoner-Wohlforth model is generalized in thispaper. The generalized IDD (GIDD) estimate, based on micromagnetic theory, is found very close to the results of relatedexperiments and numerical simulations. We show that the IDD (GIDD)estimate has a simple and explicit structure, with clear physicalmeanings for all involvedcomponents, valid for multiphase composites of nonlinear materials, andthe influence of various inclusion distribution can be taken into account.
2006, 38(3): 323-329. doi: 10.6052/0459-1879-2006-3-2005-618
Reflection and transmission of elastic waves at the interface between a fluid-saturated porous solid and a double porosity solid
The reflection and transmission characteristics of an incidentplane P-1 wave at an interface between a fluid-saturated double porositymedium and a fluid-saturated single porous solid are investigated. Thefluid-saturated single porous solid is modeled with the classic Biot'stheory and the double porosity medium is described by an extended Biot'stheory. In double-porosity media with dual-permeability there exist threecompressional waves and a shear wave. The variation of the phase velocity andattenuation of the four bulk waves in double porosity media with frequencyis studied. It is shown that the peak values of attenuation curves of P-1and S waves emerge at about 1\,kHz, and the decay of P-2 and P-3 waves ismore prominent than other bulk waves in double porosity media. Assumingno relative displacement between the fracture pore fluid and the matrix solid at the interface, the expressions of the reflection andtransmission coefficients are obtained. The effects of incident angle andfrequency on the amplitude ratios of reflected and transmitted waves arediscussed. Numerical calculations show that the amplitudes of the reflectedand transmitted P-1 waves reach the maximum values at a certain incidentangle for a constant frequency, and reach the minimum and maximumvalues, respectively, for a constant incident angle. It is also found that theamplitudes of the reflected P-2, P-3 waves and transmitted P-2 wave are farless than those of the reflected and transmitted P-1, S waves.
2006, 38(3): 330-338. doi: 10.6052/0459-1879-2006-3-2005-333
Discussion on quality testing of frame structure embedded partially in soil
There are no ready-made methods to calculate the transient responseof pile foundations under a large number of structures in actualengineering, such as a frame structure embedded partially insoil under impact. The transient response of the framestructure embedded partially in soil may providea theoretical basis for designing the marine platform, oil-linetrestle and open type wharf under impact. The method of reverberation-raymatrix for frame structures embedded partially in soil is presented in thispaper. The velocity wave of the perfect and defective frame structure embeddedpartially in soil is studied with square impulses in axial, horizontal oroblique directions. It is found that the defects of pile foundations ofthe framestructure embedded partially in soil can be identified via axial velocityunder axial or oblique impulse.
2006, 38(3): 339-346. doi: 10.6052/0459-1879-2006-3-2004-455
Numerical simulation of thin film failure with MPM
Thin metallic films under compressive loads often fail dueto delaminating away from the substrates, which has been observed in manyexperiments and arouses many researchers' interests. Recently, much researchhas been conduced to model and simulate this physical phenomenon fromtheoretical and computational aspects and most of them are based on theconventional elastic stability theory and interfacial fracture mechanics(Shen 2004). In fact, the thin film failure often involves both localizationand decohesion processes and the evolution of localization in the film isquite possible is the reason of delamination (Chen 2003), which ischaracterized by the interaction between geometrical and materialinstabilities. To simulate such a multi-physical phenomenon, a carefuldesigned model should be constructed. Before localization occurs, thin filmsundergo usually elastoplastic deformations, and after that displacement jumpappears in some local areas, which can be modeled by a decohesion-basedmodel (Schreyer et al. 2002, Chen et al. 2003). It was pointed out that theinitiation of localization could be regarded as the transition fromcontinuous to discontinuous failure modes (Chen 1996), which can bedetermined via a bifurcation analysis of the acoustic tensor.The purpose of this paper is to simulate thin film failure phenomenon withthe combination of continuous and discontinuous constitutive models and theMaterial Point Method (MPM, Sulsky et al. 1994). The MPM is chosen as a basicmethod in this paper because of its simplicity and high performance inmodeling large deformation, impact/contact, blast, penetration and otherchallenging physical processes. At the beginning of the deformations of thesegment, associated von Mises elastoplasticity constitutive model is used.Whether a local failure will appear in the segment can be identified throughthe bifurcation analysis in the plastic deformation stage, namely,localization. If localization occurs, the decohesion-based model will beadopted to describe the motions of the material points in the local regionuntil separation emerges. Under the assumptions of the deformations aresmall in the evolution of material failure and no contact occurs betweenmaterial points in a short period after separation (these assumptions arereasonable because the film failure occurs very quickly and the case afterfailure will not be considered in this paper), a special algorithm will beused to describe the motion post separation. Also we adopt a silent boundarywith viscous damping stresses to improve the computational efficiency.Numerical results show that: (1) Shear band modes are predicted easily withusing the MPM and coupled models; (2) Thin film failure modes vary withdifferent load cases and structural sizes. Failure starts from the topsurface of the film in dynamic case but from the interface of the film andthe substrate in quasi-static one. The period between bifurcation andseparation occur in the former is longer than that in the latter; (3) Themethod coupled continuous and discontinuous models is appropriate for thesimulation of material failure problems; (4) The MPM is a robust andefficient method for material modeling.
2006, 38(3): 347-355. doi: 10.6052/0459-1879-2006-3-2004-429
Stress optimization for truss-like materials based on micropolar continuum representation
In this paper, the optimum stress distribution around a holeis investigated for LCMs materials with micropolar continuum representationto reduce the computational cost. Two classes of design variables, relativedensity and cell size distribution of the truss-like materials, are to bedetermined by optimization under the given total material volume constraint.The concurrent designs of materials and structures are obtained for threedifferent optimization formulations. In the first formulation, oneminimizes the stress around the hole; in the second formulation, oneminimizes the highest stress within the whole structure. Since the yieldstrength of truss-like materials depends on the relative materialdensity, we minimize the ratio of stress over the corresponding effectiveyield strength along the hole boundary in our third formulation, whichmaximizes the strength reserve, which seems more rational. Numerical resultsfor the three objectives validate the method proposed in this paper. Theinfluence of the ply angle (angle between the principle direction of materialand the axes of system's coordinate) on the optimum result is discussed.The dependence of the optimum design on finite element meshes is alsoinvestigated.
2006, 38(3): 356-363. doi: 10.6052/0459-1879-2006-3-2005-518
Topological optimization of continuum structure under the strategy of globalization of stress constraints
Since the stress is a local quantity, a large number ofconstraints must be considered in the topology optimization of continuumstructure. This increases the computational complexity of both theoptimization algorithm and sensitivity analysis. A strategy withglobalization of stress constraints is proposed based on von Mises'yield criterion. The localstress constraints of element are transformed into the global strain energy constraints ofstructure. Based on ICM (Independent, Continuous, Mapping)method, independent continuous topological variables are introduced; asuitable set of Filter functions of element with respect to weight,allowable stress and stiffness is selected. The optimal topology model ofcontinuum structure is established with weight as objective andsubjected to strain energy constraints with multiple load cases. The bestpath transmitted force in the multiple load cases is selected successfully.Furthermore, the dual quadratic programming is applied to solve theoptimal model of continuum. In addition, the present optimal model and itsalgorithm have been implemented by means of the MSC/Patran software platformusing PCL (Patran Command Language). Numerical examples indicate that themethod is efficient.
2006, 38(3): 364-370. doi: 10.6052/0459-1879-2006-3-2005-071
Experimental studies on external explosions during venting explosions
Experimental studies were preformed to investigate thecombustion and venting process of the methane/air mixture inside acylinder by the pressure transducers and the YA-16 high-speed shadowgraphsystems controlled by a synchronization unit. The pressure-time historiesand the sequences of high-speed shadowgraphs were obtained for the externalflow field, which can follow the development of the external explosions (the secondary explosions) in explosion venting. The experimentalresults show the typical characteristics of the external explosions. Thesecond pressure peak followed the first pressure peak formed by therupture shock wave. The shadowgraphs of the external flow field also showthe secondary explosion.
2006, 38(3): 371-380. doi: 10.6052/0459-1879-2006-3-2004-538
Strongly subfeasible sequential quadratic programming method of cable tension optimization for cable-stayed bridges
A practical optimization method(strongly subfeasible sequential quadratic programming method) of cabletension optimization for cable-stayed bridges is presented, witha model for nonlinear optimization programming to obtain the forcein cables of cable-stayed bridge, in which the bendingstrain energy of the beams and cable tower of the bridge is the objectivefunction, and the cable forces are the design variable, the stress inthe structureor the cable force is the constraint condition. In order to determine theprestressing force of the cables, the influence of various geometricalnonlinearities is considered, and the strongly subfeasible sequential quadratic programmingmethod is used to solve the program. This method is used to obtain the set ofoptimal cable tensions of a cable-stayed bridge using the spatial nonlinearfinite element program. The result of analysis shows that themethod is effective.
2006, 38(3): 381-384. doi: 10.6052/0459-1879-2006-3-2005-174
The methods of cluster synchronization in chaotic networks
With the development of biological sciences and communication engineering, a lot of phenomena about cluster synchronization arediscovered and investigated. However, because of the complexity of network, the theoreticalresults about cluster synchronization are very limited. In this paper,for the case that the number of every cluster is equal to m, a coupled weightnetwork is constructed, and a sufficient condition about thesynchronization with n clusters is obtained. The effectiveness of the methods is illustrated by an example.
2006, 38(3): 385-391. doi: 10.6052/0459-1879-2006-3-2005-312
Effects on f recombination in annular hypersonic low-temperature nozzle with different contraction curves
Annular Hypersonic Low-Temperature (HYLTE) nozzle arrayis the gain generator assembly in cylindrical chemical lasers. In thispaper, double cubic and Witozinsky curves are applied to the design of HYLTEnozzle convergent contour, and two kinds of HYLTE nozzles are designed. Based on 3D Navier-Stokes equations and the realizable k-\varepsilon model, the multi-species reacting flow field of the annular HYLTEnozzles is calculated. The numerical simulation results show that bothcontraction curves can prevent the separation of boundary layers, and thedifference of fluid dynamics parameters in the divergent section is negligible.However, with the nozzle designed by Witozinsky curve the fluid velocityis higher as compared with that designed by double cubic cueve, thus the recombination of F atomis slower, and the mass rate of F atom is about 5{\%} higher. It can beconcluded that cylindrical chemical laser with a convergent section nozzledesigned by Witozinsky curve works with a higher efficiency.
2006, 38(3): 392-397. doi: 10.6052/0459-1879-2006-3-2004-346
Effects of specimen size and apllied strain rate on the plastic flow of FCC metals
The simple shear molecular dynamics (MD) simulations areperformed on single-crystal copper blocks to analyze the size and strainrate effects on face-centered cubic (FCC) metals. It is found that the yieldstress decreases with the specimen size and increases with the strain rate.Based on the theory of dislocation nucleation, a modified power law isestablished to predict the scaling behavior of FCC metals, and it agreeswell with the numerical and experimental data ranging all spatial domainfrom nano-scale to macro-scale. In the atomistic simulation at differentapplied strain rates, a critical strain rate exists for the single-crystalcopper. Below it the yield stress is nearly insensitive to the strain rate,while above it the yield stress increases rapidly with increasing strainrate. Based on the results of the MD simulation, a strain rate model isintroduced for the plastic yield stress of FCC metals at nano-scale.
2006, 38(3): 398-406. doi: 10.6052/0459-1879-2006-3-2005-378
Fracture mechanics researches on piezoelectric materials based on a novel crack-tip hybrid finite element method
Singular electro-elastic fields surrounding crack-tips ofpiezoelectric materials can be expressed as \Sigma = \beta r^\lambdaF(\theta ), in which (r,\theta)is the polar coordinate system whose origin is set at the singular point;$\la$ is the eigenvalue; F(\theta)is the characteristic angular variation function; \beta is a coefficient tobe determined. The authors have developed a new {\it ad doc} finite element methodto solve eigenvalues $\la$ and characteristic angular variation functionsF(\theta)in paper [20]. To solve all the singular electro-elastic fields,coefficient$\beta $ should be determined. In this paper a new super crack-tip hybridelement model together with an assumed hybrid stress finite element model isdeveloped to solve the singular electro-elastic fields near the crack-tip ofpiezoelectric materials. The procedure is as follows: 1) an {\it ad doc} one dimensional finite element method is developedto determine the characteristic problems; 2) The numerical results of step 1are substituted into the generalized Hellinger-Reissner variationalfunctional, and then a finite element formulation of the super crack-tipelement is derived. This new model has two obvious advantages: One is to usenumerical solutions but not analytical solutions, the other is to avoid meshrefinement near the crack-tip. To verify efficiency and accuracyof the present model, a benchmark example on the singular electro-elasticfields, stress intensity factors and electric displacement intensity factorsfor a central crack in an infinite PZT5 panel is given. Interfacial crackproblem of PZT4-PZT5 panel is also considered as a further application ofthe new model. In all examples, three kinds of electric boundaryconditions [13], i.e., impermeable boundary condition, permeable boundarycondition and conducting boundary condition on the crack surfaces, areconsidered. This model can be used in more complicated fractureproblems, such as piezoelectric wedges, piezoelectric junctions or othercomplex geometries.
2006, 38(3): 407-413. doi: 10.6052/0459-1879-2006-3-2005-272
A new method for evaluating stress intensity factors of planar crack in 3-D solid
According to the inherent relation between the crackshape and the stress intensity factor (SIF) distribution along the crack front,a gradientless iterative method is proposed for obtaining the shape and thecorresponding SIF of mode-I planar crack with a given SIF distributionfunction under the condition of Linear Elastic FractureMechanics. Numerical examples for planar cracks in through-cracked andsurface-cracked plates with limited thickness and width are presented toshow the validity and practicability of the proposed method. The effects ofvarious SIF distribution functions on the shape and the corresponding SIF ofcracks are analyzed and discussed. The presented method is shown to bean effective alternative for the evaluation of SIFs and the prediction ofshape evolution for growing cracks.
2006, 38(3): 414-420. doi: 10.6052/0459-1879-2006-3-2005-189
Study of electro mechanical coupling system by codimension-3 dynamical bifurcation
The destabilizing oscillations, which are foundin the single-machine infinite-bus power system with series compensatecapacitors, are studied with bifurcating parameters r_{sl}, r_{f}, x_{c},using the theory of Dynamical Bifurcation. Under certainbifurcating parameters, three pairs of pure imaginary eigenvalues emergesimultaneously in the above system. For the multi-parameter high-codimensionbifurcation, Center Manifold Theory is applied to simplify the equations ofthe original system. For the simplified nonlinear system, its Normal Form isobtained by means of [7], the analytical solutions are obtained by usingthe Multiple Parameter Stability Theory, Harmonic Balance Method andUnification Technique. From an analysis of solutions, some complicatedphenomena in the system are revealed: Hopf bifurcations, 2-D Toribifurcations, 3-D Tori bifurcations, 4-D Tori bifurcations and even higherdimension bifurcations. The stability of solutions is discussed indetail, the stable conditions and regions are computed for each solution. Inaddition, a detailed numerical analysis is carried out to verify thetheoretical results. The numerical results are in good agreement with thetheoretical results. The study of this paper provides some theoretical guides forthe parameter design for the stability of power system and the accidentprevention of generators.
2006, 38(3): 421-428. doi: 10.6052/0459-1879-2006-3-2005-232
Stochastic bifurcation in a duffing-van der pol system
Stochastic bifurcation of a Duffing-van der Pol system subject to adeterministic harmonic excitation and bounded noise is studied by usingthe generalized cell mapping method with diagraphes. System parameters arechosen in the range of two co-existing attractors and a chaotic saddle,during their evolution. It is found that stochastic bifurcationmostly occurs when a stochastic attractor collides with a stochastic saddle.In our study, two kinds of discontinuous bifurcations are found according tothe abrupt increase or disappearance of the attractor when it collides withthe saddle in the basin interior or on the boundary. Our study also revealsthat the bifurcation value is different from that of D-bifurcation which isdefined by the change of the sign of the top Lyapunov exponent.
2006, 38(3): 429-432. doi: 10.6052/0459-1879-2006-3-2005-256