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2008 Vol. 40, No. 1

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Numerical simulation of granular flow in ``Chinese Fish Basin''
Heng Li, Qingdong Cai
As demonstrated in experiments, highly nonlinear reactions exist in the``Chinese Fish Basin'', which finally lead tothe surface discontinuity. It is difficult to deal with such problems innumerical simulation.In this paper, Molecular Dynamics Method is employed to simulatethree-dimensional granular flow in Chinese Fish Basin.we consider particles in the container from the viewpoint ofdiscretization, without the requirement of continuous media. When thenumber of particles in the simulation is large enough, the behaviors ofgranular flow are statistically equivalent to those of the continuous media.We first develop a parallel program based on message passinginterface(MPI), which can be used to simulate large scale granularflow. Interesting phenomena in the ``Chinese Fish Basin'' aredemonstrated with our simulation results. As a result of the excitationfrom outside, energy from the boundary spreads to theinterior of the basin in the form of wave, and dissipates quickly. Andparticles spout upward near the excited points, which is in consistentto the water spouting in the real Fish Basin.
2008, 40(1): 1-8. doi: 10.6052/0459-1879-2008-1-2006-525
Numerical simulation of unsteady vortical flows by a fast Lagrangian vortex method
Baoshan Zhu
In this paper, a fast Lagrangian vortex method is used tonumerically simulate the unsteady vortical flows. Discrete vortices are usedto model the vorticity generation, accumulation and transport mechanisms forunsteady separated flow fields. The velocity field is computed using ageneralized Biot-Savart formula combined with a fast summation algorithm.The discrete vortices are transported by the local velocity field and theviscosity diffusion is considered with a corrected vortex core spreadingmodel. The effectiveness of the present method was examined throughcomparing the numerical simulation of unsteady separated flows past acylinder and a NACA0012 airfoil with available experimental results.Specific results are provided for an impulsively started NACA0012 airfoil ata high angle of attack. Detailed unsteady behavior at discrete time stepsfor the early stages of the flow development as well as the fully developedflow pattern is presented and discussed.
2008, 40(1): 9-18. doi: 10.6052/0459-1879-2008-1-2006-048
Study on the dissipative effect of approximate riemann solver on hypersonic heatflux simulation
Zuowu Li
TVD-type schemes are frequently adopted in hypersonic flowsimulation. In construction of such kind schemes, approximate Riemannsolvers are fundamental. It is investigated through analysis and numericalexamination in the present paper that how the dissipative property ofapproximate Riemann solver affects the aerodynamic heating in numericalsimulation of hypersonic flow. Numerical examples show that approximateRiemann solver severely contaminates the boundary layer resolution. If exactRiemann solver adopted, the accuracy of numerical aerodynamic heating couldbe greatly improved and the grid cell size might be coarser by a factor of10.
2008, 40(1): 19-25. doi: 10.6052/0459-1879-2008-1-2006-359
The interaction between multiple underwater explosion bubbles near free surface
Aman Zhang, Xiongliang Yao
A boundary integral method is adopted to simulate thebubble motion in the fluid field on the assumption that the fluid field isinviscid, irrotational and incompressible. A corresponding three-dimensionalcomputation program is exploited and the calculated results agree well withthe experimental data. The interaction between multiple bubbles near thefree surface including in-phase and out-of-phase bubbles is simulated withthe program presented here. From calculation it's found out that the bubbleperiod increases along with the decrease in the distance between bubblecenters because of the depression effect among multiple bubbles and theeffect is more evident especially for out-of-phase bubbles. The depressioneffect exists between all bubbles no matter whether there is a free surfaceor not. There are great differences on the dynamic behavior of in-phasebubble coupling and that of out-of-phase bubble coupling due to thedepression effect. These phenomena can provide reference for the futureresearch on the power of underwater explosion bubble induced by multiplecharges exploding simultaneously or continuously.
2008, 40(1): 26-34. doi: 10.6052/0459-1879-2008-1-2007-132
Finite element simulation of leaky lamb wave at fluid-solid interfaces excited thermoelastically by pulsed laser
Yan Zhao, Zhonghua Shen, Jian Lu, Xiaowu Ni
Based on the variation principle, the corresponding finite element equationsfor the thermoelstic and heat conduction equations are obtained. The finiteelement equations for the fluid-solid interface waves propagated along thewater-aluminum, air-aluminum interfaces are solved by using the numericalmethod of integration, and then the transient waveforms excitedthermoelastically by a pulsed laser line source are obtained. The resultsshow that the leaky Lamb wave exists at the liquid-solid interface and alsoexists at air-solid interface; in reverse to the Lamb wave, the S_0 modeof leaky Lamb wave is antisymmetric, and the A_0 is symmetric; due tothe difference of the two kinds fluid-solid interfaces, the waveforms andamplitudes of the two leaky Lamb waves are different.
2008, 40(1): 35-39. doi: 10.6052/0459-1879-2008-1-2006-065
Effects of thermal environments on the thermal shock resistance of ultra-high temperature ceramics
Weiguo Li, Daining Fang
In the present study, the temperature-dependent thermal shock resistances ofUltra-High Temperature Ceramics (UHTCs) were measured based on the currentevaluation theories of thermal shock resistance parameters, since thematerial parameters of the UHTCs are very sensitive to the changes oftemperature. The influence of some important thermal environmentparameters,such as the surface heat transfer coefficient, heat transfercondition, thermal stress decay modulus and initial temperature of thethermal shock,on the thermal shock resistance parameters, criticaltemperature of rupture and critical temperature difference of rupture of theUHTCs were studied considering the effects of temperature on the physicaland mechanical properties of the UHTCs within the range of thermal shocktemperature. The results show that thermal shock behaviour of the UHTCs isstrongly affected by the thermal environments.
2008, 40(1): 40-45. doi: 10.6052/0459-1879-2008-1-2007-081
Multiple three-dimensional cracks in fully coupled electromagnetothermoelastic multiphase composites
Bojing Zhu, Taiyan Qin
This work presents hypersingular integral equation methodto analyze the multiple three-dimensional cracks problem in fully coupledelectromagnetothermoelastic multiphase composites under extendedelectro-magneto-thermo-elastic coupled loading through intricate theoreticalanalysis and numerical simulations. First, the problem is reduced to solvinga set of hypersingular integral equations. Analytical solutions for theextended singular stresses, the extended stress intensity factors, theextended strain energy factors and the extended energy release rate near thecracks front are obtained, respectively. Then, the numerical method for thehypersingular integral equations subjected to extended coupled loads isproposed. Finally, numerical solutions of the extended stress intensityfactors and the extended strain energy factors for two interactingthree-dimensional cracks are given, and the effect of cracks orientation,interaction and shielding is discussed.
2008, 40(1): 46-58. doi: 10.6052/0459-1879-2008-1-2007-273
Accuracy controllable time-domain difference approach to calculate foundation resisting force
Xiuli Du, Jianfeng Zhao, Qiang Han
Interaction forces between foundation and structure isone of key problems in nonlinear dynamic response analysis of structuresaccounting for soil-structure dynamic interaction. Currently there are twokinds of method dealing with it: one is the direct integrity analysisapproach, the other is time-domain substructure approach. Because of farless computational cost comparison to the former, time-domain substructureapproach is very important in engineering field. The fact that foundationimpedance complexly vary with frequency makes the calculation of time-domainfoundation resisting force time-consuming. To simplify the calculation oftime-domain foundation resisting force, many lumped-parameter models havebeen proposed. Lumped-parameter model reflects the singular component offoundation impedance which is not square integrable and correspond tosimultaneous effect. Nevertheless the regular component can't be reflectedaccurately, which correspond to time-delay effect and be square integrable.Time-domain recursive model proposed by Safak (2006) used for representingtime-domain foundation resisting force can simulate the regular component offoundation impedance. But the whole essential of foundation impedance cannot be reflected in this model because the corresponding filter function hasintrinsically limitation at Nyquist frequency. Thus, time-domain foundationresisting force can not be simulated accurately. Combining lumped-parametermodel and time-domain difference recursive filter model, a time-domaindifference approach of accuracy controllable foundation resisting force isproposed. Numerical examples results demonstrate that the proposed procedurecan perfectly fit the frequency dependent impedance in interested frequencyband.
2008, 40(1): 59-66. doi: 10.6052/0459-1879-2008-1-2006-162
Effect of track support failure on dynamic response of tangent track
Xinbiao Xiao, Xuesong Jin, Zefeng Wen
In order to investigate the effect of track supportfailure on dynamic response of tangent track, a vehicle-track couplingdynamic model is established, in which the rails are assumed to beTimoshenko beams resting on the discrete sleepers. The failure situation oftrack components under the tangent track is simulated by the abrupt changesof track stiffness along the track. The effect of the discrete sleepersupports on the coupling dynamics of the vehicle and track is taken intoconsideration by the excitation model of moving sleeper supported. As to theinteraction of wheel and rail system, the creepage formulas of wheel/railrolling contact are deduced, in which the lateral, vertical and torsionalmotions of rail are taken into account. The normal forces of wheel/rail arecalculated by Hertzian contact theory and the creep forces of wheel/rail inrolling contact are decided by the nonlinear creep theory of Shen et al. Themotion equations of the vehicle/track coupling system are solved with thenew explicit integration method. Effect of zero, two, four and six tracksupports in failure situation on tangent track dynamic response is analyzedand evaluated. The numerical results indicate that track support failuregreatly affects dynamic response of tangent track. With the increasing offailure number, the wheel/rail normal forces, displacement and accelerationof track components increase quickly, which will deteriorate the track.
2008, 40(1): 67-78. doi: 10.6052/0459-1879-2008-1-2006-236
Model and application of uniformity expansion in randomized structure of intravascular stent
Jie Yang, Nan Huang, Quanxing Du
The expansion of intravascular stent may be considered as an extension in instable serial structure from the viewpoint of mechanics. Therandomization of the width and thickness of a stent will hare greatinfluence on the uniformity expansion in the instable serial structure. Inthis paper, a mathematical model to describe that problem is establishedon the basis of randomized unstable serial structure. The concept, methodand probability calculation formula of uniformity index are proposed.Regarding the serial structure made up of two expanded units, a detailedstudy is carried out on the influence of the random variation of beam thicknesson expansion uniformity indexes. We obtain the uniformity index probability'srelationships with beam thickness random variation, load variation andhardening coefficient variation. The research shows that materialharding coefficient has great effects on uniformity index when the totalexpansion displacement remains constant. The serial expansion theory ofrandom unstable structure provides an important guide to the design of new-typeintravascular stent.
2008, 40(1): 79-85. doi: 10.6052/0459-1879-2008-1-2006-646
Time-varying optimal control via canonical transformation of hamiltonian system
Zhigang Wu, Shujun Tan
This paper presents a unified canonical transformationand generating function approach, including associated numerical algorithms,for linear time-varying optimal control problems with various terminalconstraints. Generating functions are employed to find the optimal controllaw by solving Hamiltonian two-point-boundary-value problems. Thetime-varying optimal control laws constructed by the second type generatingfunction do not have infinite feedback gain at terminal time, which isdifferent from other existing solutions. Motivated by practical design oftime-varying optimal control systems, a structure-preserving matrixrecursive algorithm is proposed to solve coupled time-varying matrixdifferential equations of the generating function; derivation of therecursive algorithm is based on symplectic formulation of canonicaltransformation. To preserve symplectic structure of matrices in therecursive computation, state transition matrices of the Hamiltonian systemare calculated by Magnus series. In fact, the canonical transformation andgenerating function method leads to a geometric perspective to thedesign and computation of optimal control systems.%control systems synthesis and computation.
2008, 40(1): 86-97. doi: 10.6052/0459-1879-2008-1-2007-235
Mechanism analysis of delayed nonlinear vibration absorber
Yanying Zhao, Jian Xu
In a two-degree-of-freedom system with delayed nonlineardynamical vibration absorber, the method of multiple scales is employed tostudy its performance of vibration suppression. The amplitude-delay responsecurves of the primary system are obtained. The results show that for thedelayed nonlinear dynamical vibration absorber, the gain and the delay maybe tuned to control the vibration of the primary system. With the delayvarying for a fixed gain, it is easy to see that the vibration can besuppressed at some values of the delay under the conditions of the system isstable. The ``maximum vibration suppression point'' may be predicted atwhich the amplitude of the primary system is the minimum for a fixed gain.For different values of the gain, the amplitudes of the primary system aredifferent at their ``maximum vibration suppression point''. Correspondingly,the optimum values of the gain and the delay may be obtained to suppress theamplitude of the primary system to a minimum. The results of this paper showthat the vibration of the primary system can be suppressed about 90{\%} whenthe optimum values of the gain and the delay are obtained by comparing withthe nonlinear dynamical vibration absorber. All the analytical predictionsof this paper are in good agreement with the numerical simulation.
2008, 40(1): 98-106. doi: 10.6052/0459-1879-2008-1-2007-078
Numerical modeling of human ear for sound transmission
Yingxi Liu, Sheng Li, Xiuzhen Sun
A complete finite element model of the human ear canprovide better understanding of sound transmission. In this paper, athree-dimensional finite element model of the human ear is established,including the external ear canal, tympanic membrane, ossicular bones, middleear suspensory ligaments/muscles, and inner ear fluid. This model isconstructed based on a complete set of computerized tomography sectionimages of a healthy volunteer (right ear) to describe the complicatedstructures and boundary conditions. The validity of this model is confirmedby comparing the model-predicted motion of the tympanic membrane and stapesfootplate with published experimental data. The acoustic-structural coupledfinite element analysis among the ear canal, middle ear ossicles and innerear fluid is conducted and employed to predict the effects of ear canal,incudostapeblial joint andcochlear fluid on sound transmission mechanics. The results revealed thatthe final model is reasonable in predicting the ear acoustic mechanicalproperties.
2008, 40(1): 107-113. doi: 10.6052/0459-1879-2008-1-2007-051
Direct numerical simulation of a compressible transitional mixing layer with combustion chemical reactions
Wenbo Miao, Xiaoli Cheng, Qiang Wang
A fifth-order upwind/sixth-order symmetriccompact hybrid difference scheme coupled with a third-order explicitRunge-Kutta time-marching method is used as a direct numerical simulationalgorithm to investigate a three-dimensional temporally-developingcompressible plane free shear mixing layer with H$_{2}$/O$_{2}$ non-premixedcombustion. The reacting mixing layer with product formation and energyrelease is perturbed by a pair of conjugate oblique waves, and henceexperiences an instable transitional evolution. At the beginning oftransition, some well-known large scale coherent structures, such as${\it\Lambda}$ vortex and horseshoe vortex, are found, and a three-dimensionalparing phenomenon of two horseshoe vortices following flow instabilities isalso revealed. Furthermore, these large scale structures are approximatelysymmetric. At the last stage of the development of this flow, large scalestructures break down continuously, and small scale structures gradually getdominant. The reacting mixing layer finally behaves very similar toturbulence and shows clear asymmetry. On the analogy of the stability theoryfor incompressible boundary layer, the large scale structures obtained hereare due to a subharmonic secondary instability mechanism, which is wellknown as Herbert type secondary instability.
2008, 40(1): 114-120. doi: 10.6052/0459-1879-2008-1-2007-296
Electro-magnetic control of hydrofoil wake
Yaohui Chen, Baochun Fan, Benmou Zhou, Zhihua Chen, Hui Zhang, Hongzhi Li
An actuator, consisting of a specific array ofalternating stripwise electrodes and permanent magnets, will generate awall-parallel Lorentz force as submerged in a weakly conducting fluid, whichinfluences the flow in the boundary layer. The experiments have beenconducted in a rotating annular tank filled with a copper sulphate(CuSO$_4$)electrolyte, to investigate the flow around a hydrofoil and itselectromagnetic control. To reveal the transient behavior of controlled flowfrom the initial to the final steady state, the flow fields are visualizedby potassium permanganate (KMnO$_4$) used as a marker and record by a camera.To verify the influence of flow control on the lift and the drag of ahydrofoil, force measurements have been carried out by strain gages attachedto a fixed beam to which the hydrofoil is suspended.It has been shown from the experimental results that, for the absence of theLorentz force, there exist two kinds of vortex, i.e. shedding on the leadingedge and the trailing edge respectively, which affect each other and finallyleave the leeward surface of the hydrofoil periodically to form a wake. Theinfluences of the Lorentz force on the flow around the hydrofoil are justsomething like the variations of the attack angle. The Lorentz force instreamwise direction can suppress the flow separation and the wake, ashappened in the cases with a small or zero attack angles. In contradiction,for the reversed Lorentz force, the vortex street on the leeward surface ofhydrofoil is introduced, as happened in the cases with a big attack angle.
2008, 40(1): 121-127. doi: 10.6052/0459-1879-2008-1-2006-015
Convergence control of probabilistic structural design optimization based on performance measure approach
Ping Yi, Dixiong Yang
The evaluation of probabilistic constraints inProbabilistic Structural Design Optimization (PSDO) can be carried out usingthe recently proposed performance measure approach (PMA). The advancedmean-value (AMV) method is well suitable for PMA due to its simplicity andefficiency. However, when the AMV iterative scheme is applied to search forthe minimum performance target point for some nonlinear performancefunctions, the iterative sequences could fall into the periodic oscillationand even chaos. Then both PMA Two-level and PMA with SAP (SequentialApproximate Programming), which are based on this evaluation ofprobabilistic constraints, could yield convergent failure. In the presentpaper, the convergence control of AMV iterative procedure is firstimplemented by using the stability transformation method of chaos feedbackcontrol. The unstable fixed points embedded in the periodic and chaoticorbit are stabilized and the expected stable convergent solutions areobtained. Once the evaluation of probabilistic constraints can be carriedout successfully, the design optimization is performed by PMA Two-level orPMA with SAP. The numerical results demonstrate that the convergence controlusing stability transformation method is effective and PMA with SAP is moreefficient.
2008, 40(1): 128-134. doi: 10.6052/0459-1879-2008-1-2007-195
Time-optimal deployment of a tethered subsatellite based on differential inclusion
Hao Wen, Dongping Jin, Haiyan Hu
This paper presents the nonlinear time-optimal controlfor the three-dimensional deployment process of a tethered subsatellitemodel, which also takes tether elasticity and the mission-relatedstate-control constraints into consideration. Instead of the commonly usedstate-space model, a second-order differential inclusion formulation isexploited in this work to achieve a significant reduction of the number ofsystem variables. The optimal control is solved by discretizing the optimalcontrol problem based on a direct algorithm, and numerically solving theresulting large-scale optimization problem via an NLP (nonlinearprogramming) solver. The case studies in the paper well demonstrate theperformance of the proposed strategy.
2008, 40(1): 135-140. doi: 10.6052/0459-1879-2008-1-2007-063