力学学报

A new understanding of the nonlinear eddy-viscosity distribution for the two-dimensional separation flows

Yancheng You, Dewang Liang

A study of turbulence modeling of 2D separation flows ispresented in the paper. First, experimental data analysis of Delery'stransonic bump showed the nonlinear development of the eddy viscosity in theseparation zone. Second, it is found that the eddy-viscosity decreases in the separation partand then enlarges during reattachment and relaxation process. Third, anonlinear correlation is extracted from the experiment data and thensuccessfully applied into the Balwin-Lomax model to form a mathematicallynew and simple algebraic turbulence model. The proposed model was evaluatedwith several typical separation flows, including low speed flow over plate,transonic flow, supersonic flow and the hypersonic flow. The numericalresults are compared with the experimental data and the results obtainedfrom other models to show that the nonlinear characteristics ofeddy-viscosity proposed in this paper is correct and suitable for 2Dseparation flows.

2009, 41(2): 145-154. doi: 10.6052/0459-1879-2009-2-2008-161

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Spectral vanishing viscosity for large-eddy simulations by spectral element methods

Zhijian Rong, Chuanju Xu

Spectral Vanishing Viscosity (SVV) method was initially proposed tostabilize the computations of hyperbolic conservation laws when higher orderspectral method was employed. Recently it was found that the SVV method canalso be applied to large eddy simulations (LES) of incompressible flowswithout sub-grid scales (SGS) modeling. In this paper, a new SVV-LES methodwas proposed using Legendre spectral element discretizations. A new operatorin variational form was introduced to replace the SVV operator and theviscosity operator in NS equations in order to implement the proposedSVV-LES method in a standard spectral element code with few modificationswithout significant increase of the computational cost. A large-eddysimulation case of the lid-driven cubic cavity flow at Reynolds numberRe=12000 was carried out. The simulation results showed good agreements withthe direct numerical simulation (DNS) or experimental results to demonstratethe efficiency and robustness of the proposed SVV-LES method. In addition,the impact of the SVV control parameters on the obtained results was alsoinvestigated.

2009, 41(2): 155-161. doi: 10.6052/0459-1879-2009-2-2007-446

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A new transition/turbulence model for the flow transition in supersonic boundary layer

Liang Wang, Song Fu

A new k-ω-γ transition/turbulence model is established toconsider the instability modes associated with the compressibility. Theparticular features of the new model are: (1) the fluctuating kinetic energyk includes the non-turbulent, as well as turbulent components modelled withthe stability analysis; (2) a function for the source term in γequation isdeveloped to trigger the transition onset; (3) it is strictly based on localvariables by introducing a new length scale normal to wall and compatiblewith the modern CFD methods. The present model was numerically proved to beapplied into the analyses of natural transition and bypass transition with awide range of Mach number.

2009, 41(2): 162-168. doi: 10.6052/0459-1879-2009-2-2007-578

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Research on relationship between vortex and sound of moderately under-expanded supersonic impinging jet

Xinguang Cui, Zhaohui Yao, Xiwen Zhang

This paper studies moderately under-expanded supersonicjet impinging on flat plate by using large-eddy simulation. A third-orderupwind compact difference and a fourth-order symmetric compact scheme areemployed to discretize the nondimensional axisymmetric compressibleFavre-filtered Navier-Stokes equations in space, while the third-orderRunge-Kutta method with the TVD property is adopted to deal with thetemporal discretization. The numerical results are first validated with theexperimental data of the classic impinging jet. The shock wave and vortexstructure with different scales in the flowfield, the wave traveling uponand reflecting back, and sound sources in different locations are acquiredin the simulation. The frequencies of the change of pressure and swirlingstrength in the shear layer at different position, pressure change on theimpinging plate, and the vortex merging in the jet shear layer are obtainedwith Fourier analysis. We found that the change of pressure and swirlingstrength in the shear layer, pressure change on the impinging plate, andvortex merging in the jet shear layer are associated with impinging tone.

2009, 41(2): 169-176. doi: 10.6052/0459-1879-2009-2-2007-524

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Numerical analysis of the validity of binary scaling parameterρ∞L in nonequilibrium flow

Ming Zeng, Zhenbin Lin, Jun Liu, Zhanghua Qu

In the present study, the validity of binary scaling parameterρ∞L in nonequilibrium flow isnumerically investigated with the charactristic time of chemicalreactions similarity, thermochemical state of the flowfield, radiationtransfer equation and similarity law for hypersonic flowfield. Thenumerical results show that the nonequilibrium dissociation process isdominant in the noqequilibrium region of the flowfield when theparameter ofρ∞L is below itscritical value. Therefore, it is validated that the parameter ofρ∞L can be applied in the simulationof the nondimensional variable distributions, wall heat transfer andionization properties in the whole flow field, and molecular radiationintensity at the stagnation point. In addition, the effectsof free stream velocities, the corresponding variables and flow regionson the validity ofρ∞L are also discussed.

2009, 41(2): 177-184. doi: 10.6052/0459-1879-2009-2-2007-636

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Finite element analysis of generalized thermoelastic problems in elastic media with temperature-dependent properties

Xiaogeng Tian, Tianjian Lu, Zhanjun Zheng

Finite element nonlinear equations based on Lord-Shulman(L-S) generalized thermoelasticity theory are derived for elastic media withtemperature-dependent properties and solved directly in time domain. A caseof an infinite medium with a cylindrical hole under thermal and mechanicalshock is analyzed with the developed method. The numerical results withtemperature-dependent properties show the fluctuation of heat conduction andthe efficiency of the time domain method in solving generalizedthermoelastic problems. Furthermore, it also shows that the influence oftemperature-dependent properties are more pronounced on mechanical responseof the media with the thermal shock loading, rather than the mechanicalshock.

2009, 41(2): 185-191. doi: 10.6052/0459-1879-2009-2-2008-278

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Elastoplastic finite element analysis of shear band with couple stress theory

Bin Ji, Wanji Chen, Jie Zhao

The problems of mesh dependence and mesh refinement areexhibited in shear bands computations of softening materials withconventional finite element method, and recognized with three numericalcases by a finite element software ABAQUS. Numerical analysis shows themesh-dependence problem does not occur for the thick-walled cylinderswithout shear bands. Couple stress theory is introduced to solve thesenumerical problems as a mesoscale non-local theory and the length scaleparameter \ell is investigated \ell in details. 18-DOF triangle couplestress element, which can pass C{0 - 1} patch test, is used for the abovethree numerical cases. Numerical results show that the finite elementmethods of mesoscale couple stress theory are suitable for the shear bandscomputations.

2009, 41(2): 192-199. doi: 10.6052/0459-1879-2009-2-2007-416

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Kinked growth of an embedded elliptic crack

Zhongjun Ren, Xianghe Peng, Ning Hu, Xiaohui Liu

Based on the deformation field in an infinite isotropicelastic matrix with an embedded elliptic crack and subjected to combinedtensile and shear stress, the energy release rate and a mixed-modefracture criterion are obtained with an energy balance approach. Furthermore, an analyticalapproach is suggested for the determination of the initial kink locationand direction of the embedded elliptic crack.

2009, 41(2): 200-206. doi: 10.6052/0459-1879-2009-2-2007-364

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A novel high-order spring-dashpot-mass boundary for cylindrical-symmetry wave motions in infinite domain

Xiuli Du, Mi Zhao

A novel high-order spring-dashpot-mass model (SDMM) forconvolution integral of force-displacement relationship in time domain isproposed and applied into the cylindrical-symmetry wave motions in infinitedomain as an artificial boundary condition (ABC). First, the high-order SDMMis dynamically and numerically stable, while low- and high-frequencyinstabilities occur under the displacement-type ABCs in term of space-timeextrapolation, such as multi-transmitting formula (MTF) and Pad\'{e}boundary. Second, SDMM has higher numerical accuracy thanthe stress-type ABCs, such as viscous boundary (VB) and viscous-springboundary (VSB). Third, SDMM is strictly doubly asymptotic at low- andhigh-frequency limits, and can be degenerated to VB or VSB. Fourth, SDMM canbe incorporated simply and easily into commercial FE software by using theinternal spring-dashpot and mass elements and time-integration solvers.Several numerical cases were carried out to validate the particular featuresof SDMM.

2009, 41(2): 207-215. doi: 10.6052/0459-1879-2009-2-2007-404

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Analytical method for testing mechanical properties of artificial ossicular

Wenjuan Yao, Wu Li, Xiaoqing Li

Transmission deafness is mainly caused by the pathologicalchanges of eardrum or ossicular chain. Artificial middle ear has beenapplied in clinical treatment of conductive hearing loss. In the presentaper, an analytical method for testing mechanical properties of artificialossicular was proposed. The relationship between forced vibrationdisplacement of tympanic membrane and activated sound pressure isestablished at the random time $t$ using variation principles based onartificial middle ear structure and its mechanical hypotheses, and thecontrolling vibration equations are derived. Furthermore, the analyticalsolutions of tympanic membrane and artificial ossicular are obtained byseparation of variables and Bessel function. The theoretical results agreewell with the documented experimental data and reflect the mechanism ofsound transmission. Better sound transmission efficiency in artificialmaterial is obtained with smaller density, rather than heavier density. Theproposed analytical method is efficient and convenient for vibrationanalysis of artificial middle ear and helpful for the optimization design ofartificial ossicular.

2009, 41(2): 216-221. doi: 10.6052/0459-1879-2009-2-2008-169

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Concurrent optimum design of components layout and connection in a structure

Heting Qiao, Shutian Liu

The conventional structural topology optimization is todesign the structure layout with fixed external loads. In addition, thelinkage model of components in a structure has a great influence on theoptimal topology design of structure layout due to the load transferfunction of components connection. This paper was focused onconcurrent optimum design of components layout and connection in a complexstructure. First, a new type of material model was introduced in theconnective domain and different material distributions represented differentconnections between components. Second, the design variable is about therelative material density of loading-carrying domain and connective domain.Third, a topology optimization based the proposed approach was developed aswell as the corresponding solving technique for designing structure andconnection distribution. The effectiveness of the present design methodologyand optimization scheme is demonstrated through numerical examples.

2009, 41(2): 222-228. doi: 10.6052/0459-1879-2009-2-2007-616

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Scattering of SH-waves and ground motion by an elastic cylindrical inclusion and a crack in half space

Zailin Yang, Peilei Yan, Diankui Liu

Scattering of SH wave and ground motion in an elastichalf space containing an elastic cylindrical inclusion and a crack locatedat any position and direction are studied using Green's function, complexfunction and multi-polar coordinate system. A suitable Green's function isfirstly constructed to obtain the fundamental solution of the displacementfield for a half space (surface) with an elastic cylindrical inclusion. Inaddition, an out-plane harmonic line--source-loading is at an arbitrarypoint in half space. Meanwhile, a crack located at any position anddirection can be built in half space with crack-division technique. Thedisplacement field and stress field are obtained with elastic cylindricalinclusion and crack, and the ground motion above the elastic cylindricalinclusion is also discussed.

2009, 41(2): 229-235. doi: 10.6052/0459-1879-2009-2-2007-459

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Dynamic calculation model and seismic response for the system of soil nailing and surrounding soil

Jianhua Dong, Yanpeng Zhu

A dynamic calculation model of soil nailing structure forslope protection is proposed in the present paper. The interaction betweensoil and soil nailing is treated as linear spring and damping system relatedto velocity. The inertia of the facing upon soil nailing is simplified as anequivalent concentrated mass. Excitation equations of vibration responseunder horizontal harmonic earthquake are established, and the analyticalsolutions are obtained for steady vibration. 3D nonlinear FEM with ADINAsoftware is carried out to verify the proposed model. The results show thatthe present model is safe and credible for the design of uniform soil slope.The calculation model provides a new approach for earthquake analysis andantiseismic design of the structure protected by soil nailing.

2009, 41(2): 236-242. doi: 10.6052/0459-1879-2009-2-2007-391

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Vertical vibration of pile in radially inhomogeneous soil layers

Dongying Yang, Kuihua Wang

Based on three-dimensional axisymmetric soil model, thevertical dynamic response of pile in radially inhomogeneous soil layers wasinvestigated with the effect of soil inhomogeneity. First, the soilsurrounding the pile was subdivided into arbitrary numerous annular zones,Second, the boundary conditions and continuum assumptions of displacementand stress between adjacent soil zones were developed. Third, the dynamicequilibrium equations of each soil zone are solved from outer to innersurrounding the pile. Third, the dynamic equilibrium equation of pile isalso solved and the analytical solutions in frequency domain andsemi-analytical solutions in time domain are obtained with the coupledcondition of pile-soil interface. The theoretical results reflect theinfluences of radial soil inhomogeneity on dynamic response of the pile andthe soil.

2009, 41(2): 243-252. doi: 10.6052/0459-1879-2009-2-2007-186

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Dynamic properties of a class of vibration with isolator with solid-and-liquid mixture

This paper describes a type of new vibration isolator withsolid-and-liquid mixture (SALiM) for vibration isolation and shock absorbing.The SALiM is composed of incompressible liquid and compressible elastic solidelements. Under shock or vibration loading, the incompressible liquid caninstantly pass the pressure onto all solid elements. The deformations of allsolid elements can greatly absorb and dissipate the energy of vibrations andshocks. In this paper, hollow rubber sphere was used as solid element in theisolator. Dynamic properties of hollow rubber sphere were investigated andthe nonlinear force-displacement relation of isolator was established. Inaddition, the motion equation of the isolator and its perturbation solutionare developed. The theoertical results show good agreement with the MTSexperimental data. Furthermore, the frequency response of the isolator isevaluated theoretically and measured on a test rig to show nonlinear dynamicbehaviors.

2009, 41(2): 253-258. doi: 10.6052/0459-1879-2009-2-2008-059

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Investigation of feedback loop in the impinging jet

Caijun Gan, Feng He, Zhaohui Yao, Jinglong Yang

It is important to take noise control of impinging jetsin many engineering fields, such as a short take-off and vertical landing(SVTOL) aircraft as well as air nozzle. In general, the impinging jet noiseis associated with the relationship between the impinging tone and the scaleof vortex structure, and the propagating direction of feedback waves. In thepresent study, the propagation direction of impinging tone was investigatedwith wavelet analysis and acoustic analogy. The velocity field of impingingjet was obtained by Particle Image Velocimetry (PIV) technique anddecomposed by means of biorthogonal wavelet transform. The frequencydistribution of discrete tone was obtained from its noise field. The resultsshow that large-scale structure can be viewed as ``coustic source'' ofdiscrete tone. Moreover, the direction of upstream-propagating feedbackwaves is about 60$^{\circ}$ oriented from the impinging plane and agrees withHo's experimental results.

2009, 41(2): 259-264. doi: 10.6052/0459-1879-2009-2-2007-460

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Effective mechanical properties of solid filled by hollow nanospheres

Bo Zou, Zixing Lu

The hollow nanospheres with scientific and technologicalinterest can be used as fillers in preparation of composite materials. Ingeneral, hollow nanospheres have more significant surface effect in filledmaterials than solid nanoparticles. The objective of this paper is toresearch the influence of surface/interface stress on the mechanicalbehavior of solid containing hollow nanospheres. Based on the generalizedself-consistent principle, a four phase model incorporatingsurface/interface stress effect is developed to derive the elastic fields ofthe solid under uniaxial loading and to obtain the closed-form solutions forthe effective elastic constants of the solid. In addition, the sizedependence of nanocomposites is also analyzed. The numerical results showthe difference from the classical results of the effective elastic constantsand the circumferential stress. Furthermore, the effective mechanicalproperties of the solid are dependent on the volume fraction, thesurface/interface properties, the outer radius and the wall thickness of thehollow nanosphere. The results of this paper are helpful to fabricate thecomposite materials with hollow nanospheres.

2009, 41(2): 265-273. doi: 10.6052/0459-1879-2009-2-2008-214

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Mechanical behavior of 2d periodic honeycombs under in-plane uniaxial compression

Bo Wang, Xiong Zhang, Shengli Xu

In the present study, polyvinylchloride (PVC) andpolypropylene (PP) ``based honeycomb structures with different inner celltopologies, such as Kagome, Triangle and Diamond, are fabricated with the``Strip slotting- Assembling-Welding'' technique. The quasi-static crushbehaviors under in-plane compression are experimentally investigated forKagome, Triangle and Diamond cell structures. The Charge Couple Devices(CCD) camera and digital image correlation (DIC) method are applied toobtain the the whole strain-field of the structures. Experimental resultssuggest that the energy absorption performance of Kagome structure issuperior to others with the same materials volume and structural sizes. Inaddition, a special rotation deformation mechanism of Kagome honeycombstructures is addressed. Moreover, numerical analyses of Kagome and Trianglecells under low velocity impact are studied in comparison with the resultsfrom the known Hexagonal cells. The numerical results show that the Kagomecells with the rotation deformation behavior have better energy absorptionperformance than triangle and hexagonal cells. Both experimental andnumerical results indicate great sensitivity of the local honeycombmorphology to deformation and energy absorption.

2009, 41(2): 274-281. doi: 10.6052/0459-1879-2009-2-2007-400

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Dynamic characteristics of electrostatically actuated mems under parametric excitations

Wenming Zhang, Guang Meng, Kexiang Wei

A dynamic model for thetime-variable-electric-capacity-type electrostatically actuatedmicro-electro-mechanical systems (MEMS) under parametric excitations ispresented with the effect of squeeze film damping. The harmonic balance (HB)method is applied to simulate the frequency response of this system underthe combined parametric and forcing excitations. The effects of the appliedvoltages and frequency ratios on the frequency responses of the system arediscussed. In addition, the nonlinear dynamic characteristics of this systemare studied with the control parameters of the amplitude of the alteringcurrent voltage, frequency ratio and squeeze film damping ratio. Thetheoretical results indicated the nonlinear dynamic characteristics,bifurcation and chaos of the electrostatically actuated MEMS underparametric excitations. Furthermore, it was also indicated that the effectof squeeze film damping on the dynamic characteristics of the system cannotbe ignored. This investigation provides an understanding of the nonlineardynamic characteristics of electrostatically actuated MEMS under parametricexcitations at micro-scale.

2009, 41(2): 282-288. doi: 10.6052/0459-1879-2009-2-2007-598

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