力学学报

Gas flows through micro-pipes with different cross-section shapes

Jianzheng Jiang, Qing ShenJing Fan

The information preservation (IP) method and the direct simulation MonteCarlo (DSMC) method are employed to investigate gas flows throughmicro-pipes with the circular, semi-circular, hexagonal or rectangular crosssections, respectively, as an important issue in thedesign and optimization of MEMS devices. The IP and DSMC results agree wellwith each other, and are compared with the numerical solutions of the BGKmodel equation given by other researchers. For low Mach number casesin micro-pipe flows, the IP method demonstrates the statistically convergentefficiency superior to DSMC. The investigation shows that the cross-sectionshapes of micro-pipes considerately affect their mass flow rates. A relationbetween the mass flow rate and the equivalent Knudsen number for circular,semi-circular, hexagonal and rectangular cross sections is suggested throughfitting the IP and DSMC results.

2007, 23(2): 145-152. doi: 10.6052/0459-1879-2007-2-2005-377

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The study of flow transition process induced by oblique wave instability in a supersonic flat-plate boundary layer

The spatial large eddy simulations of the transition process and thefull turbulence in a supersonic flat-plate boundary layer at a free-streamMach number M_\infty = 4.5 and a Reynolds number Re = 10000 arecarried out by solving the three-dimensionalcompressible Favre-filtered Navier-Stokes equations with a hybrid method of a fifth-order upwind compact difference anda sixth-order symmetric compact difference. The compact storagethird-order explicit Runge-Kutta method is applied for the time-integration. Thesub-grid scales are formulated according to the modified Smagorinskyeddy-viscosity model. Based on the linear stability theory, a pair of themost unstable oblique first mode disturbances is imposed on the inflowboundary and the evolution of flow from laminar, transition to fullturbulence, is simulated successfully. The instant and statistical parametersare obtained, and numerical results show a good agreementwith the relevant flat-plate boundary layer theory. Especially the linearand weakly nonlinear growth of disturbance, the appearance of staggered$\Lambda $-vortex pattern, and the evolution of $\Lambda $-vortex intohairpin vortex are consistent with related findings in literature.

2007, 23(2): 153-157. doi: 10.6052/0459-1879-2007-2-2005-301

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Local structure and its absolute scaling law of the most intermittency in turbulence signals

Qiang Fu

In this paper, the most intensive structure proposed firstin Hierarchical-Structure (H-S) model is further studied, and it isconcluded that there exists an absolute scaling law for this structure,and the statistical absolute scaling behavior is only produced by the local andstrong intermittence structure. In a statistical theory, it is essentialto consider the local fluid structures, especially, the strong intensivestructures.

2007, 23(2): 158-161. doi: 10.6052/0459-1879-2007-2-2005-531

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A study on disturbances evolution in supersonic mixing layer with spanwise curvature

Lin Qian, Jisheng Luo

In order to enhance the mixing efficiency, the effects of spanwise curvature, spanwisevelocity and Mach number are studied by the method of DNS. When the spanwisevelocity is fixed, the larger the spanwise curvature, the larger growth rate of the 3-Ddisturbances will be for the 3-D compressible mixing layer with thespanwise curvature. The increase ofspanwise velocity can also enhance the ability of blending when the spanwise curvature is not zero.The spanwise vorticity produced by high frequency disturbance wave will break down and stretchin the course of evolution but this phenomenon is not found in the lowfrequency disturbance cases. With a high Machnumber, the most instable disturbance still has a large growth rate for the mixing with spanwisecurvature and velocity. Therefore, it is an effective method for enhancing the mixing.

2007, 23(2): 162-170. doi: 10.6052/0459-1879-2007-2-2006-156

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Ignition characteristics of the shock wave focusing in combustive gases

Honghui Teng, Chun Wang, Bo Deng, Zonglin Jiang

The two-dimensional plane shock wave focusing with the parabolicreflectors in combustive gases is numerically simulated, and the ignitioncharacteristics of the detonation initiation are investigated. In thestoichiometric hydrogen/air mixtures under 20\,kPa, the shock wave focusing withthe incident Mach number 2.6$\sim$2.8 will generate two ignition zones. One isderived from the reflection shock convergence; the other is derived fromthe high temperature zone, which is induced by Mach Reflection on theparabolic reflectors. Then the focusing shock wave with the incident Mach number2.6$\sim$2.8 will induce the detonation initiation via deflagration-to-detonationtransition. The initiation points locate on the tube wall, the parabolicreflector and near the second ignition point, separately. The correspondinginitiation mechanisms are the shock wave reflection on the tube wall, the shockreflection on the parabolic reflector, and the interaction of theignition-induced shock and the deflagration induced by the second ignitionzone, respectively. Different ignition and detonation initiation processesresult in various wave systems in the flow field, and lead to different wavedynamic processes of the detonation wave propagation.

2007, 23(2): 171-180. doi: 10.6052/0459-1879-2007-2-2005-578

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Multi-scale energy transfer in near-wall region of turbulent channel flow

Hongtao Jia, Chunxiao Xu, Guixiang Cui

The multi-scale energy transfer in near-wall turbulence is studied byorthonormal wavelets and the database of channel turbulence obtained bydirect numerical simulation. By a multi-scale decomposition of the flow fieldin streamwise and spanwise directions, the difference of energy transferbetween these two directions is investigated. It is found that the energy transferin the streamwise direction is dominated by back scatter, while in thespanwise direction, there is an obvious forward transfer, which is notconfined in the viscous sublayer only like that in the streamwise direction.With a lager filter width, the forward energy transfer in the spanwise directionbecomes dominant.

2007, 23(2): 181-187. doi: 10.6052/0459-1879-2007-2-2006-136

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Numerical study on mass exchange characteristics of cavity flameholders for scramjet applications

Mingbo Sun, Jianhan Liang, Zhenguo Wang

Mass exchange characteristics of cavities for scramjetapplications within a supersonic cold flow are investigated.Calculations are carried out using the hybrid RANS/LES method to predict unsteadystate flowfields. The key cavity parameters include cavityaft wall angle and cavity length to depth ratio (L/D). The hybrid model captures the large scale unsteadiness and reveals the evolvementof cavity free shear layer. For pressure fluctuation spectra, thetheoretical prediction agrees quite well with some calculated data.The hybridRANS/LES data suggest that both the cavity shape and the size have a significanteffect on the mass exchange processes. Cavities with larger $L/D$ have a longerresidence time. For cavities with smaller L/D, the residence time reduces as theaft wall angle decreases. The opposite is true for cavities with larger$L/D$. These calculated results provide some new insight for cavityflamehoder design.

2007, 23(2): 188-194. doi: 10.6052/0459-1879-2007-2-2006-187

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Study on propagation of nonlinear flexural waves in the beams

Zhengfeng Liu, Xiaohong Wang

By means of Hamilton variational principle, a nonlinearflexural wave equation for beams taking account of the geometricnonlinearity caused by the large deflection and the dispersive effectof rotational inertia in the beams is derived in this paper. Results ofqualitative analysis of the nonlinear evolution equation show that for theequation there exists homoclinic or heteroclinic orbits on the phase plane, whichcorrespond to a solitary wave or shock wave solution, respectively. Nonlinearflexural wave equation is solved by the Jacobi elliptic functionexpansion method.Two kinds of exact periodic solutions of the nonlinear equations areobtained, that is, the shock wave solution and the solitary wave solution.The necessary condition for existence of exact periodic solutions, shock solution andsolitary solution is discussed, which is consistent with thequalitative analysis. By using the reductive perturbation method, two kindsof nonlinear Schr\"{o}dinger equations are derived from the nonlinear flexuralwave equation. Taking into account of large deflection and rotaryinertia of beams,the existence of NLS solitary wave in the beams is possible in theory.

2007, 23(2): 195-201. doi: 10.6052/0459-1879-2007-2-2006-365

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Experimental study on particle-laden turbulent reacting flow in a combustor with staged air injection

Xiaochuan Zheng, Shusheng Yuan, Jian Zhang, Hongtao Zhang, Lixing Zhou

The Three-Dimension Laser Particle Dynamic Analyzer (PDA) wasused in the present experimental study. The instantaneous gas andparticle velocities were measured for the particle-laden turbulent reactingflow in a combustor with staged air injection. Theinstantaneous gas velocity was also measured. The distributions of time-averaged axial and tangential velocities,root mean squares of axial and tangential fluctuating velocities, andsecond-order correlation moments of axial and tangential fluctuatingvelocities were obtained both for the gas and particle phases and for thesingle gas phase.

2007, 23(2): 202-209. doi: 10.6052/0459-1879-2007-2-2005-545

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Influence of cavitator parameters on formation and development of supercavity

Liping Jia, Kaiping Yu, Jiazhong Zhang, Cong Wang, Yingjie Wei, Haibin Wang

Based on the way how to form supercavity, a series ofprojectile experiments and moderate-speed tunnel experiments were carriedout to study the formation and development of the natural and ventilatedsupercavities in this paper. The processes of forming supercavities were recordedand discussed. The influence of cavitator parameters on the critical cavitationnumber and critical ventilation coefficient was analyzed. Qualitativefeatures of the supercavity size change were obtained. It is shown that thecavitator diameter and coutour have a similar influence on thenatural and ventilated supercavity sizes. Supercavity size increases withcavitator diameter and the formation of supercavity for a bluntcavitator is easier than for a cone cavitator under the same conditions.A cavitator of relatively small diameter might not be able to form aventilated supercavity, mainly because the natural cavitation number isnot small enough. Furthermore, the research shows that the cavitator diameter has animportant effect on the fineness ratio of the ventilated supercavity, whichis not the same as the natural supercavity. Finally, the perspective futureresearch on cavitators is discussed.

2007, 23(2): 210-216. doi: 10.6052/0459-1879-2007-2-2005-584

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Study on the surface deformation in buoyant-thermcapillary convection using the optical bar lines method

Feng Yuan, Li Duan, Qi Kang

An optical diagnostic system with image processor isdeveloped for study of the kinetics of Buoyant-Thermcapillary Convection.The convection, surface deformation in a rectangular cavity withsidewalls of different temperatures are investigated. Thesurface deformations are calculated with the correlation analysis. Thepresent experiment demonstrates that the surface deformation is relatedwith the temperature gradient, surface tension and buoyancy.

2007, 23(2): 217-222. doi: 10.6052/0459-1879-2007-2-2005-523

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The quasi-solid-liquid phase transition of non-uniform granular materials and their constitutive equation

Shunying Ji

Granular materials can be regarded neither as solid media, nor as liquid media,but behave as solid or liquid media under some conditions, and eventhere is a quasi-solid-liquid phase transition. Granular materials can bemodeled with a plastic constitutive model or the kinetic theory ofmolecular dynamics in the quasi-static or fast flow state, respectively.However, in the quasi-solid-liquid phase transition, the constitutive modelis still an open problem. To develop an effective constitutive model forgranular materials in the phase transition, the basic dynamiccharacteristics of granular materials should be determined in details.In this study, a simple shear flow of granular materials is simulated witha 3D discrete element model (DEM) in various concentrations and shear rates,and the phase transition between fast flow and quasi-static flow isobtained. Since the granular materials are normally of various sizes undernatural conditions, the particles of granular flow modeled here are in amulti-size state. Based on the simulated results, it is found that themacro-stress is independent of shear rate in the solid phase, and is a linearfunction of the square of the shear rate in the liquid phase. In thequasi-solid-liquid phase transition, the macro-stress shows a complexcorrelation with the shear rate. Based on the simulated variables ofmacro-stress, contact time number, coordination number, and particle numberof clusters, etc., the basic characteristics of granular materials in thephase transition are analyzed in details. The effective frictioncoefficient, net contact time number and coordination number at some medium concentrations can be treated as thephase transition point. Adopting various friction and restitutioncoefficients, the granular systems still have apparent quasi-solid-liquidphase transition, but their transition points are different.Based on the dynamic behaviors of granular materials in different phases,especially from the relationship between macro-stress and shear rate, anexponential constitutive model for multi-size granular materials isdeveloped, and some parameters are determined based on the simulation data.With the physical experimental results measured in a shear cell, the form ofthis constitutive model, i.e. the relationship between macro-stress andshear rate in different flow states, is validated.

2007, 23(2): 223-237. doi: 10.6052/0459-1879-2007-2-2005-605

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Study on propagation of nonlinear flexural waves in the beams

Zhifang Liu, Tiefeng Wang, Shanyuan Zhang

By means of Hamilton variational principle, a nonlinearflexural wave equation for beams taking account of the geometricnonlinearity caused by the large deflection and the dispersive effectof rotational inertia in the beams is derived in this paper. Results ofqualitative analysis of the nonlinear evolution equation show that for theequation there exists homoclinic or heteroclinic orbits on the phase plane, whichcorrespond to a solitary wave or shock wave solution, respectively. Nonlinearflexural wave equation is solved by the Jacobi elliptic functionexpansion method.Two kinds of exact periodic solutions of the nonlinear equations areobtained, that is, the shock wave solution and the solitary wave solution.The necessary condition for existence of exact periodic solutions, shock solution andsolitary solution is discussed, which is consistent with thequalitative analysis. By using the reductive perturbation method, two kindsof nonlinear Schr\"{o}dinger equations are derived from the nonlinear flexuralwave equation. Taking into account of large deflection and rotaryinertia of beams,the existence of NLS solitary wave in the beams is possible in theory.

2007, 23(2): 238-244. doi: 10.6052/0459-1879-2007-2-2006-165

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An investigation of sub-pixel displacements registration algorithms in digital image correlation

Bing Pan, Huiming Xie, Fulong Dai

The sub-pixel registration algorithm is considered as a keytechnique to improve displacement measurement accuracy in a digital imagecorrelation. Various types of sub-pixel registration algorithms have beendeveloped. However, few quantitative researches have been reported toevaluate their performances. This paper investigates three types of mostcommonly used sub-pixel displacement registration algorithms in terms ofregistration accuracy and computational efficiency using computer-simulatedspeckle images and real experimental images. A detailed examination of theperformances of each algorithm reveals that the Newton-Rapshon Method isthe most accurate and stable. Accordingly, it is highly recommended touse this method in real applications.

2007, 23(2): 245-252. doi: 10.6052/0459-1879-2007-2-2006-053

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An improved level set method for structural topology optimization

Jianhua Rong

In practice, a continuum structure is usually designed with tractions applied to a part of its boundary and prescribeddisplacements imposed on other part of the boundary. The design domains of practicalstructures are often limited and significantly affect the final optimaldesign of the structures. Structural boundaries under tractions andprescribed displacements should be treated as a subset of zero level set inthe level set methods. However, structural optimization methods based onlevel set movements do not consider these realistic requirements. Toovercome the limitations of current level set methods and the stopping issueof structural boundary movements, this paper constructs new normal speedsrequired by level set movements. And the convergence characteristics of structuraltopology optimization series solutions obtained by the proposed normalspeeds are studied. Then, we implement the algorithm of the objective functionfor a problem with the strain energy as the objective function and with material volume as a constraint by useof several robust and efficient numerical techniques of level set methods.The benefits and advantages of the proposed method are illustratedthrough two 2D examples.

2007, 23(2): 253-260. doi: 10.6052/0459-1879-2007-2-2006-135

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Smog visualization technique of asymmetric vortices on forebody at high wind speed

Nan Bo, Xueying Deng, Yankui Wang

We have obtained a clear, integrated and steady image of vortices athigh wind speed (60m/s) in the routine wind tunnel by setting a smokeorifice on the surface of the slender cylinder body and infusing theatomized oil with the new type of liquid droplet seeding generator. Asimple technique is developed to measure the vortice position bycalibrating at the same state and drawing grids in the same scale. Itprovides a useful technical platform for the research of Reynolds numbereffect on asymmetric vortices at a forebody.

2007, 23(2): 261-266. doi: 10.6052/0459-1879-2007-2-2006-262

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Constrained optimum control theory: application to aerodynamic design

Zhili Tang

The constrained optimum aerodynamic design method isdeveloped in the framework of control theory in order to implement allthe constraints implicitly and automatically. With the constrainedadjoint method developed in this paper , only the boundary condition ofadjoint equations and the gradient computation need to be modifiedslightly as compared with Jameson's original unconstrained formula,other terms are maintained thesame. It turns out that the control theory basedoptimization method is very suitable not only for the designs with a largenumber of design variables but also for the designs with constraints.

2007, 23(2): 273-277. doi: 10.6052/0459-1879-2007-2-2006-100

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An exact solution for periodic open type parallel cracks

Junhua Xiao, Chiping Jiang

Periodic parallel cracks in an infinite medium underfar-field inplane tensile stress are investigated. By using thesingular analysis of the complex stress function at the concentrated loadpoint and the tips of cracks, as well as combining periodicity of thehyperbolic function, a closed form solution of the stress intensity factorto the problem is obtained. A comparison of the present solution withexisting numerical results, shows a good agreement. The presentexact solution can be used to study the interaction ofmulti-cracks and the structural integrity assessment.

2007, 23(2): 278-282. doi: 10.6052/0459-1879-2007-2-2006-111

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Instability of incompressible thermo-hyperelastic tubes

Jiusheng Ren, Changjun Cheng

Instability of non-uniform deformations of an incompressiblethermo-hyperelastic tube, subjected to internal pressure and axial stretch,is examined within the framework of finite elasticity. When the inflationpressure is small, a thin-walled tube undergoes a uniform inflation. Butwhen the inflation pressure is larger than a certain critical value, thethin-walled tube undergoes a strikingly non-uniform deformation. One partbecomes highly distended as a bubble while the rest remains lightlyinflated. But a thick-walled tube always undergoes a uniform inflationeven if the pressure attains a very high value. A critical thickness for thetube to have an instability deformation is given based on the deformation curves along with its slope. Furthermore, theeffect of axial stretch and temperature on the deformation is discussed.

2007, 23(2): 283-288. doi: 10.6052/0459-1879-2007-2-2006-328

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