力学学报

Zheng Quanshui

2012, 44(1) doi: 10.6052/0459-1879-2012-1-lxxb2012-001

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Phenomenological model and numerical analysis of collective interaction of primary vortex

Wubing Yang Qing Shen Qiang Wang

A phenomenological model of collective interaction of primary vortex of mixing layers is built on the linear stability theory in this paper. The model can be used to determine the influence of the phase shift of the subharmonic disturbance wave on the nonlinear evolving process of the primary vortex. The results indicate that the evolving process of the primary vortex can be classified as tearing phenomenon, symmetric collective interaction and asymmetrical collective interaction. The tearing phenomenon and symmetric collective interaction are special phenomena and occur only at particular phase shift points, while the asymmetrical collective interaction is common and proceed through pairing one by one.

2012, 44(1): 1-12. doi: 10.6052/0459-1879-2012-1-lxxb2011-029

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Unsteady separation of flow around airfoil with local elastic structure

Peng-Fei Lei Jiazhong Zhang Jiahui Chen

For flow around airfoil with local elastic structure at low Reynolds number, the unsteady flow separation excited by the self-induced oscillation of local elastic structure has been analyzed in detail. The arbitrary Lagrangian Eulerian-characteristic-based split (ALE-CBS) scheme is developed to simulate the flow field with moving boundary. Moreover, Galerkin method is used to approximate the governing equations of the local elastic structure. The analysis is focus on the influences of the local elastic structure on the flow separation and airfoil performance. Further, different unsteady separation phenomena are studied from both Eulerian and Lagrangian viewpoints. The results show that local elastic structure of airfoil has significant effect on the unsteady separation and streamline structure, and can enhance the lift performance by the moving separation on airfoil surface, resulting in reattachment. Compared with Eulerian description, the Lagrangian description of separation can reveal the nature of lift enhancement and momentum transfer from main flow to boundary.

2012, 44(1): 13-22. doi: 10.6052/0459-1879-2012-1-lxxb2011-158

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Numerical Analysis of the Effect of an Inclined Coil on Thermomagnetic Convection of Air in a Porous Cubic Enclosure

Changwei Jiang Hesong Li Donglin Chen Er Shi Xianfeng Zhu Mao Li

Thermomagnetic convection of air in a porous cubicenclosure with an inclined electric coil is numerically investigated undermicrogravity environment. Biot-Savart's law was used to calculate magneticfield. The momentum equations and energy equations were solved by the DarcyModel and the local thermal non-equilibrium model. The results show that thenatural convection of air is strengthened in the porous cubic enclosure withthe increase of \gamma number and Da number. The resultedconvection is symmetrical in terms of the angle at x_{\rmeuler}=45^\circ when the range of inclination angleis from 0^\circ to 90^\circ. The coil inclination changes theNu_{\rm m} number and a local maximum is obtained at x_{\rmeuler}=45^\circ for every case. Localminima are obtained at x_{\rm euler}=0^\circ and 90^\circ.

2012, 44(1): 23-29. doi: 10.6052/0459-1879-2012-1-lxxb2010-847

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Nonlinear thermal flutter of heated curved panels in supersonic air fow

Zhichun Yang Jian Zhou Yingsong Gu

A nonlinear aeroelastic model for a two-dimensionalheated curved panel in supersonic air flow is established by using Galerkinmethod. The von Karman large deflection theory and the modified pistontheory appended with static aerodynamic loading are used in the formulation.The static deflection of a cylindrical curved panel is studied by numericalsimulation using Newton iterative approach. Then the stability boundarycurves under different temperature elevations are obtained by using Lyapunovindirect method. The motion equations of curved panel are solved byRunge-Kutta method, time history and phase plots of curved panel flutterresponses are depicted and corresponding bifurcation diagrams are obtainedfor better understanding of the subcritical and supercritical flutterresponses of curved panels with different initial height-rises underincreasing dynamic pressure and static thermo-aerodynamic loading (STAL).The results demonstrate that the flutter boundary drops significantly withincreasing temperature elevation for small curvature panel, whereas, theflutter boundary almost keeps the same value for large curvature panel. Theflutter dynamic behaviors of curved panels differ from those of flat panelssignificantly. Curved panels may enter chaos from static stable point whenconsidering temperature elevation effects, and static stable point and LCOmotion also exist in the chaotic motion area. For larger curvatures, chaoticmotions will not occur, however the supercritical flutter motions exhibit alimit strip oscillation in which the vibration amplitudes restrained in alimited range.

2012, 44(1): 30-38. doi: 10.6052/0459-1879-2012-1-lxxb2010-853

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Mechanism analysis about cavitation collapse load of underwater vehihles in a vertical launching process

Yiwei Wang Chenguang Huang Tezhuan Du Xin Fang Naigang Liang

Pressure pulses generated by cavitation collapse when vehicles launching through the free surface will form the key load which decides the strength of structures. Consequently, it is very significant to investigate the mechanism of cavitation evolution and collapse. Firstly, a typical vertical launching process was simulated, and time sequences of pressure distribution gained were verified by experimental results. Through the analysis about flow fields, mechanism for the occurrence and evolution of cavitation collapse was investigated. Furthermore, a physical model of collapse pressure was established, by which influence of important factors such as cavity thickness, thickness of water layer, sound speed were studied. Finally, relative issues about the similarity law of scaled tests and load-reduction measurements were discussed.

2012, 44(1): 39-48. doi: 10.6052/0459-1879-2012-1-lxxb2011-139

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Experiments on water entry of high-speed slender body and the resulting supercavitation

Honghui Shi Hao-Lei Zhou Yan Wu Huixia Jia Xiaoping Zhang Suyun Zhou Lite Zhang Ruoling Dong Chao Wang

This paper presents an experimental study on the fluiddynamic processes of water entry of a slender body in some different cases.The impact effect between slender body and water surface after water entryof a slender body are recorded at real time by a high-speed camera. Thedevelopment process of supercavitation which is induced by high-speedslender body is visualized clearly. The oscillation of water surface afterwater entry of a slender body and the instability of the motion of slenderbody in some different cases are analyzed in detail. The velocities ofslender body after entry water are calculated from experiment data.According to our analysis to the variation tendency of the slender body'svelocity, the effect of supercavitation on drag reduction is validated.

2012, 44(1): 49-55. doi: 10.6052/0459-1879-2012-1-lxxb2011-062

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Experimental study on interaction of inphase bubbles

Shiping Wang Aman Zhang Yunlong Liu Chao Wang

The study of bubble-bubble interaction has many valuableapplications in fields of fluid mechanics. But there are still manydifficulties in theoretical and numerical studies presently. Therefore,experiments using electronic spark to generate bubbles are designed in thispaper to investigate the interactions of two bubbles and bubbles with freesurface. The experiments are carefully controlled and the two bubbles aregenerated within 67\mus which can be considered as inphase. Manyphenomena can be found such as fusion, mushroom shape and split, jettingtoward, jetting direction change, jetting away and so on. Two feature parameters, dimensionlessdistance and period difference, are concluded to classify the phenomena oftwo inphase bubbles interaction, which aims to offer experimental referencesto the study of multi- bubble interactions.

2012, 44(1): 56-64. doi: 10.6052/0459-1879-2012-1-lxxb2010-772

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A two-phase numerical model for non-equilibrium sediment transport

Xin Chen Xiping Yu

A numerical model for non-equilibrium sediment transportis developed based on Reynolds averaged two-phase flow equations. Differentfrom most of the previous models, the present one does not require anempirical formula to deal with the pick-up and settling of sediment over thebed. The model includes the interactions between particles, and betweenfluid and particles. The two-phases are coupled through the interphaseforces. The model is employed to predict the longitudinal variation of thesediment concentration profile over an eroding bed under a steady uniformflow. Computational results agree reasonably well with the availableexperimental data and are evidently more accurate than the analyticalsolution. The relevant turbulent diffusion and gravity settling are alsodiscussed.

2012, 44(1): 65-70. doi: 10.6052/0459-1879-2012-1-lxxb2010-527

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Experiments on two-phase flow characteristics in a catenary riser system with the gas and liquid mixture transportation

Song Gao Wei Li Yunxiaing You Zhong Yu Tianqun Hu

Severe slugging is an undesirable flow phenomenon for apipline-riser system with the gas-liquid mixture transportation in oceanengineering. In present paper experiments were performed for the two-phaseflow characteristics in a horizontal/ declination pipeline-catenary risersystem with the gas-liquid mixture transportation, and flow patterns wereidentified by series combinations of gas and liquid superficial velocities,including severe slug, intermittent and oscillation flows. The formationmechanisms of these flow patterns were presented and the conditions wherethe severe slug flow can be produced in the catenary riser were obtained.The results show that the severe slug flow in a catenary riser hasremarkably periodic characteristics and consists of four stages in a circle,including slug formation, slug production, slug blowout and liquid fallback,respectively, where the characteristics of the flow parameters in each stagewere given. Moreover, the formation mechanisms of severe slug flows in bothcatenary and vertical risers were compared and analyzed, and a remarkabledifferentiation in the slug formation stages for the two types of risers wasobserved, where the formation procedure of a mixture liquid slug with bothgas and liquid first occurs before the pure liquid slug in the catenaryriser can be produced, however, there is no occurrence of such a procedureof the mixture liquid slug for the vertical riser.

2012, 44(1): 71-81. doi: 10.6052/0459-1879-2012-1-lxxb2011-223

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An arithmetic method of segmenting moving aeolian sand particles' images from background information of digital high-speed photography images

Fanmin Mei Chanwen Jiang

To deeply understand dynamic evolutionalmechanism of initial of aeolian sand particles by multiple factors, it isvery critical to measure precisely liftoff velocities and trajectories ofsand particles with different movement types. Although the high-speedphotography illuminated by intensive and continuous laser is an effectivemethod for obtaining the above information, the kinds of high- speedphotography images cannot be processed precisely by overlapping image methoddue to very low contrast ratio of objectives to backgrounds and significantdiscrepancy between two frame images. As a result, a new arithmetic methodof image segmentation is proposed on basis of a principle of variation ingray level difference between two frame consecutive images. The cases showthat the new arithmetic method can segment successfully saltating particlesfrom immobile bed by selecting appropriate threshold value of gray leveldifference between two continuous images and by adopting adaptive binarymethod. The new arithmetic method plus a minimum distance matching method ofparticles tracking velocimetry (PTV) can retrieve precisely sand particlestrajectories near the bed as sand particles concentration is low.

2012, 44(1): 82-87. doi: 10.6052/0459-1879-2012-1-lxxb2010-637

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Modeling of the flow characteristic in an axial-flow rapid pressure swing adsorption bed

Xiangjun Liu Yingshu Liu Yongling Li Hui Zhang

The gas flow characteristic in an adsorbent bed is avital problem for further studying the mechanics of gas separation process.In this paper, a comprehensive mathematical model of gas flow and adsorptionin an adsorbing bed, which based on mass and momentum conservation law, isestablished. A typical cyclic process of an axial-flow rapid pressure swingadsorption is numerically studied. The flow patterns in different cyclicperiod for pressurization, adsorption, depressurization, desorption andpurge, are obtained. The flow characteristics and their difference from thegas flow in an empty bed and a no-adsorption bed are also studied.

2012, 44(1): 88-95. doi: 10.6052/0459-1879-2012-1-lxxb2010-602

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The theoretical analysis on multi-mode of the instability of longshore currents

Chun-Ping Ren Zhili Zou

Thepopular theory for the instability of longshore currents is thelinear shear instability theory. It is assumed that theinstability mode with the largest growth rate dominates theinstability of longshore currents. However, the assumption cannotbe used to some case from the experimental results. In the presentpaper, milti-mode unstable process (or behavior) has been analyzedwhich is in good agreement with our previous experiment results.Velocity profile has great effects on the growth mode of theinstability of longshore currents. Specially, variations can leadto multi-mode of the instability of longshore currents, viz. morethan two peaks occur in growth rate curve. In present paper, weanalyze the effect of frontshear and backshear simultaneousvariations and individually of the both on the multi-mode of theinstability of longshore currents using analytic velocityprofiles. The analysis shows that the wave development(orphenomena, formation，evolution) in our experiment can beattributed to the frontshear instability.

2012, 44(1): 96-105. doi: 10.6052/0459-1879-2012-1-lxxb2010-380

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Nonlinear flow equations for heavy oil in porous media

Tongyu Yao Yanzhang Huang Jishan Li

The gas flowcharacteristic in an adsorbent bed is a vital problem for furtherstudying the mechanics of gas separation process. In this paper, acomprehensive mathematical model of gas flow and adsorption in anadsorbing bed, which based on mass and momentum conservation law,is established. A typical cyclic process of an axial-flow rapidpressure swing adsorption is numerically studied. The flowpatterns in different cyclic period for pressurization,adsorption, depressurization, desorption and purge, are obtained.The flow characteristics and their difference from the gas flow inan empty bed and a no-adsorption bed are also studied.

2012, 44(1): 106-110. doi: 10.6052/0459-1879-2012-1-lxxb2010-829

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The properties of stopping are investigated for off-lane bus station

Yujuan Liang Yu Xue

Basedon the Nagel-Schreckenberg traffic flow model, a cellularautomaton model of mixed traffic flow considering bus station ontwo-lane is proposed via introducing lane-change rule. Numericalsimulation indicate that the traffic flow in the bus stationswithout stopping-lane has a certain characteristics under thecondition of period boundary, that is to say, there is a power-lawscaling relationship between mean-velocity and density in thejamming phase over a medium density of vehicles.

2012, 44(1): 111-116. doi: 10.6052/0459-1879-2012-1-lxxb2010-654

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The evolution of bell and kink solitary waves in microstructured solids

Shuang-Shan Wang Naranm

Firstly, the simple model which describes the one-dimensional longitudinal wave propagation in dissipation-dispersion nonlinear solid is derived based on the Mindlin theory and the Murnaghan model. Secondly, the microstructural effect on bell and kink solitary wave evolution is simulated, by using the finite difference method. The results show that with the weakening of microstructural effect, the amplitude attenuation and asymmetric characteristic of bell solitary wave become more and more obvious; with the enhancement of microstructural effect, the “hat” shape change emerging at the top of kink solitary wave and the corresponding asymmetric characteristic become more and more obvious.

2012, 44(1): 117-123. doi: 10.6052/0459-1879-2012-1-lxxb2011-010

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A study of dynamic combined compression-shear loading technique based on hopkinson pressure bar

Wen Zheng Song-Lin Xu Chao Cai Shisheng Hu

This paper presents a new combined compression-shear testtechnique based on Hopkinson pressure bar to investigate the dynamicresponse of materials. The desired compression-shear loading were applied bythe beveled ends with different angles. The data processing methods arestudied and verified by the finite element analysis. A series of experimentson common metal were performed at the same impact velocity with the loadingangles ranging from 0$^{\circ}$ to 60$^{\circ}$. It shows that this method canprovide combined compression-shear loading, and achieve a new experimentalmethod to investigate the dynamic mechanical properties of materials underimpact multiaxial loadings.

2012, 44(1): 124-131. doi: 10.6052/0459-1879-2012-1-lxxb2011-103

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Dynamic UH model for sands and its application in FEM

Yang-Ping Yao Zheng Wan Zhenhua Qin

Complex stress-strain relationship is exhibited forsaturated sands under cyclic loading conditions. The large deformation andphenomena of cyclic mobility occur during liquefaction. In order to simulatethe above mechanical behaviors of sands simply and effectively, a dynamicconstitutive model which can be used to describe stress-strain relationshipfor sands under dynamic loading conditions is proposed on the basis of UHmodel for overconsolidated clay. There are three specific revisions in thispaper: (1) Ratio between the length of long axis to that of short axis forellipse yielding surface is defined as the function for slope of rotationalaxis which can be used to reflect stress-induced anisotropy. (2) Rotationalhardening rule is introduced into the proposed model to reflectstress-induced anisotropy. (3) A unified hardening parameter is establishedby coordinating rotational hardening rule and critical state behavior.Comparison between model prediction and test results demonstrates that theproposed model can be conveniently used to simulate stress-strainrelationship under dynamic loading conditions for sands. Dynamicconstitutive model is also embedded into FEM program. Stress-strainrelationship of sands for soils foundation is simulated. Simulated resultshave shown that the proposed model can be applied into geotechnicalengineering practice conveniently.

2012, 44(1): 132-139. doi: 10.6052/0459-1879-2012-1-lxxb2010-740

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A corrected damage law for high cycle fatigue

Fengping Yang Qin Sun Jinheng Luo Hua Zhang

It is an effective method to use continuum damagemechanics (CDM) to solve fatigue problems. A corrected damage law for highcycle fatigue is postulated to accord with experimental data based on thelatest Lemaitre damage law. Stress amplitude and mean stress can be takeninto account in this corrected damage law. Take 2A12-T4 aluminum alloy as anexample, the material parameters were gotten for this correction damage model.Let this model be an UMAT subroutine of ABAQUS. Fatigue lives of 14 loadingsituations for two components were computed. The result shows that the meanerror between experimental and computational result is about 15%, whichshows this corrected fatigue damage law can preferably forecast high cyclefatigue life for metallic components.

2012, 44(1): 140-147. doi: 10.6052/0459-1879-2012-1-lxxb2010-594

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Delay effect on the relaxation oscillations of a van der pol oscillator with delayed feedback

Yuanguang Zheng Chengdai Huang Zaihua Wang

This paper investigates the relaxation oscillations ofthe van der Pol oscillator with delayed feedback. Firstly, the stability ofslow manifold is determined and the bifurcation analysis on the fastsubsystem is carried out by means of stability switches. It is shown thatthe structure of the slow manifold changes essentially when the delayexceeds some critical value. Secondly, on the basis of geometric singularperturbation theory, it is shown that a small amplitude oscillation occursin the slow process of the relaxation oscillations due to the delay-inducedHopf bifurcation, and the period of the relaxation oscillations is shortenedas the delay increases. As demonstrated in the numerical simulations,oscillation with small amplitude in the slow process can be resulted frominner layer or Hopf bifurcation, or the both.

2012, 44(1): 148-157. doi: 10.6052/0459-1879-2012-1-lxxb2011-244

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An identification method of multi-source dynamic loads based on independent component analysis

Xun Xu Jinping Ou

This study proposes an identification method ofmulti-source dynamic loads based on independent component analysis, in orderto detect the wave pattern of the load subjected to a structural systemwhose configurational information is totally unknown. The method is based onthe principle that the response of structure is a convolution of load andcorresponding structure impulse response; also, it assumes that individualload sources are statistically independent to each other. When compared withthe existing load identification methods, the features of the methoddeveloped in this study embody three merits: (1) The structuralconfiguration, such as distribution of structural mass, structural stiffnessand damping ratio, could be unknown, and the independence among the actualloads is taken as the goal of optimization; (2) The independence ofindividual identified loads is measured using their mutual information, andthe correlation at different orders is eliminated by the use of gradientdegressive algorithm, so that the independence among detected loads isguaranteed; (3) Loads could be identified from the standpoint of wavepatterns. Numerical simulation indicates that the algorithm is robust onmeasuring point, noise, structure and input load. By normalization, thevalue of the correlation coefficient between identified and actual loads isapproximately 1. Therefore, this method successfully integrates the existingknowledge on load into the load detection algorithm, and could make aconfident estimation of the actual value, which contributes in the practicalsignificance of the developed method.

2012, 44(1): 158-166. doi: 10.6052/0459-1879-2012-1-lxxb2011-107

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Importance measure of correlated variables in polynomial output

Wenrui Hao Zhenzhou Lv Pengfei Wei

With the case of the quadratic polynomial outputs withoutcross-term, the correlated and uncorrelated contributions by correlatedinput variables to variance of output response are derived analyticallythrough the properties of the multi-dimensional correlated normaldistribution and conditional distribution. The results of examplesdemonstrate that the derived analytical expressions are correct. The derivedanalytical expressions can be used directly in recognition of thecontribution by input variables in quadratic or one-order polynomial outputwithout cross terms and can be compared for other new algorithms. Thismethod can also be extended to higher order polynomial with cross terms, tosolve the recognition of contribution by input variables in more complicatedoutputs.

2012, 44(1): 167-173. doi: 10.6052/0459-1879-2012-1-lxxb2011-056

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Wave interaction with double-cylinder structurer with arc-shaped porous outer wall

Jun Liu Gao Lin Jianbo Li

The scaled boundary finite element method (SBFEM) isapplied to solve the problem of hydrodynamic interaction between theshort-crested wave and the circular cylinder circumscribed arc-shaped porousstructure. The porous arc is extended to form an imaginary circularcylindrical interface. As a result, the entire computational domain isdivided into one bounded domain and one unbounded domain. The porouscoefficient of the whole imaginary circular interface is represented by adiagonal matrix G_0. Analytical procedure is applied in thereduced direction, and only the boundary of the exterior cylinder needs bediscretized to reduce spatial dimension by one. In addition, the presentapproach can meet the boundary condition at the infinity automatically.Hankel and Bessel functions are chosen as the basis functions for thesolution SBFEM equations. Comparisons are made between the results solved bySBFEM and those by acquired analytical solution or solutions by othermethods in the literature. The results show that the proposed approachyields excellent results with quite few discretized nodes and quickconvergence. The influence of varying wave parameters and structureconfiguration on the system hydrodynamics is extensively examined. Theseresearch results are of practical significance to the hydrodynamic analysisand design for the circular cylinder circumscribed arc-shaped porousstructure.

2012, 44(1): 174-178. doi: 10.6052/0459-1879-2012-1-lxxb2011-200

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Numerical simulation of the hydrodynamics of self-propelled fish swimming

Liang Wang Zongfang Chen Qiang Fu Rende Miao Ming Wang

Based on a novel method of force analysis, the thrust anddrag forces of self-propelled fish are redefined, and the difficulty indistinguish the thrust and drag in fish swimming is overcome. Then, anadaptive ghost-cell immersed boundary method is used to simulate the 2Dself-propelled carangiform swimming. Simulation cases are carried out forReynolds number in the rang of 309 \le Re \le 14581 (viscous flow) andRe=\infty (inviscid flow). The results show that: (1) The Strouhal numberdecreases with increasing the Reynolds number. If the Reynolds number tendstowards infinite, the Strouhal number approaches 0.25; (2) For all Reynoldsnumber, the main part of the thrust is the pressure component. The viscouspart of the drag is larger than the pressure part when Re<3000, while therelationship will be reversed when Re>3000; (3) The thrust efficiencyincreases with increasing the Reynolds number and the maximum efficiency isabout 70%. The result show that the carangiform swimming rule suit thehigh Reynolds situation.

2012, 44(1): 179-183. doi: 10.6052/0459-1879-2012-1-lxxb2010-697

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Dynamic substructure method for propagation of elastic-plastic wave induced by impact

Pengbo Qian Xiaochun Yin Yunian Shen Jun Yang

The dynamic substructure method was proposed to accountfor propagation of elastic-plastic waves in flexible components induced byimpact. A dynamic model using the substructure technique was established andits governing equations in modal coordinates were derived from the finiteelement theory and the substructure synthesis method. The existence of thenormal modes in the indicated waves and the convergence of the truncation ofthe normal modes were proved. Numerical cases are illustrated forlongitudinal and transverse impact of flexible bars. The simulation results,the comparisons with their analytical solutions, and calculations of thethree-dimensional dynamic finite element method, show that the presentmethod is convergent and valid.

2012, 44(1): 184-188. doi: 10.6052/0459-1879-2012-1-lxxb2011-186

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2012, 44(1): 189-194. doi: 10.6052/0459-1879-2012-1-lxxb2012-018

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2012, 44(1): 195-196. doi: 10.6052/0459-1879-2012-1-lxxb2012-019

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