力学学报

VIV DEVELOPING PROCESS OF A FLEXIBLE CYLINDER UNDER OSCILLATORY FLOW

Wang Jungao, Fu Shixiao, Xu Yuwang, Song Leijian

Offshore floating structures would bring the catenary risers moving in the water periodically under sea loads, then to generate relatively oscillatory flow between the riser and the water particles. Such oscillatory flow would easily trigger the "intermittent VIV" at sag-bend of the catenary riser. Experimental investigations on the behaviors of a 4m long straight flexible cylinder in the relatively oscillatory flow were carried out in this paper by forcing it oscillating with different combinations of both maximum reduced velocity U_R_max and Keulegan-Carpenter number (KC) in still water. Fiber brag grating (FBG) strain sensors were used to measure the VIV responses of the model cylinder. Meanwhile, modal analysis was adopted to process the experimental data, and three VIV developing process in oscillatory flow including "building-up", "locking-in" and "dying-out" were firstly proposed. Furthermore, effects on VIV in oscillatory flow from both reduced velocity U_R_max and KC were discussed and summarized. Finally, normalized time ratio contour plots of three VIV developing phases in different maximum reduced velocities were obtained.

2014, 46(2): 173-182. doi: 10.6052/0459-1879-13-277

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APPLICATION OF A HARMONIC BALANCE METHOD IN RAPID PREDICTIONS OF DYNAMIC STABILITY DERIVATIVES

Chen Qi, Chen Jianqiang, Yuan Xianxu, Xie Yufei

Harmonic balance method is constructed on the base of the Fourier series expansion. In the method, the unsteady solution process of a periodically unsteady flow is transformed into coupled solution processes of several steady flows, and then the whole time history of the unsteady aerodynamic forces and moments are rebuilt from the steady results. A rapid prediction method for dynamic stability derivatives is established, utilizing the harmonic balance method. In this way, the dynamic supersonic flow around a pitching winged missile is numerically simulated, with the dynamic derivative in pitch obtained via integration method. The results agree well with those from experiments. The computational efficiency could achieve about thirteen times of that of the dual-time-stepping method, while the order of computational accuracy being the same. The harmonic balance method is then utilized to investigate the effects of reduced frequency on the computation of dynamic derivative in pitch within a broad range. The results show that, with the decrease of the reduced frequency, the variation of the dynamic derivative in pitch is great, and in some cases even sign change could happen. At last, the applicability of the present method at high angles of attack flow is also studied, aiming at the strong nonlinearity of dynamic flow fields in this case. Results show that good agreement could be achieved with the wind tunnel data.

2014, 46(2): 183-190. doi: 10.6052/0459-1879-13-145

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STUDY OF TURBULENT VORTEX AND HYDRAULIC DYNAMICS IN TRANSIENT SHEET/CLOUD CAVITATING FLOWS

Zhao Yu, Wang Guoyu, Huang Biao, Hu Changli, Chen Guanghao, Wu Qin

Studies are presented for a Clark-Y hydrofoil fixed at an attack angle of α=8° at a moderate Reynolds number, Re=7×10⁵, for both noncavitating and sheet/cloud cavitating conditions. The numerical simulations are performed via the commercial code CFX using a transport equation-based cavitation model, and the turbulence model utilizes the large eddy simulation (LES) approach with a classical eddy viscosity subgrid-scale turbulence model. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding, in accordance with the quantitative features observed in the experiment. The primary frequency, St =0.85, of the hydrodynamic fluctuations can be observed for noncavitation. It is induced by the shedding of the vortex structures at the trailing edge of the hydrofoil. The primary frequency, St =0.34, of the hydrodynamic fluctuations is induced by the growing up and shedding of the cavity, which can be observed for sheet/cloud cavitation. At the same time, some medium amplitude peaks are observed ranking from St =0.5 to St =1.5. These are due to the divergence influences from cavitation in different phases. These influences may lead to changes of vortex shedding frequencies at the trailing edge of the hydrofoil.

2014, 46(2): 191-200. doi: 10.6052/0459-1879-13-177

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TEMPERATURE MEASUREMENTS IN SIMULATED MARS ATMOSPHERES BASED ON THE CN RADICAL EMISSION SPECTRUM

Lin Xin, Yu Xilong, Li Fei, Zhang Shaohua, Xin Jianguo, Zhang Xinyu

Temperature measurements behind the strong shock waves for simulated Martian atmosphere were presented in this paper. Based on the inherent molecular structure characteristics of the CN radicals, the energy level distribution, the transition frequency and Einstein spontaneous emission transition probability were systematically analyzed and numerically studied. Meanwhile, the FWHM of apparatus function was measured experimentally to be Lorentzian profile of value 0.154nm by using of a narrow line width diode laser. The dependence of the spectral structure on the rotational temperature and vibrational temperature were numerically analyzed in detailed. In shock-tube experiments, the emission of CN (B²Σ⁺→X²Σ⁺) system measurements were performed behind a strong shock wave in a CO₂-N₂ mixture with two di erent conditions of initial pressure and velocity. Rotational and vibrational temperatures behind the strong shock wave, and the radiation structure of the shock layer, including induction, relaxation and equilibrium processes were obtained through analysis of time gating optical emission spectra with nanosecond temporal resolution.

2014, 46(2): 201-208. doi: 10.6052/0459-1879-13-224

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TWO-PHASE FLOW CHARACTERISTICS IN Y-JUNCTION MICROCHANNEL

Liu Zhaomiao, Liu Likun, Shen Feng

Droplets formed in different Y-angles (45°, 90°, 135°, 180°) and flow flux of two-phase in Y-junction microchannels are studied by making use of micro-PIV, high speed digital microscopic system and numerical simulation in this paper. It is found that the shearing action impels the formation of dispersed phase droplet in the squeezing mechanism, and the smaller Y-angle results in the bigger shearing action suffered by dispersed phase. The continuous phase velocity profile is asymmetric parabolic distribution in droplet generation process. When Y-angle is less than 180°, it does not affect the droplet diameter size but will speed up the droplet generation as it decreases. The droplet size and generated cycle will be the largest in the case of Y-angle being 180°. It is indicated that Capillary number affects droplet size and generation time simultaneously. The increasing capillary number of continuous phase will make the acting force from continuous phase to dispersed phase more intensive in the junction of the two phases in the in-plane velocities in the continuous phase and lead to dispersed droplet rupture more easily.

2014, 46(2): 209-216. doi: 10.6052/0459-1879-13-228

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LABORATORY STUDIES ON THE STAIRCASE STRUCTURE OF DOUBLE-DIFFUSIVE CONVECTION

Wan Wei, Qu Ling, Zhou Shengqi

In the present study, the evolution of double-diffusive convection is explored in a linear stratified salt-water system, where the uniform heating is provided from below and the constant temperature is applied from above. By using the variances of vertical profiles of temperature and shadowgraph images, it is found that the generating and merging of the staircases occur during the experiment. Based on the temperature difference across the system, the whole evolution process can be divided into two stages. In the temperature difference increase stage, the generation of new staircase happens at the top of the old ones, while the merging event typically occurs between the lowest staircase and its overlaying one. The staircase number increases because that the generating rate of new staircase is faster than the merging rate. In the temperature difference decrease stage, the existing staircases disappear progressively. It is interesting that the bottom boundary of system can feel the happen of the merging events of the lowest staircase, which means that the dynamics process in the local region can have effect on the other regions of system. The thickness of the lowest staircase (h) is much thicker than those of others, and its temporal dependence is in the form of h~τ^0.7, here τ is the dimensionless time.

2014, 46(2): 217-223. doi: 10.6052/0459-1879-13-230

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A NOVEL LATTICE BOLTZMANN MODEL SIMULATING GAS-LIQUID TWO-PHASE FLOW

Shi Dongyan, Wang Zhikai, Zhang Aman

Based on the lattice Boltzmann free-energy model, a novel model is developed to simulate the gas-liquid two-phase flow with great density ratio in the viscous field. To improve the accuracy, the transfer rate control of the particle number density between two adjacent points is added to the original model, and the differential relaxation of the collision term is considered. Also, to avoid the numerical instability problems caused by the large density ratio, the six point and nine point differential schemes are used to solve ∇ and ∇2, respectively. Different from the traditional LBM implementation process, the single-step operation is divided into two steps in the paper. Unconsidering the gravity, the bubble motion is simulated and the results are compared with those from the exited models. It shows that the newly developed model has higher accuracy and numerical stability. Also, the deformation and the vortex formation of a rising bubble under gravity and the interaction of two bubbles in the horizontal and vertical directions are simulated. In the process, the mass conservation and the volume incompressibility are verified.

2014, 46(2): 224-233. doi: 10.6052/0459-1879-13-243

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EFFECTS OF FORMATION DAMAGE ZONE ON BOTTOM-HOLE PRESSURE RESPONSE OF PARTIALLY PENETRATING WELLS

Ouyang Weiping, Liu Yuewu, Wan Yizhao

The effect of formation damage zone due to well drilling on partially penetrating wells is different from that on open-hole wells. In order to analyze the effect of damage zone on pressure response at the well bottom, this paper presents a 2D axial symmetry porous flow model for partially penetrating well. The model considers the actual formation damage zone around the wellbore and reservoir permeability anisotropy. The bottom-hole pressure response curves and pressure fields of partially penetrating wells are obtained by using the FEM method. The analysis of the pressure response curves and pressure fields shows that five flow regimes may appear in the pressure response process of partially penetrating wells. The early-time radial flow and the ellipsoidal flow are typical characteristics of partially penetrating wells. The effect of damage zone is studied. It shows that the skin factor S in traditional methods is not the mechanical skin factor S_d due to the formation damage. The dimensionless wellbore storage coefficient cannot combine with the mechanical skin factor. The wellbore pressure obtained from traditional methods is modified. The formula for total skin factor of partially penetrating wells is verified. Those conclusions provide theoretical guidance for the transient pressure data interpretation and productivity prediction of partially penetrating wells.

2014, 46(2): 234-240. doi: 10.6052/0459-1879-13-183

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MEASUREMENT OF DYNAMIC STRENGTH OF LY12 ALUMINUM UNDER MAGNETICALLY DRIVEN QUASI-ISENTROPIC COMPRESSION

Luo Binqiang, Wang Guiji, Tan Fuli, Zhao Jianheng, Sun Chengwei

It is difficult to fully understand the yield strength of materials under high pressure and high strain rate loading. At present, strength measure under high pressure is mainly based on plate impact technique, in which the effects of strain rate and temperature increase during loading process on material dynamic strength are difficult to resolve. In this work, Lagrangian wave speed and strength of LY12 aluminum under magnetically driven quasi-isentropic compression are studied using CQ-4, a compact strip-line pulsed power generator for isentropic compression experiments. The optimizations of loading electrode and sample configuration, as well as experimental data processing are discussed in detail. Meanwhile, Lagrangian wave speed of LY12 aluminum along loading and unloading path and yield strength under quasi-isentropic compression up to 12GPa are obtained in a good accuracy.

2014, 46(2): 241-247. doi: 10.6052/0459-1879-13-227

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ASYMPTOTIC ANALYSIS OF SOLID SPHERE SUBJECTED TO THERMAL SHOCK UNDER FRACTIONAL ORDER GENERALIZED THERMOELASTICITY

Wang Yingze, Wang Qian, Liu Dong, Song Xinnan

Based on fractional order generalized thermoelasticity, one dimensional problem of a solid sphere subjected a thermal shock is studied. The transient characteristics of thermal shock is considered to derive the approximate solutions of displacement, temperature and stresses by means of the Laplace transform technique and the asymptotic properties of Bessel functions. Numerical simulation has been conducted for an isotropic solid sphere with the boundary subjected to a thermal shock. The propagation of thermal wave and thermal elastic wave, and the distribution of each physical field in the different values of the fractional order parameter are obtained. The results show that the fractional parameter has a significant effect on propagation of two waves and distribution of each physical field, which can be regarded as an influence factor of the thermal relaxation time, and can change the effect of thermal shock by constraining the influence of the delay effects on thermal behaviors.

2014, 46(2): 248-254. doi: 10.6052/0459-1879-13-287

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SYNERGISTIC DAMAGE MECHANIC MODEL FOR STIFFNESS PROPERTIES OF COMPOSITE LAMINATES

Shen Haojie, Yao Weixing, Wu Fuqiang

In connection with diffused damage in composite laminates, a synergistic damage mechanic model was proposed for the stiffness properties. The model included the microcosmic responses of the physical damage and macroscopic performance of the material's stiffness. In micro-level, mesoscopic RVE (representative volume element) model was established to obtain crack opening displacement and crack sliding displacement, which were used to define the damage tensor. In macro-level, through homogenizing the material strain and the surface displacement of the damage, the relationship of the stiffness matrix of unidirectional laminate or laminates in damage statue and damage tense was set up. As matrix crack for example, the constitutive relations of the laminates with transverse and longitudinal cracks were constructed, respectively. The influences of the transverse matrix cracks on the stiffness properties of the laminates [±θ/90₄]_S were analyzed with the present model and showed that it is capable to predict the reduction of the stiffness properties resulted from the damage in the laminates.

2014, 46(2): 255-263. doi: 10.6052/0459-1879-13-255

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A TIME-VARIANT RELIABILITY ANALYSIS METHOD FOR NON-LINEAR LIMIT-STATE FUNCTIONS

Huang Xinping, Jiang Chao, Han Xu

Time-variant reliability problems appear in the engineering practice when loads stochastically change or the material properties of the structure deteriorate in time. In this paper, a time-variant structural reliability analysis method for non-linear limit-state function is presented. In this method, the stochastic process in the limit-state function is first discretized. Each discretized limit-state function is linearized at the most probable point (MPP), and it is further simplified into a time-invariant reliability analysis problem which is then solved by using the traditional first order reliability method (FORM). Three numerical examples are analyzed to demonstrate the effectiveness of the present method.

2014, 46(2): 264-272. doi: 10.6052/0459-1879-13-190

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SUBSTRUCTURE METHODS OF GEOMETRIC NONLINEAR ANALYSIS FOR MEMBER STRUCTURES WITH HINGED SUPPORTS

Wang Gang, Qi Zhaohui, Wang Jing

Along the longitudinal direction, a slender truss structure is divided into several substructures. Due to that the nodal displacements are small in the embedded coordinate systems of substructures, the degrees of freedom of the internal nodes can be reduced to the ones of the interface nodes. Considering that the left and right ends of the substructure remain rigid sections during deformation, the interface nodal displacements would be reduced to the ones of the section central points. Each substructure would be reduced to be a generalized two-node beam element, in which the degree of freedom would be reduced sharply. Large displacement and rotation are important causes of the geometric nonlinearity of slender member structures. Based on the co-rotational method, an embedded coordinate system is defined, and the equilibrium equations of nodal forces for substructure elements and the tangential stiffness matrix are formulated. Taking into account of slender truss structures containing mutually hinged rigid bodies in the actual construction machinery, the convention of the nodal forces and their derivatives with respect to the independent and non-independent degrees of freedom are formulated. At last, numerical examples of sub-arm condition for crawler cranes are presented, in which the displacements of the boom structures under different load conditions are obtained. The numerical examples prove the validity of the presented method.

2014, 46(2): 273-283. doi: 10.6052/0459-1879-13-345

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LOW-GRAVITY LIQUID SLOSHING IN CYLINDRICAL TANKS UNDER PITCHING EXCITATION

Wu Wenjun, Yue Baozeng

The curved free surface of liquid in a cylindrical tank caused by surface tension under low-gravity environment is considered. The dominant modal vibration function of liquid sloshing under pitching excitation is selected as the basic function of velocity potential. The generalized state equation of liquid sloshing system is introduced by expanding the lateral sloshing boundary condition of the free surface to a Fourier-Bessel series, and the formulas of sloshing characteristics including wave height, sloshing frequencies, sloshing force and sloshing moment are also deduced, respectively. Through numerical calculation, the dynamic responses of sloshing characteristics are studied when the tank under pitching excitation. And the convergence, applicability and correctness of the present algorithm are validated.

2014, 46(2): 284-290. doi: 10.6052/0459-1879-13-236

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A NEW HIGHLY ROBUST GRID DEFORMATION TECHNIQUE AND ITS APPLICATION

Huang Jiangtao, Gao Zhenghong, Zhou Zhu, Liu Gang, Zhao Ke

In order to solve the multi-quaternion interpolation problem, quaternion is exponentially mapped to lie algebra space firstly, and the IDW interpolation method is combined to propagate the boundary perturbation to space. Consequently, the new grid deformation technique with high robustness is established based on quaternion. Aiming at the low efficiency due to large matrix computation, the proposed method takes advantage of the characteristic of quaternion method that can keep the boundary deformation in high-order consistency with elastic wall, and constructs the hierarchical deformation strategy that avoids the large matrix computation for the whole flow field. Furthermore, the infinite interpolation (TFI) which has strongly logical holding ability is combined in the hierarchical blend strategy. The embedded parallelism of multi-area, overlapping, patched grid deformation technology is utilized to establish the parallel program for grid deformation based on ''peer to peer'' programming concept and MPI library functions. Finally, a typical example of aircraft wing-body for aerodynamic aeroelasticity analysis is used to demonstrate the computational efficiency and robustness of proposed method by comparing with existing methods. Moreover, the hierarchical deformation technique is applied to the jig shape design of a regional aircraft, the efficiency and robust of the new type of the dynamic mesh technique is verified.

2014, 46(2): 291-299. doi: 10.6052/0459-1879-13-121

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FINITE ELEMENT ANALYSIS OF HUMAN RIB FRACTURE UNDER VARIOUS IMPACT LOADING CONDITIONS

Wang Fang, Yang Jikuang, Li Guibing

This study aimed at investigating the mechanism of the human rib fracture under various impact loading conditions based on different failure models. For this purpose, a validated FE thorax model was utilized for analysis of the rib fractures. Based on the human anatomical structures, the human thorax FE model consists of ribs, vertebras, sternum, costal cartilages, internal organs, and soft tissues. Material properties used in this model were based on the published literature. The phenomenon of human rib fractures was simulated in different configurations, including structural experiments of single rib and human thorax frontal crash experiments with a cylinder impactor. Based on different rib fracture failure models in human injury biomechanics, the rib fractures from simulations were analyzed and compared with the impact responses obtained from all of the experiments from the literature. The simulation results with the FE model showed that the applicability of rib fracture failure model would depend on the loading conditions. It was proved that the FE model could be used in research of human rib fracture biomechanics under various impact loading conditions in vehicle traffic accidents.

2014, 46(2): 300-307. doi: 10.6052/0459-1879-13-247

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SIDE FORCE CONTROL ON SLENDER BODY BY VORTEX GENERATORS

Zhai Jian, Zhang Weiwei, Gao Chuanqiang, Zhang Yanhua, Ye Zhengyin

There is a large side force on the slender body at high angle of attack (AOA). Vortex generators (VG, a micro delta wing) are fixed on the tip of the slender body with 10° semi-apex angle as actuators in this paper. Side forces can change approximately proportional to roll setting angle of VG along the model axis at high AOA. Moreover, the effects of the parameters of VG, such as half-wingspan length, sweepback of lead edge and AOA have been researched. It is found that the vortex generators with 6mm half-wingspan and 45° sweepback show good performance on the presented slender body at a series of AOAs. This device is very simple that can be used in engineering in the future.

2014, 46(2): 308-312. doi: 10.6052/0459-1879-13-232

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A SHEAR VISCOSITY MODEL OF POLYMER MELT CONSTRUCTED BY BEZIER CURVE

Yang Xiaodong, Shen Changyu, Li Qian

A shear viscosity model of polymer melt is proposed based on a quadric Bezier curve to improve the model's descriptive precision. The model is characterized by piecewise functions in a logarithmic coordinate. Linear functions are adopted to represent the two linear sections of the Newton region at lower shear rates and the power law region at higher shear rates. A quadric Bezier curve is applied to describe the transitional region between the two linear regions. The three curves are connected smoothly by a control polygon which is formed through the extension lines of the two linear curves of the Newton region and the power law region. At any temperature, the end point of the Newton region at lower shear rates and the start point of the power law region at higher shear rates are predicted accordingly. The data fitting examples show that the precision of the proposed model turns out to be obviously higher than that of the Cross-Arrhenius model.

2014, 46(2): 313-317. doi: 10.6052/0459-1879-13-163

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MULTI-VARIABLE SELECTION METHOD IN CONTACT/IMPACT DYNAMICS

Wang Jianyao, Hong Jiazhen, Liu Zhuyong

In flexible multi-body dynamics with contact/impact, multi-variable method (MVM) which is based on appended contact constraint model is proposed. With this method, two types of variables are used to describe the flexible body deformation: small superposed deformation is depicted with finite element nodal coordinates in contact region and modal coordinates in non-contact region respectively, thus this method takes account of both accuracy and efficiency. This method is extended to three-dimensional spatial contact issue which is more complicated than the planar one, and the numerical simulation of a longitudinal impact between two rods agrees well with the experiment result. To solve the variable selection problem, the influences on result accuracy of node position, modal orders and material parameter are studied. Based on this, the optimal multi-variable selection is realized which reduces the DOFs to the maximum extent and also achieves accuracy in the same time.

2014, 46(2): 318-322. doi: 10.6052/0459-1879-13-166

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REVIEW OF THE NATIONAL SYMPOSIUM ON FUNDAMENTAL SCIENTIFIC ISSUES FOR MARINE STRUCTURES AND EQUIPMENTS

Zhou Jifu, Yan Kai, Zhan Shige, Zhang Panfeng, Meng Qingguo, Ji Peiwen

The national symposium on fundamental scientific issues for marine structures and equipments held on November 29-30, 2013 is briefly introduced. The invited reports are reviewed by category. The viewpoints from free discussion and focusing discussion on what kinds of marine structures or equipments and what scientific fronts should be paid specific attentions in the future are summarized.

2014, 46(2): 323-328. doi: 10.6052/0459-1879-14-021

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2014 Vol. 46, No. 2

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