力学学报

TURBULENT MIXING AND FRACTAL STRUCTURE AT A DENSITY INTERFACE IN A STABLY STRATIFIED FLUID

Zhang Shuang, John Z. Shi

Laboratory mixing box experiments were undertaken to examine turbulent mixing and fractal structure at a density interface in a stably stratified two-component fluid (fresh on salt), subjected to shear-free turbulence induced by an oscillating grid within the salt water layer. The density interface was visualized by adding fluorescein and dye into the salt water layer. A total of 12 runs were made. Measurements were made of (a) the height of the mean density interface above the bottom of the mixing box; (b) the densities of the fresh water and salt water layers. Photographs and videos were made of the two-dimensional and three-dimensional density interfaces. Calculations were made for (1) the entrainment velocity; (2) the overall Richardson number (Ri₀); and (3) the fractal dimension of the two-dimensional and three-dimensional density interfaces. The entrainment rate decreases with an increasing overall Richardson number. It can be expressed as Ri_o to the -3/2 or -7/4 power. This indicates that the rate of mixing deceases with decreasing turbulence intensity. Fractal dimension of the two-dimensional density interface is larger than 1, while that of the three-dimensional density interface is larger than 2. Fractal structures are present on the two-dimensional and three-dimensional density interfaces. Fractal dimension decreases with an increasing overall Richardson number. This suggests that the density interfaces become smoother with decreasing turbulence intensity.

2015, 47(4): 547-556. doi: 10.6052/0459-1879-14-367

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CONTROL MECHANISM OF THERMAL ACTUATOR IN SUPERSONIC ROUND JET

Yan Hong, Lin Ke

Large eddy simulation (LES) is applied to study the effect of the thermal actuators on the vertical structures with a Mach 1.3 round jet. The thermal actuators are modelled as heat sources inside the groove. The noise reduction and mixing enhancement at two different actuation modes (m =±1 and m =±4) are explored. Results show that radial and circumferential velocity fluctuations are increased due to the actuation effect. It promotes the formation of streamwise vertical structure especially on the flapping plane at the mode m =±1. The aerodynamic noise distribution covers a wide range of frequencies with high amplitude at high frequencies. It is found that the actuation weakens aerodynamic noise in the range of high frequencies while the wall noise may be increased due to the actuation effect.

2015, 47(4): 557-570. doi: 10.6052/0459-1879-14-379

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EFFECTS OF HIGH FREQUENCY BLOWING PERTURBATION ON A TURBULENT BOUNDARY LAYER

Wang Yanpin, Guo Hao, Liu Peiqing, Huang Qianmin

An experimental study is conducted on a zero pressure gradient flat plate for investigating the effects of a periodical perturbation on the turbulent boundary layer over the flat plate. This experiment is focused on studying the effects of high frequency blowing on statistical characteristicss of near wall turbulence. By measuring and analyzing streamwise velocity signals at different streamwise locations with and without a periodical perturbation induced by a synthetic jet actuator, the conclusion of the experiment indicates skin friction reduction can be achieved downstream of the slot by applying high frequency periodical blowing perturbation. Owing to the intensity of the perturbation in the turbulent boundary layer is attenuating along the streamwise, the interaction between the perturbation and turbulent flow structures is attenuating. However, the negative spanwise vortexes induced by the high frequency perturbation are nearly of the same scale as the structures of bursting events, which directly impact the statistics of production and evolution of near wall coherent structures. As a result, the outcomes of bursting detection methods like VITA in the experiment show a contradictory phenomenon to the mechanism of skin friction reduction in low frequency blowing or steady blowing.

2015, 47(4): 571-579. doi: 10.6052/0459-1879-14-381

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GROUND EXPERIMENTS ON THE INSTABILITY OF THERMOCAPILLARY CONVECTION IN LARGE SCALE LIQUID BRIDGE

Wang Jia, Wu Di, Duan Li, Kang Qi

In this paper, PIV and thermal infrared camera are used to observe the flow field structure and temperature distribution respectively. In large Prandtl number condition, the critical temperature difference or the corresponding Marangoni number will tend to decrease with the increase of volume ratio and the ratio of height to diameter, besides, the fluid field can flow from stable state via unstable state to oscillation and will change along with the change of high aspect ratio. Traveling wave will appear when the Marangoni number exceeds the critical value, and chaos will follow with higher Marangoni number.

2015, 47(4): 580-586. doi: 10.6052/0459-1879-14-309

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UNCERTAINTY QUANTIFICATION AND GLOBAL SENSITIVITY ANALYSIS OF TRANSONIC AERODYNAMICS ABOUT AIRFOIL

Wu Xiaojing, Zhang Weiwei, Song Shufang, Ye Zhengyin

Considering the randomness of Mach number and angle of attack, the non-intrusive polynomial chaos method is employed to analyze the uncertainty and the corresponding global sensitivity indexes of transonic aerodynamics for the NACA0012 airfoil. In the paper, the uncertainty analysis and global sensitivity analysis about the aerodynamic loads, flow field and the aerodynamic coefficients are presented. The results of uncertainty analysis show that the flow characteristics in the shock disturbance region and the boundary-layer separation region are sensitive to the input uncertainties. This is the main reason for the aerodynamic performance fluctuations caused by parameter uncertainties. From the results of global sensitivity analysis, the fluctuations of flow characteristics near the shock wave region are dominated by Mach number. Moreover, the coupling effect between Mach number and angle of attack is significant and cannot be ignored in shock disturbance region. However, this coupling effect is very weak from the results of aerodynamic coefficients.

2015, 47(4): 587-595. doi: 10.6052/0459-1879-14-372

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STUDY ON CFD-BASED NUMERICAL VIRTUAL FLIGHT TECHNOLOGY AND PRELIMINARY APPLICATION

Chang Xinghua, Ma Rongy, Zhang Laiping, He Xin

Based on dynamic hybrid mesh and the coupling solver of N-S equations, rigid body dynamic equations and flight controlling law, a CFD-based numerical virtual flight technique is presented. A wing/store separation case is examined to validate the coupling solver. Finally, preliminary applications of this numerical method are carried out, including the attack angle controlling process, the acceleration load controlling process of a missile with and without Mach number varying. These cases demonstrate the robustness and accuracy of the present solver.

2015, 47(4): 596-604. doi: 10.6052/0459-1879-14-320

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RESEARCH ON ANALYTICAL AND NUMERICAL SOLUTIONS OF A MOVING BOUNDARY MODEL OF SEEPAGE FLOWIN LOW- PERMEABLE POROUS MEDIA

Liu Wenchao, Yao Juny, Chen Zhangxin, Liu Yuewu, Sun Haiy

The modes of non-Darcy seepage flow in low- permeable porous media with threshold pressure gradient belong to the moving boundary problems with strong nonlinearity. In this paper, a moving boundary model of one- dimensional non-Darcy seepage flow in low- permeable porous media with threshold pressure gradient is studied for the case of a variable pressure at the inner boundary. A similarity transformation method and a spatial coordinate transformation based finite difference method are applied to obtain the exact analytical solution and numerical solution of the moving boundary model, respectively. Research results show that the moving boundary model has a unique exact analytical solution, which also strictly verifies the accuracy of the numerical solution; and when the value of threshold pressure gradient tends to zero, the exact analytical solution of the moving boundary model of non-Darcy seepage flow can reduce to the one corresponding to Darcy's seepage flow. The formation pressure distribution curves with non- zero dimensionless threshold pressure gradient from these solutions exhibit the characteristics of compact support, which is obviously different from those corresponding to Darcy's flow model. Therefore, the study on the unsteady seepage flow problem in low- permeable porous media should take into account the effect of moving boundary condition. The presented research improves the theory of non-Darcy seepage flow in low- permeable porous media, and also builds theoretical foundation for the technologies of well testing interpretation and reservoir numerical simulation involved in the development of low- permeable oil and gas reservoirs.

2015, 47(4): 605-612. doi: 10.6052/0459-1879-14-385

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LARGE EDDY SIMULATION OF SAND RIPPLE EVOLUTION USING DISCRETE PARTICLE METHOD

Ji Chunning, Liu Danqing, Xu Dong

This paper numerically simulates the evolution of sand ripples in a turbulent open channel flow by using a methodology in which three numerical technologies were combined, i.e. the large eddy simulation, the "point-particle" immersed boundary method and the discrete particle method with coupled "event-driven" and "spring-dashpot" models. The accuracy and reliability of the numerical model were verified by comparing the numerical results of bed-load transport rate of a featureless sand bed with the results from empirical formulas at different Shields numbers. After that, the numerical model was applied in simulating the evolution process of sand ripples in a turbulent open channel flow. The time variations of the sediment transport rate, the length and height of the sand ripples, the maximum, averaged and minimum values of the effective bed location, the shape drag of the sand ripples and the bulk velocity were investigated. It was found that several sand ripples were developed from an initially flat sand bed in a short time period with tU_b/h ≈ 100. After that, the sand ripples grew up gradually and an significant coalescence was observed during tU_b=/h from 1600 ～ 2000. The sand ripples' height increases approximately linearly when their number is constant, while the mean sand ripples' length is invariant. With the increasing sand ripple height, the sediment transport rate and the bulk velocity decreases gradually, while the shape drag of sand ripples increases gradually. However, when the sand ripples merge, a rapid increasing pattern is observed in the curve of their height, together with large jumps observed in the curves of the transport rate, the bulk velocity and the shape drag of sand ripples. Under the same flow conditions, the sediment transport rate of a featured sand bed is lower than that of a featureless sand bed.

2015, 47(4): 613-623. doi: 10.6052/0459-1879-14-254

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EFFECTIVE STRESS PRINCIPLE OF NON-EQUILIBRIUM EVOLUTION AND LONG TERM STABILITY ANALYSIS OF ROCK MASS STRUCTURE

Zhang Long, Liu Yaoru, Yang Qiang

After excavation, the disturbed natural rock mass tends to be in non-equilibrium evolution state and affects the safety and stability of engineering structure. The time-dependent deformation and damage evolution are the cores of the non-equilibrium evolution process of rock mass structure. In this paper, the effective stress principle of non-equilibrium evolution is proposed within thermodynamics with internal state variables. The effective stress, which can really derive non-equilibrium evolution process, is only a portion of total stress. The rate of inelastic strain and energy dissipation rate can be expressed in form of effective stress, and concept of inelastic complementary energy is proposed. A creep constitutive equation with damage is derived through giving specific complementary energy density function and evolution function of internal state variables. Parameters identification of degraded one-dimension equation is conducted under one dimensional scene through uniaxial creep test of analogue material by load and unload method. Viscoplastic strain rate, rate of energy dissipation and inelastic complementary energy can be calculated, and the comparative discussion is illustrated. The results indicate that the difference between rates of inelastic strain is minor in primary and secondary creep stages but is major in tertiary stage because of theoretical error. The integral value of rate of energy dissipation in domain and inelastic complementary energy can characterize the non-equilibrium process of structure in actual effect and driving potential perspective respectively, and the latter is a more applicable one to assess the long-term stability of structure. At last, a case about deep buried tunnels is shown and its long-term stability is studied.

2015, 47(4): 624-633. doi: 10.6052/0459-1879-14-173

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A NEW MULTIAXIAL FATIGUE LIFE PREDICTION MODEL BASED ON THE NONPROPORTIONAL ADDITIONAL DAMAGE

Jiang Chao, Deng Qun, Li Bochuan

Based on the critical plane approach, this paper proposed a multiaxial low cycle fatigue life prediction model to correctly account for the non-proportional fatigue life reduction. Different from traditional critical plane models, in which only consider the effect of non-proportional additional cyclic hardening, the new model takes into account the influence of loading paths on fatigue life by introducing a non-proportional additional damage coefficient into the fatigue damage parameter. By taking the maximum shear strain plane and the maximum damage plane as the critical plane respectively, this model can also reflect the importance of the selected critical plane on the predicted life. Demonstrated by using the experiment data of eight kinds of materials from different published references, this new model is capable for application under both proportional and non-proportional loading conditions, which is very convenient for engineering application.

2015, 47(4): 634-641. doi: 10.6052/0459-1879-15-050

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ROBUST TOPOLOGY OPTIMIZATION DESIGN OF STRUCTURES WITH MULTIPLE-UNCERTAINTY LOAD CASES

Fu Zhifang, Zhao Junpeng, Wang Chunjie

The uncertainties existed in practical applications have great effect on the performance of structures, so it is necessary to introduce uncertainty in structural conceptual design. Robust topology optimization under multiple load cases with uncertainty was studied, where the magnitude and direction of each load are treated as random variables and their probability density functions are given. The weighted sum of the mean and standard deviation of the structural compliance is minimized. According to the superposition principle of linear theory, computational method for expected and variance of structural compliance was proposed. Sensitivity analysis method was developed based on the expressions of the expected and variance of compliance. For 2D structure with M load cases, the expected compliance and variance of structures as well as sensitivity information can be obtained for each load case, and then the object function as well as sensitivity can be achieved readily. In each load case, the expected compliance and variance of structures as well as sensitivity information can be obtained by solving the equilibrium equation under 2n deterministic load cases, where n is the number of uncertain loads. Algorithm of structural robust topology optimization to minimize the weighted sum of expectation and standard deviation of compliance under the constraint on the material volume was proposed and verified by numerical examples. The numerical examples also demonstrated the robustness of topology optimization results under multiple load cases with uncertainties. The proposed algorithm can be readily generalized into 3D cases.

2015, 47(4): 642-650. doi: 10.6052/0459-1879-15-072

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MULTIAXIAL PHENOMENOLOGICAL COMPRESSIBLE CONSTITUTIVE PARAMETERS FOR CLOSED-CELL ALUMINUM FOAMS

Zhang Jian, Zhao Guipingy, Lu Tianjian

A three-dimensional (3D) finite element model for real closed-cell aluminum foam specimen was constructed by employing the microfocus X-ray CT system, 3D reconstruction program and the commercially mesh generation program. By changing the boundary conditions of the 3D finite element models for real closed-cell aluminum foam specimen, eleven various stress states including uniaxial (sides coupling), hydrostatic and proportional compression loading were applied for analysis. The yield surface parameters of three compressible elasto-plastic constitutive models were obtained from numerical results. In testing hydrostatic compression, the crushable foam model with isotropic hardening in ABAQUS showed very serious deviation, especially at large strain levels. Chen-!-Lu constitutive models lightly underestimated the hydrostatic yield stress. The present volumetric hardening model was seem to give accurate predictions for both uniaxial and hydrostatic compressions.

2015, 47(4): 651-663. doi: 10.6052/0459-1879-15-086

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THE RESEARCH OF 2-DIMENSIONAL STANDINGWAVES ON ANNULAR PLATE

Fang Yizhong, Wang Gang, Shen Han, Cui Xintu, Liao Deju, Feng Raohui

The analytical solution of Chladni figures on a thin metal plate is a difficult problem in theoretical acoustics. The problem can be solved quite completely if the plate is circular or rectangular and the vibration frequency is low, but the solution becomes rather difficult if the plate is annular and the frequency is high. In this paper, the two-dimensional standing waves on an annular plate (Chladni figures) are investigated both experimentally and theoretically at two kinds of boundary conditions, the free outer edge with simply supported inner edge and both free edges , respectively. It is found that the Chladni figures can be precisely controlled by adjusting the vibrating frequency and position of the vibration source. Three kinds of patterns have been observed, only having circular nodal lines, only having radial nodal lines, and having both of the two kinds of nodal lines, distinguishedly. Furthermore, the approximate radial wave velocities, the radii of standing wave nodal circles in different frequencies, and the elastic modulus of the plate are also obtained. The results of experiments well correspond with those from the analytical solutions.

2015, 47(4): 664-671. doi: 10.6052/0459-1879-15-023

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INVESTIGATION ON SHAPED CHARGE PENETRATING INTO CONCRETE TARGETS

Wang Cheng, Wang Wanjuny, Ning Jianguo

Experiments for penetration into concrete by shaped charges with different liner materials, different cone angles, different liner thicknesses at different standoffs were performed in this paper. The influences of liner material, cone angle, liner thickness and standoff on crater diameter, hole diameter, crater depth and penetration depth were analyzed. Resistance of concrete target was calculated using the cavity expansion theory; penetration depth and hole diameter were predicted using the modified Bernoulli's equation and two-phase cavity expansion theory, and the theoretical results are consistent with the experimental ones. The formation processes of 57 different shaped charge penetrators with AUTODYN software were simulated, and the penetration processes into concrete for several typical shaped charge penetrators were also simulated. The simulation results of hole diameter and penetration depth are in good agreement with the experimental ones. Mechanism of crater formation under the action of shaped charge was investigated, which indicates that the mechanism of crater formation for aluminum liner is different from that for steel and copper liner.

2015, 47(4): 672-686. doi: 10.6052/0459-1879-14-336

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PHYSICS OF LASER PROPULSION UNDERWATER: EXPERIMENTS AND MODELING

Wu Xianqian, Wang Yiwei, Huang Chenguang

In the present research, physics of laser propulsion underwater was investigated by experiments and numerical simulation. Two physical processes of laser propulsion were observed in experiments. One is laser-matter interaction during laser irradiating propelled object, in which the laser induced plasma with short duration and high amplitude was generated. The object was propelled under the pressure of plasma. Another is bubble pulsation after the annihilation of plasma, resulting in the movement of object under bubble pressure with relative long duration. In addition, high speed of object was also observed for high impedance medium around the object and for propulsion near free surface of water. Based on the experiments, a physical model as well as simulation method were developed, by which the characteristics of laser propulsion underwater, including applied pressure and resistance histories, laser induced bubble pulsation, etc. were obtained. The simulated results agreed well with experiments, providing a valuable insight into the physics of laser propulsion underwater.

2015, 47(4): 687-698. doi: 10.6052/0459-1879-14-253

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BURSTING OSCILLATIONS AS WELL AS THE BIFURCATION MECHANISM INDUCED BY FAST SUBSYSTEM WITH MULTIPLE BALANCES

Chen Zhangyao, Chen Yaguang, Bi Qinsheng

By introducing subcircuit module and taking suitable values for the parameters as well as the characteristics of the nonlinear resistance, a four-dimensional generalized Hartley model whose fast subsystem has multiple balances is established. Based on the multiple balances as well as stabilities of the fast subsystem, bifurcation sets are derived, which divide the parameter space into different regions. In each region, nonlinear dynamical behaviors as well as the bifurcation patterns corresponding to different critical conditions are obtained. Two typical cases with different bifurcations are investigated, in which two different bursting oscillations with multiple balances of the fast subsystem involved are presented. Combining with the bifurcation analysis of the fast subsystem, the mechanism of the alternation between quiescent state and the spiking state is explored, which reveals that multiple balances of the fast subsystem not only may cause multiple quiescent states and spiking states to involve a periodic burster simultaneously, but also may lead to the multiplicity of patterns of bursting oscillations.

2015, 47(4): 699-706. doi: 10.6052/0459-1879-14-353

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A BRIEF INTRODUCTION OF COMPLETED KEY PROGRAM PROJECTS ON MECHANICS IN 2014

Zhang Panfeng, Zhan Shige, Xu Xianghong, Sun Zhongkui

The paper briefly introduced the completion and evaluation of 12 NSFC key program projects on mechanics in 2014. The projects list and the evaluation assessments provided by expert committee have been given in detail.

2015, 47(4): 707-711. doi: 10.6052/0459-1879-15-223

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