力学学报

STATIC SPREADING OF DROPLET IMPACT ON SOLID SURFACE：INFLUENCE FACTOR

Chen Shi, Tao Ying, Shen Shengqiang, Li Dewei

The droplet property has an important effect on the spreading area of a droplet impact on the solid surface. The theoretical method has been established to develop the mathematical model of the droplet based on the static force balance. We first obtained the mathematical expression of the relationship among the static spreading radius, the droplet physical parameters and the contact angle. A computational fluid dynamics (CFD) model was used to simulate drop dynamics on the solid surface. The static spreading radius and the static height solved by theoretical analysis are compared with those from simulation results. Theoretical results show reasonably good agreement with the simulation data. It has been demonstrated that for the different droplets on solid surface, the static spreading radius is determined with the density, the volume, the surface tension coefficient and the contact angle, and without the velocity.

2014, 46(3): 329-335. doi: 10.6052/0459-1879-14-012

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GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES

Li Zhihui, Jiang Xinyu, Wu Junlin, Peng Aoping

Based on the gas-kinetic unified algorithm (GKUA) for flows from rarefied transition to continuum, the effect of rotational non-equilibrium is investigated involving the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant, then the unified Boltzmann model equation involving rotational non-equilibrium effect is presented for various flow regimes. The molecular velocity distribution function is integrated by the weight factor on the energy of rotational motion, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The discrete velocity ordinate technique and numerical quadrature methods are applied to discretize the velocity space, and the gas-kinetic finite-difference numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in rotational non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of the Boltzmann kinetic model equation involving rotational non-equilibrium effect is presented for the whole range of flow regimes. As the applications of the GKUA, the hypersonic flows of diatomic gas involving rotational non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-25, the two-dimensional planar Ramp flow with the whole range of Knudsen numbers of 9×10^-4-10 and the three-dimensional re-entering hypersonic flows around sphere, tine double-cone and spacecraft body. The computed results match the relevant experimental data, DSMC results, and the solutions of the generalized Boltzmann equation (GBE) and ellipsoidal statistical (ES) model equation well. It is tested and validated from this study that the GKUA solving the Boltzmann model equation in rotational nonequilibrium can simulate the complex hypersonic flow problems and flow mechanisms from high rarefied free-molecule flow to continuum flow regimes with good reliability and precision.

2014, 46(3): 336-351. doi: 10.6052/0459-1879-13-246

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STUDIES ON THE AUTOIGNITION CHARACTERISTICS OF RP-3 AVIATION KEROSENE

Liang Jinhu, Wang Su, Zhang Can, Zhang Shengtao, Fan Bingcheng, Cui Jiping

In a shock tube preheated at a constant temperature of 135℃, the ignition delay characteristics of RP-3 aviation kerosene were studied behind reflected shock waves by monitoring the steepest rise of the characteristic emission of OH radical at 306.5nm. Experimental conditions covered a wider temperature range of 800～1450K, at pressures of 0.05, 0.1 and 0.2MPa, equivalence ratios of 0.5, 1 and 1.5, and oxygen concentration of 20% (mol). Under low-pressure conditions, the experimental results of ignition delay time were correlated with the temperature, pressure, stoichiometry, and the concentrations of kerosene and oxygen. The comparison between current data and the previous high-pressure results shows that a critical temperature exists about the effect of equivalence ratio on the ignition behavior of RP-3 kerosene. For the higher temperature range above the critical temperature, ignition delay time increases with increasing equivalence ratio, but decreases with increasing equivalence ratio for the lower temperature range below the critical temperature. This critical temperature also rises with decreasing the pressure. Meanwhile, the ignition process of kerosene was simulated by using three kinds of kerosene combustion kinetic models, and the comparison was made between the experimental and calculated results. The results show good agreement between experimental data and the prediction based on the model of Honnet et al. at high pressure of 2.2MPa, but some differences at lower pressures. The sensitivity analyses for different pressures indicate that the three-body reaction (H+O₂+M=HO₂+M) shows a slight inhibitory effect on kerosene ignition at high pressures, but a promoting effect at low pressures.

2014, 46(3): 352-360. doi: 10.6052/0459-1879-13-305

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STUDY ON ANALYSIS METHOD OF “THREE BOX” IN HEAT AND MASS TRANSFER PROCESS OF RESERVOIR MEDIA

Wang Zhiguo, Zhang Lei, Zhang Wenfu, Jia Yongying, Yin Chailing

The composition and structure of reservoir porous media are varied. It is di cult to obtain its full parameters, and the accurate description and analysis become di cult as well. In addition, the hydraulic conditions and mechanism of seepage process in porous media are complex, and there also has thermo-hydro-mechanical coupling e ect in porous media. So the current analysis methods and models have certain limitations. This paper presents the REV (representative elementary volume) description method of reservoir porous media. Based on the REV, the author established blackbox model, gray-box model and white-box model of porous media, and proposed "black box → gray box → white box" analysis process in porous media. Also based on black-box and gray-box models, the calculation formulas of REV thermal conductivity were derived, and heat balance equation of heat and mass transfer process was given. Combined with our reservoir thermal recovery situation, this paper analyzed the variation of the thermal conductivity and the characteristics of heat and mass transfer in steam drive, and obtained some useful results. This paper provided a new idea and method to analyze the heat and mass transfer in porous media.

2014, 46(3): 361-368. doi: 10.6052/0459-1879-13-379

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NUMERICAL SIMULATION FOR NAVIER-STOKES EQUATIONS BY PROJECTION/CHARACTERISTIC-BASED OPERATOR-SPLITTING FINITE ELEMENT METHOD

Shui Qingxiang, Wang Daguo

A novel finite element method, which is projection/Characteristic-based operator-splitting finite element method, is proposed for the prediction of unsteady incompressible N-S equations. In each time step, the equations are split into the diffusive part, the convective part and the pressure correction part. The temporal discretization of the convective part is performed by an exact characteristic-Galerkin method. The convective part is solved explicitly and a multistep technique is introduced to enlarge the calculation precision. The plane Poisseuille flow, the driven square flow and the flow over a circular cylinder are conducted to validate the model. It is show that the numerical results are close to reference results. In particularly, for the driven square flow at Re=10000, the flow becomes periodical in time and small vortex structure can be simulated.

2014, 46(3): 369-381. doi: 10.6052/0459-1879-13-253

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GAS WAVE IN FUNCTIONALLY GRADED MAGNETO-ELECTRO-ELASTIC COUPLED STRUCTURE

Zhao Xing, Liu Sai, Liu Jinxi

This paper investigates the propagation behaviors of air gas waves between a homogenous magneto-electro-elastic (MEE) half-space and a functionally graded MEE layer. The properties of functionally graded magneto-electro-elastic plate are assumed to vary exponentially in the direction of the thickness, and the surface is mechanically free and subjected to two kinds of electromagnetic boundary conditions. The dispersion equations are derived, and the numerical examples are provided to show the influences of graded variation, layer thickness and the electromagnetic boundary conditions on the phase velocity. The obtained results are of significance for the applications of functionally graded MEE materials to acoustic wave devices.

2014, 46(3): 382-388. doi: 10.6052/0459-1879-13-294

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NONLINEAR UNIFIED STRENGTH MODEL OF GEOMATERIALS

Du Xiuli, Ma Chao, Lu Dechun

The failure of material can be concluded to the shear fracture and each material has a specific shear sliding surface. The shear strength is the function of normal stress on sliding surface. A series of shear sliding surface is unified and nonlinear unified strength model of geo-materials is proposed. Sliding surface of nonlinear unified strength model is isoclinic surface in β stress space. The Strength surface of nonlinear unified strength model is circular conical surface in the β stress space and a series of conical surfaces are continuous smooth and convex in principal stress space. The nonlinear unified strength model can be illustrated as a curve between the Drucker-Prager and SMP in deviatoric plane, and as a straight line in meridian plane. There are only three mechanical parameters in the model which have definite physical meanings. Compared with large numbers of data under true triaxial tests, the applicability of nonlinear unified strength model is verified to different materials. And the proposed model can describe the nonlinear strength property of various materials reasonably.

2014, 46(3): 389-397. doi: 10.6052/0459-1879-13-312

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INSTABILITY OF SHAFT EXCAVATION AND MECHANISM OF ROCKBURST

Yin Youquan, Li Ping'en, Di Yuan

On the basis of stability theory and the analytical solutions of thick-walled cylinder of elasto-plastic material, the post-yield equibrium path of shaft excavation is tracked and adopted to stability analysis of the surrounding rock. The results show that the instability of surrounding rock and the occurrence of rockburst depend not only on the post-peak property of stress-strain total curve of rock material, but also on the type of equilibrium path curves during excavation of shaft. The equilibrium path curve describes the post-yield behaviour of the structure of surrounding rock, and can only be classified into two types. A point on the curve of one type is corresponding to a stable stage of the equilibrium, which accumulates plastic deformation but the instability not occurs. The other type is related to limit-point-type instability and displacement snap-through. The equilibrium path curve of shaft excavation is a key factor of inducing rockbursts of surrounding rock. The limit-point-type instability and displacement snap-through are possible mechanism of rockbursts in homogeneous rock.

2014, 46(3): 398-408. doi: 10.6052/0459-1879-13-308

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AN IMPROVED RESPONSE SURFACE METHOD BASED ON THE RESONABLE SUBDOMAIN

Zhao Weitao, Qiu Zhiping

The concept of reasonable subdomain is defined based on the theory of structural reliability in the paper. The size of domain around the design point which gives the main contribution to the failure probability is well-defined by using the reasonable subdomain. The failure points can be distributed in the reasonable subdomain in terms of a given probability. The proposed reasonable subdomain can solve the problem that the size of main domain influencing failure probability is not given obviously. Then, an improved response surface method is also proposed based on the reasonable subdomain. The proposed method can ensure that there is no fitting error of the response function at the design point, and can better fit the limit state function in the reasonable subdomain. The failure probability is evaluated by using the importance sampling Monte Carlo simulation. In order to improve the evaluation accuracy of failure probability, the evaluation method of subdomain is applied according to the locations of sample points. Numerical examples are shown that the proposed method has high accuracy and efficiency for both explicit and implicit limit states.

2014, 46(3): 409-416. doi: 10.6052/0459-1879-13-339

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A NEW SEMI-ANALYTIC ALGORITHM OF NEARLY SINGULAR INTEGRALS IN HIGH ORDER BOUNDARY ELEMENT ANALYSIS OF 3D POTENTIAL

Hu Zongjun, Niu Zhongrong, Cheng Changzheng

By analyzing the geometric feature of 8-noded quadrilateral element in three dimensional boundary element method (3D BEM), the relative distance is first defined as the approach degree from a source point to the high order surface element. And then a local polar coordinate ρθ is built which origin point is the project point of the source point on the element surface. The approximate singular kernel function is constructed corresponding to the nearly singular integral on high order surface elements in 3D potential BEM by a series of deduction, which has the same singularity as the nearly singular kernel function. The leading singular part is separated by subtracting the approximate kernel function from the original kernel function. Thus the nearly singular surface integrals on high order elements are transformed into the sum of both the non-singular integrals and singular integrals. The former can be efficiently computed by the Gaussian quadrature. The integral variables ρ and θ of the later are separated in the local polar coordinate. The singular surface integrals with respect to polar variable ρ are firstly expressed by the analytic formulations. Then the surface integrals are transformed into the line integrals with respect to variable θ, which can be evaluated by the Gaussian quadrature. Consequently, the new semi-analytic algorithm is established to calculate the nearly strongly and hyper-singular surface integrals on high order element in 3D potential BEM. Some numerical examples about the high order BE analysis for 3D heat conduction problems are given to demonstrate the efficiency and accuracy of the present semi-analytic algorithm. In comparison with the published regularization algorithm which is applied to calculating the nearly singular integrals on 3-noded triangular element, the present semi-analytic algorithm with 8-noded quadrilateral element can evaluate the potentials and potential gradients of inner points more close to the boundary. Moreover, the semi-analytic algorithm can be applied to more efficiently analyze thin structures in 3D potentials.

2014, 46(3): 417-427. doi: 10.6052/0459-1879-13-353

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A DIRECT METHOD FOR EVALUATING LINE INTEGRALS WITH ARBITRARY HIGH ORDER OF SINGULARITIES

Gao Xiaowei, Feng Weizhe, Yang Kai

This paper presents a new direct method for evaluating arbitrary singular boundary integrals appearing in 2D boundary element analysis. Firstly, geometry quantities on a curved line element are expressed using those projected on a tangential line. Then, singularities involved in the integrals are analytically removed by expressing the non-singular part of the integration kernel as power series. A set of formulations for computing the first and second derivatives of intrinsic coordinates with respect to local orthogonal coordinates are also presented in the paper for the first time. Since the coordinate transformation is at the real spatial scale, the operation is straightforward and convenient, and can be applied to treat arbitrary high order of singular integrals. Finally, some examples are given to verify the correctness and stability of the presented method.

2014, 46(3): 428-435. doi: 10.6052/0459-1879-13-248

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AN ARBITRARILY MIXED EXPLICIT-IMPLICIT ASYNCHRONOUS INTEGRATION ALGORITHM BASED ON UNIFORM DISCRETIZATION FORMAT

Zhang Weiwei, Jin Xianlong

Dynamical finite element method requires solving system information at each time step, and the computational effort is much larger than solving the static ones. Thus, to improve computational efficiency and save computational effort is one the of the main research content in dynamics. The present paper introduces an arbitrarily mixed explicit-implicit asynchronous integration algorithm based on uniform Newmark discretization format, for the efficiently solving of the large and complex dynamic systems. The overall dynamical system can be partitioned into different parts according to the physical and mechanical properties, as well as the requirements of solution accuracy, and the system equation can be solved in multi-scale both at the space domain and time domain. According to the inherent message passing mechanisms of the explicit and implicit algorithm, a variable boundary treatment method was adopted to avoid the accumulation of errors at the asynchronous boundary. The simulation time steps were dynamically determined and corrected according to the energy balance checking, which can effectively prevent the emergence and development of the instability. Numerical example shows that the proposed algorithm can greatly reduce the consumption of computing resources while maintaining high accuracy, thus it has a high practical value.

2014, 46(3): 436-446. doi: 10.6052/0459-1879-13-260

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RESEARCH FOR ATTRACTING REGION AND EXIT PROBLEM OF A PIECEWISE LINEAR SYSTEM UNDER PERIODIC AND WHITE NOISE EXCITATIONS

Kong Chen, Liu Xianbin

Exit behaviour is one of the significant phenomena of stochastic nonlinear systems, other than the theory of random dynamical system, the exit problem is an another way to investigate the stochastic stability for a stochastic nonlinear system. The piecewise linear system is a classical model in non-linear dynamics, for which, the stochastic excitation leads to a stochastic system, not a rigorous random dynamical system, and then the theory of random dynamical system is not applicable. Thus, in order to learn the stochastic dynamical behaviours for a piecewise linear system that is under a periodic and a Gaussian white noise excitations, its exit behaviour is examined in the present paper via investigating the mean first-passage time which is one of the most important quantities within exit problem and is also used to quantify the global stability of a stochastic system. Some numerical experiments are designed to investigate the deterministic dynamical behaviors in the case that only the periodic excitations are added, and based upon the Monte Carlo simulation, the other numerical procedures are designed to reveal the exit behavior of the system that is under both periodic and Gaussian white noise excitations. In order to obtain the analytical expression of the mean first-passage time, van der Pol transition and stochastic averaging method are firstly applied to simplify the system, then singular perturbation method and ray method are used to quantify the mean first-passage time. Comparing the analytical results with the analog ones, we conclude that if the attracting boundary is fractal, the two results are far different; otherwise if the attracting boundary is smooth enough, the two results match very well.

2014, 46(3): 447-456. doi: 10.6052/0459-1879-13-300

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MATHEMATICAL MODELING AND EXPERIMENTAL STUDY ON SIT-TO-STAND PROCESS BASED ON ASSISTIVE STANDING-UP ROBOT

Wang Zhiqiang, Jiang Hongyuan, Roman Kamink

The new assistive standing-up robot followed the rule of sit-to-stand movement was developed. Mathematical model during standing-up motion was built by using Newton-Euler approach for kinetics analysis. Force and moment equilibrium equations were obtained and simulation model was built in Simulink by standing up with robot-aided, robot and arms supported and robot, arm and lower limbs of weakness of muscle strength. By means of assistive standing-up robot and sensors, force and moment were measured and analyzed. The results show that standing-up robot can be efficiently used to assist the rising, especially in initial stage, in spite of sit-to-stand aided-method. Arm-supported standing-up maneuver can keep the posture balance and stable, and has compensation ability of necessary force and moment of lower extremity, particularly close to upright standing posture,and force and moment can be predicted accurately by the standing posture simulation model. Lower limbs of deficient muscle strength play limited role to assist the rising.

2014, 46(3): 457-464. doi: 10.6052/0459-1879-13-304

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AN INVESTIGATION OF BIOMECHANICAL MECHANISMS OF OCCUPANT FEMUR INJURIES UNDER COMPRESSION-BENDING LOAD

Jiang Xiaoqing, Yang Jikuang, Wang Bingyu, Zhang Weigang

Occupant femur fractures occur frequently under compression-bending load in the frontal crashes of passenger cars. In order to explore the injury mechanisms and tolerances of occupants' femur in this load condition, a finite element model of the lower extremity in the sitting posture was developed based on the anatomy of a 50th percentile male. Then the model was validated against two types of cadaver tests, including three-point dynamic bending test of the femur and the axial impact test on the knee-thigh complex. A study of femur fractures under compression-bending load has been carried out using an analytical model of the curved beam. Furthermore, six virtual tests were conducted using the validated finite element model. The results show that the location of bone fractures and the tolerance of the femur depend on both bending load and axial compression. With the increasing preload of the bending moment from 0 to 676Nm, the femur fracture location was shift from the femoral neck to the shaft. Regarding the tests with fractures occurring in the femoral neck, the tolerance of the femur is between 285 and 296Nm. For the other tests with fractures located in the femoral shaft, the tolerance of the femur is between 381 and 443Nm. The results indicated that the femur fractures always occurred at the femoral neck in axial impact tests on the knee-thigh complex, but in real world car frontal impacts the femoral shaft fractures can be observed frequently.

2014, 46(3): 465-474. doi: 10.6052/0459-1879-13-282

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EXPERIMENTALLY STUDY OF THE RICHTMYER-MESHKOV INSTABILITY AT N₂/SF₆ FLAT INTERFACES BY DIFFRACTED INCIDENT SHOCK WAVES AND RESHOCK

Liu Jinhong, Zou Liyong, Cao Renyi, Liao Shenfei, Wang Yanping

The developments of Richtmyer-Meshkov instability at gas interface subjected to a diffracted incident shock wave of low Mach number and reshock wave have been experimentally studied using the high-speed schlieren photography. The planar shock wave diffracted over a cylindrical column produces local perturbation at the gas interface. It has been demonstrated that the thickness of the interface grows slowly under the incident shock wave, while spike and bubble are clearly observed upon reshock. Moreover, the interaction between the reshock wave and the boundary layer generates wall vortices, which accelerates the development of turbulence mixing zone (TMZ). The post-reshock growth rate of TMZ is almost independent of pre-reshock conditions and in good agreement with the prediction of Mikaelian model. The reflected rarefaction wave from wall-end also accelerates the development of TMZ.

2014, 46(3): 475-479. doi: 10.6052/0459-1879-13-355

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A WAVELET THRESHOLDING DENSITY-BASED ADAPTIVE IMPORTANCE SAMPING METHOD

Dai Hongzhe, Xue Guofeng, Wang Wei

This study develops an efficient adaptive importance sampling method based on nonlinear wavelet thresholding for reliability analysis. In the proposed method, the pre-sampling samples, which fall in the failure region, are used to estimate the density via the nonlinear wavelet thresholding estimator, and the density obtained is applied as the near-optimal sampling density to implement the importance sampling. Compared with the kernel density estimator, the nonlinear wavelet thresholding density estimator has a high degree of flexibility in terms of convergence rate and smoothness, moreover, the choice of the initial parameters slightly affects the accuracy of the method. Therefore, the proposed method can achieve comparable accuracy with fewer pre-sampling samples and improve the computational efficiency of the traditional method. Numerical examples show that the proposed method is applicable for wide-range reliability problems with multi-design points or noisy limit state functions.

2014, 46(3): 480-484. doi: 10.6052/0459-1879-13-303

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THE INTRODUCTION OF APPLICATION PROJECTS ON MECHANICS IN 2014

Zhan Shige, Zhang Panfeng, Wang Lifeng, Xu Xianghong

The paper introduced the applications for NSFC programs on mechanics in 2014. The statistics of application projects for General Programs, Young Scientists Fund, Fund for Less Developed Regions, Key Programs, Excellent Young Scientists Fund, National Science Fund for Distinguished Young Scholars and Joint Research Fund for Overseas Chinese Scholars and Scholars in Hong Kong and Macao are presented and compared with applications in 2013.

2014, 46(3): 485-486.

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