力学学报

RESEARCH DEVELOPMENTS OF SMOOTHED PARTICLE HYDRODYNAMICS METHOD AND ITS COUPLING WITH FINITE ELEMENT METHOD

Hu Dean, Han Xu, Xiao Yihua, Yang Gang

The merits and shortcomings are existed simultaneously in finite element method (FEM) and smoothed particle hydrodynamics (SPH) method, in which these methods are established based on Lagrange system. In order to makes use of high computational efficiency of FEM and advantages of SPH method, such as naturally simulation of large deformation of material, the coupling algorithm of FEM with SPH method is presented to calculate region of small deformation by FEM and simulate region of large deformation by SPH method. In this paper, the research and application of FEM, SPH and FEM-SPH coupling algorithm are reviewed. And the problems existing in these methods are also discussed. Finally, the computational accuracy and efficiency of FEM, SPH and FEM-SPH coupling algorithm are investigated by a numerical example, which is a reference for research fellows.

2013, 45(5): 639-652. doi: 10.6052/0459-1879-13-092

PDF

MOLECULAR SIMULATION OF DRIVEN CAVITY FLOWS WITH HIGH REYNOLDS NUMBER

Fei Fei, Fan Jing

Cavity flow is simulated using the diffusive information preservation (D-IP) method. The D-IP method is a molecular simulation scheme based on a viewpoint of molecular diffusion, and it greatly releases the time step and cell size limitations of the DSMC method that become too strict to meet as the Reynolds number increases. The Reynolds number in the present calculations ranges from 10² to 10⁴, while the time step and cell size of D-IP are tens of times or even hundreds of times more than the molecular mean collision time and mean free path, respectively. The stream-wise distributions, as well as the fine structures of vortices, obtained by the D-IP method, are compared with the numerical solutions of the Navier-Stokes equations and found to be in good agreement.

2013, 45(5): 653-659. doi: 10.6052/0459-1879-13-064

PDF

THE RENORMALIZATION-GROUP ANALYSIS FOR THE STATISTICAL PROPERTIES OF RAPIDLY ROTATING TURBULENCE

Wang Xiaohong, Zhou Quan

The statistical properties for rapidly rotating turbulence are investigated using the renormalization-group method. With the renormalized perturbation, the high wavenumber velocity components are taken to be average successively. The calculations show that the renormalized viscosity, which represents the influence of the high wavenumber velocity components upon the low wavenumber velocity components, tends to zero at the limit of the rotational angular velocity Ω → ∞. It indicates that the Coriolis force will impede the nonlinear interactions among different wavenumber velocity components. At the limit Ω → ∞, the turbulent energy cascade will diminish to zero. Consequently the flow tends towards laminarization as the turbulent fluctuations disappear. The calculations also show that the space-time Fourier velocity components tend to two-dimensionalization and the spherically averaged energy spectrum have the scaling behavior E(k) ∝ k^-3 for rapidly rotating turbulence.

2013, 45(5): 660-665. doi: 10.6052/0459-1879-13-047

PDF

AN EFFICIENT SOLUTION FOR 2D RAYLEIGH-BÉNARD CONVECTION USING FFT

Xu Wei, Bao Yun

The computation efficiency of direct numerical simulation (DNS) for Rayleigh-Bénard (RB) convection in rectangular containers is studied. For unsteady flow of RB convection, the solution of pressure Poisson's equation is a key issue affecting the computation efficiency in the whole solving process. Combined with fast Fourier transform (FFT) and chase method, a direct solution of pressure Poisson's equation is presented. Comparing the precision and speed with hopscotch overrelaxation iteration, it is found that the direct solution of pressure poisson equation for RB convection using FFT is efficient. The results of temperature fields for the plume and the large scale circulation, and the change of Nu number for series Ra numbers are given.

2013, 45(5): 666-671. doi: 10.6052/0459-1879-12-334

PDF

DIRECT NUMERICAL SIMULATION OF TURBINE CASCADE FLOW WITH HEAT TRANSFER EFFECTS

Zhu Haitao, Shan Peng

Low-Reynolds number flow has a significant effect on the performance of high-altitude aircraft engines, especially the turbine parts. In this paper, the low-Reynolds number flow around a turbine cascade was numerically simulated by directly solving the two-dimensional compressible Navier-Stokes equations using a finite difference scheme with 7th-order. The flow Reynolds number is 241800 based on the blade chord, and there exists thermal conduction on the turbine blade surfaces. In the time-averaged flowfield, the pressure on the blade surface agrees well with the experimental data. So does the distribution of Stanton number, except in the turbulence region on the suction surface. For the instantaneous flow, the unsteady flow near the entrance of cascade passage is very weak. But, at the trailing edge of the blade, there exists periodical vortex-shedding on both the pressure and suction surfaces. The vortex-shedding makes the total pressure in the cascade passage and the wake varies periodically, and the main frequency in the wake is double of that in the cascade channel. Besides, the distribution of the second order statistic of pulse velocity in the wake is similar to that of the flow around the cylinder.

2013, 45(5): 672-680. doi: 10.6052/0459-1879-12-356

PDF

STABILITY OF ULTRATHIN LIQUID FILM EVOLUTION WITH SURFACTANT

Ye Xuemin, Jiang Kai, Shen Lei, Li Chunxi

For an ultrathin liquid film thickness less than 100 nm, instability often accompanies ultrathin liquid film flow driven by surfactant on solid substrate. In present paper, the process of film evolution under the effect of disjoining pressure was simulated with three evolution equations for the film thickness, surfactant interfacial and bulk concentration, which are derived in lubrication approximation. The effects of characteristic parameters on the stability of evolution process are analyzed, and the coincidence between the stability prediction based on linear theory and the simulation results with nonlinear characteristic equation derived with regular modules method is compared. Results show that van der Waals forces promote the instability characteristic while Born repulsion depress it; the secondary instability occurs on the depression section of the film under the condition of small capillary number, which results in a dewetting structure formation ultimately; the increasing of initial value of the film thickness and surfactant bulk concentration enhances the stability of film evolution, however, the increasing of interfacial concentration and the adsorption coefficient leads to an opposite effect instead.

2013, 45(5): 681-689. doi: 10.6052/0459-1879-12-381

PDF

AN APPROXIMATE MODEL OF UNSTEADY AERODYNAMICS FOR HYPERSONIC PROBLEMS AT HIGH ALTITUDE

Han Hanqiao, Zhang Chen'an, Wang Famin

The paper introduces a local piston theory with viscous correction for the prediction of hypersonic unsteady aerodynamic loads at high altitude where viscous interaction cannot be ignored. A semi-empirical relation for the determination of effective shape for this method at high Mach number and high altitude is presented based on steady Navier-Stokes equations, and validation of the relation is also completed by numerical method. Furthermore, a series of two-dimensional numerical examples with various Mach numbers, angles of attack and operating altitudes for typical thin airfoil and typical blunt airfoil are provided. The unsteady aerodynamic force coefficients are in well agreement with the unsteady Navier-Stokes predictions with altitude in the range of 40 to 70 km and Mach number in the range of 10 to 20. Compared with classical piston theory and local piston theory based on steady Euler equations, this model performs much better at high Mach number and high altitudes when the viscous interaction effects are strong. This model can be applied in supersonic/hypersonic problems with wide range of Mach number, angle of attack and altitude, and has much higher computational efficiency than unsteady Navier-Stokes equations.

2013, 45(5): 690-698. doi: 10.6052/0459-1879-12-382

PDF

THE NUMERICAL STUDY OF LATTICE BOLTZMANN METHOD BASED ON DIFFERENT GRID STRUCTURE

An Bo, Sang Weimin

In this paper, we mainly focus on the different grid structures used in lattice Boltzmann method (LBM). We present corresponding methods for each grid structure. As we know, in the numerical simulations based on the traditional LBM, the standard uniform grid is always hired. This is up to the discrete velocities on the grid node. Yet, it is a thorny question when the LBM is employed to solving problems with complex boundaries, due to the grid structure of standard uniform grid itself. And this shortcoming would decrease the applicability of LBM. Besides, for those complicated flows, it is necessary to have enough meshes to capture the flow information in the zones where the flow state changes fiercely. In another word, if there are too many grids, it will greatly enlarge the computational burden with the use of standard uniform grid. On the other side, if the grids are not enough, it is hard to get a satisfied result. This dilemma greatly decreases the efficiency of LBM. For solving those questions above, we use different grid structures to improve the applicability and efficiency of LBM. In this paper, we perform the simulations of the lid-driven flow of cavity, flow around cylinder and flow around airfoil as our numerical cases.

2013, 45(5): 699-706. doi: 10.6052/0459-1879-12-333

PDF

A STUDY ON JET PHENOMENON OF R₂₂ GAS CYLINDER UNDER THE IMPACT OF SHOCK WAVE

Wang Ge, Guan Ben

The jet formation of a heavy gas cylinder under planar shock wave impact is a very interesting phenomenon which is closely associated with the gas properties and the shock wave strength. It is worthwhile to investigate the complex wave structure in this process due to its academic value. The R₂₂ cylinder jet formation process under planar shock wave impact is simulated using Level Set method to capture the gaseous interface, and rGFM to define the interfacial boundary conditions. The development of wave structure is elucidated, typical wave patterns that lead to the jet formation is highlighted, and the reason of the jet formation is expounded from a perspective of wave pattern. Cases with different shock strengths are presented in this study. It is found that the shock strength plays an important role in determining the formation of jet and even the characteristics of the jet structure if the jet is formed. A critical shock strength is concluded beyond which the jet cannot be formed. It is expected that the presented results could guide and verify the experimental results.

2013, 45(5): 707-715. doi: 10.6052/0459-1879-12-380

PDF

INTERNAL SOLITARY WAVE LOADS EXPERIMENTS AND ITS THEORETICAL MODEL FOR A CYLINDRICAL STRUCTURE

Huang Wenhao, You Yunxiang, Wang Xu, Hu Tianqun

Series experiments are conducted to investigate interaction characteristics of internal solitary waves with a cylindrical structure in a large-scale gravity type density stratified tank. Based on KdV, eKdV and MCC theories for internal solitary waves in a two-layer fluid of finite depth, a theoretical predicting model is established for internal solitary wave loads on a cylindrical structure, and the applicability conditions for these internal solitary wave theories are presented in order to apply such a load predicting model. It is showed that the horizontal load on the cylindrical structure due to the internal solitary wave consists of the horizontal Froude-Krylov, added mass and drag forces, respectively, which can be determined by Morison formula, while the vertical load mainly is the vertical Froude-Krylov force which can be obtained from the dynamic pressure induced by the internal solitary wave. Results for series experiments show that the added mass coefficient can be taken to be a constant value of approximately 1.0, and there exists an exponential function relationship between the drag force coefficient and the Reynolds number based on the velocity field induced by the internal solitary wave. Moreover, the numerical results based on the theoretical predicting model have good agreement with experimental ones. The investigation provides a practical theoretical model for predicting internal solitary wave loads on marine engineering structures due to internal solitary waves on the basis of the series experiment results.

2013, 45(5): 716-728. doi: 10.6052/0459-1879-12-298

PDF

EXPERIMENTAL AND THEORETICAL INVESTIGATIONS ON THE VELOCITY OSCILLATIONS OF DYNAMIC CRACK PROPAGATING IN BRITTLE MATERIAL TENSION

Zhang Zhenya, Duan Zhong, Zhou Fenghua

To study the propagating behavior of a dynamic crack in brittle material, an experimental technique was developed to measure the propagation speed of a fast crack in a preloaded brittle polymethylmethacrylate (PMMA) strip. The experimental results show that for each preloaded strip, the crack arrives at a steady velocity v₀ after a short acceleration stage, when the crack propagation is self-similar. The steady propagation velocity was found to be an increasing function of the energy G_c stored in the preloaded strip, which means that the material has a "speed toughening" property. When the crack speed exceeds a threshold, the crack speed exhibits apparent oscillations. This crack speed oscillation corresponds to the microscopic periodic grooves on the fractured surface. Further increase of the pre-stored elastic energy results in the curving, micro-branching, and full bifurcations of the cracks. Based on the energy conservation theory, a dynamic model is established to describe the motion of the crack. This motion equation is used to explain the crack speed oscillations during propagations.

2013, 45(5): 729-738. doi: 10.6052/0459-1879-13-056

PDF

RESEARCH OF CONSTITUTIVE RELATION CORRECTION OF GEOTECHNICAL MATERIALS AND THEORETICAL SOLUTION DUE TO PILE-SOIL INTERACTION

Gao Zikun, Shi Jianyong

The size of modulus is directly related to the value of pre-consolidation pressure and the additional volume strain due to pile-soil interaction for geotechnical materials. First, the paper analyzes the main factors of constitutive models for the materials, considering its changes with depth and volumetric strain. Tensile modulus in Duncan-Chang constitutive model is revised based on the above analysis. Then, the mechanical model due to pile-soil interaction is established considering the effect of the displacement boundary of the interaction and the above-mentioned non-linearity of the materials. The theoretical solutions of soil displacement, strain and stress, are obtained based on the variation principle. Finally, comparisons are made to prove the reasonability of the results, using the classical CEM results and the passive soil pressure theory.

2013, 45(5): 739-745. doi: 10.6052/0459-1879-13-005

PDF

DYNAMIC ANALYSIS OF SPINNING DEPLOYMENT OF A SOLAR SAIL COMPOSED OF VISCOELASTIC MEMBRANES

Zhao Jiang, Liu Cheng, Tian Qiang, Hu Haiyan

In recent years, increasing attention has been paid to the spinning deployment technology of solar sails for spacecraft. Such a solar sail can be regarded as a rigid-flexible multibody system mainly composed of a central rotating hub, a number of flexible thin tethers, sail membranes and tip masses. In order to model the sail membrane, a viscoelastic finite element of thin plate is proposed via the absolute nodal coordinate formulation (ANCF) and the efficacy of the finite element is testified first. Then, a simplified spinning deployable "IKAROS" model is established by using the absolute-coordinate-based (ACB) method in combination with ANCF and the natural coordinate formulation (NCF). Afterwards, a large set of stiff equations of system dynamics is solved by using the Generalized-α method. Therefore, the deployment dynamics of the system is well analyzed and the influence of the viscoelastic damping in the membranes on the deployment dynamics is discussed.

2013, 45(5): 746-754. doi: 10.6052/0459-1879-13-002

PDF

DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE SUSPENSION WITH TIME DELAY

Shen Yongjun, Zhao Yongxiang, Tian Jiayu, Yang Shaopu

The dynamical analysis on a single degree-of-freedom semi-active suspension system with time delay is completed in this paper, where the limited relative displacement control is adopted in this system. The first-order approximately analytical solution is obtained by the averaging method, and the stability condition is set up based on Lyapunov theory. The results show that the steady-state amplitude of the approximate solution and the stability conditions are all periodic functions of time delay, and have the same period as the excitation one. Through the comparison of the amplitude-frequency curves obtained by the approximate solution and the numerical method, the correctness and satisfactory precision of the approximate solution are verified. The chattering phenomenon of semi-active control existing in high frequency is also explained. Moreover, the passive suspension is also researched analytically and compared with the semi-active one, and the results confirm the superiority of semi-active suspension. Finally, the effects of some key system parameters on control performance, including the control clearance, time delay and minimum damping ratio, are discussed.

2013, 45(5): 755-762. doi: 10.6052/0459-1879-13-017

PDF

THE EVOLUTION CHARACTERIZATION OF LIBRATIN POINT ORBITS AND APPLICATION RESEARCH

Cheng Yu, Yuan Jianping, Luo Jianjun

In the context of three-body problem, the behavior of trajectory in the vicinity of the smaller primary is difficult to predict because of the complicated gravity. The most challenging problem in preliminary design is to effectively select an appropriate initial solution. The periapsis Poincaré maps are applied to analyze the short-term and long-term behaviors of libration point orbits in planar three-body problem. The design space is significantly reduced and classified into escape and capture regions according to the periapse location. For short-term escape orbit, the homoclinic and heteroclinic trajectory design methods are present, and two-level differential correction is utilized to solve the position discontinuity problem at the patch point. For the long-term capture trajectory, several typical periodic and quasi-periodic orbits are achieved. Furthermore, the prograde trajectory is usually quasi-periodic, and proves much more stable than retrograde trajectory. With the application of periapsis Poincaré maps, the initial state corresponding to different type of trajectory is quickly determined, which provides a fast and available design tool for specific mission.

2013, 45(5): 763-771. doi: 10.6052/0459-1879-12-353

PDF

TR PIV INVESTIGATION ON THE LAGRANGIAN HAIRPIN VORTICES INDUCED BY A CUBIC DISTURBANCE

Quanji Zhuojun, Jiang Nan, Tang Zhanqi

The hairpin vortices structure induced by a cubic disturbance with a frequency of 2.1 Hz are investigated by time-resolved particle image velocimetry (TR PIV) from both the Euler and Lagrangian view. Firstly, the hairpin vortices' heads could be clearly distinguished form the side-view database, which also indicates that the hairpin heads lift up when convecting down streamwise. Then, the finite-time lyapunov exponents (FTLE) method is utilized to describe the lagrangian hairpin vortices induced by the cubic. It could be seen that FTLE clearly shows both the projection of the hairpin heads and the hairpin necks in the streamwise and spanwise plane. Furthermore, two-point correlation of FTLE at different reference positions along the streamwise indicate that the hairpin vortices statistically with an increasing inclined angle with the flat plate while they are moving downstream.

2013, 45(5): 772-776. doi: 10.6052/0459-1879-12-361

PDF

WIND TUNNEL FREE-FLIGHT TEST WITH BIPLANAR OPTICAL SYSTEM ON THE SPINNING BLUNT CONE

Jiang Zenghui, Chen Nong

Wind-tunnel free-flight tests with biplanar optical system were conducted at Mach 6 in the hypersonic wind tunnel, to investigate the dynamic stability of the spinning blunt cone. Due to the application of a two-plane orthogonal optical system in wind-tunnel free-flight tests, both views in horizontal and vertical plane can be recorded synchronizingly. And the two views of coning motion can also be observed directly. With the record angular motion results in both views, identification method of biplanar is studied. Then the static and dynamic derivative coefficients of the models are acquired, and dynamic stability criterion is obtained.

2013, 45(5): 777-781. doi: 10.6052/0459-1879-12-358

PDF

THE OSCILLATION MODE OF INCOMPRESSIBLE CAVITY FLOW

Li Huan, Fang Tao, Wu Fangliang, Li Wanping

The numerical calculation of the cavity flow using 2D-LES method has been conducted to examine how the momentum loss thickness and inflow velocity at the cavity leading edge affect the cavity flow oscillations, and how the length-to-depth ratio of the cavity is related to the oscillation modes of the cavity flow. PIV measurements of cavity flows verify the credibility of the results of numerical calculation. The results show that the friction velocity determines whether or not the flow of water over the cavity will oscillate. The instantaneous vortex structures and the cavity drag coefficients identify two typical modes of oscillation, the shear layer mode and wake mode. The key factor that determines the oscillation mode is the length-to-depth ratio of the cavity.

2013, 45(5): 782-786. doi: 10.6052/0459-1879-12-213

PDF

AN APPLICATION OF THE CBS SCHEME IN THE FLUID-MEMBRANE INTERACTION

Sun Xu, Zhang Jiazhong, Huang Biwu

A finite element scheme for the fluid-membrane interaction is proposed. First, governing equations for the incompressible flow and the elastic membrane are presented. Then, the proposed algorithm is discussed in detail. By this method, an improved characteristic-based split (CBS) scheme is combined with the dual-time stepping method and taken as the flow solver, and the Aitken method is applied to accelerate the convergence of the iteration. The governing equation of the structure is discretized by the Galerkin finite element method and the Generalized-α method, and the obtained nonlinear algebraic equations are solved by the Newton-Raphson method. Moreover, the spring analogy method is used for mesh moving, and the flow and structure solvers are loosely coupled. Finally, the proposed method is applied to a benchmark problem, namely, the driven cavity with flexible bottom, and the stability and accuracy of the proposed method are verified. In addition, it is found that the convergence rate of the flow solver can be increased significantly by the Aitken method.

2013, 45(5): 787-791. doi: 10.6052/0459-1879-13-003

PDF

MAGNETO-THERMO-ELASTIC COUPLED DYNAMICS EQUATIONS OF AXIALLY MOVING CARRY CURRENT PLATE IN MAGNETIC FIELD

Hu Yuda, Zhang Jinzhi

The theory of In this study, magneto-thermo-elastic coupled dynamics modeling for axially moving carry current plate in magnetic field is investigated. Considering geometric nonlinearity and thermal effect, the expressions of kinetic energy, strain energy and virtual work done by external force were derived. The nonlinear force-electro-magneto- thermo-elastic coupled vibration equations of an axially moving current-conducting thin plate were deduced for the first time in this paper by using Hamilton principle. Based on the Maxwell equations, considering the corresponding electromagnetic constitutive relations and electromagnetic boundary conditions, the electrodynamics equations and electromagnetic forces expressions of axially moving carry current thin plate in general magnetic field were derived and thermal conduction equation caused by Joule heat was also presented. Numerical example shows that magnetic field carries significant effect on the bifurcation characteristics. These results are expected to be a theoretical reference for further analysis of this case.

2013, 45(5): 792-796. doi: 10.6052/0459-1879-12-330

PDF

2013, 45(5): 797-814.

PDF

2013 Vol. 45, No. 5

NoticeMORE+

Exquisite ArticlesMORE+

Download Center

Author Center