力学学报

LARGE-EDDY SIMULATION AND DOUBLE-AVERAGING ANALYSIS OF OPEN-CHANNEL FLOW OVER A PERMEABLE BED

Han Xu, He Guojian, Fang Hongwei, Fu Songy

This study focuses on the double-averaging (DA) turbulence characteristics of flow over an idealized permeable bed using the large-eddy simulation (LES). To discuss the spatial heterogeneity, the vertical distributions of DA velocity, DA Reynold shear stress (RSS), DA form-induced shear stress (FISS) and turbulence intensities in different positions are analyzed. It is shown that the spatial heterogeneity has a little influence in the upper flow region, and the distribution of DA velocity corresponds to the logarithmic law. The Von Karman constant obtained is significantly less than the normal value because of permeability. In the vicinity of bed, the spatial heterogeneity has a significant effect on the velocity distributions, which match with a polynomial series and a linear series respectively. Within the permeable bed, the peak velocity at lower pore is 1.55 times larger than that at upper pore. Above the crest bed level, the DA Reynolds shear stress is 95% of the total DA shear stress. The DA form-induced shear stress is 15% of the total DA shear stress occurring at the virtual bed level. The distributions of turbulence intensities in different positions show some discrepancies, which result from the spatial heterogeneity.

2015, 47(5): 713-721. doi: 10.6052/0459-1879-14-382

HTML PDF

NUMERICAL INVESTIGATION ON FLOW STABILITY OF RAYLEIGH-B?NARD CONVECTION OF COLD WATER IN A RECTANGULAR CAVITY COOLED AND HEATED SYMMETRICALLY RELATIVE TO THE TEMPERATURE OF DENSITY MAXIMUM

Hu Yupeng, Li Yourongy

In order to understand the special phenomena and laws of Rayleigh-Bénard convection of fluids with density extremum, a series of three-dimensional numerical simulations on Rayleigh-Bénard convection of cold water in a rectangular cavity when its horizontal walls were cooled and heated symmetrically relative to the temperature of the density extremum by using finite volume method is carried out. Flow structures and their bifurcation series are obtained, and the effects of the density extremum character, the Rayleigh number, the thermal boundary condition and the aspect ratio on Rayleigh-Bénard convection are discussed. The results demonstrate that the system of Rayleigh-Bénard convection of cold water with density extremum is much more stable than that of common fluid, and the flow structures and their bifurcation series are much more complex. Multiple flow patterns can coexist at a constant Rayleigh number and hysteresis phenomenon is observed in the flow evolution. The system loses its stability more easily and the heat transfer ability enhances with the increase of the aspect ratio. The system for conducting sidewalls is much more stable than that for insulating sidewalls and the heat transfer ability weakens. Furthermore, heat transfer correlations are proposed according to the multiple linear regression.

2015, 47(5): 722-730. doi: 10.6052/0459-1879-15-171

HTML PDF

NUMERICAL INVESTIGATION ON THE ASYMMETRIC VIBRATION AND SYMMETRY HYSTERESIS OF FLOW-INDUCED VIBRATION OF TWO SIDE-BY-SIDE CYLINDERS

Chen Weilin, Ji Chunning, Xu Wanhai

Flow-induced vibration of two side-by-side circular cylinders at Re= 100 is numerically investigated. The cylinders are constrained to oscillate in the cross-flow direction with a center-to-center spacing ratio s/D = 2.5 and 5.0. The mass ratio of the cylinders is 2.0 and the reduced velocity is U_r= 2.0 ～ 10.0. The results show that, for the case with s/D = 2.5, asymmetric vibrations of the two side-by-side cylinders is observed in 4.0 < U_r< 4.8, while the symmetry hysteresis is observed in 4.4 < U_r< 4.8. However, for the case with s/D = 5.0, both two phenomena disappear and the vibration responses of two side-by-side circular cylinders are close to those of an isolated circular cylinder. Moreover, it was found that the lift and drag coefficients of the two cylinders also showed asymmetric features in the asymmetric vibrations region. When the two cylinders oscillate with different amplitudes, the gap flow stably biases to one of the cylinders and thus leads to a wide-narrow near-wake pattern. The cylinder with the narrower near-wake has larger vibration amplitude, drag and lift forces than the other one with the wider near-wake. A detailed explanation on the mechanisms of the asymmetric vibration and symmetry hysteresis is presented from the point of view of near-wake patterns before and after the asymmetric vibration occurs.

2015, 47(5): 731-739. doi: 10.6052/0459-1879-15-007

HTML PDF

NUMERICAL SIMULATION OF BROWNIAN COAGULATION AND MIXING OF NANOPARTICLES IN 2D RAYLEIGH-B?NARD CONVECTION

Xu Feibin, Zhou Quan, Lu Zhiming

In the present simulations, the first three moments of the particle size distribution of nanoparticles in a two dimensional Rayleigh-Bénard convection system are calculated with the combination of SIMPLE algorithm and the Tayler-series expansion method of moments (TEMOM) to probe into Brownian coagulation and mixing of nanoparticles. Driven by Brownian coagulation, diffusion and thermal convection, the number concentration of nanoparticles decreases, while the average volume increase generally as time goes on. The temporal evolution of nanoparticles can be divided into three stages, named the diffusion stage, the mixing stage and the fully mixing stage respectively. The correlation coefficients between moments of nanoparticles and the temperature, and relative standard deviation of moments experience distinct characteristics in three stages. The long-time behavior for moments of nanoparticles is obtained and is in good agreement with the asymptotic solution. Finally, the time to attain such an asymptotic solution is investigated and its dependence on Ra, Sc_M and Da is also determined numerically. The results show that the time decreases logarithmically when Ra and Sc_M increase, while it increases linearly when Da increases.

2015, 47(5): 740-750. doi: 10.6052/0459-1879-15-062

HTML PDF

FINITE ELEMENT ANALYSIS OF STRAIN GRADIENT MIDDLE THICK PLATE MODEL ON THE VIBRATION OF GRAPHENE SHEETS

Xu Wei, Wang Lifeng, Jiang Jingnong

The dynamics equation of the Mindlin middle thick plate model based on strain gradient theory is formulated to study the vibration of single-layered graphene sheets (SLGSs). Analytical solution of the natural frequency for free vibration of Mindlin plate with all edges simply-supported is derived. A 4-node 36-degree-of-freedom (DOF) Mindlin plate element is proposed to build the nonlocal finite element (FE) plate model with second order gradient of strain taken into consideration. This FE method is used to study the influences of the size, vibration mode and nonlocal parameters on the scale effect of vibration behaviors of SLGSs, which validates the reliability of the FE model for predicting the scale effect on the vibrational SLGSs with complex boundary conditions. The natural frequencies obtained by the strain gradient Mindlin plate are lower than that obtained by classical Mindlin plate model. The natural frequencies of SLGSs obtained by Mindlin plate model with first-order shear deformation taken into account are lower than that obtained by Kirchhoff plate model for both strain gradient model and classical case. The small scale effect increases with the increase of the mode order and the decrease of the size of SLGSs.

2015, 47(5): 751-761. doi: 10.6052/0459-1879-15-074

HTML PDF

A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua

Hu Wenfeng, Liu Yihua

Based on the Refs.[1-3], boundary displacement functions are treated as state variables and introduced into the state equation. The exact solutions are presented for the rectangular thick single and laminated plates with clamped edges. In the solving process, the state equation becomes a homogeneous equation from a nonhomogeneous one and the intermediate process to solve undetermined constants is omitted. The displacement boundary conditions are satisfied strictly on clamped edges, and it is not necessary to divide the layer with same material into some sub-layers. Therefore the obtained solutions are more accurate. Additionally, a new calculating method of the stresses on the clamped edges is proposed and more exact boundary stresses can be obtained. The results of two examples show that the present solutions have better constringency and higher precision, and are approaching to FEM solutions well than the existing exact solutions, especially on the clamped edges.

2015, 47(5): 762-771. doi: 10.6052/0459-1879-15-033

HTML PDF

STUDY OF THE SUBSTRATE CRACK PENETRATION MECHANISMS IN CRACK-DETECTED COATING SYSTEM

Sun Yang, Wang Biao, Wang Qiaoyun, Liu Mabao

The two-phase model and three-phase model of crack penetration/deflection at the interfaces in the crack-detected smart coating system were established utilizing the energy-based criterion. The effects of the relative crack growth length, the elastic mismatch parameters and the thickness of the interface layer on the ratio of energy release rates for the penetrated and deflected cracks were studied by the finite element method. When the substrate crack reaches an interface between substrate and driving layer, the results show that the ratio of energy release rate not only has a strong dependence on elastic mismatch between driving layer and substrate, but elastic mismatch between sensing layer and driving layer for the thinner driving layer as well. Moreover, with increase of the thickness of the driving layer, the dependence on elastic mismatch between sensing layer and driving layer decreases gradually. Compared with the experiment results, the numerical results can interpret the interface behavior of substrate crack and can be used for the optimization design of the crack-detected coating sensors.

2015, 47(5): 772-778. doi: 10.6052/0459-1879-15-142

HTML PDF

SHAKEDOWN ANALYSIS OF THERMAL BARRIER COATINGS BASED ON CYLINDER MODEL

Xu Yingqiang, Sun Jian, Li Wanzhong, Zhang Yichi, Chen Yaya

Due to thermal expansion misfit and temperature dependent material parameters among layers of thermal barrier coatings (TBCs), the interfacial stress-strain fields become more complicated under thermal loading, which affecting the TBCs stability and spalling failure directly. In this study, the convex and concave microscopic structure around TBCs interface is simplified as multi-cylinder model, with the classic shakedown theorem, Tresca yield criterion and incremental failure criterion, an analytical method of TBCs shakedown analysis is established, in addition, avoiding the time integral and mathematical programming. The variation between material yield strength and temperature is simplified as bilinear relationship, and the stability of typical TBCs is analyzed by using the method of compensation transformation to simplify the solving process. The results show that the stability limit can be obtained facility by using the analytical model of shakedown analysis based on the cylinder model. Stability limit of TBCs was significantly higher than the elastic limit, and the regional stability limit in convex area is higher than concave area around the interface, which indicates that failure prior to occur in concave area. The larger the radius of curvature of the substrate and the thickness of TBCs, the higher the stability limit, and those analysis results are consistent with the experimental results. The shakedown analysis method of TBCs built in this study has a great significant influence on the further research on stability of TBCs considering the creep.

2015, 47(5): 779-788. doi: 10.6052/0459-1879-15-073

HTML PDF

DYNAMIC MODELING AND ANALYSIS OF LARGE-LOOP COUPLED BY ATTITUDE CONTROL AND POGO FOR LARGE LIQUID ROCKETS

Wang Qingwei, Tan Shujun, Wu Zhigang, Yang Yunfei, Chen Yu

Coupling effect always exists between structural vibration, attitude and propulsion system because of the spatial distribution characteristics of the structural vibration mode of large liquid rockets. The coupling model of attitude control-structure-propulsion system is derived to investigate the effects of the propulsion system on the stability of attitude control system. The coupling is based on mechanism that the effects of attitude control system on the attitude motion and structural vibration as well as the interaction of propulsion system and structural vibration. By including the coupling factors between the propulsion system, structural system and attitude control system, the large-loop coupling model can be used to investigate the coupling stability of the large-loop coupling system. Besides, the coupling model can be directly used for frequency-domain analysis and time-domain simulation for the non-singularity. Based on this model, the effects of the propulsion system parameters-pump gain and accumulator energy value to the stability of attitude control system are analyzed by frequency domain analysis and time domain simulation. The results show that the variations of parameters-pump gain and accumulator energy value not only result in the instability of structural vibration but also lead to the instability of attitude motion. It is concluded that it is necessary to take the effect of POGO loop into count in the design of attitude control system.

2015, 47(5): 789-798. doi: 10.6052/0459-1879-15-137

HTML PDF

OPTIMAL SINGLE IMPULSE MANEUVER FOR SPACECRAFT CLUSTER FLIGHT

Wang Wei, Yuan Jianping, Luo Jianjun

The optimal single-impulse maneuver for spacecraft cluster flight is studied in this paper. Based on Gauss' variational equations, the optimal conditions and solutions for time-fixed and time-unfixed case are provided via the periodic condition of nonlinear relative motion. For the time-fixed case, the problem is also treated from the perspective of energy matching condition. In this case, the problem is transformed into seeking for the extremum of a quadratic equation or the solution of a single-root algebraic equation, and the optimal semimajor axis is derived, as well as the optimal velocity impulse. For the time-unfixed case, the problem can be solved by numerical algorithms or transformed into pursuing for the solution of a multi-root algebraic equation with the aid of Fourier-Bessel functions. In the end, the proposed method is validated by several carried out illustrating examples.

2015, 47(5): 799-806. doi: 10.6052/0459-1879-14-386

HTML PDF

THE INFLUENCE OF ONE-TO-ONE INTERNAL RESONANCE ON RELIABILITY OF RANDOM VIBRATION SYSTEM

Wang Haoyu, Wu Yongjun

Based on first-passage model, the reliability problem of two degrees-of-freedom random vibration system under Gaussian white noise excitations is studied analytically. In the case of 1:1 internal resonance, the equations of motion of the original system are reduced to a set of Itô stochastic differential equations after averaging. The backward Kolmogorov equation and the Pontryagin equation, which determine the conditional reliability function and the mean first-passage time of the random vibration systems, are constructed under appropriate boundary and (or) initial conditions, respectively. To study the influence of the internal resonance on the reliability, the averaged Itô stochastic differential equations, the backward Kolmogorov equation and the Pontryagin equation in the case of non-internal resonance are also derived. Numerical solutions of high-dimensional backward Kolmogorov equation and Pontryagin equation are obtained. The results of resonant case and non-resonant case are compared. It is shown that 1:1 internal resonance can greatly reduce the reliability. All the analytical results are validated by Monte Carlo digital simulation.

2015, 47(5): 807-813. doi: 10.6052/0459-1879-15-058

HTML PDF

A LCP METHOD FOR THE DYNAMICS OF PLANAR MULTIBODYSYSTEMS WITH IMPACT AND FRICTION

Wang Xiaojun, Wang Qi

This paper is presented to show the modeling and numerical method for the dynamics of the planar multi-rigid-body system with contact, impact and Coulomb's dry friction. The multibody system consists of the rigid bodies which are linked with ideal joints and driving motors, so the system constraint equations included two parts, scleronomic constraint equations and rheonomic constraint equations. Based on the theory of contact mechanics, the local deformations in contact bodies are taken into account and the normal forces of contact surfaces are expressed as nonlinear functions of relative penetration depth and its speed during impact between two bodies. The Coulomb dry friction model is used to describe the tangential frictional forces of contact surfaces. Using the concept of friction saturation and the relative acceleration of the contact point in the tangential direction, the complementarity conditions and formulations about the friction law are given. The problems of detecting stick-slip transitions of contact points and solving frictional forces in stick situation are formulated and solved as a linear complementarity problem (LCP) by the event-driven scheme. The dynamical equations of the system are obtained by Lagrange's equations of the first kind and Baumgarte stabilization method in order to reduce the constraint drift and solve the system motion, normal contact forces and tangential friction forces as well as ideal joint constraint forces and driven constraint forces in the system. Finally, the numerical example of a planar multi-rigid-body like flat beater is given to analyze its dynamical behavior and show the availability of the method in this paper.

2015, 47(5): 814-821. doi: 10.6052/0459-1879-15-168

HTML PDF

STUDY ON IMPLICIT IMPLEMENTATION OF THE UNIFIED GAS KINETIC SCHEME

Mao Meiliang, Jiang Dingwu, Li Jin, Deng Xiaogang

The current explicit unified gas kinetic scheme (UGKS) is very time-consuming for high speed flows due to the massive phase space mesh demand, which is a bottleneck for complex engineering problems. In order to improve the efficiency, the motion and collision term in the model equation is implicitly treated and the evolving time averaged flux across the cell interface is introduced, then the implicit UGKS can be obtained applying the approximate LU decomposition on the matrix of the governing equations. The tests on the flows over a cylinder with different freestream Mach numbers show that the implicit method can give the same result as the original explicit method with a properly chosen evolving time step. Meanwhile, the computational efficiency can be improved by 1-2 orders.

2015, 47(5): 822-829. doi: 10.6052/0459-1879-14-408

HTML PDF

APPLICATION OF LAGRANGIAN BOUNDARY CONDITIONS BY CHARACTERISTICS METHOD USING TIME-LINE INTERPOLATION IN SPH

Gong Xiangfei, Zhang Shudao, Yang Jiming

Boundary conditions is an important research topic in the practical application of computational fluid dynamics. A new Lagrangian boundary conditions framework is constructed by characteristics method using time-line interpolation and is applied in SPH. Compared with methods within Euler framework this method is obvious and easily carrying out for the same formulations in inflow zone and in outflow zone whether for subsonic flow or supersonic flow. SPH numerical simulation in various wave inputs shows the feasibility of the method.

2015, 47(5): 830-838. doi: 10.6052/0459-1879-14-412

HTML PDF

NODE-BASED SMOOTHED POINT INTERPOLATION METHOD: A NEW METHOD FOR COMPUTING LOWER BOUND OF NATURAL FREQUENCY

Du Chaofan, Zhang Dingguo

A meshfree method called node-based smoothed point interpolation method (NS-PIM) is proposed for static analysis of cantilever beam and dynamic analysis of rotating flexible beam for the first time. Gradient smoothing technique is utilized to perform the numerical integration required in the weakened weak (W2) form formulation. The shape functions are approximated using linear interpolation functions, which can be used to solve the 4th order differential equation. In static problems, the cantilever beams with two loading conditions are analyzed, and the results are compared with the analytic solution, which shows a high accuracy of this method even if using linear shape functions. A further study shows that if more than 9 modes were used in the assumed mode method, the result will be divergent. In dynamic problem, the natural frequencies of a rotating flexible beam are analyzed. Simulation results of the NS-PIM are compared with those obtained using finite element method (FEM) and assumed modes method (AMM). It is found that NS-PIM can provide unique lower bounds of natural frequencies, while FEM and AMM can provide upper bounds of natural frequencies. That means we can get more accurate results for the problems by using FEM and NS-PIM in case that exact solution can't be obtained. The NS-PIM has easier shape functions and less independent variable than FEM, and can provide lower bounds of natural frequencies, with a great value of application and dissemination.

2015, 47(5): 839-847. doi: 10.6052/0459-1879-15-146

HTML PDF

INFLUENCE OF SHAPE FUNCTIONS AND TEMPLATE SIZE IN DIGITAL IMAGE CORRELATION METHOD FOR HIGHLY INHOMOGENEOUS DEFORMATIONS

Xu Xiaohai, Su Yong, Cai Yulong, Cheng Teng, Zhang Qingchuan

Digital image correlation (DIC) method and its reliability and accuracy are commonly accepted in the measurements of affine deformations since it obtains comparable results with strain gauges. However, in engineering measurements, there are always substantial local deformations with high strain gradients such as the Portevin-Le Chatelier (PLC) bands, deformations near gaps and crack tips. In these situations, because the results within the contact areas are smoothed, strain gauges are restricted. Here DIC method can be employed to solve this problem. Problems that the calculation parameters (the order of shape functions, template size, etc.) seriously impact on the results and often make it difficult to get reliable results. In this paper, the deep mechanism that how the shape functions and the size of the templates impact on the accuracy of DIC results is discovered via analyzing PLC bands with different gradients in tensile tests and simulated bands. Second-order shape functions are more suitable than first-order shape functions to describe local deformations according to the simulation results. A gist is proposed that the results of second-order shape functions are reliable and accurate when the relative error between first- and second-order shape functions is less than 10%.

2015, 47(5): 848-862. doi: 10.6052/0459-1879-15-119

HTML PDF

DISCUSSION ON DUPUIT FORMULA OF BOTTOM-WATER CRITICAL RATE AND A NEW COMPUTATIONAL METHOD

Han Guofeng, Chen Fangfangy, Liu Yuewu, Zhu Yongfengy, Ma Xiaopingy

The determination of critical rate is a key issue of high-efficient development of bottom-water reservoirs, while in the Dupuit formula of bottom-water reservoirs' critical rate, it is unreasonable that the critical rate monotonously increase with the reduction of perforating level. In fact, checking the derivation process of Dupuit formula, there is an implied condition that the top of water cone just at the well bottom. However, it is found that it can't keep a stable water cone at well-bottom when producing with the critical rate computed by Dupuit formula. In the paper, a new computational method has been established without the assumption of water-cone top at well bottom. It assumes that it is a kind of radial flow at the upper and a kind of hemispherical flow at the lower around the well bottom. The example shows that the new method could optimize the perforating level and gain the critical water-cone height. The project case demonstrates that the method gained in this study is more correspond to reality.

2015, 47(5): 863-867. doi: 10.6052/0459-1879-15-043

HTML PDF

DYNAMIC FRACTURE ANALYSIS OF FUNCTIONALLY GRADED MATERIALS BY RADIAL INTEGRATION BEM

Gao Xiaowei, Zheng Baojing, Liu Jian

In this paper, the radial integration boundary element method is presented to analyze dynamic fracture mechanics problems of functionally gradient materials. The fundamental solutions for homogeneous, isotropic and linear elastic solids are used to derive the boundary-domain integration equations by weighted residual method and this approach leads to domain integrals appearing in the resulting integral equations. The radial integral method (RIM) is employed to transform the domain integrals into boundary integrals and thus the boundary-only integral equations formulation can be achieved. The Houbolt method is utilized to solve the resulted system of time-dependent algebraic equations from the discretization. Numerical results are given to demonstrate the efficiency and the accuracy of the present method.

2015, 47(5): 868-873. doi: 10.6052/0459-1879-15-150

HTML PDF

STABILITY ANALYSIS OF FLOW PAST AN ELASTICALLY-SUSPENDED CIRCULAR CYLINDER

Li Xintao, Zhang Weiwei, Jiang Yuewen, Ye Zhengyin

An identification technique is used to construct reduced order models (ROMs) for the cylinder wake flow at subcritical Reynolds numbers (Re <47) using CFD simulation data. ROM-based aeroelastic models are then found by coupling the structural motion equations and ROMs. The impacts of structural frequency, mass ratio and mount style on the instability boundaries are investigated. It is found that self-excited oscillations, accompanied by vortex shedding are possible at Re as low as 20 for one freedom transversely suspended cylinder, as the structural frequency gets close to that of the most unstable mode of flow. The release of rotational freedom could further increase the instability of the coupled system and the critical Re can be reduced to 18. ROM-based method not only has high efficiency but also profoundly shows that the inherent instability of the coupled system is induced by the unstable of the structure mode. Therefore, in the unstable region, the vibration frequency of the coupled system is synchronized with the natural frequency of the cylinder.

2015, 47(5): 874-880. doi: 10.6052/0459-1879-14-307

HTML PDF

THE SUPPORTED PROJECTS ON MECHANICS OF NSFC IN 2015

Zhan Shige, Zhang Panfeng, Xu Xianghong, Sun Zhongkui

The paper brief introduced the supported NSFC projects for General Programs, Young Scientists Fund, Fund for Less Developed Regions on mechanics in 2015. The projects list is also given.

2015, 47(5): 881-898.

HTML PDF

2015 Vol. 47, No. 5

NoticeMORE+

Exquisite ArticlesMORE+

Download Center

Author Center