力学学报

Study of the nonlinear lift coefficient of the symmetrical airfoil at low reynolds number near the 0o angle of attack

The nonlinear effect of the lift coefficient of thesymmetrical airfoil near the 0$^{\circ}$ angle of attack occurs at low Reynoldsnumber. It may be disadvantageous for control. The 3rd order Roe schemedeveloped by Rogers was used to solve the unsteady incompressibleNavier-Stokes equations, in the temporal direction the 2nd ordertwo-step method was accepted, to numerically simulate the flowfield laminarseparation vortex structure and the lift coefficient of the symmetricalairfoil SD8020 at low Reynolds number ($Re=40\,000$, 100\,000) at differentangle of attack. The correctness of the simulation was proved by comparingthe present CFD results with the experiment. Through the analysis and studyto the time-averaged result of the numerical simulations, the newtrailing-edge laminar separation bubble model for the airfoil near the0$^{\circ}$ angle of attack was described in this paper, which is different fromthe classical laminar separation bubble model both in the inner structureand the development with the angle of attack. And this model was used tostudy and explain the mechanisms of nonlinear effect of the lift coefficientof the symmetrical airfoil at low Reynolds number at low angle of attack.

2006, 38(1): 1-8. doi: 10.6052/0459-1879-2006-1-2005-110

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Schlieren visualization and numerical simulation on gaseous detonation propagation through a bend tube

Gaseous detonation propagation through a semi-circle bendtube was experimentally and numerically investigated. The laser schlierensystem was employed to obtain the images of detonation front at thedifferent position. The 2nd additive semi-implicit Runge-Kutta methodand 5th order WENO scheme were respectively used to discretize the timeand space terms of reactive Euler equations. Detailed chemical reactionmodel was utilized to describe the processes of detonation chemicalreactions. The contours of pressure, temperature, OH mass fraction,numerical cellular pattern and average detonation speed were obtained.Experimental and numerical results show that, influenced by the rarefactionwaves and compression waves, the detonation front is distorted. Due to theshallow curvature of the bend tube, the detonation front is not so seriouslydistorted and there is no evidence of detonation failure. The leading shockalong the concave wall is much stronger than that along the convex wall. Thereaction zone along the convex wall is also wider than that along theconcave wall. The triple-point number decreases in the process of detonationpropagation through the bend tube, and therefore the detonation wave isdegenerated. However, it can be recuperated to self-sustaining cellulardetonation at the exit section. The computed detonation flow field, cellularpattern and average speed are qualitatively consistent with those from theexperiments.

2006, 38(1): 9-15. doi: 10.6052/0459-1879-2006-1-2004-491

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An iterative stabilized fractional step algorithm for finite element analysis in high-viscosity fluid flows

Stabilized fractional step algorithm has been widelyaccepted for numerical solution of the incompressible N-S equations. Basedon Guermond's works, the stability of the fractional step algorithm requiresthat the time step size should be larger than a critical value. However, inmodeling of high-viscosity fluid flows, existing explicit and semi-implicitversions of the algorithm require to use smaller time step sizes due totheir explicit nature, which reduces the efficiency of the numericalsolution procedure and very often conflicts with the minimum time step sizerequirement presented to ensure the stability of the fractional stepalgorithm. The purpose of this paper is to present a modified version of thefractional step algorithm, which allows much larger time step sizes thanthose for the preceding ones. The method is based on introducing aniteration algorithm. Numerical experiments in the cavity flow and the planePoisseuille flow problems demonstrate the improved performance of theproposed modified version of the fractional step algorithm, which is furthersuccessfully applied to numerical simulation of the polymer injectionmolding process with high efficiency.

2006, 38(1): 16-24. doi: 10.6052/0459-1879-2006-1-2004-405

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Direct Numerical Simulation of Finite-Inertia Particle Collision in Isotropic Turbulent Flow

In this paper, direct numerical simulations (DNS) were conducted to study particle collisions in a stationary isotropic homogeneous turbulent flow, with the aim to investigate the influence of turbulence on particle collision rates of various finite-inertia particles. It is found that the behavior of finite-inertial particle collision is very complicated, both the Saffman & Turner theory(Stk=τp/τk =0) and kinetic theory( Stk=￥) can't correctly predict it. For particles of Stk <1 the collision rate increases sharply as Stk increases; at Stk ~1, collision rate reaches a peak value; As Stk continues to increase, collision rate slowly decreases at first and then increases to reach another peak at Stk ~3 (corresponding to Eulerian integral time scale). As particle inertia continues to increase, collision rate begins to decrease slowly to reach the kinetic theory. Both of the peak value is about 30 times of zero inertia limit. To further understand the mechanism of finite-inertia particle collision in isotropic turbulence, two major effects of turbulent flow on particle collision, namely turbulent transport effect and preferential concentration effect, are investigated and are represent qualitatively using radial relative velocity <|wr|> and radial distribution function g(R) of colliding particle pairs respectively. Both effects tend to increase collision rates, leading to the observed complex behavior. The results showed that preferential concentration effect is the main contribution factor for the peak of particle collision rate near Stk~1, while both preferential concentration effect and turbulent transport effect contributing to the peak near Stk~3, with much stronger turbulent transport effect herein. Statistical analysis of the data also showed that the probability density function(pdf) of relative radial velocity between two colliding particles does not fit for Gaussian distribution for different Stokes number. Instead, due to the effect of different scales of motions in turbulent flow, the shape of the pdf appears to belong to a family of exponential distributions with powers in the exponent that vary with the Stokes number.Keywords: Isotropic Turbulence, DNS, Finite Inertia, Particle Collision Rate, Preferential Concentration Effect, Turbulent Transport Effect

2006, 38(1): 25-32. doi: 10.6052/0459-1879-2006-1-2005-002

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Analyses on Magnetoelastic Initial Post-buckling and Sensitivity to Imperfection for Ferromagnetic Beam-Plates

Based on a generalized variational principle ofmagnetoelasticity for soft ferromagnetic plates, the magnetoelasticstability and post-buckling as well as sensitivity to imperfection areanalytically investigated in the present paper to the ferromagnetic beam-plateswith cantilevered, simply-supported, clamp-supported boundary conditions.The analyses are carried out by means of perturbation technique for theouter and inner fields of ferromagnetic beam-plate and classical Koitertheory. The results achieved show that the stability of cantileveredbeam-plates is sensitive to initial imperfection but is not sensitive toinitial imperfection for simply-supported and clamped beam-plates. Thereasonable explanation is suggested qualitatively for the phenomenon thatthe predicted critical magnetic field of magnetoelastic buckling are alwayslarger than the measured values from experiments.

2006, 38(1): 33-40. doi: 10.6052/0459-1879-2006-1-2004-468

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Creep buckling of viscoelastic plates with geometrical nonlinearity

The creep buckling behavior of viscoelastic plates withinitial deflections, subjected to axial compressive force, is analyzed. Thevon Karman nonlinear geometry equations are introduced in the thesis andstandard linear solid model is employed. In order to change the nonlinearintegral equations to a nonlinear algebraic equation which can be solved byusing a standard subroutine, the trapezium method is used to calculate thehereditary integral expression, then the creep deformation of viscoelasticplate is obtained. Meanwhile, the instantaneous critical loads, durablecritical loads are obtained. On the other hand, the problem of creepbuckling is analyzed by using the linear geometric theory, an analyticalsolution of deflection varying with time is obtained. The influence ofgeometry nonlinearity on the creep buckling of viscoelastic plates isstudied.

2006, 38(1): 41-48. doi: 10.6052/0459-1879-2006-1-2004-143

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A stress artificial boundary in FEA for near-field wave problem

The stability and accuracy of local artificial boundary are two important criterions for evaluating its applied value in engineering. In this paper, a stress artificial boundary condition was developed by mixing the planar waves and the scattered waves transmitting into the linear elastic infinite media through artificial boundary. For the proposed boundary condition, the responses of boundary nodes and finite element nodes are calculated by the same integral method, and its stability condition is also the same as the finite element integral method. Numerical examples demonstrate that the accuracy of the proposed boundary is higher than that of existing viscous boundaries, viscous-spring boundaries, the first-order transmitting boundary and the second-order transmitting boundary.

2006, 38(1): 49-56. doi: 10.6052/0459-1879-2006-1-2004-442

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Structural robust design concerning static and dynamic performance based on perturbation stochastic finite element method

The perturbation-based stochastic finite element analysis incorporating structuraloptimization techniques is employed in the structural robust design problem. In the framework ofthe second-order perturbation-based stochastic finite element method, the computational schemesfor the expected value and the variance of the structural performance functional as well as theirsensitivity are proposed. The robust design of structures is formulated as a multi-criteriaoptimization problem, in which both the expected value and the standard deviation of theobjective function are to be minimized. The robustness of the design feasibility is also accountedfor by involving the variability of the structural response in the constraints. The optimizationproblem is converted into a scalar one and solved by a gradient based optimization algorithm. Todemonstrate the applicability of the presented method, numerical examples are given.

2006, 38(1): 57-65. doi: 10.6052/0459-1879-2006-1-2004-524

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Sensitivity Analysis and Design Optimization Methods for Problems of Heat Transfer with Phase Change

The design optimization and sensitivity analysis methodsfor the problems of transient heat transfer with phase change have beenresearched in the paper. On the basis of phase-change temperature fieldsolution with the finite element, time difference, and equivalent heatcapacity methods, the numerical method to compute the first-orderderivatives of temperature with respect to design variables is proposed. Twocomputational schemes of the direct method and the adjoint method have beengiven, and their characteristics have been discussed. The optimization modeland algorithm are built for the transient temperature filed with phasechange. These methods have been implemented within the software JIFEX forfinite element analysis and design optimization. The numerical results ofexample problems are given to illustrate the accuracy of sensitivityanalysis and the effectiveness of design optimization.

2006, 38(1): 66-72. doi: 10.6052/0459-1879-2006-1-2004-130

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An Particle Tracing Scheme for Fokker-Planck Equation in Finite Analytic/Monte Carlo Methods

Fokker-Planck equation for Stochastic system with whitenoise is reduced to velocity state vector, and the analytic solution of thereduced Fokker-Planck equation is obtained. The hybrid scheme in FiniteAnalytic/Monte Carlo methods is developed to simulate constant parameterscomplete Fokker-Planck equation and complete Fokker-Planck equation withvariable $F(X)$. It is shown that the results obtained from the numericalalgorthm are in good agrement with the analytic solutions, and that thesimulating PDF is smoothed when calculated particles number is 10$^{5}$, andthe simulating average moments are about to analytic solutions whencalculated particles number is 300. This work described here is first partof a long-term study in pursuit of a new simulating scheme for two-phaseflows.

2006, 38(1): 73-78. doi: 10.6052/0459-1879-2006-1-2004-150

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Incompatible Numerical Manifold Method

This paper deduces the additional incompatible displacement terms on internal parameters for three-dimensional elasticity problems, establishes the improved incompatible numerical manifold method. Based on eliminating the internal parameters, the expressing formula of element strain matrix and element stiffness matrix are given. Calculating accuracy and computing efficiency can be greatly increased by incompatible numerical manifold method without adding generalized degrees of freedom. In order to apply this method to engineering, an explicit treatment of incompatible numerical method is provided. To illustrate the stability of the present approach, numerical examples are analyzed. It is shown that this method produces highly accurate and stable results.Keywords: numerical manifold method; incompatible element; additional displacement term; generalized degree of freedom; static concentration

2006, 38(1): 79-88. doi: 10.6052/0459-1879-2006-1-2004-521

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J2 Perturbation Analysis of Relative Orbits in Satellite Formation Flying

$J_{2}$ perturbation has a great effect on the relativemotion of low-earth orbiting satellites in formation flying and has effecton lives of satellites directly. $J_{2}$ perturbation makes the relativeorbit drift in the in-track direction, nutation or procession. Firstly, thispaper investigates the magnitudes of the first order approximations andinfluencing factors for drift rate, nutation rate and procession rate.Secondly, a rule is given to estimate the relationship of drift and rotationfor a relative orbit. Finally, using the rule, effects of the differences inorbital elements of leading satellite and following satellite on the driftand rotation of the relative orbit are investigated. The conclusions in thepaper could be as the reference to determine initial orbital elements ofsatellites formation design when considering $J_{2}$ perturbation.

2006, 38(1): 89-96. doi: 10.6052/0459-1879-2006-1-2005-117

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Dynamics and Control of a Flexible Hub-Beam System with Considering the Effect of Damping

In this paper, dynamics and control of a flexible hub-beam system is investigated with considering effect of damping. Dynamic expression with containing damping is presented. Active controller is designed using optimal tracking control theory. Three kind of damping are considered: structural damping, wind damping, and damping at bearing of the hub. In wind damping, viscous wind damping and square wind damping are considered. Since active controller is a function of mode coordinates, extraction method of modal coordinate from actual physical measurements is developed. Simulation results indicate that the simplified first-order approximation coupling model presented is valid for dynamic description of flexible hub-beam system and so is available for control study. Damping has important effect on dynamic characteristics of the system. In the case that angular velocity of large motion of the system is low, desired motion trajectory may be achieved by using optimal tracking controller and the vibration of the beam caused by the large motion may be suppressed by this controller at the same time.

2006, 38(1): 97-105. doi: 10.6052/0459-1879-2006-1-2004-353

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Study on some breakdown forms and characteristics of leading edge vortex over delta wings

Since the discovery of vortex breakdown phenomenon, manytheoretical and experimental studies have been conducted. However, up todate the understanding of vortex breakdown is not enough or comprehensive.Vortex breakdown is an unsteady process and a breakdown vortex has verycomplex structure. The vortex breakdown phenomenon is concerned with afighter aerodynamic characteristics and buffeting. Farther investigation onthe vortex breakdown phenomenon is very important. It is well known thedominate vortex breakdown forms over delta wings are spiral and bubble form.However many other forms of vortex breakdown have been found in thevortex flow in a tube. A lot of flow visualization on vortex breakdown overdelta wings show that the spiral breakdown form is a dominant form. Othershave found that there are two new forms of vortex breakdown: one is doublespiral and another is filiform spiral form, which appears on delta wingswith smaller sweep angle. Recent years particle image velocimeter (PIV)technique is developed rapidly and applied in flow measurement. At certaindegree quantitative measurement of vortex breakdown phenomenon could beconducted.Based on experimental results of flow visualization and PIV measurement somebreakdown forms and characteristics of leading edge vortices over deltawings are analysed and discussed in this paper. It is shown that for spiralbreakdown the helix sense of the vortex core is opposite to the direction ofthe main vortex rotation and double spiral vorticity distributionperpendicular to the vortex axis is identified. Besides that different ideafrom existed explanation in lot of papers about spiral wave mechanism inbreakdown vortex flow is also presented.

2006, 38(1): 106-111. doi: 10.6052/0459-1879-2006-1-2004-126

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The analyses of gravity waves in a rectangular elastic fluid-shell coupled system

The theory and experiment about gravity waves in arectangular elastic fluid-shell coupled system are presented in thispaper. A set of equations are constructed according to fluid and vibrationtheory. Based on the boundary and initial conditions of the system, thevelocity potential of the fluid and the surface wave function of the firstgravity wave are obtained. Through the numerical calculation for theequations, the time response curves and response spectrum are given to thefirst gravity wave. The results show that when gravity wave appears, theshell acts as pendulum and the gravity wave's motion is harmonic.Furthermore, the effects of exciting force and the frequency to the systemare also discussed. Only when the force is large enough to conquer theviscid resistance and the frequency is near a certain constant, gravitywaves are engendered, which is the result of resonance vibration. At thesame time, the experimental study is processed. The phenomena observed areresonance without gravity wave if the system is excited on the shell with ahorizontal force and the force is large enough but the frequency out of thescope. When all the conditions are met, large-amplitude and low-frequencygravity waves are observed. All the experimental results show goodqualitative agreement with the theoretical results.

2006, 38(1): 106-112. doi: 10.6052/0459-1879-2006-1-2004-319

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An effective numerical approach for interaction of macrocrack with mircocracks

In this paper, an effective numerical approach forinteraction of macrocrack with microcracks in plane elastic media ispresented. By extending Bueckner's principle suited for a single crack to ageneral system containing multiple interacting cracks, the original problemis divided into a homogeneous problem (the one without cracks) subjected toremote loads and a multiple-crack problem in an unloaded body with appliedtractions on the crack surfaces. Thus, the results in terms of the stressintensity factors (SIFs) can be obtained by taking into account the latterproblem, which is analyzed easily by means of the Hybrid DisplacementDiscontinuity Method proposed recently by the author. The examples given byCai and Faber (see, Cai H, and Faber KT. 1992, On the use of approximatemethods for microcrack shielding, ASME J. Appl Mech 59, 497$\sim$501) for the interaction of a macrocrack withmicrocracks are exemplified here. It is found that the presentapproximation method is very simple andeffective for microcrack shielding problems.

2006, 38(1): 112-117. doi: 10.6052/0459-1879-2006-1-2005-042

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Solving helmholtz equation by least-square collocation method based on reproducing kernel particle method

Helmholtz equation often arises while solving boundaryvalue problems of partial differential equation by eigen function method. Inphysics, Helmholtz equation represents a stationary state of vibration inthe fields of mechanics, acoustics and electro-magnetics. In this paper, aleast-square collocation formulation for solving Helmholtz equation withDirichlet and Neumann boundary conditions was established. The unknowninterpolated functions were first constructed based on reproducing kernelparticle method and Helmholtz equation was then discretized by pointcollocation method. The variance errors of unknown function in each discretepoint are minimized by a least-square scheme to arrive at the finalsolution. To verify the proposed method, a wave propagation problem and aboundary layer problem of Helmholtz equation were solved. Numerical resultsby the present approach are compared with exact solutions and those bysmooth particle hydrodynamics (SPH) method. Numerical examples show that thepresent method displays better accuracy and convergence than the classicalSPH method for the same density of discrete points.

2006, 38(1): 118-122. doi: 10.6052/0459-1879-2006-1-2004-235

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Effects of mechanical strain different load parameters on proliferation of lung adenocarcinoma cell in vitro

The effects of waveform, frequency, cycle number andelongation on proliferation of human lung adenocarcinoma cell line A549 werestudied by FX-4000 strain unit. Image analysis revealed that cellularproliferation rate(PR) reduced significantly at squarewave group, The PR hadno distinct difference at heartwave, trianglewave and sinewave groupcompared with control after A549 cells were subjected to 0\%$\sim $15{\%}elongation for 2\,h. The PR reduced significantly at 0.5\,Hz and 1.0\,Hzgroup, ThePR had no distinct difference at 0.3\,Hz and 0.7\,Hz group after A549 cells weresubjected to squarewave for 2\,h. The PR had no distinct difference at15{\%}, 20{\%} and 25{\%} elongation for squarewave group. It indicates thatA549 cells do respond to physiological strain in vitro. The effects ofsquarewave and 1.0\,Hz tension was distinct for A549 cells proliferation.

2006, 38(1): 123-126. doi: 10.6052/0459-1879-2006-1-2004-324

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Strategy of selecting points via number theoretical method in probability density evolution analysis of stochastic response of structures

The newly developed probability density evolution method(PDEM) is capable of capturing instantaneous probability density functionand its evolution of linear and/or nonlinear stochastic response ofstructures. In the occasions that multiple random parameters are involved inthe structural properties and external excitations, the strategy ofselecting representative points required in the PDEM is of paramountimportance to the accuracy and efficiency. Enlightened by the NumberTheoretical Method successfully employed in high-dimensional numericalintegration, the strategy of selecting points via Number Theoretical Methodis proposed in the present paper. Further, making use of the sphericallysymmetric properties or the radial attenuation properties of the jointprobability density function, the points scattered over themulti-dimensional hypercube selected by the Number Theoretic Method aresieved once again such that only the points inside the multi-dimensionalhyper-ball are retained. With the proposed strategy of selecting points, thestochastic response analysis involving multiple random parameters is almostas efficient as the problem involving only one single random parameter.

2006, 38(1): 127-133. doi: 10.6052/0459-1879-2006-1-2005-054

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