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2004 Vol. 36, No. 2

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Effects of pressure-gradient on turbulent counter-gradient transport
By using Reynolds Stress Closure Model (RSM) and k-e Model, the turbulent field of wing flow is numericallysimulated. In most practical situations, flows with changing pressuregradient are familiar, these pressure gradients may induce strongmodifications of turbulent structure, accordingly, affect the diffusion andtransportation process of turbulence. The effects of pressure gradient oncounter-gradient transport phenomena are studied. The computational resultsshow that RSM model can describe the CGT phenomena while k-e model cannot. Negative turbulent energy production appears in the result ofRSM, but it behaves differently with CGT: it gradually shrinks until theposition of the wing central part is reached, where it vanishes; while theCGT region exists all along. This fact shows that CGT phenomena is moregeneral than negative turbulent energy production. The pressure gradienttakes an important effect on the region of negative turbulent energyproduction and counter-gradient transport. In the CGT region, the relationbetween turbulent Reynolds stress and mean velocity gradient is nonlinear.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2002-278
A MCA model for molecular diffusion in turbulent reactive flows
In the PDF approach of turbulent reactive flows, the convection and reaction terms are closedbut the molecular diffusuion term is unclosed. The currently existing models for the moleculardiffusion are either empirical or introduced via external parameters, and it has been verifiedthat they are not valid for such physical processes as the diffusion process. In this paper,a stochastically mapping approximation approach is developed to model the effect of moleculardiffusion. A length scale is introduced by a two-point joint probability density function,to account for the evolutions of the conditional diffusion. Numerical simulation shows thatthe approach is able to predict the evolution of the variances, dissipation rates, conditionaldiffusion and PDFs in the diffusion process.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2002-378
Numerical simulations of suspension motion of irregular shaped particles via the lattice Boltzmann method
In this study, we combine the Newtonian mechanics with lattice Boltzmannmethod(LBM) to simulate the motion of irregular shaped particle suspensions.A moving boundary method to follow the motion of moving particles is used,which can not only trace the motion of particles for a long time, but also increasethe speed of computation and decrease the usage of computer memory.We also analyze in detail of the forces acted on the elliptical andirregular particle suspensions. In the study, with the comparison of ourresults of the motion of elliptical particles with others results of themotion of long square particles, reasonable physical explanations of thecomplex phenomena are found, which can be used as a guideto understand the motion of particle suspensions with more general irregular shapes.It is shown that the lattice Boltzmann method is as accurate as the finite elementmethod in the simulation of motion of particlesuspensions and has a lot of advantages, such as fast and can handle complex boundarieseasily. The code of LBM is much shorter than other CFD methods and isparticularly suitable for large scale parallel computation.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2002-408
Renewal precise time step integration method of structural dynamic analysis
The precise time step integration method proposed forlinear time-invariant homogeneous dynamic system can give precise numericalresults approaching to the exact solution at the integration points.However, it is more or less difficult when the algorithm is used to thenon-homogeneous dynamic systems due to the inverse matrix calculation andthe simulation accuracy of the applied loading. By combining the Gaussquadrature method and state space theory with the calculation technique ofmatrix exponential function in the precise time step integration method, anew precise time step integration method (that is renewal precise time stepintegration method) is proposed. The new method avoids the inverse matrixcalculation and the simulation of the applied loading and improves thecomputing efficiency. In particular, the method is independent to thequality of the matrix ${\pmb H}$. If the matrix ${\pmb H}$ is singular or nearly singular,the advantage of the method is remarkable. The proposed method in this paperis a unconditionally stable algorithm having an arbitrary order of accuracy.Numerical examples are given to demonstrate the validity and efficiency ofthe algorithm.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2002-420
Influence of inclusions on bi-materials interface crack
With the continuity conditions of stress and displacement on materialinterface, complex potentials solutions for a bi-material infinite platewith an elliptical inclusion under uniaxial tension are given. The stressfield of a bi-material infinite plate with an elliptical inclusion and asemi-infinite interface crack are given on the base of the complexpotentials solutions obtained above. And the corresponding stress intensityfactor $K$ is given. The influences of the position, the shape,material property, and different material combinations of inclusion on the stressintensity factor $K$ are calculated. The results indicate that the distance ofinclusion from crack tip and the property of inclusion have remarkableinfluence on the stress intensity factor $K$, and these influences vary notablywith different material combinations, whereas the shape of inclusion haslittle influence on $K$. When the inclusion is soft, the shield effect isoccurred for $K$; conversely, it is inverse shield.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-057
A study of destabilizing oscillation in the mechanics and electricity coupling system by dynamical bifurcation method
Based on mechanical and electrical analytical dynamics,we established equations about vibration coupled with mechanics andelectrics in AC motor set. Using the theory of differential dynamic system,destabilizing oscillation of the AC motor's were analyzed with electricityand mechanics coupling. By Center Manifold, theory of stability with multipleparameters and unification technique to analyze the high-codimbifurcation occurring in the system, the Normal Form of the originalsystem is obtained. The bifurcation situation and the stabilization of thebifurcation solution are discussed in detail. In addition, a detailednumerical analysis is made, its results are in agreement with the theoreticresults. Also, we got the further result in vibration when AC motor lose itsstability.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-067
Double-balloon dynamics model
In this paper a double-balloon dynamic model is presentedfor a whirling yarn of a ring spinning machine with balloon control ring,considering influences of running speed of the yarn, tangential directionair drag and gravitational force on the yarn as well as inertia of the yarn,normal direction air drag and tension of the yarn. Although dynamictreatment of the connecting condition of the yarn at the balloon controlring is very important both for analytical theory and practical applicationto control of ring spinning machine, there have never been derived dynamicanalytical theory considering many practical parameters. In the paper theauthors derived condition equations of the yarn contacting to the controlring, taking account of reaction force of the ring to the yarn andfrictional force between the ring and the yarn. Obtained equations canderive numerically the shape of whirling yarn (balloon shape, inclinationangle of the yarn to bobbin axis) and the yarn tension, if the certainvalues of the system parameter such as diameters of the traveler guide ringand balloon control ring, heights of yarn guide and control ring above thetraveler guide, air drag coefficients of the yarn, coefficient of frictionalforce of control ring to the yarn, revolution speed of the bobbin, etc. aregiven. Numerical calculations results proved validity of the theory. Thetheory derived is applicable to on-line and real time control of the yarntension of ring spinning machine.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-083
Investigation on stability of 3-d supersonic mixing layer and method of enhancing the mixing
A useful method of enhancing the mixing for supersonicmixing layer is improving flow dynamics instability. In this paper, thethree-dimensional (3-D) compressible mixing layers with spanwise curvaturewas discussion. According to analyses of flow dynamics stability, thethree dimensional disturbances have lager rate of amplification, have betterability of blending in normal direction of mixing layer and can enhance themixing for 3-D compressible mixing layer in this compressible mixinglayers. This characteristic is also for supersonic and hypersonic mixinglayer, which is useful method of enhancing the mixing for supersonic andhypersonic mixing layer.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-123
Dynamic reliability analysis of stochastic truss structures under stationary random excitation
A method of calculating dynamic reliability of stochastictruss structures under stationary random excitation is discussed in thispaper. Considering the randomness of the structural physical parameters andthe geometric dimensions parameters and utilizing the random variable'sfunctional moment method and the algebra synthesis method, the mean valueand the variance of the mean square value of the structural displacement andstress response and stationary random excitation are computed firstly fromthe expressions of structural stationary response in frequency domain. Andthen the expressions of the mean value and the variance of stochastic trussstructural dynamic reliability are educed from the Poisson formula ofcalculating dynamic reliability. Finally, the influence of the random ofstructural physical and geometric dimensions parameters on the structuraldynamic reliability is analyzed through the examples, validating thefeasibility of this method.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-151
Stresses of cohesionless solids flow in water-sediment mixture
The stresses of the cohesionless solids flow in water-sedimentmixture is a difficulty in the solid-liquid two phase theory. On the basesof the expansion model, the kinetic theory, and the continuous media theory,the stress constitutive relation of cohesionless solids flow withconsideration of the coefficient of elastic collision restitution has beenobtained, which included the friction stress, the slide stress, and thecollision stress. A critical value ($\tau _c / \tau _e < 0.02$, $\tau _c$ represents the time experienced by a given particle between two consecutivebinary collisions, $\tau _e $ is the particle relaxation time) was applied tojudge whether the friction stress and the slide stress could be neglected. Asimulation of water-sediment flow in inclined chute was carried out toemploy the new stress constitutive relation, and the calculated result wasgood agreement with the experiment data.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-156
Micropolar effects in thin film lubrication
Thin film lubrication (TFL) has been a research hot spotin recent years, which leaves many black areas to tribologists. Themicropolar theory for fluids is adopted to account for the microstructureand microrotation in TFL. Simulation results reveal that micro-polarity willgive rise to an increase in effective viscosity. Micro-polarity has littleeffect on the pressure profile and film shape, but has an influence on thefilm thickness in TFL. The effective viscosity grown with micro-polarity isin very close to that of experimental results presented in a preceding work.The present work will shed some light into the mechanism of TFL.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-177
On the problem of piezoelectric solid with an elliptic hole
An electroelastic analysis is performed on a transverselyisotropic material containing elliptic hole, which subject to a uniformstress field $\sigma ^\infty $ and a uniform electric displacement field$D^\infty $ at infinity while the surface of the hole is free of tractionand electrically open. Taking PZT-4 ceramic into consideration, the resultsbased on the exact electric boundary conditions and the impermeable electricboundary conditions are all obtained. It can be seen that the relatedresults of these two electric boundary conditions are entirely identicalwhen the hole is a circular hole. The impermeable electric boundarycondition is becoming incorrect with the elliptic hole degenerating into acrack. A comparison between these present results and the related resultsshows that the present results are validity. It also shows that some resultsgiven by Sosa are incorrect maybe due to his calculation, not theimpermeable electric boundary.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-187
On asymmetry of ventilated supercavity of underwater vehicle
For all its attracktiveness due to a low hydrodynamic drag, the motion of a supercavitating vehiclein a cavity is a more complicated and paradoxical process than that of space craft. Moving in avaper- or gas- filled , the cavitating vehicle loses buoyancy------the main advantage of motion inwater, and thus need dynamic means to maintan its weight in cavity. To keep the balance andstability of the motion, supercavitating underwater vehicle need asymmetrical supercavitatingflow patterns. In order to explore the asymmetrical supercavitating flow patterns, a series ofexperiments were conducted to investigate asymmetry of ventilated supercavity's configuration.Supercavitation is initiated by ventilating at moderate flow speed. By analyzing and measuring thephotos of supercavity under conditions of various Froude number, attack angle of model andcavitator, the relations between supercavity asymmetry and the factors those arose it were foundqualitatively and quantitatively. The result indicated that whencompound parameter $F_r^2(1+\sigma)$ isgreater than 50, the asymmetrical deformation caused by gravity is less than 5‰. Theasymmetrical supercavitating flow pattern can satisfy the requirement of supercavitating motion ofunderwater vehicle.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-190
The probability density evolution method for dynamic reliability assessment of nonlinear stochastic structures
An original approach for dynamic reliability assessmentof nonlinear stochastic structures is proposed. In the past few years, a newmethod, named the probability density evolution method, has been developed,showing versatile capability in engineering stochastic mechanics such as thestochastic response analysis of either linear or nonlinear structures ineither static or dynamic occasions. In the method, the probability densityevolution equation, a first order quasi-linear partial differential equationin terms of the joint probability density, is deduced and uncoupled to aone-dimensional partial differential equation, which is easy to benumerically solved combining the deterministic dynamic response analysis ofstructures, such as the precise integration method or Newmark-Beta timeintegration method, and the finite difference method. Therefore, theinstantaneous probability density function, rather than the second orderstatistical characteristics such as the mean, the covariance function andthe power spectrum density and so on which are focused on by traditionalstochastic finite element methods, of the response quantities of interestcan be obtained. In the present paper, the probability density evolutionmethod is applied to assess the dynamic reliability of stochasticstructures. To achieve the purpose, an absorbing boundary conditioncorresponding to the failure criterion of the first passage problem isimposed on the probability density evolution equation. Solving theinitial-boundary-value partial differential equation problem with anumerical algorithm will give the ``remaining'' probability density functionof the response. The dynamic reliability can then be assessed throughintegrating the ``remaining'' probability density function over the safedomain. The numerical algorithm is studied in detail where an adaptive TVDdifference scheme is presented. In contrast to the widely usedlevel-crossing process based reliability assessment approach, in theproposed method the mean out-crossing rate, which is usually obtainedthrough the Rice formula, is not needed, nor the properties of thelevel-crossing process such as the Poisson and Markovian assumption.Therefore the proposed method is expected to have a high accuracy. An8-story frame structure with bilinear hysteretic restoring force, which issubjected to seismic excitation, is investigated. The results of dynamicreliability assessment are compared with those evaluated by the Monte Carlosimulation. The investigation shows that the proposed approach is of highaccuracy and efficiency.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-202
An exact solution of angle-ply laminated cylindrical panels in cylindrical bending with imperfect interfaces
An exact elasticity analysis is presented for the cylindrical bending problem of simply-supported angle-ply laminated cylindrical panels featuring interlaminar bonding imperfections. Alinear spring-layer model is adopted to describe the interfacial imperfections. New physicalvariables are introduced to rewrite the basic equations, and the corresponding state-spaceformulations are established. A variable substitution technique is then employed to transfer the stateequation into the one with constant variables, of which the solution can be obtained exactly. It isshown that the effect of weak interfaces can be easily taken intoconsideration by integrating the so-called interfacial transfer matrix into the global transfer matrix.Numerical comparison is firstly made with other exact solution inliterature for perfect angle-ply laminated cylindrical panels and goodagreement is obtained, thus validating the correctness ofthe algebra as well as program of the present method. For an imperfect cross-ply laminatedcylindrical panel, results are then compared with those obtained by an extended zig-zag shell theory.It is shown that when the compliance constants of weak interfaces increase, the shell theorybecomes more and more inaccurate. Thus, for a laminated shell structure with bondingimperfections, the applicability of various two-dimensional approximate theories as well asnumerical methods should be carefully clarified. The results of an unsymmetric five-layeredcylindrical panel further show that the presence of weak interfaces generally reduces the transverseshear stress level at the interfaces; but for some particular values of compliance constants, thetransverse shear stresses may increase at certain perfect interfaces. This will lead to a dangeroussituation because high transverse shear stress is generally one of the most important causes of theinterlaminar shear failure. Thus, the effect of weak interfaces should be precisely evaluated forpractical laminated structures.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-213
Influence of thickness effects on impact responses of beam
In Euler-Benoulli beam theory, Timoshenko beam theory andordinary high order beam theories considering cross-section warping, thenormal strain in the thickness direction is neglected, which can induce someerrors in the analysis of transient responses which involved highfrequencies. In elasticity the beam can be assumed to be in a state of planestress, i.e., there is no any assumption on longitudinal and transversedisplacements, so the beam is a two-dimensional beam. In present study theimpact problem of a particle on a two-dimensional beam is analyzed byindirect mode superposition method which is a semi-analytical method, bythis method the problem of solving the equilibrium equation with singularright term ( point impact force) is avoided. The impact of a particleagainst a simply-supported two-dimensional beam whose modes can be obtainedanalytically and the frequency equation is explicit, is taken as an exampleto investigate the thickness effects on the transient responses, and thecomparisons of results of the two-dimensional beam with that of Timoshenkobeam, demonstrate that the thickness effects play an important role in theanalysis of beam impact problem. The effects of dilatational (longitudinal)and distortional (shear) waves on dynamic responses such as impact loads arediscussed.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-285
Analysis and simulation of discharging residual rocket Propellants in orbit
To diminish the generation of space debris, the residualpropellants in the storage tank of a final-stage rocket have to bedischarged after the satellite-rocket separation. An analysis shows that thepropellant jets under the discharge conditions, once entering the space,will break up into a number of liquid droplets. The droplets diffuse in thehigh vacuum, while gaseous molecules successively evaporate from the dropletsurfaces. This process yields a rarefied vapor and droplet field around thefinal-stage rocket. This article employs the Lagrange means to tracktrajectories and evaporation processes of the droplets, and employs thedirect simulation Monte Carlo (DSMC) method to calculate motion andcollisions of the gaseous molecules. Macroscopic quantities of interest,such as the flow fields, surface pressure, shear stress and heat flux, etc.,are obtained through statistically averaging the corresponding microscopicquantities. This scheme is validated to simulate a steam plume around awater jet into vacuum,and the calculated Pitot pressure distributions inthe radial direction agree with Fuchs and Legge's measured data . The schemeis then applied to three dimensional rarefied vapor and droplet plumesarising from original and new manners discharging in orbit the residual fuel1,1-dimethyl-hydrazine of a CZ-4B final-stage rocket. The calculation showsthat the original manner may lead to quite large disturbance moments beyondthe rocket attitude-control range, whereas the new manner very smalldisturbance moments within the range. These predictions are supported by theremotely measured data of flights
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-286
Stochastic resonance in bistable duffing oscillators and its dynamical
The method of moments is applied to the bistable Duffingoscillators driven by Gaussian white noise and weak periodic force, and theconverging rate of the method is found dependent on the damping size,namely, with the same nonlinear parameter, it converges quicker if thedamping coefficient is larger. Since the method of moments can make usdisclose more general characteristic than only using numerical simulations,the results derived from the method of moments along with the numericalsimulation results can make us to find relations between stochasticresonance and stochastic dynamical behavior. With the method of moments, themono-peak and double-peak resonant structures in the system are disclosedwith the spectral amplification factor for different drive frequencies forthe case of the larger damping coefficient. To explain the derived resonantstructure, the dependence of nonzero frequency peaks peaked out fromfluctuating spectral density on noise intensity is investigated, and thedouble-peaked resonance is found to be resulted from the intrawellvibrations and the above potential barrier vibrations, which is amodification to the previous result. The study confirms there are threepossible resonant sources, i.e. interwell jump, intrawell vibration andabove-barrier vibration in the considered system, and the results haveimportance in statistical mechanics.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-293
The general lie symmetries and non-noether conserved quantities
In this paper, the authors study the non-Noether conservedquantities of Birkhoffian systems by using the general Lie symmetries, andderive a theorem about non-Noether conserved quantities. An example ispresented to illustrate the applications of the results.
2004, 36(2) doi: 10.6052/0459-1879-2004-2-2003-381
The incremental Young's moduli in the rat small intestine caused by
Biomechanical remodelling of the rat small intestineafter treatment with epidermal growth factor (EGF) subcutaneously for 2 days(n=6), 4 days (n=6), 7 days (n=6), and 14 days (n=4) was studied. Theincremental circumferential, longitudinal and cross moduli close to the invivo state were computed from bi-axial test data (combined inflation andaxial stretching) by a least square method. The moduli in thecircumferential direction and the longitudinal direction differed in allgroups, i.e. the mechanical properties were anisotropic in both normal andEGF-treated rats. Time-dependent variation existed for the Young's moduli inall directions during EGF treatment (P<0.05). The circumferential modulusdecreased during the first 7 days of EGF treatment and it almost remodelledback to that of the control group after 14 days treatment. The incrementalmodulus in the circumferential direction ranged between 17.4kPa and 24.2kPa.The modulus in the longitudinal direction ranged between 22.9kPa and 32.4kPa.The longitudinal modulus after 4 days EGF treatment was significantly largerthan that of control group (P<0.02). The cross modulus decreased during thefirst 4 days of EGF treatment thereafter it increased to a maximum at 7days. The values for the cross moduli were between 4.7kPa and 6.6kPa. Inconclusion, the mechanical properties in the intestinal wall are anisotropicand remodel during treatment with EGF.
2004, 36(2): 171-176. doi: 10.6052/0459-1879-2004-2-2003-188