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2006 Vol. 38, No. 2

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The effect of electrostatic force on the evolution of saltaing population of wind-blown grains
A theoretical model is suggested to mathematically describe the evolutionand the wind feedback mechanism of the wind-blown grain flow. In thistheoretical model, the coupling interaction between the wind flow andsaltantgrains and the effect of electrostatical force are considered and the windfield is regarded as changing with time. The time for the entire systemto reach a steady state, the variation curves of the saltant grain numberand the grain transport rate with time, the mass-flux profiles and windprofiles at a steady state are calculated based on this theoretical model.These calculation results are well in agreement with the experimentaldata with the average charge-mass ratio of 60μC/kg.
2006, 38(2): 145-152. doi: 10.6052/0459-1879-2006-2-2005-057
Control of circular cylinder wakes at relatively high Reynolds numbers
Chuanping Shao
A narrow strip has bee introduced as an element to controlcircular cylinder wakes at Reynolds numbers Re=3.0×10 3~2.0× 10 4. The strip is 0.18D (D is diameter of the cylinder) wide, 0.015D~0.025D thick and as long as the cylinder. The long margins of the strip are parallel to and coplanar with the cylinderaxis. The strip is fixed by a row of small rods distributed along a meridianand perpendicularly connected to the surface of the cylinder. The rods havebeen proven to have negligible influence on the flow. The control parameteris strip position, which can be determined byλ/(0.5D)-(unified) distance between the cylinder axis and the length-wise centerline of the strip, and β-angle of attack of the strip.The experiment was conducted in a low turbulence wind tunnel of test section2m long, 60cm wide and 60cm high. Two circular cylinders ofdiameter D=3cm and 5cm were tested respectively in the range ofβ=0°~ 180° and λ/(0.5D)=1.1~3.8. The overall information of the cylinder wake was visualizedby smoke-wire technique and the detailed local information offluctuating velocity was detected by a hot-wire anemometry at various pointsfrom Y/(0.5D)= -6.0 to 6.0 at a stream-wisestation X/D=12.5.Visualization pictures and power spectra of fluctuating velocities show thatvortex shedding on both sides of the cylinder can be effectively suppressedif the strip is located in a certain zone in the near wake. The effectivezones at Re=6.3×103, 1.0×104 and 1.64×104 have been found out with accuracy 0.1 of λ/0.5D and 2.5° of β. The zone enlarges slightly with theincrease of Re in the range tested.Distributions of turbulence intensity for variousβfrom0° to 180° at λ/(0.5D)=2.9 and Re=1.64×104 have been measured. Compare with the case without control, the turbulence intensity on both sides of the wake isreduced when βis in the range of 0°~ 50° or in the vicinity of 180°. However, in the range β=60°~ 120°, an increase appears on the side where the stripresides, while no increase presents on the opposite side.Total resistance on cylinder and control element for variousβfrom 0°to 180°at λ/(0.5D)=2.9 and Re=1.64×104 has been evaluated by momentum integrationusing measured velocity profiles. It shows that the total resistance in therange ofβ=0°~ 40° and in the vicinity of β=180° is obviously smaller than the resistance on bare cylinder. The maximum reduction of resistance is about 32%, which happens atβ=25°~ 30°.All the results mean, local passive interference of the strip can induceglobal changes of the wake at high Reynolds numbers.
2006, 38(2): 153-161. doi: 10.6052/0459-1879-2006-2-2005-241
Flow field analysis of annular hylte nozzle array without base purge
The annular Hypersonic Low Temperature (HYLTE) nozzle arrayis a gain generator of cylindrical high power chemical lasers. In thispaper, a novel design of HYLTE nozzle without base purging is presented.Based on 3D Navier-Stokes equations and the realizable k-\varepsilon model, the multi-species reacting flow field of the annular HYLTE nozzle iscalculated. The numerical simulation results show that eddies along the flowdirection and highly twisted contact surfaces between fuel and oxidizer aremajor factors for rapid mixing and reacting rate of HYLTE. Multi spectralaser outputs are compared between the old HYLTE nozzle design and the newone, which shows that with the new HYLTE design, a total of 3kW output power can beextracted from 1g F atom reacting gas by BCAR resonator, howerver, only1.6kW can be extracted with the old design. In addition, the new design notonly simplifies the fabrication of the complex HYLTE nozzle, but alsoreduces theconsumption of He used in the high-energy chemical DF laser.
2006, 38(2): 162-169. doi: 10.6052/0459-1879-2006-2-2004-449
Mixed finite element method for coupled thermo-hydro-mechanical in unsaturated porous media
A mixed finite element for coupledthermo-hydro-mechanical (THM) analysis in unsaturated porous media isproposed. Displacements, strains, the net stresses for the solid phase;pressures, pressure gradients, Darcy velocities for pore water and pore airphases; temperature, temperature gradients, the heat flux of the three phasemixture are interpolated as independent variables. The weak form of thegoverning equations of coupled thermo-hydro-mechanical problems in porousmedia within the element is established on the basis of the Hu-Washizuthree-fieldvariational principle. The proposed mixed finite element formulation isthenderived. For geometrical non-linearity, the co-rotational formulationapproach is used. Numerical results demonstrate the capability and theperformance of the proposed element in modelling progressive failurecharacterized by strain localization.
2006, 38(2): 170-175. doi: 10.6052/0459-1879-2006-2-2005-162
Numerical simulation for cone indentation of metallic foams and the reverse analysis
Indentation testing is a popular method used to determinethe mechanical properties of materials. In this paper, finite elementsimulations are carried out for cone indentation of metallic foamswith 80 different material parameters. The numerical results combinedwith the dimensionless analysis method are used to establish therelationship between the cone indentation behavior and the elastoplasticmaterial parameters of metallic foams. Based upon the relationship, areverse analysis is developed so that the elastoplastic properties ofmetallic foams can be extracted from the cone indentation data.Obtained results show that the Young's modulus, yield strength, and plasticcompression coefficient of metallic foams can be unambiguously determined bythe developed reverse method. However, some supplement information is needed inorder to evaluate the densification strain.
2006, 38(2): 176-184. doi: 10.6052/0459-1879-2006-2-2005-128
Electroelastic interaction between a piezoelectric screw dislocation and a circular coated inclusion with interfacial cracks
The electroelastic interaction between apiezoelectric screw dislocation and a circular coated inclusion withinterfacial cracks is investigated. With the complex variable method,the general solutions of the complex potentials in the matrix, the coatinglayer and the inclusion regions are derived. As illustrative examples, solutions in the form of explicit series are presented in the case of one interfacialcrack. Based on the obtained complex potentials, the image force on thepiezoelectric screw dislocation is then calculated by using the generalizedPeach-Koehler formula. The equilibrium position of the dislocation isdiscussed in detail for various crack geometries, coating layer thicknessesand piezoelectric material property combinations. The results show that theinterfacial cracks have a significant perturbation effect on the motion of thepiezoelectric screw dislocation near the coated circular inclusion and thetrapping power of the coated inclusion with interfacial cracks is higherthan that of a perfectly bonded one. The critical value of the crack length or the material constant of the coating layer may be found to changethe original direction of the image force.
2006, 38(2): 185-191. doi: 10.6052/0459-1879-2006-2-2005-150
Self-similar solutions to mode iii interface crack subjected to variable loadings Pxmtn
By the method of complex functions,self-similar solutions are obtained for a mode III interface cracksubjected to variable loadings Pxmtn. The problems discussed can be transformed into Riemann-Hilbert problems by this method, thenanalytical solutions are obtained by self-similar functions.Using those solutions and the superposition theorem, the solution toarbitrarily complex problems can be obtained.
2006, 38(2): 192-198. doi: 10.6052/0459-1879-2006-2-2004-391
Investigation on impact behavior of concrete
This paper presents two damage constitutive models,namely, the damage visco-elastic constitutive model and the coupledconstitutive model of damage and plasticity, to describe the impact behaviorof concrete. A comparison between the model prediction and theexperimental results shows that the damage visco-elastic constitutivemodel is not adequate to describe the plastic deformation inconcrete, with increase of impact velocity. The damageconstitutive model coupled with plasticity accounts for such effects asmodulus degradation due to micro-cracking, the increase of bulk modulus andplastic strain due to micro-voids collapse. Therefore, it describesvery well the impactbehavior of concrete subjected to shock loading.
2006, 38(2): 199-208. doi: 10.6052/0459-1879-2006-2-2005-172
Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity
In this paper, the scatting of SH-wave by asemi-cylindrical hill above a subsurface cavity in half-space is studiedbased on the idea of match up, by using complex functions andmulti-polar coordinates. During the solution, we divide the solutiondomain into two. Thefirst one is a circle domain, including the boundary of the hill, andthe second one consists ofall of the rest parts. A solution is constructedin the circle domain, where satisfies the condition that stress is zero atthe hill edge and arbitrary at the other part. In the second domain, including asemi-cylindrical canyon and a subsurface cavity in the half-space,the scattered wave function is constructed, which satisfies the condition of stress free atthe horizontal surface. Then, by using the moving coordinate method, thetwo solutions are matched up on the junction interface, satisfying the boundary conditionat the subsurface cavity edge. The problem can be reduced tosolve a set of infinite linear algebraic equations. Finally thecomputational results of surface displacement are presented togetherwitha discussion.
2006, 38(2): 209-218. doi: 10.6052/0459-1879-2006-2-2004-508
A 1-D time-domain method for 2-d wave motion in elastic layered half-space by antiplane wave oblique incidence
A 1-D finite element method in time domain is developed inthis paper, which can be used to calculate the wave motion of free field inelastic layered half-space by antiplane SH wave oblique incidence. When thelayered half-space is discretized, the vertical element size is determinedconforming to the simulation accuracy; the horizontal element sizeis determined automatically by the horizontal apparent wave velocity and thediscrete time step in the step-by-step calculation, and then the elements aredivided virtually. Artificial boundary is constructed on the bottom ofthe computational area and the input wave motion is transformed into an equivalentload, which is applied on the nodes of the boundary. Then, the finite elementmethod with lumped mass and the central difference method are combined to establish the wave motion equations in 2-D finite element model.Since the displacement of any node in the finite element model can berepresented by that of the adjacent node in the horizontal direction, the 2-Dwave motion equations can be transformed into 1-D equations. By solving the1-D equations, the displacement of nodes in one vertical line can beobtained. Finally, the wave motion in elastic half-space is obtained basedon the propagation characteristics of traveling wave. Both the theoreticalanalysis and the numerical results demonstrate that the proposed methodfeatures high accuracy and good stability.
2006, 38(2): 219-225. doi: 10.6052/0459-1879-2006-2-2005-294
Thermodynamic analysis of multiphase periodic structures based on a spatial and temporal multiple scale method
A spatial and temporal multiscale asymptotichomogenization method simulating the wave propagationproblem in periodic multiphase materials is systematically studied.Generalized function field governing equations of wave propagation are expressedin a unified form with both inertia and velocity items. Amplified spatialand reduced temporal scales are, respectively, introduced to account forspatial and temporal fluctuations and nonlocal effect of the homogenizedsolution due to material heterogeneity on different time scales. The model isderived from the higher-order homogenization theory with multiple spatialand temporal scales. By combining various orders of homogenized functionfield equations, the reduced time dependence is eliminated and then thefourth-order differential equations are derived. To avoid the necessity ofC1-continuity in finite element implementation, the C0-continuousmixed finite element approximation of the resulting nonlocal equations offunction field is put forward. Non-Fourier heat conduction and thermaldynamic problem are computed to demonstrate the efficiency and validity ofthe theories and models developed and indicate the disadvantages of theclassical spatial homogenization.
2006, 38(2): 226-235. doi: 10.6052/0459-1879-2006-2-2004-519
An experimental investigation on coherent structures in near wall region of channel turbulent flow using DPIV
The channel turbulence isstudied experimentally by using a double frame straddling CCD camera DPIV system. Throughthe analysis of enormous data obtained from the experiment,the spatial structure and its evolution characteristics, together withthe time history ofturbulence in the near wall region, are obtained. The experimental resultreveals that the phenomena such as ejection, sweep and variety ofinstantaneous velocity profiles of turbulence bear a direct physical relationwith the evolution of the clockwise transverse vortex flowing downstream. Theexperimental result explains the form and the evolution of inflexion ofthe instantaneous velocity profile when the clockwise transverse vortexpasses through it. From the experimental result, we can explain some characteristicmechanism of large scale structure. The experimental result also shows thatDPIV system can provide quantitative and qualitative informationconcerning turbulence spatial characteristics and is suitable forexperimental studies on turbulence in the near wall region.
2006, 38(2): 236-245. doi: 10.6052/0459-1879-2006-2-2005-119
Velocity distribution in compound channels with vegetated floodplains
The authors experimentally studied the velocitydistribution of flows in different types of vegetations such as arbors,shrubs and grass. The experimental procedures and the principle of ADV formeasuring the local velocities are described in detail. For vegetations onthe floodplain, the authors chose plastic grass, duck feathers and plasticstraws as model grass, model shrubs and model arbors, respectively. ADV wasused to measure the local flow velocities for different typesof vegetation on the floodplain, discharges and flume slopes. All measuredstreamwise velocities follow a logarithmic distribution fornon-vegetated floodplain, and obey S-shaped distribution for vegetatedfloodplain. The S-shaped distribution divides the flow into three regions.The range of every region is related to the flow depth, lateral location andvegetation type. For different types of vegetation, the S-shapeddistribution is different. In the meantime, it is found that the velocity inthe main channel increases and that on the floodplain decreases after thefloodplain is vegetated. The increasing or decreasing degree is related tovegetation type. Furthermore, the influences of bed slope on local velocitydistribution for different types of vegetation are distinct.
2006, 38(2): 246-250. doi: 10.6052/0459-1879-2006-2-2004-511
Logarithmic singularity in an arc crack problem
This paper investigates an arc crack in an infinite plateunder antisymmetric loading on the crack faces. In other words,the tractions on the two crack faces are the same in magnitude and indirection. Complex variable method is used to solve theabove-mentioned problem. The stresses and the displacements are expressedthrough two complex potentials. After some manipulations, the problem isreduced to a Riemann-Hilbert problem for the complex variable functions,which can be solved in a closed form. The stress intensity factors at thecrack tips can be determined as usual. At the vicinity of the crack tips,the logarithmic terms can be found from the obtained complex potentials.From the logarithmic terms, the logarithmic singularity at the crack tipis defined and evaluated, in a closed form.
2006, 38(2): 251-254. doi: 10.6052/0459-1879-2006-2-2005-134
A new multiaxial fatigue model considering the influence of tensile dwell time
The influence of tensile dwell time on fatigue was usedto define a CFI (Creep -Fatigue Interaction) factor, that characterizesthe nonlinear interaction of creep damage and fatigue damage. A hightemperature multiaxial fatigue model with energy-type parameters based on thecritical plane approach was proposed. The model considers both theexperimentalobservation of fatigue fracture and the tensile dominant effects of crackinitiation, propagation and fracture under biaxial fatigue loading. Themodel has a ``unified'' ability of modeling the multiaxial fatigue lifeunder different temperatures, various loading properties and dwell time. Thematerial life constants in the model are temperature-independent andloading-independent, and the method may be generalized to other dominanteffects of fatigue to build multiaxial fatigue models. The constantsfor Udimet720 Li, a superalloy used for turbine disc, were obtained byfitting the test data under uniaxial low cycle fatigue loading with dwelltime. The model was applied to predict the fatigue life of cruciform underbiaxial cyclic loading with dwell time at elevated temperatures based on thestress-strain results by a viscoplastic finite element analysis method.Errors are within a factor of 2, that is, within the engineeringrequirement margins. The validity and accuracy of the model were verified.
2006, 38(2): 255-261. doi: 10.6052/0459-1879-2006-2-2005-022
Impact response of an unrestrained modified Timoshenko beam
In this paper, the modified motion equation of Timoshenkobeam is first introduced, which is then compared with that ofTimoshenko beam. The orthogonality conditions of the modifiedTimoshenko beam, where the rotary inertia caused by the shear deformation isconsidered, are derived. The impact response formulas of an unrestrainedmodified Timoshenko beam under the impact of a lumped mass are deduced, andthe corresponding numerical examples are analyzed. The evaluationresults are compared with the impact response of the classical unrestrainedTimoshenko beam with the same lumped mass. Finally, the effects ofthe beam stiffness and impact mass ratio on the response are discussed.
2006, 38(2): 262-269. doi: 10.6052/0459-1879-2006-2-2004-380
Numerical study on the influence of a symmetrical stenosis at the carotid sinus on the flow in the carotid bifurcation
The operation of ring constraining, which produce a symmetricalstenosis to artery, was a usually used method to establish an animal modelor in vitro arterial atherosclerosis model because the straitness degree canbe controlled easily and quantitatively. However, it is unknown howthe flow field will be changed, and whether the flow field is similar tothat under physiological stenosis when a ring constraining employed tobifurcation or bended artery. To understand the flow in bifurcation arteryunder a ring constraining, carotid bifurcation with a symmetrical stenosisto the carotid sinus was instanced. The velocity profile, the secondary flowand the distribution of wall shear stress in the stenosed carotidbifurcation were numerically studied. The results were compared withthose inthe healthy carotid bifurcation. It was shown that the flow field in thecarotid sinus, especially, the distribution of wall shear stress, waschanged. Low wall shear stress was axis-symmetrically distributed on thewall of the backward site of stenosis. Based on the influence of low wallshear stress on atherosis, it was prompted that atherosis might take placeaxis-symmetrically in the backward site of stenosis. It is obviouslydifferent to the physiological process of atherosis. Therefore, it isindicated that the symmetrical stenosis is not suitable for simulating thecarotid sinus stenosis. To simulate the physiological stenosis in thecarotid sinus, an asymmetrical stenosis should be employed.
2006, 38(2): 270-275. doi: 10.6052/0459-1879-2006-2-2005-353
Rigid-flexible coupling dynamics of a flexible beam with three-dimensional
In this paper, the modeling theory of rigid-flexible coupling dynamics of aflexible beam with three-dimensional large overall motion is studied. Basedon the precise strain-displacement relation, the rigid-flexible coupling dynamicequations are derived using the velocity variational principle, in which thevirtual power of the torsion force and the inertial torque of the beamelement are included and the geometric nonlinearity is taken into account.Finite element method is employed for discretization. Simulation of aspatial beam system is used to show the influence of torsion and crosssection rotary inertia on the dynamic performance of the system.Conservation of energy in case of free motion is shown to verify the proposed nonlinear model. It is shown that the torsiondeformation influences not only the axial angular velocity of the hub,but also the lateral angular velocity of the hub and the bendingdeformation of the beam.
2006, 38(2): 276-282. doi: 10.6052/0459-1879-2006-2-2005-101
The bifurcation of noisy bistable Duffing oscillator's moment equations and stochastic resonance
In this paper, the relationship between thebifurcation of noisy bistable Duffing oscillator's moment equations andstochastic resonance of this system is studied. According to therelationship, the mechanism of stochastic resonance of the bistable Duffingoscillator is revealed from another viewpoint. First, the momentequations of the bistable Duffing oscillator in the presence of Gaussiandistributed white noise and weak periodic signal are obtained on the basisof It$\hat{\rm o}$ equation. Second, the bifurcation behavior of its momentequations with noise intensity as their bifurcation parameter is analyzed.Third, the relationship between stochastic resonance of the bistable Duffingoscillator and the behavior of bifurcation of the moment equations is studiedquantitatively. Finally, the mechanism ofstochastic resonance of the bistable Duffing oscillator is presented fromanother viewpoint, that is, the transfer of the energy distribution of thefirst moment of the original system response occurs because of occurrence ofbifurcation of the moment equations with noise intensity bifurcation parameter,and the transfer makes the energy of system response concentrate in thefrequency component whose frequency is equal to that of input, then the weaksignal is amplified and stochastic resonance occurs.
2006, 38(2): 288-293. doi: 10.6052/0459-1879-2006-2-2004-414