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2006 Vol. 38, No. 4

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Statistics of conditionally filtered dissipation and diffusion in large eddy simulation
In the large eddy simulation of turbulent reacting flows, thefiltered reaction terms are unclosed. It is difficult to construct thesubgrid scale (SGS) model for filtered reaction terms due to the absenceof a universal energy cascade process, which is the foundation of SGS modelsin fluid turbulence. With the conditional filter approach, theSGS models for conditionally filtered reaction terms can be closed, butconditional diffusion and dissipation have to be modeled. We use a directnumerical simulation of turbulent mixing to investigate the scale-dependenceof the conditional filtered diffusion and dissipation. The results show that theconditional filtered diffusion depends on large scales, but the conditionalfiltered dissipation depends on both large and small scales. The effectsof small scales on the conditional filtered dissipation have to be includedin its SGS models.
2006, 38(4): 433-437. doi: 10.6052/0459-1879-2006-4-2004-500
Penetration mode and drag reduction research in hypersonic flows using a counter-flow jet
More and more people believe that opposing jetscan reduce the drag, which are obtained by the interaction of high speedcounter- flow jets and bow shock. It improves the performance of aircraft byshifting the flow field (shock wave structure and boundary layer)around the aircraft, changing the physical and aerodynamiccharacteristics ofthe aircraft. The flow field over the sphere and truncated cone, withcounter-flow jets, is investigated in the present paper. It takes intoaccount theeffect of the thermo-chemical non-equilibrium in the flow field. Two steadyflow modes of a truncated cone are obtained: short penetration mode (SPM) and long penetration mode (LPM). Details of bothmodes are studied. The transient phenomena during the transition from onemode to another are also investigated. The shock bifurcation phenomenon isstudied and the relation between flow field's stability and jettotal-pressure ratio is obtained. The numerical experiment reveals acritical state for theoscillatory fluid motion. The control parameter is the stagnation pressureratio between the on-coming stream and the counter-flow jet. At a lowinjection pressure, the jet is compressed, penetrates through the bowshock and forms a multi barrel structure. When the counter-flow jet isgenerated by a sufficient high stagnation pressure, it will assume a singlebarrel structure. When the jet pressure is in the critical range, a largeamplitude oscillation will occur and the drag attains its minimum value. Theuse of counter-flow jets in drag reduction is analyzed. The main factorsin the drag reduction's efficiency are also studied.
2006, 38(4): 438-445. doi: 10.6052/0459-1879-2006-4-2005-067
Experimantal research on infrared radiation in hypersonic flow around blunt
This paper reports our experimental research on infraredradiation in reentry flows. The experiments are conducted in the oxygen-hydrogendetonation driven shock tunnel JF-10. Total enthalpy of the particular runamounts to 15.5 MJ/kg, pressure in the reservoir is 19.6 MPa, and thegenerated free stream velocity is approximately 5 km/s. InSb multi-elementinfrared imaging system is used to measure the infrared radiation.Taking a sphere-nosed blunt cone as the test model, the transverse infraredradiation power profiles in the shock layer and wake are obtained. The datashow some unique features. Infrared radiation is weak near the wall, strongand relatively uniform in the middle region of the shock layer, and becomesweak again in the outer part of the shock layer. In the wake, the radiationis the strongest near the symmetric axis and becomes weaker monotonically whiledeparting from the axis.
2006, 38(4): 446-451. doi: 10.6052/0459-1879-2006-4-2004-496
A two-layer mathematical model for oil spill transport and transformation in the sea
A computer model for simulation of oil slick transport inseas by a Lagrangian discrete parcel algorithm is proposed. Oil spilled in awater body, regardless of whether it is originated as a surface or subsurfacespill, consists of a floating surface slick and suspended oildroplets in the water column. In this algorithm the oil slick is viewed as alarge number of small parcels of equal mass and their discrete path and massare followed and recorded as functions of time relative to a reference gridsystem in space. The movement of each parcel in the sea is affected by thewind, water current, and concentration of surrounding parcels. The transport of spilled oil is governed by advection, horizontal spreading,turbulent diffusion, evaporation, dissolution, emulsification, theinteraction of oil with the shoreline, and sedimentation. In addition,photochemical reactions and biodegradation can also affect thecharacters of the oil andreduce the amount of oil over a long period of time. The model simulatesboth continuous and instantaneous oil spills, not only oil spills, butalso ofother toxic matter. American Princeton Ocean Model is applied in thispaper as the hydraulic model. Sample simulations for oil spills in Bohai arepresented.
2006, 38(4): 452-461. doi: 10.6052/0459-1879-2006-4-2005-007
Study on the mechanism and simulation method for wall burning process
While burning solid fuels, like biomass, coal andwaste, wall-burning will occur to a certain extent. With the coal-fired liquid-bath combustor as an example, the mechanism of coaldeposition, movement and combustion on the molten surface are discussed.In order to overcome the limitation of existing simulation methods for burningcharacteristics in the liquid-bath combustor, this paper proposes awall-burning model considering the slag flow condition and gives a totalcomputational frame work. From the comparison of simulation results with severalother methods, their difference and properties are analyzed, whichcan provide a guidance for the simulation of liquid-bathcombustor and guidance for the simulation of biomass or wastecombustion.
2006, 38(4): 462-470. doi: 10.6052/0459-1879-2006-4-2005-358
Mathematical model and numerical method for simulation of coupled chemo-thermo-hydro-mechanical process in concrete subjected to fire
A hierachical mathematical model for analyses of coupledchemo-thermo-hydro-mechanical behavior in concretes subjected to fire ispresented. The concretes are modeled as unsaturated deforming reactiveporous media filled with two immiscible pore fluids. The mathematical modelconsists of a set of coupled, partial differential equations governing themass balance of the dry air, the mass balance of the water species, the massbalance of the matrix components dissolved in the liquid phases, theenthalpy (energy) balance and momentum balance of the whole medium mixture.The thermo-induced desalinization process is particularly integrated intothe model. A mixed weak form for the finite element solution procedure isformulated for the numerical simulation of chemo-thermo-hydro-mechanicalbehaviors. Special considerations are given to spatial discretization ofthe hyperbolic equation with non self-adjoint operator nature. Numerical resultsdemonstrate the performance and the effectiveness of the proposed model andits numerical procedure in reproducing the coupled chemo-thermo-hydro-mechanicalbehavior in concretes subjected to fire.
2006, 38(4): 471-479. doi: 10.6052/0459-1879-2006-4-2005-242
Study on a two-dimensional generalized magneto- thermoviscoelastic problem subjected to ramp-type heating
In this paper, a two-dimensional problem ofmagneto-thermoviscoelasticity with relaxation time in a perfectly conductingmedium is studied. With Laplace transform (for time variable) and Fourier transform(for one space variable), the exact expressions for field quantitiesare obtained in the transformed domain. The resulting formulations are applied toa semi-space problem subjected to ramp-type heating at the surface. Usingnumerical inverse method, the results are obtained and shown graphically when the acrylicplastic material is considered. Also a comparison is made between theresults obtained using the generalized thermoviscoelastic theory andthoseobtained using the conventional thermoviscoelstic theory and thermoelastictheory.
2006, 38(4): 480-487. doi: 10.6052/0459-1879-2006-4-2005-240
Finite element model with equivalent beam elements of single-walled carbon nanotubes
Graphite sheet and single-walled carbon nanotube areintegrated through Carbon-Carbon (C---C) covalent bonds. Under the assumption ofsmall deformation, the potential of C---C bonds can be described by a harmonicfunction, with the same form as the strain energy function of beamelements, so beam elements can be used to describe C---C bonds. This paperpresents a finite element model with equivalent beam elements, which canperfectly replace the harmonic potential to describe the bond stretching,bond angle variance, inversion angle variance and torsion of the C---C bonds.By the analysis of graphite sheet under typical loads, the parameters of theequivalent beam elements and the relation of the parameters of theequivalent beam elements vs the C---C bonds are obtained. By using the model,the elastic properties for achiral nanotubes are calculated. The results arein good agreement with the existing results.
2006, 38(4): 488-495. doi: 10.6052/0459-1879-2006-4-2005-328
Frictional contact analysis of a finite plate with multiple elliptical holes and closed cracks
Based on the mathematical programming procedure of thecontact problem with friction and using the complex potential method in theanisotropic plane theory of elasticity, an efficient approach is presentedto deal with the frictional contact of a finite anisotropic plate containingmultiple elliptical holes and cracks subjected to arbitrary loads. Thecomplementary parameters introduced to the contact boundary are expandedinto Fourier series, and the linear complementary model considering thecrack closure is obtained by means of the Faber series expansion, conformalmapping and the least square boundary collocation technique. Some examplesare given to demonstrate the validity and effectiveness of the method.Numerical results indicate that the present method enjoys many advantages suchas high accuracy, good convergence, and is convenient to be used toinvestigate effects of crack closure on the fracture parameters of structures.
2006, 38(4): 496-504. doi: 10.6052/0459-1879-2006-4-2005-263
Wolff's law based topology optimization for continuum structure
Wolff's law in biomechanics states that the bone continuallyadapts to its mechanical environment through cell-based remodeling oftrabecular surfaces and the local microstructure tends to align with theprincipal directions of the stress. The objective of the present research is todevelop a new rule-based method for continuum topology optimization based onWolff's law. The major ideas of the present approach are as follows.Firstly, the structure is to be optimized as a piece of bone whichobeys Wolff's law. Secondly, the process of finding the optimal structuraltopology is equivalent to the ``bone'' remodeling/growth process. Thirdly,the remodeling rule can be explained as follows: During the process ofgrowth, at any material point in the structure, if the absolutevalues of one of its principal strains is out of a given interval of referencestrain, then the material in the local microstructure along the correspondingdirection should be adjusted. If theabsolute values of all its principal strains locate in the interval, the material point is in a state of equilibrium of remodeling.Finally, the global optimization of structure requires all material pointsto be in the state of remodeling equilibrium under the loading conditions.In order to express the microstructure and the anisotropic behavior of amaterial point, a second rank positive and definite fabric tensor isintroduced. The relative density of a point in design domain expressed bythe invariants of the fabric tensor through the mathematical condensation ofthe porous medium based on the stiffness-equivalence rule is used to displaythe optimal topology of structure. Examples are given to show the validityand capability of the proposed approach for the optimal topology design ofcontinuum structures.
2006, 38(4): 505-513. doi: 10.6052/0459-1879-2006-4-2005-219
The damage coupled thermo-mechanical (TM) model for rock failure process and applications
Based on the heterogeneous characteristics of rock atmesoscopic level, the thermal-mechanical coupled behavior during the failureprocess of rock subjected to thermal stress is analyzed with elastic damagemechanics and thermal-elastic theory. A mesoscopic thermal-mechanical (TMModel) coupling model, implemented in RFPA, is proposed, which can beused to study the damage and failure process, as well aselastici stresses for the coupled thermo-mechanical rock problem. With thenumerical model, the damage and associated mechanical property evolutionof mesoscopic structure in rocks subjected to TM loading can beanalyzed.Numerical simulation is carried out to investigate the stability of the rockpillar in a Hard Rock Laboratory. The numerically obtained stress field,failure pattern of pillar rock and associated AE events all agree wellwith the in-situ data, which shows that the proposed model isreasonable and effective, and may provide guides for theexperiment design and associated applications.
2006, 38(4): 514-521. doi: 10.6052/0459-1879-2006-4-2005-452
Integrated design of porous materials and structures with scale-coupled effect
It is known that structural behaviors of cellularsolids are dictated by the topology of the dense and porous regions,with a complex arrangement of microstructures of different sizesand topologies. In this paper, an integrated design methodology usingRepresentative Volume Element(RVE) scale is proposed for the globalstiffness maximization of the overall structure and the local design ofRepresentative Volume Element based on multi-scale computing. Influences ofRepresentative Volume Element aspect ratio, scale, and periodic arrangementstyle such as translation, symmetric pattern on the optimal design areinvestigated using the super-element method. By means of the dualoptimization scheme and perimeter constraint, Representative Volume Elementsare efficiently optimized with checkerboards being eliminated. Numericalresults show that the proposed method can be used in the design ofporous materials such as honeycomb panels and hierarchical cellular sandwichpanels and the hierarchical cellular materials scale effects are wellrepresented. Thisprovides an innovative design concept for the lightweight structures.
2006, 38(4): 522-529. doi: 10.6052/0459-1879-2006-4-2005-209
Study on Characteristics of Railway Bogie Structural Vibrations under Train Running through a Switch
The general train model, with three high-speedrolling-stocks and a track system, passing through a switch, is developed,considering the elasticity of the track foundation andmodeling the bogie frames as elastic bodies. The excitations caused by arailway switch and the dynamic loads acting on a railway elastic bogie frameare simulated and analyzed. By theMBS-postprocessor FEMBS$^{ -1}$, these loads are transferred back tothe FE-code, in which the stress distributions for the whole bogie aresimulated by means of the ANSYS-code, high stressed locations areidentified, and time histories for the stresses at the locations aresimulated and analyzed.The simulating results of thetrain model and one rolling-stock model, including the time histories for the stresses in the bogie frame are compared with those obtainedin the real field test. The frequency spectrums of the dynamic stressesshow that thestructural vibrations of the bogie frames in the train are differentfrom those of one rolling stock. The dynamic tensile stresses and compressive stressesin the bogie frames while the train passing through a crossing vee are allhigher in magnitude than those in a railway car. It indicates that the onerolling-stock model is only suitable for primary designs, calculations andanalyses, while the train model should be adopted in order to analyzestructural characteristics more accurately. According to the frequencyspectrums of the dynamic stresses of bogie frames, frequency domain of thestresses may be divided into three vibration zones, that is, the firstfrequency zone corresponding to the stresses while train passing a curve,the secondcorresponding to those while train passing through a crossing vee and turnout ofswitch, and the third corresponding to the natural eigenmodes ofthe elastic bogie frame.
2006, 38(4): 530-539. doi: 10.6052/0459-1879-2006-4-2005-369
Optimized design of waverider with high lift over drag ratio
A family of optimized hypersonic waverider derived fromconical flow fields is generated and studied; the detailed viscous effectsare included within the optimization process using the referencetemperature methods. A non-linear simplex method is used to find thewaverider configuration for the maximum lift over drag ratio, viscousoptimization is completed at Mach number 6, attitude 30km, andcone angle from 5^{\circ} to 10^{\circ}. Shapes of waveriderwith high lift over drag ratio are obtained, and the resultsare verified with CFD. The results show that for the optimized designwaverider, the lift over drag ratio of waverider is the maximum at acertain cone angle; the skin friction drag and wave drag are nearlyequal; volumetric efficiency, slenderness,span over length ratio increase with the cone angle.
2006, 38(4): 540-546. doi: 10.6052/0459-1879-2006-4-2005-021
Experimental observations of inception cavitation vortices around a hydrofoils
The inception cavitation around a 2D-hydrofoil in the boundary layer of a non-separated turbulent flow was studiedexperimentally. The cavitation inceptions were observed by ahigh speed video camera, and the velocities around the hydrofoil weremeasured by a 2D-LDV. It is shown that the inception cavitation bubbles aregenerated along with a hairpin-shaped vortex coherent structure in theboundary layer of the non-separated turbulent flow. The developingprocess of an inception cavitation bubble vortice comprises generation,expanding, collapse, rebound and re-collapse. It is concluded that theinception cavitation has dual characteristics of both bubbles and coherentstructures.
2006, 38(4): 547-552. doi: 10.6052/0459-1879-2006-4-2005-020
Solving generalized piezothermoelastic problem by fem with different theories
The generalized piezothermoelastic coupled governingequations are formulated in generalized thermoelasticity theories: G-Ltheory and L-S theory. For a short time duration, the finite element method isproposed to solve the partial differential equations directly in the timedomain. The developed method is applied to a two-dimensional generalizedpiezothermoelastic problem of a thick piezoelectric plate of infinite extentsubjected to thermal shock on its surface. Temperature distributions as wellas displacement, stress and electric potential distributions areobtained and representedgraphically. Comparisons are made with the results predicted by theclassical piezothermoelastic theories. It is shown that the present methodis an effective and exact numerical analysis method for the generalizedpiezothermoelastic problem.
2006, 38(4): 553-558. doi: 10.6052/0459-1879-2006-4-2005-456
Impact fracture analysis of functionally gradient bi-material interface with weak/micro-discontinuity
The concepts are clarified and a classification is suggested with respect to thestrong-discontinuous, weak-discontinuous, micro-discontinuous andall-continuous interfaces. A mechanical model is established forimpact fracture problems of functionally gradient elastic bi-materialinterfaces with weak discontinuity. Integral transform is used to deriveCauchy singular integral equation for the crack, and the allocation methodis used to obtain numerical solutions. It is indicated that, the weakdiscontinuity and the micro-discontinuity have significant effects on stressintensity factors, and the micro-discontinuity is a kind of connection of interfacial mechanical property better than the weakdiscontinuity. By assuming the mechanical property of the FGM at one side of theinterface to be the lower-rank terms of Taylor series with respect to that at the otherside, the interface will become micro-discontinuous. The first rankmicro-discontinuity is enough to reduce the stress intensity factorsnotably, however, the higher-rank terms, which are equal to or higher thanthe second rank, have less effect on stress intensity factors. To reduce theweak discontinuity or to make the interface micro-discontinuous are allbeneficial to the enhancement of the capacity of the FGMs interface toresist impact fracture, i.e. to the enhancement of the interfacialtoughness.
2006, 38(4): 559-564. doi: 10.6052/0459-1879-2006-4-2005-095
A method of establishing generalizedmaxwell model for viscoelastic materia
The generalized Maxwell model, which describes stressrelaxation modulus, is usually used for analyzing the rheologicalcharacteristics of viscoelastic materials. While data of relaxation modulusobtained from experiments are usually expressed as Kohlrausch-William-Watts(KWW) function, which is in an exponent-spread form. In the paper, thefitting of KWW function to the generalized Maxwell model is turnedinto the equality of two matrixes, which is equivalent to make the1-norm of the matrix difference infinitely small. Minimumvalue of the 1-norm is achieved by introducing the generalized inverse ofmatrix. At last, taking the minimum value of the 1-norm as the objectivefunction, and relaxation time as the constraint condition, a simplex methodis used to optimize the minimum value of the 1-norm. A new computationalmethod for fitting of KWW function to the generalized Maxwell modulus by means of MATLAB software is proposed.
2006, 38(4): 565-569. doi: 10.6052/0459-1879-2006-4-2005-132
Nonlinear dynamic stability for piezoelectric laminated plates with damage
On the basis of the anisotropic damage theory andpiezoelectric theory, the nonlinear governing equations for piezoelectricmoderately thick laminated plates with damage subjected to a parametricexcitation are derived through applying the energy principle and Lagrangeequation. Employing the incremental harmonic balance method, a solution forthe nonlinear dynamic stability of the piezoelectric moderately thicklaminated plates with damage is obtained. In the numerical examples, theinfluences of damage parameters and piezoelectricity on the nonlineardynamic stabilities are discussed andthe inherent features about the coupledmechanics and electricity are revealed. A comparison is made with available data.
2006, 38(4): 570-576. doi: 10.6052/0459-1879-2006-4-2005-214