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2008 Vol. 40, No. 6

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An experimental study on head-on collision of detonation with shock
ZHU Yu-Jian
An experimental study on head-on collision of adetonation wave with shock wave in a straight tube was carried out. Highspeed streak schlieren photography was used to illustrate the interactingflow field, and smoke foils were adopted to record the detonation cellularstructure around collision. Based on the theories of shock wave andclassical CJ detonation, the theoectical analyses were also performed toacquire its steady solution and the essential characteristics. Theexperimental showed that the steady wave system after collision consists ofa shock wave and a detonation wave followed by a rarefaction wave fan, whichis consistent with the CJ solution of 1-D theoretical analysis. The initialwave pressure has no effect on the wave system and the initial temperatureremarkably affects the wave and flow velocities. Meanwhile, the strength ofthe incident shock wave has the most important influence on the transmittedflow system, that is, strong shock induces the whole flow field towards theshock direction. Rarefaction is inevitable in the system unless the incidentshock tends to Mach one, and stronger shock usually results in more expandedrarefaction zone. Experimental study also revealed that the detonation waveexperiences a transit process after collision, where it first slows down andthen bursts into an overdrived detonation which then undergoes a subsequentequilibrium process towards CJ state. This transit process usually developsunsteadily in the highly irregular mixture. Seroius decoupling of shock andflame may occur in some region, and the decoupled flame could rapidlydevelop new cellular detonation even before it overtakes the decoupledprecursor shock. Very fine cellular traces printed by this kind ofdetonation were observed in our smoke foil results.
2008, 40(6): 721-728. doi: 10.6052/0459-1879-2008-6-2007-450
Hydrodynamic simulation and the effect of centrifugal forcefor chemical mechanical polishing process
Taiyuan Gao, Ming-jun Li, Limin Hu, Zhi Gao
Chemical mechanical polishing process is a combination ofchemical dissolution and mechanical action. The mechanical action of CMPinvolves hydrodynamic lubrication. In this paper, the modified Reynoldsequation with centrifugal force is investigated and solved by means ofChebyshev acceleration method with successive over-relaxation algorithm, toobtain the effects of centrifugal force on the slurry pressuredistributions. The numerical results show that it is markedly different forthe pressure distribution and the same tendency for dimensionless resultantforces and moments along with standard nominal clearance, rolling angle,pitch angle and pad angular velocity, obtained from the Reynolds equationswith and without centrifugal force terms, though the values of dimensionlessresultant forces and moments are different, with the significant effect ofthe pad angular velocity.
2008, 40(6): 729-734. doi: 10.6052/0459-1879-2008-6-2007-436
Numerical simulation of complex flow with multi lateral jets interactions
Jianqiang Chen, Yifeng Zhang, Dingwu Jiang, Meiliang Mao
In this paper numerical simulations and theoreticalanalyses on complex flow with multi lateral jets interactions are presented.The NND scheme with high resolution is adopted to simulate the complexflow phenomena related to lateral jet interaction accurately and a LU-SGS implicit algorithm is usedto accelerate the converging process. A multi-block patched grid techniqueis introduced to obtain the suitable grids system, which can map the jetaccurately. The influences of the difference schemes, types of limiters,topologies of grids and flow models (laminar or turbulence) on interactionflow structures and pressure distribution are investigated, and the vortexstructures, wave structures and aerodynamic characteristic induced bylateral jet interaction are also studied. And then detailed flow simulationstudies for a typical vehicle with multi lateral jets interaction arecarried out. This highlights the complex nature of the three dimensionalinteraction phenomena and also provides insight into the physics of the flowmechanism. The influences of the jet parameters, such as the number andlocation of lateral jet, and the flow conditions, such as flight Machnumber, angle of attack, altitude on flow structures and aerodynamic forcesare analyzed. The good comparisons between the computational results and theexperimental data for the pressure distributions are obtained. It isdemonstrated that the numerical method developed in this paper can beavailable to simulate the complex flow field with multi lateral jetsinteractions and predict the aerodynamic forces in the flow.
2008, 40(6): 735-743. doi: 10.6052/0459-1879-2008-6-2008-020
The ausmpw scheme based on adaptive algorithm of interpolating multiwavelets applied to solve euler equations
Yang Sun, Boying Wu, Guotai Feng
The high order precision and high resolution of the highorder schemes are very important for complex flow field. In this paper, thenew AUSMPW scheme based on adaptive algorithm of interpolating multiwaveletswas investigated in order to decrease the numerical oscillation and increasethe numerical accuracy for discontinuity, such as shock wave. Theinterpolating multiwavelets is used for multilevel decomposition of thefunction, and the method of the valve's value is used to construct adaptivegrid. Arbitrary precision can be achieved theoretically. The pressure anddensity obtained in the algorithm are compared with those from originalAUSMPW scheme, TVD scheme and WENO scheme. The numerical results demonstratethat the modified AUSMPW scheme has higher resolution, stronger chaseableability and lower numerical dissipation.
2008, 40(6): 744-751. doi: 10.6052/0459-1879-2008-6-2007-374
Efficiency analysis of magnetic field configuration in MHD flow control
Chun-Hian Lee
Influences of the magnetic field configuration on theheat flux density distribution along a ballistic reentry vehicle surfacewere numerically investigated with the low magnetic Reynolds numberapproximation of MHD (Magnetohydrodynamics) model. The numerical resultsshow the distinct difference of the effects on the heat flux densitydistribution of the two magnetic dipoles with the same magnitude anddifferent orientations, indicating the efficiency problem in heat fluxmanagement by utilizing MHD method. Due to the influences of the magneticdipoles on the energy conversion mechanism of the flow, the principles ofthe magnetic field configuration in heat flux mitigation are developed.
2008, 40(6): 752-759. doi: 10.6052/0459-1879-2008-6-2007-376
Modeling of the NOx and SOx formation in pulverized coal combustion with detailed reaction mechanism
The present work introduces a numerical simulationapproach to calculate the concentration profiles of CO, NOx, andSOx, and study the effects of combustion temperature and pulverizedcoal particle size on NO formation during pulverized coal combustion coupledwith detailed chemical reaction mechanism and CFD software. The numericaldata are validated with the experimental ones. The results show that thereis significant effect of the combustion temperature and not obvious effectof coal particle size on the NO formation. Increasing temperature obviouslyenhances NO concentration. There might exist different temperature pointscorresponding to the fast rate of NO formation for various coals. Meanwhile,combustion temperature has effect on the release process of SOx andlittle effect on the final concentration of SOx.
2008, 40(6): 760-768. doi: 10.6052/0459-1879-2008-6-2006-540
Elastic wave propagation in honeycomb materials
Yuesheng Wang
In this paper, the elastic wave propagation in honeycombmaterials is investigated based on the dispersion relations. The Block waveswill be generated due to the periodicity of the honeycomb structure.Consequently, the dispersion relation (also called the band structure) isdivided into separate bands. The wavelet theory is employed to calculate theband structures of aluminum (Al) and polypropylene (PP) honeycomb materialswith three typical lattice structures, namely, square, triangular andhexagonal. The material parameters and the displacements of the honeycombmaterials are deduced into the wavelet forms associated with biorthogonalperiodic basis functions. The wave equations are also reduced to Eigenvalueproblems characterized by the Bloch theorem and variational theory. Thetheoretical results show that the significant effect of lattice structuresand the little effect of the material types of the honeycomb materials arefound on the elastic wave propagation. All three lattice cases do notexhibit the complete band gaps and only the square and triangular casesexhibit the directional band gaps. Furthermore, a wider directional band gapis achieved in the triangular case than in the square case in the widerpropagating direction at lower frequencies.
2008, 40(6): 769-775. doi: 10.6052/0459-1879-2008-6-2007-508
Effective continuum model of grid material based on couple-stress theory
The effective properties of grid material based onclassical continuum model have been widely investigated. Moreover, gridmaterial is often used as thin-walled structures and the corresponding sizeof macro-structure (L) has the same magnitude with the characteristic length(l_{m}) of the grid material. The purpose of this paper is to introduce aneffective couple-stress continuum model to describe the performance of gridmaterial when L \approx l_{m} and to recommend a method to calculatethe effective moduli of the model. The representative volume element(RVE) method Dirichlet boundary conditions is proposed. The effective beamstiffness of couple-stress continuum is deduced with a new parameter\delta as for the couple-stress influence factor. The theoreticalanalysis is validated with finite elements (FE) solutions with the casesof some typical grid materials. The results show that couple-stresscontinuum model can be used to evaluate grid material and obtain theeffective material parameters. The couple-stress effect is obvious onlywhen L \approx l_{m}. Furthermore, thecharacteristic length of the grid material is influenced by the relativitydensity, the size of the base cell and the geometry.
2008, 40(6): 776-785. doi: 10.6052/0459-1879-2008-6-2007-379
Meso-failure of sandstone under temperature effects and DSCM study on deformation field
Zuo Jian, pingHeping Xie, Huaiwen Wang, Yuan Fang
The meso-failure progress of sandstone under temperatureeffects was observed and studied in-situ through Scanning Electron Microscopy(SEM). The SEM observations under thermal-mechanical coupling effects showedthe brittle fracture on the different places, independent bearing mineralsand the bifurcated cracks in the sandstone sample. The numer of microcracksor the branch cracks near the main crack was large below the temperature of100°C and small over 150°C. Within the temperature from25°C to 300°C, the fracture toughness of sandstone increased firstly and thendecreased. There was the threshold temperature of 150°C forsandstone at meso-scale. With the rising temperature, the failutre ofsandstone will obtain the transition from brittle to ductile behavior.Sandstone failure modes were experimental observed, such as transgranular,intergranular and mixed mode. Meanwhile, the deformation field of sandstonewas measured using digital speckle correlation method (DSCM).
2008, 40(6): 786-794. doi: 10.6052/0459-1879-2008-6-2007-292
Undrained shear strength for K0{K}_{0}K0 overconsolidated clays K01)}K0
Yangping Yao
The unified equation of the undrained shear strengths isdeduced by combining K0K_0 K0 overconsolidated clay model, the function ofrotating angle, the critical state conditions of the clay and thetransformed stress tensors based on SMP criterion. The stress Lodeangle K0\theta K0 and the rotating angle K0\omega K0 under the triaxialcompression and extension condition, and under the plane strain compressioncondition are applied to develop the corresponding undrained shear strengthequations, respectively. The theoreticalresults for K0K_0 K0 overconsolidated clays are in good agreement with theexperimental data.
2008, 40(6): 795-803. doi: 10.6052/0459-1879-2008-6-2007-444
Vibration response of stay cables induced by axial narrow-band random excitation
In this paper, the stochastic differential equations ofstay cables under axial narrow-band random excitations are derived with theconsideration of cable sag and variation of cable tension along cables.Gaussian and the first order non-Gaussian closure solutions are deduced withthe cumulant closure scheme. A numerical case of the cable A20 with a lengthabout 330\,m of No.2 Nanjing Bridge over Yangtze River is carried out toobtain the cable vibration response. Monte-Carlo method is applied to verifythe theoretical solutions in the present work. Moreover, the effects ofexcitation frequency on the vibration response of the cable are investigatedwhen the ratio value of the central excitation frequency to naturalfrequency of the cable is 1 or 2. Some new conclusions are summarized in thepresent study.
2008, 40(6): 804-811. doi: 10.6052/0459-1879-2008-6-2007-650
Grazing Bifurcation of a Cantilever Vibrating System with One-sided Impact
Grazing bifurcation is a special bifurcation behavior ofnon-smooth dynamical systems. In the present paper, grazing bifurcations ofa cantilever system with one-sided impact is investigated. Firstly, thelocal discontinuity mapping and Poincar\'{e} mapping of the vibrating systemare developed. Secondly, numerical simulation with the impacting clearanceas the bifurcation parameter are carried out to obtain two types ofgrazing bifurcations of the system, which are different from those of rigidimpact systems. Finally, it is further shown that the local discontinuitymapping can be also used to investigate grazing bifurcation of non-smoothdynamical systems with high order nonlinear terms.
2008, 40(6): 812-819. doi: 10.6052/0459-1879-2008-6-2007-522
A numerical method for the stability analysis of ventilated supercavity
Jiazhong Zhang, Yingjie Wei, Cong Wang
A numerical method was developed to calculate unsteadyventilated supercavity based on the Logvinovich principle of independence ofthe cavity sections expansion. The case of the stability of unsteadyventilated supercavity was carried out. The numerical results indicated thatthe stability criterion proposed by Semenenko was available for ventilatedsupercavity. Moreover, a surface disturbance wave of the supercavity mayfirst arise and then disappear for the stable supercavity, while it will bein the self-induced oscillation for the unstable supercavity. The amplitudeof disturbance wave increased gradually to induce the periodic orquasi-periodic pulsation of supercavity.
2008, 40(6): 820-825. doi: 10.6052/0459-1879-2008-6-2007-588
Analysis of yield surface and crack tip plastic zone of Kagome lattice structure
Yueqiang Qian, Xinming QIU, Xiong Zhang
Effective stiffness and yield surface of Kagome latticestructure are investigated in the paper. The shape function of singularyield surface is a convex domain in the plane enclosed within four straightlines. The plastic zone of crack tips of mode I and mode II cracks in theinfinite half plane are estimated with the singular yield surface andvalidated with finite element simulation, which are more precise than thosewith Mises smooth yield surface. Thus Kagome could be simplified asisotropic continuum only in elastic deformation; meanwhile, in the case ofmaterial yielding or the strong singular stress field, the strength ofKagome lattice depends on the direction of principal stress.
2008, 40(6): 826-833. doi: 10.6052/0459-1879-2008-6-2007-109
Stress-strength interference model including model uncertainty
Model uncertainty of design variables is investigatedbased on traditional stress-strength interference model in this paper. Modeluncertainty source was first studied and a random variable H was introducedto describe the uncertainty. The distribution of parameter H and itscalculation method H corresponding to different sample sizes were given.Finally, an interval stress-strength interference model with modeluncertainty was developed with.the algorithm of reliability index \beta .The results show that the proposed model in the present paper is suitablefor describing the model uncertainty.
2008, 40(6): 834-839. doi: 10.6052/0459-1879-2008-6-2007-411
Dual boundary element analysis of rectangular-shaped cracks in graded materials
Hongtian Xiao, Zhongqi Yue
This paper analyzes the rectangular-shaped crack in the graded materials byusing the dual boundary element method. The method is based on thefundamental solutions for multilayered solids and uses a pair of boundaryintegral equations, namely, the displacement and traction boundary integralequations. The former is collocated exclusively on the uncracked boundary,and the latter on one side of the crack surface. The displacement and/ortraction are used as unknown variables on the uncracked boundary and therelative crack opening displacement (i.e., displacement discontinuity) istreated as an unknown quantity on the crack surface. The layered techniqueis used to analyze the variation of parameters of the graded interlayer.Numerical examples of stress intensity factors (SIFs) calculation are givenfor the rectangular-shaped crack parallel to the graded interlayer. Theresults show that the SIFs obtained with the present formulation are in verygood agreement with existing numerical results. The nonhomogeneous parameterand the distance of the crack from the interlayer exert an obvious influenceon the SIFs of the rectangular-shaped crack in the graded material.Furthermore, it may be shown that the proposed method can be used to analyzedifferent cracks subject to complex loads in graded materials and to modelthe non-homogeneous solids with multiple interacting cracks.
2008, 40(6): 840-848. doi: 10.6052/0459-1879-2008-6-2008-082
Boundary element analysis of the stress intensity factors for the v-notched structures
Zhongrong Niu, Changzheng Cheng, Zongjun Hu, Jianqiao Ye
In this paper a new way is proposed to determine thegeneralized stress intensity factors of the plane V-notch structures byboundary element method. Firstly, a small sector around the V-notch tip isdug out from the V-notch structure. Based on the assumption of an asymptoticstress field in the V-notch tip region, evaluation of stress singularitiesof the sector zone are transformed into an eigenvalue problem of theordinary differential equations. Then the solutions of the eigenvalueproblem provide the singularity orders and associated eigenvectors of theV-notch. Hence the displacements and tractions on the arc of the abovesector are expressed as the linear combination of the finite terms of theseries expansion with different singular orders. Secondly, the boundaryelement method is used to model the V-notch structure removed the smallsector, in which the boundary conditions along the arc edge from cutting thesector are expressed by the above linear combination. Consequently, thegeneralized stress intensity factors and the stress field of the V-notchedstructure are obtained through the boundary element analysis. Finally, twonumerical examples are given to show the effectiveness of the presentmethod.
2008, 40(6): 849-857. doi: 10.6052/0459-1879-2008-6-2007-387