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2011 Vol. 43, No. 4

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Numerical research on the complicated structures on the oblique detonation wave surface
Teng Honghui Wang Chun Zhao Wei Jiang Zonglin
The oblique detonation waves are simulated numerically to study the fine structures on the detonation surface, with Euler equations and the one step chemical reaction model. Two kinds of complicated structures are observed on the oblique detonation surface. One is composed of the transverse wave and triangle flame, which is special on the oblique detonation surface. The other is similar to the cellular structure on the normal detonation surface, but rarely observed on the detonation surface before. Simulation results demonstrate that they have similar mechanisms and can be converted into each other. Their formation and evolution processes are influenced by the inflow Mach numbers and the activation energy values.
2011, 43(4): 641-645. doi: 10.6052/0459-1879-2011-4-lxxb2011-004
Numerical simulation of nozzle's flow field based on mixed implicit iteration-analysis algorithm for two equation turbulence model
Hu Haiyang Bai Peng
The flux modification of Harten's second-order TVDscheme, coupled with implicit iteration-analysis algorithm, is employed toovercome the computational stiffness of k-ε turbulence model.Internal flow field of an axisymmetric nozzle and internal-external flowfield of a two-dimensional nozzle are simulated to confirm the improvementof calculation efficiency by the above methods when using improved multigridstrategy. The calculation results are compared with experimental data.
2011, 43(4): 646-652. doi: 10.6052/0459-1879-2011-4-lxxb2010-288
Mechanism of drag reduction by spanwise oscillating lorentz force in turbulent channel flow
Dong-Jie Mei Fan Baochun Chen Yaohui Ye Jingfang
Numerical simulations and experiment research are bothcarried out to investigate the control of spanwise oscillating Lorentzforces on a turbulent channel flow. The variation of the streaks and theskin friction drag are obtained through the PIV system and the dragmeasurement system, respectively. The flow field in the near-wall region isshown through direct numerical simulations utilizing spectral method. Theexperiment results are consistent with the numerical simulation onesqualitatively, and both indicate that the streaks are tilted into thespanwise direction and the darg reduction utilizing spanwise oscillatingLorentz forces can be realized. The numerical simulation results reveal moredetails of the drag reduction mechanism which can be explained as thespanwise fluctuating vortices generated, from interaction between the induced longitudinal vortices and intrinsicturbulent flow in the near-wall region can make the longitudinalvortices tilted and oscillated to suppress the turbulent intensity andlead to drag reduction.
2011, 43(4): 653-659. doi: 10.6052/0459-1879-2011-4-lxxb2010-334
A Roe-related semi-lagrangian method
Tian Baolin Shuanghu Wang
An algorithm for 1D and 2D Euler equations was proposedby combining the Roe scheme and the semi-Lagrangian method based oncharacteristic theory. The finite volume method (FVM) is cast in a flux formand thus guarantees the numerical conservation. We calculated the flux atthe cell boundary by using its value at the boundary's center, which couldmake the algorithm second-order accuracy in time. The semi-Lagrangian methodwith characteristic theory was implemented to trace the fluid particles. Thecharacteristic velocities were modified based on Roe average to locate thedeparture points. The interpolation by ENO reconstruction made the algorithmfree of limiters. The high order algorithm is simple and convenient toimplement. The numerical results showed that it was competitive comparingwith other schemes.
2011, 43(4): 660-666. doi: 10.6052/0459-1879-2011-4-lxxb2010-635
Numerical simulation of the viscoelastic flows for PTT model by the SPH method
Yang Bo Ouyang Jie Jiang Tao
The smoothed particle hydrodynamics (SPH) method isapplied to simulate the viscoelastic flows governed by the PHan-Thien-Tanner(PTT) constitutive equation. First of all, the validity of the SPH methodfor viscoelastic flows is verified by comparing the numerical solution of aPTT fluid in the planar Poiseuille flow with those in literatures. And then,a viscoelastic free surface flow is simulated to consider about a drop of aPTT fluid impacting a rigid plate. Furthermore, the effect of theelongational parameter is investigated. The results show the flexibility ofthe SPH method for viscoelastic free surface problems. In particular, asimplified artificial stress is adopted to resolve the problem of thetensile instability. Numerical results obtained are in good agreement withthose simulated by other mesh-based methods.
2011, 43(4): 667-673. doi: 10.6052/0459-1879-2011-4-lxxb2010-223
Experimental investigation and simulation on the marangoni convection in a binary mixture
Zhu Zhiqiang Chen Shuling Liu Qiusheng Tong Shaoli
A typical binary aqueous solution with positive surface tension-temperature gradientwas experimentally and numerically studied. In this present paper, the surface tension of a1-pentanol aqueous solution was found to grow with the increase of the temperature under specificconcentration and temperature range. To verify this special phenomenon, flow fields of the1-pentanol aqueous solution under different horizontal temperature gradients were visualized andmeasured in a rectangular cavity by means of PIV method. And an inverse Marangoni convectiondifferent from that in pure liquid layer was investigated. For comparison, a numerical simulationwas carried out to obtain the velocity distribution along the free surface of the 1-pentanol aqueoussolution layer under same horizontal temperature gradients. Both results obtained by theexperimental observation and numerical simulation were found to display similar tendency.
2011, 43(4): 674-679. doi: 10.6052/0459-1879-2011-4-lxxb2010-490
Impact of basset force on the movement of soluble bubble in fluid
Heng-Dou Tian Jin Liang-an Chi Wei Fang Yi Han Yundong Wang Yong
To analyze the impact of Basset force on the solublebubbles' movement in fluid, a dynamic coupling model was proposed inconsideration of the coupling relationship between the rising velocity andthe mass transfer rate of bubbles. According to the calculation and analysisof ammonia bubble absorption, it could be concluded that Basset force hadsignificant impact on the movement of soluble bubbles. Hence, anondimensional parameter ($\eta $) and its calculation method wereintroduced to scale the impact on bubbles of Basset force. With thepresented model and the parameter $\eta $, the analysis of risingprocess of bubbles in water indicatesthat the gas solubility coefficient $H$, which is the decisive parameter,determines the impact intensity of Basset force on bubbles. The impact couldbe ignored when $H<10^{-4}$, while the impact intensity increases sharplywhen $H>10^{-4}$. Furthermore, the smaller the bubbles are, the greaterthe impact intensity of Basset force is. However, the relationship betweenthe depth of bubbles' location and the impact intensity is weak.
2011, 43(4): 680-687. doi: 10.6052/0459-1879-2011-4-lxxb2010-069
Study on bubbles interaction with a flexible boundary
Wang Shiping Zhang Aman Liu Yunlong Yao Xiongliang
From the basic phenomenon of interaction between bubbleand flexible boundary, the numerical model of pulsing bubble coupled withflexible boundary is established based on the potential flow theory in thispaper. Buoyancy and surface tension are taken into account in the simulationof bubble dynamics near flexible medium. The pressure profile around thebubble in the fluid field is plotted to explain the formation cause of the`mushroom' shape bubble and the numerical results are in good agreement withexperiment data. Interaction of two bubbles and flexible boundary is alsoexplored and the numerical model is validated by contrast with theexperimental data of Robinson and Blake. It is found through numericalcalculation that buoyancy, the elastic coefficient and density ratio are themain parameters that influence bubble dynamics. This work aims to providereferences for study on dynamic behavior of bubble near flexible boundary.
2011, 43(4): 688-698. doi: 10.6052/0459-1879-2011-4-lxxb2010-415
Effects of elasticity of substrate on dewetting process of evaporating ultra-thin liquid film
Li Zhen Hu Guohui Zhou Jijie Zhou Zhewei
The effects of substrate elasticity on instability anddynamics of the horizontal evaporating ultra-thin liquid film areinvestigated in the present study. The evolution equation for the thicknessof liquid film is derived based on long-wave approximation. The effects ofsubstrate elasticity, Van der Waals forces and evaporation of liquid areexamined by both linear stability analysis and numerical simulation. Theresults indicate that increasing substrate elasticity or decreasing thesurface tension of liquid can enhance the development of perturbations,change the wavelength of interfacial wave, and be helpful to the rupture ofthe liquid film. The evaporation of liquid will promote the instability offilm and accelerate the rupture process.
2011, 43(4): 699-706. doi: 10.6052/0459-1879-2011-4-lxxb2010-459
Simulation of variation of projectile nose during high-speed penetration into concrete
He Liling Chen Xiaowei
A formula for estimating total mass loss of projectilewas developed with the assumptions of the peeling of molten surface inprojectile nose as the primary cause of mass loss and the frictional heattotally accepted by projectile. In combination of the linear relationshipbetween friction work and work done by pressure, the receding displacementof every point on projectile surface, which is vertical to the projectilesymmetry axis, is obtained based on the formula for estimating total massloss. Thereby, the variation of projectile shape is simulated. The shape ofresidual projectile, the depth of penetration (DOP) and projectile mass lossobtained by calculation are in good consistency with the correspondingexperimental results.
2011, 43(4): 707-715. doi: 10.6052/0459-1879-2011-4-lxxb2010-476
ICM method with high accuracy approximation for topology optimization of continuum structures
Sui Yunkang Xuan Donghai Shang Zhen
The topology optimization model of continuum structures with stress’ and displacement’s constraints is formulated, applying ICM (Independent Continuous and Mapping) method of high accuracy approximation, in which the exponential type function is adopted as fast filter function. Stress constraints are globalized by use of structural distortional strain energy density. Displacement constraint is explicited by use of unit virtual load method. The constraint limit values are normalized to solve the mismatch of the order of two kinds of constraints. The parameter selection of fast filter functions of exponential type with different properties is given. The examples of single loading case and multiple loading cases have shown that the ICM method of high accuracy approximation is available and efficient to solve the topology optimization of continuum structures with multiple constraint types.
2011, 43(4): 716-725. doi: 10.6052/0459-1879-2011-4-lxxb2010-503
Fail-safe optimal design of truss structures based on robust optimization
Du Jianming Guo Xu
Traditional fail-safe optimal design was always performedbased on a prior assumed failure mode. However, the assumed failure mode maynot necessarily be the most dangerous one, and if this is the case, then thereliability of the obtained optimal solution cannot be guaranteed. Tocircumvent this difficulty, in the present paper, fail-safe optimal designis carried out in a robust optimization framewok. The problem is formulatedin a Bi-level form. The upper level program aims at finding the optimaldesign variables while the lower level program is solved to find the worstcase failure mode. In order to find the global optimal solution of the lowerlevel program, a mixed 0-1 programming is proposed and solved with thebranch-and-bound algorithm. The effectiveness of the proposed approach forfail-safe design and optimization are illustrated by some numericalexamples.
2011, 43(4): 725-730. doi: 10.6052/0459-1879-2011-4-lxxb2010-460
New orthogonality relationship of plane elasticity in sectorial region and its variational principle
Guo-lin Hou Alatancang Chen
In the plane elasticity sectorial region problem, an off-diagonal Hamiltonian operator is obtained by constructing new dual vectors and using virtual circumferential coordinate in spatial domain to mathematically analogize the time variable in temporal domain of Hamiltonian system. The operator possesses some structural characteristics that the elements of main diagonal are zero and skew diagonal entries are symmetric operators. Two independent and symmetrical orthogonality sub-relationships are discovered. By selecting dual vectors appropriately, the new orthogonality relationships in the rectangular coordinates are generalized into the polar coordinates for isotropic plane elasticity problems. By using integral form, a variational principle which is relative to differential form is derived, and moreover, a complete functional expression is proposed.
2011, 43(4): 731-736. doi: 10.6052/0459-1879-2011-4-lxxb2010-597
Time-domain dynamic modeling and active control of offshore platform
Liu Song Cai Guoping Dong Xingjian
This paper presents the studies on low-order time-domaindynamic modeling and active control of an offshore platform. Firstly, basedon the input-output data of the system, the method of Observer/Kalman filteridentification (OKID) is used to identify the Markov parameters of thesystem. Then a low-dimensional state-space model of the system isestablished by using the eigensystem realization algorithm (ERA). The LinearQuadratic Gaussian (LQG) controller is designed based on the low-dimensionalstate-space model. Finally, the controller designed is introduced into thefinite element model of the system to verify the effectiveness of thecontroller. Numerical results indicate the effectiveness and feasibility ofthe studies in this paper.
2011, 43(4): 737-745. doi: 10.6052/0459-1879-2011-4-lxxb2010-373
Bifurcation and responses analysis of two-dimension panel with external excitation in subsonic flow
Li Peng Yang Yiren Lu Li
Along with the development of high speed multiple unitetrain and intercity railroad, the high speed technology has become thedevelopment direction of train. With the increase of speed, the aerodynamicproblems of such train are emerging, while neglected in low speed. Futuretrains will increase their speeds substantially, and if so, aerodynamicforces may influence train running safety and affect passenger's comfort. Sothe aeroelasticity of high speed train is the problem to be urgently andpromptly solved. Because the high speed train adopts stream line design todecrease running resistance, lots of panel structures such as body skin arewidely used. When train runs with lower speed, these panel structures willvibrate with small amplitude and can not be inhibited at all. But undercombined aerodynamic forces and wheel-rail excitation, complicatedaeroelasticity phenomena of these panel structures may occur.The bifurcation and responses of two-dimension panel with externalexcitation in subsonic flow are studied in this paper. Based on thepotential theory of incompressible flow, the aerodynamic pressure for airacting on the top side of the panel is acquired. The wheel-rail excitationis simplified as external forcing acting on the panel. The cubic stiffnessand viscous damper in middle of the panel are considered. The nonlineargoverning motion equations are reduced to a series of ordinary differentialequations by the Galerkin method. The Runge-Kutta numerical method is usedto conduct numerical simulations. The distribution of non-single periodareas of the panel system are indicated in differential parameter planes.The effect of three dimensionless parameters, namely viscous dampingcoefficient $\sigma $, external forcing amplitude $\beta $ and dynamicpressure increment $\Delta \lambda $, is emphatically investigated.The results of this paper show that the pitchfork bifurcation occurs withthe increase of dynamic pressure, and the number and stability of theequilibrium points change after the dynamic pressure exceeds the criticalvalue. In differential single period regions, the system motion trajectoriesin phase-plane portraits change rhythmically.1. In the parameter plane $\sigma$-$\beta$, the number of non-singleperiod regions decreases with the increase of $\sigma $; the non-singleperiod regions and single period regions appear alternately with theincrease of $\beta $.2. In the parameter plane $\Delta \lambda$-$\beta$, the non-single periodregion number firstly increases and then decreases with the increase of$\Delta \lambda $; the non-single period regions and single period regionsappear alternately with the increase of $\beta $.3. In the parameter plane $\sigma$-$\Delta \lambda$, the non-single periodregions present asymmetric double-peak structure when $\Delta \lambda > 0$;the non-single period region number firstly increases and then decreaseswith the increase of $\sigma $.4. The route from periodic motion to chaos is via doubling-periodbifurcation.
2011, 43(4): 746-754. doi: 10.6052/0459-1879-2011-4-lxxb2010-194
Nonlinear vibratory characteristics and bifurcations of shrouded blades
Wang Yanqing Guo Xinghui Liang Hongkun Li Jian Jin Chengwu
A shrouded blade is investigated in this paper. The nonlinear equation of vibration isobtained in consideration of frictions between two shrouds, damping and geometriclarge-deformation. The system is discretized by Galerkin's method. The averaging method isapplied to study the nonlinear response of the discrete modal equations, and nonlinearfrequency-response curves are gained. It can be found that the results obtained by the averagingmethod agree well with those from numerical simulation. The stability of periodic solutions of thesystem is also investigated. The bifurcation phenomenon of the averaged equations is studied indetail by the theory of nonlinear vibrations. The results show the change process and nonlineardynamic characteristics of the periodic solutions of averaged equations. The analytical results inthis study indicate that the frictions between two neighboring shrouds have great effect on thenonlinear resonance characteristics of the second order of this system. For the continuous changeof friction directions between two neighboring shrouds, the frequency-response curve of thesecond order becomes incontinuous and two different resonant frequency domains occur. As timepasses, the vibrational amplitude of the system will jump from one frequency-response curve tothe other between the two frequency domains in periods of T/4 continually, resulting in thevibrational response of the blade falls greatly.
2011, 43(4): 755-764. doi: 10.6052/0459-1879-2011-4-lxxb2010-487
imulation research of a passive dynamic walker with round feet based on non-smooth method
Duan Wenjie Wang Qi Wang Tianshu
Passive dynamic walkers can steadily walk down gentleslope under only action of gravity without any drivers and controls, andthey have human-like characteristic of walk and high energy efficiency. Thestudy on them has a key role in designing robots and medical prosthetics.Hence, it has attracted considerable public concern in recent years.The contact configuration of the biped walkers also varies correspondinglydue to the transitions between feet and ground from slip to stick or fromcontact to detachment. For the non-smooth and nonlinear model with variablestructure, it is generally to simply regard the model as an invertedpendulum fixed at each foot in turn by means of McGeer' Step-to-Step method.Here are the basic assumptions of the traditional method (Step-to-Stepmethod): There is no slip between feet and ground, and plastic collisionoccurs at heelstrick while conserving angular momentum. In addition, it isassumed that stance leg and swing leg change instantaneously and no impulseacts on the swing foot. Although the traditional method is widely employed,the shortcomings of the method can not be neglected as follows: Firstly, slipphenomenon can not be dealt with; secondly, no direct simulation or experimentresults support the assumption of angular momentum conservation of passivedynamic walker about heelstrike; thirdly, it is not suitable for analyzinggeneral movements of the biped walker.Planar straight-legged passive dynamic walker with round foot can beconsidered as a multibody system with unilateral constrains. Based ondifferential inclusions and complementary methods, the theory of non-smoothmultibody dynamics with unilateral constraints has been well established, bywhich the multi-contact problems with friction and impact could beefficiently solved. In this paper, this passive walking phenomenon issimulated by using the non-smooth dynamic method. We mainly analyze theCoulomb friction and Newton impact phenomenon between feet and ground. Dueto the collisions, the whole dynamical equation and contact laws are set upon base of impulse-velocity level. After establishing the complementaryrelationships of all contact laws, a linear complementary problem instandard form is given. And then, we choose a one-step mid-pointtime-stepping method for numerical simulation. The programming with thenon-smooth method is easier than that of the traditional method.The following conclusions are obtained from numerical simulations in thispaper: (1) If there is no slip and the collisions are plastic, thesimulation results agree with those of the traditional methods, whichindicate that the assumptions of the Step-to-Step method are reasonable. (2)In the case of slip and plastic impact, stable periodic gaits could also befound with some suitable parameters. For this case, the friction coefficienthas a significant effect on the average walking velocity in tangentialdirection. (3) If elastic impact occurs without slipping, passive dynamicwalkers could also steadily walk down slopes with several collisions at thetransition from swing leg to stance leg. Small normal coefficient ofrestitution has little effect on average walking speed. (4) The simulationresults show that for a small normal coefficient of restitution and a largefriction coefficient, it is easy for passive dynamic walkers to realizestable periodic gaits.
2011, 43(4): 765-774. doi: 10.6052/0459-1879-2011-4-lxxb2010-277
Preconditioning technique in slightly compressible model
Cong Chenghua Deng Xiaogang Mao Meiliang
A novel slightly compressible model(SCM) is very efficientfor low Mach number flow, in which it does not have to satisfy thedivergence-free condition in order to get the solutions of theincompressible Navier-Stokes equation by time marching method. Theefficiency and precision of SCM is studied. Preconditioning technique hasbeen introduced into SCM for acceleration of convergence. Then thepreconditioned equations and its characteristic system including thepreconditioned construct of flux are recommended. By numerical simulationswith the cases of circular cylinder, cavity flow, NACA0012 and 6:1 prolatespheroid, SCM is proved to be efficient and precise; on the other hand, itshows that preconditioning technique plays an important role in accelerationof convergence and improves the precision of results. SCM would be appliedto engineering simulations in the future.
2011, 43(4): 775-779. doi: 10.6052/0459-1879-2011-4-lxxb2010-530
Kriging-HDMR metamodeling technique for nonlinear problems
Tang Long Wang Hu Li Guangyao
Some large-scale structural engineering problems need tobe solved by metamodels. With the increasing of complexity anddimensionality, metamodeling techniques confront two major challenges.First, the size of sample points should be increase exponentially as thenumber of design variables increases. Second, it is difficult to give theexplicit correlation relationships amongst design variables by popularmetamodeling techniques. Therefore, a new high-dimension modelrepresentation (HDMR) based on the Kriging interpolation, Kriging-HDMR, issuggested in this paper. The most remarkable advantage of this method is itscapacity to exploit relationships among variables of the underlyingfunction. Furthermore, Kriging-HDMR can reduce the correspondingcomputational cost from exponential growth to polynomial level. Thus, theessence of the assigned problem could be presented efficiently. To prove thefeasibility of this method, several high dimensional and nonlinear functionsare tested. The algorithm is also applied to a simple engineering problem.Compared with the classical metamodeling techniques, the efficiency andaccuracy are improved.
2011, 43(4): 780-784. doi: 10.6052/0459-1879-2011-4-lxxb2010-494
A regularized boundary element method for anisotropic potential problems
Zhang Yaoming Liu Zhaoyan Li Gongsheng Qu Wenzhen
The presentation is mainly devoted to the research on theregularized BEM formulations for homogeneous anisotropic potential problems.Based on a limit theorem for the transformation from domain integralequations into boundary integral equations (BIEs) and a novel decompositiontechnique to the fundamental solutions, the regularized BIEs with indirectunknowns, which don't involve singular integrals, are established. Comparedwith the existing methods, the presented method can solve theconsidered problems directly instead of transforming them into isotropicones, and for this reason, no inverse transform is required. In addition,this method doesn't require to calculate multiple integral as the Galerkinmethod, but rather evaluate CPV integrals indirectly, and so it is simpleand easy to program. Furthermore, the proposed gradient BIEs are suited forthe computation of ${\partial u}/{\partial x_i } (i =1,2)$ on the boundary, not only limited to normal flux ${\partial u}/{\partial n}$. Especially, for the boundary valueproblems with elliptic boundary, an exact element is developed to model itsboundary with almost no error. The convergence and accuracy of the proposedalgorithm are investigated and compared for several numerical examples,demonstrating that a better precision and high computational efficiency canbe achieved.
2011, 43(4): 785-789. doi: 10.6052/0459-1879-2011-4-lxxb2010-639
Dynamics of hub-variable section beam systems
Chen Sijia Zhang Dingguo
The dynamics of a hub-variable section beam system which is rotating in a plane is investigated,where the beam is a flexible one. Both the transversal deformation and the longitudinal deformation of the flexible beam are considered. And in the total longitudinal deformation the non-linear coupling term, also known as the longitudinal shortening caused by transversal deformation, is considered here. The approach of assumed modes is used to describe the deformation of the flexible beam. The rigid-flexible coupling dynamic equations of the system are established via employing the second kind of Lagrange’s equation. Then dynamic characteristics of both of the hub-tapered beam system and the hub-trapezium beam system undergoing large overall motions are investigated in details by using numerical simulation. The results obtained in the investigation indicate that: The ratio in width, the ratio in height, the variable section position of the trapezium beam will have a larger impact to the dynamic response and the chord-wise bending natural frequencies.
2011, 43(4): 790-794. doi: 10.6052/0459-1879-2011-4-lxxb2010-650