#### Table of Content

18 March 2010, Volume 42 Issue 2
Research paper
An improvement of tsien's equation of state in high-temperature and high-pressure gases
Bo Zhao Jiping Cui Jing Fan
2010, 42(2):  151-158.  DOI: 10.6052/0459-1879-2010-2-2009-029
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According to the general principle of molecular dynamics theory and the Lennard-Jones Devonshire(LJD) liquid theory, H.S.Tsien given an fundamental equation of state for gases at high temperatures and pressures. Tsien's EOS has physical foundation, high accuracy eqlicit temperature, and simple form. In this paper, we tested the applicability of LJD liquid theory in high-temperature and high-pressure gases by constant volume-temperature molecular dynamics, and obtained exact MD calculations for high temperature and pressure gases EOS. Based on the MD exact numerical solution. The AAD between theaso data and the improved Tsien's Eos cesults is less than 10%. in high density vesign.
Experimental research on complex eddy viscosity modeling of multi-scale coherent structures in wall turbulence
Aidong Guo Nan Jiang
2010, 42(2):  159-168.  DOI: 10.6052/0459-1879-2010-2-2008-568
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In the dynamics equation of coherent structures with periodical phasic average, Reynolds stress term \tilde {r}_{ij} = - (\langle {u}'_i {u}'_j \rangle - \overline {{u}'_i {u}'_j } ) that noncoherent structures contributes to coherent structures, is taken into the model, in which the velocity strain rate of coherent structures is multiplied by a complex eddy viscosity coefficient, as follows: \tilde {r}_{ij} = \nu _T \Big[ \dfrac{\partial \tilde {u}_i }{\partial x_j } + \dfrac{\partial \tilde {u}_j }{\partial x_i } \Big] + \dfrac{1}{3}\delta _{ij} ( \tilde {r}_{kk} ) , where \nu _T is a complex eddy viscosity coefficient. Eddy viscosity coefficient is defined to be a complex, supposing that there exist phase difference between velocity strain rate of coherent structures and the Reynolds stress. The phase relation has been experimentally measured between velocity distortion \dfrac{\partial \tilde {u}}{\partial y} of multi-scales coherent structures in turbulent boundary layer over smooth plate and the Reynolds stress, \tilde {r}_{12} and analyzed in a close-circuit low-speed wind tunnel based on the expression \tilde {r}_{12} = \nu _T \Big[ \dfrac{\partial \tilde {u}}{\partial y} + \dfrac{\partial \tilde {v}}{\partial x} \Big]. Through the phase difference analysis between the Reynolds stress and the velocity distortion of coherent structures in wall turbulence during the bursting process of coherent structures, conclusions can be drawn as following: Relaxation time in dynamic interaction between the turbulence of coherent structures with macroscopical scale and movement distortion of coherent structures can't be ignored. Hence, there exist phase difference between Reynolds stress component that noncoherent structures contribute to coherent structures and the velocity distortion of coherent structures. It is an important factor that needs to be taken into account for eddy viscosity modeling theory for non-steady turbulence macrostructure. The above phase difference depends on not only the scale of coherent structures, but also the detail of physical burst process of coherent structures, such as eject and sweep. The phase of the Reynolds stress is posterior than that of velocity distortion of coherent structures in ejecting process, while anterior in sweeping process. In addition, phase difference between them does not vary with boundary normal positions in logarithmic sublayer.
CFD based virtual flight simulation of square cross-section missile with control in longitudinal flight
Yang Tao Zhaolin Fan Jifei Wu
2010, 42(2):  169-176.  DOI: 10.6052/0459-1879-2010-2-2008-497
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The simulation of virtual flight based on computational fluid dynamics (CFD) is now becoming possible together with the incorporation of a controller with control surface commands and control surface deflections. This paper investigates CFD-based virtual flight for a generic square cross-section missile configuration in longitudinal motions. The incorporation of the flight mechanics equations and a controller into the CFD solver loop, a multi-block structured-grid scheme with both the control surface deformations and the rigid motion of the aircraft, are described. This study is helpful to a wider effort towards the simulation of guide and navigation, and validates flight stability in nonlinear aerodynamics regions. The virtual flight simulation of square section missile with control in longitudinal flight are presented including holding angle of attack and prescribed maneuver about incidence decreasing with required angle. The availability of the coupling method and the trim arithmetic are proved in the virtual flight simulations through the two typical maneuver actions.
A coupled Eulerian-Lagrangian method based on level set and its applications
Zupeng Jia Xijun Wei
2010, 42(2):  177-182.  DOI: 10.6052/0459-1879-2010-2-2008-308
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In this paper a coupled Eulerian-Lagrangian method based on level set for multi-material compressible fluid flow involving large deformation is presented. In the scheme, a Lagrangian method is used in the domain with small deformation while an Euler method is used in the domain with large deformation. The interface is treated by a new level set method and the Ghost Fluid method. Furthermore, an explicit compatible finite element method is employed as the Lagrangian method. In this Lagrangian method, the finite element method is used to discretize the fluid equations in terms of the framework of compatibility, an edge-centered artificial viscosity is used to capture shocks, and the subzonal perturbed pressure is used to resist spurious and unresolved grid motions. A vertex-centered finite volume method based on approximate Riemann solver is used as the Eulerian method. In this Eulerian method, an HLLC numerical flux adapted to various equations of state are employed, a second order accuracy in space is achieved by using a reconstruction of primitive variables based on WENO approach. An explicit two-stage Runge-Kutta time-stepping scheme is used in discretization of time. A new method to determine the signs of the level set function and a new technique to compute the velocities of the projection points of the Ghost points on the interface are proposed. Numerical examples show the accuracy as well as the robustness of the method.
Numerical simulation of airflow movement in human mouth-throat model during cyclic respiratory pattern
Xinxi Xu Xiuguo Zhao Shulin Tan Yajun Liu Zhenhai Gao
2010, 42(2):  183-190.  DOI: 10.6052/0459-1879-2010-2-2008-482
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The method of CFD was used to study airflow movement characteristics in human mouth-throat model. We investigated the airflow patterns in human mouth-throat model, and the effect of airflow movement on the wall of the mouth-throat model and the aerosols deposition were discussed. During the inhalation phase, the airflow separates gradually near the outer wall of the pharynx and near the outer wall for the upper part of the trachea downstream of the glottis with, and the features of the separation zone appearing is gradually formed. During the exhalation phase, the high velocity zone is created near the outer wall of pharynx and near the outer wall of the larynx. During the cyclic respiratory pattern, the high axial velocity zone and secondary flow are generated intermittently, eventually to induce the intermittent appearance of the high shearing strength stress zone appears intermittently. The direction of the shear stress acting on the wall vary varies periodically, which not only result in the increase of the probability of the wall strain and tissue injury, but also lead to aerosol deposition easily in these areas at the same time.
On three-dimensional numerical simulation of interstitial fluid flow of inter osseous membrane
Wei Yao Yeliang Shen Guanghong Ding
2010, 42(2):  191-196.  DOI: 10.6052/0459-1879-2010-2-2008-587
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Interstitial fluid flow is an important component of the microcirculation and interstitial environment, yet there is few direct in vivo measurement of it within human body. Therefore, computational and mathematical models are employed to investigate the fluid flow especially within cortical bone and ligaments. This article is to investigate the interstitial fluid flow in inter osseous membrane on lower limb, where the distribution of capillaries is regular parallel arrays on certain direction which is approximate to the direction of parallel collagen fibrils. It' rational to consider the interstitial space as a porous media and set up a three dimensional filtration model to study the flow field. The govern equations of the model is Brinkman equation and conservative equation. A CFD software (FLUENT) is used to executive the numerical simulation. There are some interesting results. First, interstitial fluid penetrating through capillary' walls at artery sections can flow along the direction of parallel capillaries, and then some interstitial fluid is absorbed by capillary at vein sections and others outflow at the exit. That is, under parallel capillary distribution condition, there may exit the directional interstitial fluid flow. Second, the interstitial fluid flow can be evidently influenced by collagen fibrils. Due to the existence of collagen fibrils in the interstitial space, the velocity distribution of the interstitial fluid flow tends to be uniform, which is in favor of the physiological activities of cells. So collagen fibrils are very important to the organism. Third, pressure is also an important factor to influence the interstitial fluid flow. The increases of pressure near artery ($p_{a})$ and pressure near vein ($p_{v})$ can both accelerate the interstitial fluid flow, while increase of pressure in interstitial space ($p_{i})$ can decelerate the interstitial fluid flow. Therefore, changing the pressure in capillaries can adjust the microenvironment which cells live in. Changing the pressure in interstitial space has more effective effect than pressure changing in capillaries. As we all know, when the tissue is undergone the external force, the pressure in the interstitial space will be changed, so the interstitial fluid flow will also be changed. It may be a potential reason that naprapathy has a curative effect on the microcirculation in tissues.
Fluid-structure interactional numerical simulation of erosion-corrosion failure of reducer in multiphase flow
Guofu Ou Jie Qiu Zuchao Zhu Yanping Wang Genfu Xu
2010, 42(2):  197-204.  DOI: 10.6052/0459-1879-2010-2-2008-693
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In order to research the failure of reducer, we focused on the protective corrosion product film formed on the wall of reducer and investigated the mechanism of erosion-corrosion damage caused by interaction of corrosion and fluid. The mathematical model of fluid-structure interaction was established. N-S equation of viscosity liquid and control equation of solid area of corrosion products are postulated with Arbitrary Lagrange-Euler (ALE). The interaction between multiphase liquid in boundary layer within pipe wall and the damage of protective erodent products film is analyzed. Applying with the Femlab software, the deformation of protective erodent products film in three different ways were analyzed, including different flows in reducer, different structures of reducer and different specifications of reducer. The numerical simulation result indicated that the deformation of protective erodent products film is relatively small, when the following conditions are satisfied, such as the fluid flows from the small inlet to large outlet, the concentric reducer and the relatively small difference of two end calibers of reducer. The obtained results can be used in erosion protecting and technical modification for the reducer.
The study on the sedimentation of solid particle influenced by thermal convection using direct numerical simulation
Jianzhong Chang Kang An Hantao Liu
2010, 42(2):  205-211.  DOI: 10.6052/0459-1879-2010-2-2008-649
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Based on the study of isothermal inert particle sedimentation, the Arbitrary Lagrangian-Eulerian technique was used to solve the problem of solid particle sedimentation with thermal convection including the energy equation, according to varying the solid-fluid density ratio, that is, the particles settle in different Reynolds number. The results show that the thermal convection induces the variety of flow field and asymmetry. While setting in hot fluid, the direction of thermal convection is the same as that of particle sedimentation, and there are vortex shedding arisen by thermal convection. During the sedimentation of hot particle in the cold fluid, the warm wake forms a strong upward thermal plume. With the increasing of Reynolds, the setting particles undergo three stages: steady motion with and without overshoot; weak and strong oscillations, and irregular oscillations.
Studying on the penetration depth of penetrator with including the effect of mass abrasion
Jun Zhao Xiaowei Chen Fengnian Jin Ying Xu
2010, 42(2):  212-218.  DOI: 10.6052/0459-1879-2010-2-2009-009
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Mass abrasion is observed on the nose of a projectile when it strikes concrete target at high velocity, which significantly affect the penetration performance. To evaluate the influence of the mass abrasion on the depth of penetration (DOP), an empirical relationship between the nose factor of the residual projectile after abrasion and the initial impact velocity is constructed according to the published experimental data. Based on the dynamic cavity expansion theory, considering the varying nose shape and the instant mass of a projectile, a modified model is proposed to calculate the DOP of kinetic energy penetrator. The modified model demonstrates that an upper limit of DOP exists due to the mass abrasion of projectile, which also had been confirmed by different experimental data.
Boundary layer effect and thin body structure in bem for potential problems
Yaoming Zhang Yan Gu Jeng-Tzong Chen
2010, 42(2):  219-227.  DOI: 10.6052/0459-1879-2010-2-2009-079
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In boundary element analyses, when a considered field point is very close to an integral element, the kernels' integration would exist various levels of near singularity, which can not be computed accurately with the standard Gaussian quadrature. As a result, the numerical results of field variables and their derivatives may become less satisfactory or even out of true. This is so-called boundary layer effect''. Therefore, the accurate evaluation of nearly singular integrals plays an essential role to obtain highly accurate and reliable results by using boundary element method (BEM). For most of the current numerical methods, especially for the exact integration method, the geometry of the boundary element is often depicted by using linear shape functions when nearly singular integrals need to be calculated. However, most engineering processes occur mostly in complex geometrical domains, and obviously, higher order geometry elements are expected to be more accurate to solve such practical problems. Thus, efficient approaches for estimating nearly singular integrals with high order geometry elements are necessary both in theory and application, and need to be further investigated. As is well known, for high order geometry elements, the forms of Jacobian and integrands are all complex irrational functions, and thus for a long time, the exact evaluation of nearly singular integrals is a difficult problem or even impossible implementation. In this paper, a new exact integration method for element integrals with the curvilinear geometry is presented. The present method can greatly improve the accuracy of numerical results of nearly singular integrals without increasing other computational efforts. Numerical examples of potential problems with curved elements demonstrate that the present algorithm can effectively handle nearly singular integrals occurring in boundary layer effect and thin body problems in BEM.
n the fourth order tensor valued function of the stress in return map algorithm
Mingxiang Chen
2010, 42(2):  228-238.  DOI: 10.6052/0459-1879-2010-2-2009-016
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The inversion of a fourth order tensor valued function of the stress and its transformation to the second order tensor are required in the return map algorithm for implicit integration of the constitutive equation. Based on a set of the base tensors which are mutually orthogonal, this paper presents an effective methodology to perform those tensor operations for the isotropic constitutive equations. In the scheme, two of the base tensors are the second order identity tensor and the deviatoric stress tensor, respectively. Another base tensor is constructed using an isotropic second order tensor valued function of the stress. The three base tensors are coaxial. By making use of the representation theorem for isotropic tensorial functions, all the second order, the fourth order tensor valued functions of the stress involved can be represented in terms of the base tensors. It shows that the operations between the tensors are specified by the simple relations between the corresponding matrices. The inversion of a fourth order tensor is reduced to the inversion of corresponding 3\times 3 matrix, and its transformation to the second tensor is equivalent to transformation of 3\times 3 matrix to 3\times 1 column matrix. Finally, some discussions are given to the application of those transformation relationships to the iteration algorithm for the integration of the constitutive equations.
Material design of permeability coefficient based on adaptive mesh
Shengli Xu Gengdong Cheng
2010, 42(2):  238-244.  DOI: 10.6052/0459-1879-2010-2-2008-730
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Finite element mesh size has considerable effect on the result of optimum design when the topology optimization method based on design variable of element (node) is used to design structure and material. The cell should be divided into very small size grids for no-slip boundary condition at fluid-solid interface in microstructure design of material permeability. Material microstructure design with inverse homogenization method based on adaptive mesh is studied in this paper. The objective function is maximizing isotropic permeability coefficient. The finite element mesh near fluid-solid interface will be refined adaptively during optimization iteration process for decreasing computing scale of optimization problem. With this algorithm, the material microstructure is obtained to be uniform from different initial density distributions. The result illustrates the effectiveness of our method.
Multi-objective optimization for sheet metal formnig of drawing with successive response surface method
Guangyong Sun Guangyao Li Gang Zheng Zhihui Gong
2010, 42(2):  245-255.  DOI: 10.6052/0459-1879-2010-2-2007-532
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This paper describes a multi-objective optimization of drawbead geometrical parameters of automotive panel using successive response surface method. The existing response surface method has a low precision in the entire design space, and conventional single-objective optimization design does not provide for multi-objective conditions and has been used to optimize only a single objective. The present method updates the region of interest (ROI) in the design space by panning and zooming. In each ROI, a set of pareto optimal solutions of equivalent drawbead restraint force,are obtained to minimize the defects of crack and wrinkle by combining design of experiments, successive response surface method and multi-objective particle swarm optimization. Through the minimum distance method, a solution with best forming approach is obtained from the pareto optimal solutions, and it is used as the center point of the next region of interest. The optimal drawbead restraint force will be obtained by the iterative procedure. The optimal design geometric parameters of drawbead can be obtained using the optimal drawbead restraint force and genetic algorithm. These optimal parameters can be efficiently used to improve the forming properties of sheet. Numerical examples indicate that the present method has higher precision and practicability compared with the existing techniques.
A new structural topological optimization method based on design space adjustments
Jianhua Rong Qiang Zhang Sen Ge Rangke Mu
2010, 42(2):  256-267.  DOI: 10.6052/0459-1879-2010-2-2008-766
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Although a discrete solid and void structural topology is typically desired, a continuous material density design field is usually assigned to the material points within the design domain to spatially indicate regions of solid and void material. The solid isotropic microstructure with penalization material (SIMP) formulation is easy to implement in a finite element (FEM) framework. However, the material in those regions, where the values of density variables are between 0 and 1, is artificial. It is necessary to deal with those regions after the optimum topological configuration is obtained. Then a new constraint, labeled the sum of the reciprocal variables (SRV), for 0/1 topological design was introduced to obtain 0/1 topology solutions. The structural design domain need be divided into some finite element mesh when structural topology optimization is made. Some optimization problems may need a large finite element mesh, the authors propose a new structural topological optimization method based on design space adjustments in order to solving this problem and obtaining 0$/$1 topology solutions. In topology optimization, a design space is specified by the number of design variables, and their layout or configuration. The proposed procedure has one efficient algorithm for adjusting design space. First, the rational approximation for material properties (RAMP) is adopted to design the topology structural stiffness matrix filter function, and the design space can be adjusted in terms of design space expansion and reduction. This capability is automatic when the design domain needs expansion or reduction, and it will not affect the property of mathematical programming method convergences. Second, to get a clearer topological configuration at each iteration step, by introducing the discrete condition of topological variables, integrating with the original objective and introducing varying displacement constraint limit measurements, optimal series models with multi-constraints is formulated to make the topological variables approach 0 or 1 as near as possible. Third, a heuristic algorithm is given to make the topology of the design structure be of solid/empty property and get the optimum topology during the second optimization adjustment phase. Finally, incorporating an incomplete second-order series expansion for structural displacements, a new continuum structural topological optimization method is proposed. The computational efficiency is enhanced through the size reduction of optimization structural finite model and the adoption of the displacement iterative solving method during two optimization adjustment phases. The three simulation examples show that the proposed method is robust and practicable.
Concurrent hierarchical optimization for structures composed of modules considering size effects
Jun Yan Ling Liu Xiaofeng Liu Jiadong Deng
2010, 42(2):  268-274.  DOI: 10.6052/0459-1879-2010-2-2008-694
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The concurrent optimization model and algorithm for modular structures are developed in this paper. The effects of actual size of the basic design module on optimization results are investigated for structures composed of periodic modules. The size of modules can greatly affect the optimization results of configuration and distribution of basic design modules. The concurrent optimizations of macro structures and design modules are implemented by introducing independent densities in macro-structure and micro-module hierarchies as design variables. The optimal designs of configurations of macro structure and modules in two hierarchies are obtained via topology optimization and penalty technique. The interactions of structures and modules can be considered automatically by the optimization model. Two numerical examples with single load and multi loads are presented to validate the proposed optimization model and algorithm.
The occurrence conditions and trajectory constructions for low energy cislunar transfers
Ming Xu
2010, 42(2):  275-289.  DOI: 10.6052/0459-1879-2010-2-2008-708
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The paper deals with the occurrence conditions and trajectory constructions for low-energy transfers in the cislunar space, from the views of libration point theories and nonlinear dynamical techniques. The classical concept of libration'' is unavailable for spatial bicircular model (SBCM) because of the time-dependent perturbations. So the equivalent equilibrium is defined according to the geometry of instantaneous Hill's boundary, i.e., LL_{1} or LL_{2}. The altitudes of periapsis and eccentricities of all the lunar capture trajectories are presented via the Poincare map, and the minimum energy to capture on the lunar surface is deduced which is quite different from ones obtained in circular restricted three-body problem (CR3BP) and Hill Models. The asymptotical behaviors of invariant manifolds flown from libration point or Halo orbit are destroyed by SBCM: the durations flown in and out of the libration point or Halo orbit have shifted from infinite to finite, and the directions have changed from reversible to nonreversing. The minimum energy cislunar transfer is acquired by the trajectory transiting LL_{1} point, and the (M,N)- loopy transiting trajectories are attained by transiting LL_{1}-Halo orbits. Similarly, the minimum energy of weak stability boundary (WSB) transfer is induced by the trajectory transiting LL_{2} point, and the earth's escape and lunar capture windows for WSB transfers are yielded by transiting LL_{2}-Halo orbits. All three transfer manners, as low-thrust, impulse and WSB, are applied to the transfer from Earth to Moon and the insertion of the distant retrograde orbit (DRO).
ode localization prediction criterion for T-tail structure
Zhichun Yang
2010, 42(2):  290-299.  DOI: 10.6052/0459-1879-2010-2-2008-588
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Mode localization is often an unexpected dynamic phenomenon in weakly-coupled symmetric structure, and it arises from small imperfections (less than 5{\%}) which perturb the symmetry. Such imperfections typically result from random manufacturing or assembly imprecision. Mode localization prediction is an important problem in T-Tail structure design because some drastic localized vibration phenomena occur during ground vibration test of T-Tail aircraft. Mode localization is dependent not only on mistuning, but also on coupling intensity. In this paper, we define the degree of mode localization with the peak amplitude ratio and the coupling intensity with stiffness ratio of horizontal stabilizer to fin in T-Tail structure. The influence of mass mistuning on mode localization and frequency loci veering of T-Tail structure is studied. Based on the mass mistuning model, four different criterions are proposed to predict the occurrence of mode localization in T-Tail structure from four view points, which are the peak amplitude ratio, coupling mistuned ratio, ordinary eigenvalue perturbation method and eigenvalue perturbation method for nearly equal frequencies, respectively. The numerical simulation results for a T-Tail structure model indicate that mode localization is most likely to occur in T-Tail structure consisting of weakly coupled substructures---horizontal stabilizer and fin. Moreover, when localization occurs, the first two bending vibration modes in T-Tail structure are prone to localization, and only one of the two mode frequencies is changed by parameter mistuning to induce frequency loci veering phenomena. The results of this study also demonstrate the feasibility and effectiveness of the proposed four predicting criterions of mode localization, and thus provide a reference solution to the prediction and design of mode localization of this kind structure.
The quasi-variational principles of rigid-body dynamics and their applications
Lifu Liang Qingyong Guo
2010, 42(2):  300-305.  DOI: 10.6052/0459-1879-2010-2-2008-637
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The Reference [1] points out that recent studies to solve the problems of flexible multi-body dynamics mainly depend on the numerical, quantitative methods and almost no one involves in the analytical discussion due to the complexity of flexible multi-body configuration. It is unfavorable to profoundly understand the essence of nonlinear mechanics of the system and to predict the feature of overall dynamics of the system. Therefore, it is the need to study theoretical analysis of flexible multi-body system. Of course, this is a very complex problem and it takes a very long time to solve this problem. The research of this paper carries out to adapt this need. For flexible multi-body, if we think that external forces on the deformable body (including body force and surface force) are non-conservative forces, which also lead to non-conservative forces on the rigid body, that is, the resultant force and the resultant couple acting on center of mass are non-conservative generalized forces. This research is to apply the quasi-variational principles of non-conservative system to the theoretical analysis of the flexible multi-body dynamics. Because of the complexity of the problem, it is divided into several sub-tasks: 1. To study the quasi-variational principles of rigid-body dynamics and their applications. This is the main subject of this paper; 2. To study the quasi-variational principles of flexible single-body dynamics and their applications. This subject has been published in Science in China''; 3. To study the quasi- variational principles of flexible multi-body dynamics and their applications. This subject has been written in Ph.D. thesis. In this paper, the quasi-variational principles of rigid-body dynamics are established. The quasi-stationary conditions of the quasi-variational principles of rigid-body dynamics are deduced. The generalized quasi-variational principles of rigid-body dynamics are established. The approach to seek analytical solution and numerical solution of rigid-body dynamics is illuminated by using generalized quasi-variational principles. Finally, the advantage of applying variational methods to the study of the rigid-body dynamics is validated by calculation examples.
Brief Report
Asymptotic solution of thermocapillary convection of thin two-layer system in an annular cavity
Yourong Li Shuangcheng Wang Wanyuan Shi Shuangying Wu
2010, 42(2):  306-311.  DOI: 10.6052/0459-1879-2010-2-2008-751
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The convection phenomena in two-layer liquid systems have attracted great attention in the past two decades, mainly owing to their relevance in nature and in many engineering applications. Many works have been carried out to investigate the thermocapillary convection in two-layer liquid systems in rectangular cavities or in infinite horizontal layers. However, few studies focused on the convection phenomena in two-layer liquid systems in the annular cavity. In order to understand the basic characteristics of thermocapillary convection of the thin two superposed horizontal liquid layers subjected to a radial temperature gradient in an annular cavity, an approximate analytical solution is obtained using asymptotical analysis. The cavity is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. Results show that the expressions of velocity and temperature field in the core region are the same as the results obtained by Nepomnyashchy et al (Physics of Fluids, 2006, 18: 032105) when thin annular pool approaches to thin two-dimensional slot. The numerical experiments are also carried out to compare with the asymptotic solution. It is found that there is a good agreement between the asymptotic solution and numerical result in the core region.
Experimental study on the characteristics of ctac solution flow in the rectangular channel
Weiguo Gu Dezhong Wang Yasuo Kawaguchi Hongxia Zhang
2010, 42(2):  312-318.  DOI: 10.6052/0459-1879-2010-2-2008-444
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In the dilute surfactant drag-reducing flow, the slight viscoelasticity of solution affects the energy dissipation process of the flow, and this flow exhibits special fashion different from laminar flow or turbulent one in Newtonian fluid. The study on the modification of turbulent structures by the viscoelasticity of the solution is important to clarify the drag reduction mechanism of surfactant solution flow. In this paper, drag reducing flow of dilute surfactant solution in the two dimensional rectangle channel has been investigated experimentally. To grasp the instantaneous velocity u-v in x-y plane, particle image velocimetry (PIV) is employed. The experiments pay attention to Reynolds number ranging from 10000 to 40000 and concentration of additive CTAC (a kind of cationic surfactants) from 25 to 100ppm on the flow. As for the additive CTAC concentration of 25, 40, 60 and 100ppm, the fanning friction factor decreases and drag reduction (DR) increases with the increase of mass concentration below the critical Reynolds number. The surfactant solution with 40ppm at Re=40000, compared with water flow, shows DR of more than 70%. The instantaneous distribution of velocity, vorticity, and correlation of velocity fluctuation is analyzed. Statistics calculation is carried out based on 500 velocity fields which are measured by PIV. The results exhibit that the drag-reducing flow shows the approximate characteristics of the laminar flow. The wall-normal velocity fluctuation of drag-reducing flow is damped, which causes the decrease of turbulence transportation and Reynolds shear stress comparing with the turbulent water flow. The streamwise velocity fluctuation of drag-reducing flow shows the streamwise developed band-like distribution. This pattern indicates the new characteristic of turbulence transportation in drag-reducing flow.
An optimal algorithm of the generalized jacobi method
Fengqiang Shen
2010, 42(2):  319-324.  DOI: 10.6052/0459-1879-2010-2-2008-043
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An optimal algorithm of the generalized Jacobi method is developed to solve the generalized eigen-problems in the finite element analysis of structural problems. Novel operations in this optimal algorithm are adopted to define the threshold estimation for the off-diagonal elements and the convergency criteria in the sweeping iterations, so that the present algorithm is applicable to the original structural problems, not only with the positive-definite matrices, but also with the general symmetric matrices so long as their eigenvalues are all real numbers. This paper has proved the optimal algorithm mathematically.
Three-dimensional analysis for static bending and free vibration of functionally graded rectangular plate
Fengxi Zhou Shirong Li
2010, 42(2):  325-331.  DOI: 10.6052/0459-1879-2010-2-2007-576
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The state equation of functionally graded rectangular plate were established with the state variables of three displacement components and three stress components, based on the three-dimensional linear elastic theory by using of state space method. Considering simply supported boundary conditions, the static bending and free vibration problems of a three-dimensional functionally graded rectangular plate were numerically solved by shooting method with that the material properties through the thickness coordinate are assumed to obey the exponent law dependence. Effects of the volume fraction distributions of constituent materials, and thickness-to-side ratio of functionally graded rectangular plate on the dynamical and static responses were studied. The present algorithm can be used to research the three-dimensional elastic response of functionally graded materials.
Nonlinearity system identification method with parametric excitation based on the incremental harmonic balance method
Suguang Dou Min Ye Wei Zhang
2010, 42(2):  332-336.  DOI: 10.6052/0459-1879-2010-2-2008-770
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In this paper, the incremental harmonic balance for nonlinearity identification (IHBNID) is presented for the modeling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinearity identification (HBNID) and IHBNID are also studied and compared by using the numerical simulation. Considering the Mathieu-Duffing equation as an example, the effectiveness of the IHBNID can be verified. With the aid of the new method, the derivation procedures of the incremental harmonic balance method are simplified. The results show that the IHBNID is highly efficient for computation, and its performances excel in those of the HBNID, such as the computation accuracy and the noise resistance.
Reachable domain of a satellite with a coplanar impulse applied
Dan Xue Junfeng Li Fanghua Jiang
2010, 42(2):  337-342.  DOI: 10.6052/0459-1879-2010-2-2008-772
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This paper studies the reachable domain of a satellite after a coplanar single impulse with fixed magnitude applied. On the assumption that all of the generated trajectories are ellipses due to the small amplitude impulse, the reachable domain is bounded. According to the definition of the envelope of the curve family in a plane, the boundary of reachable domain is revealed respectively for three situations, namely, the point to apply impulse is fixed and the direction is arbitrary, the point to apply impulse is arbitrary and the direction is fixed, both the point to apply impulse and the direction are arbitrary. The simulation results verify the validity of the present approach. The conclusion has no restriction on the eccentricity of the initial elliptic orbit, and fits for the situation of initial elliptic orbit with large eccentricity.