应用数学和力学

2005 Vol. 26, No. 10

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Probability Distribution Function of Near-Wall Turbulent Velocity Fluctuations

ZHOU Ji-fu, ZHANG Qiang, LI Jia-chun

2005, 26(10): 1135-1142.

Abstract(2513) PDF(1211)

Abstract:
By large eddy simulation (LES), turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuations were obtained and compared with the corresponding normal distributions. By hypothesis test, the deviation from the normal distribution was analyzed quantitatively. The skewness and flatness factors were also calculated. And the variations of these two factors in the viscous sub-layer, buffer layer and log-law layer were discussed. Still illustrated were the relations between the probability distribution functions and the burst events) sweep of high-speed fluids and ejection of low-speed fluids) in the viscous sub-layer, buffer layer and log-law layer. Finally the variations of the probability distribution functions with Reynolds number were examined.

Two-Dimensional Algebraic Solitary Wave and Its Vertical Structure in Stratified Fluid

SU Xiao-bing, WEI Gang, DAI Shi-qiang

2005, 26(10): 1143-1151.

Abstract(2636) PDF(689)

Abstract:
The algebraic solitary wave and its associated eigenvalue problem in a deep stratified fluid with a free surface and a shallow upper layer were studied. And its vertical structure was examined. An exact solution for the derived 2D Benjamin-no equation was obtained, and physical explanation was given with the corresponding dispersion relation. As a special case, the vertical structure of the weakly nonlinear internal wave for the Holmboe density distribution was numerically investigated, and the propagating mechanism of the internal wave was studied by using the ray theory.

Dynamic Behavior of Two Collinear Permeable Cracks in a Piezoelectric Layer Bonded to Two Half Spaces

QU Gui-min, ZHOU Zhen-gong, WANG Biao

2005, 26(10): 1152-1160.

Abstract(2565) PDF(598)

Abstract:
The dynamic behavior of two collinear cracks in a piezoelectric layer bonded to two half spaces under harmonic anti-plane shear waves was investigated by means of Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. The boundary conditions of the electrical field were assumed to be the permeable crack surface. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. Numerical examples were presented to show the effect of the geometry of the interacting cracks, the piezoelectric constants of the materials and the frequency of the incident waves upon the stress intensity factors. The results show that the dynamic field will impede or enhance the propagation of the crack in a piezoelectric material at different stages of the frequency of the incident waves. It is found that the electric displacement intensity fact ors for the permeable crack surface conditions are much smaller than the results for the impermeable crack surface conditions.

Exact Solution and Its Behavior Characteristic of the Nonlinear Dual-Porosity Model

TONG Deng-ke, ZHANG Hong-qing, WANG Rui-he

2005, 26(10): 1161-1167.

Abstract(2337) PDF(520)

Abstract:
A nonlinear dual-porosity model considering a quadratic gradient term is presented. Assuming the pressure difference between matrix and fractures as a primary unknown, to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the blocks from the fractures was furnished with a quasi-steady-state flow in the blocks. Analytical solutions were obtained in a radial flow domain using generalized Hankel transform. The real value cannot begotten be cause the analytical solutions were infinite series. The real pressure value was obtained by numerical solving the eigen-value problem. The pressure law of the changes of nonlinear parameters and those of dual-porosity parameters was studied, and the plots of typical curves are given. All these result can be applied in well testanalysis.

A Universal Approach for Continuous or Discrete Non-Linear Programmings With Multiple Variables and Constraints

SUN Huan-chun, WANG Yue-fang, CHAI Shan

2005, 26(10): 1168-1174.

Abstract(3717) PDF(1558)

Abstract:
A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their first-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.

Optimum Design Based on Reliability in Stochastic Structure Systems

AN Wei-guang, SUN Ke-lin, CHEN Wei-dong, WANG Bin-sheng, CAI Yin-lin

2005, 26(10): 1175-1182.

Abstract(2853) PDF(742)

Abstract:
The optimum design method based on the reliability is presented to the stochastic structure systems(i. e. the sectional area, length, elastic module and strength of the structural member are random variables) under the random loads. The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given. First, the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique(PNET) method were obtained, after derivation calculus, the expressions of the sensitivity analysis for the system reliability were obtained. Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.

Path Integral Solution of the Nonlinear Dynamic Behavior of Structure Under Wind Excitation

WANG Zhong-gang, CHENG Hua, DENG Hong-zhou

2005, 26(10): 1183-1190.

Abstract(3302) PDF(985)

Abstract:
A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito's stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted. Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and robustness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.

Interval Analysis of the Fuzzy-Random Heat Conduction in the Composite Tubes

LIU Chang-hong, CHEN Qiu

2005, 26(10): 1191-1197.

Abstract(2391) PDF(829)

Abstract:
During the analysis of stability heat conduction in the composite tubes and when the temperature boundary conditions were the random conditions, first equations of the mean values and variances of the random thermal function were transformed. Secondly when the heat conduct parameters were the fuzzy numbers and the temperature boundary conditions were the random numbers, interval equations of the heat conduction were presented. Thirdly compared with the interval results between in the interval analysis and in the confidence interval, the result in the interval analysis is larger than that in the confidence interval. Moreover the error expecting equation was presented. Finally, with upper (lower) approximation in rough set theory, a new method of the interval analysis to deal with the stability heat conduction was presented.

Axisymmetric Flow Through a Permeable Near-Sphere

F. Ayaz

2005, 26(10): 1198-1208.

Abstract(2667) PDF(468)

Abstract:
An analytical approach is described for the axisymmetric flow through a permeable near-sphere with a modification to boundary conditions in order to account permeability. The Stoke sequation was solved by a regular perturbation technique up to the second order correction in epsilon representing the deviation from the radius of nondefor med sphere. The drag and the flow rate were calculated and the results were evaluated from the point of geometry and the permeabilty of the surface. An attempt also was made to apply the theory to the filter feeding problem. The filter appendages of small ecologically important aquatic organisms were modeled as axisy mmetric permeable bodies, therefore a rough model for this problem was considered here as an oblate spheroid ornear-sphere.

Diamond Port Jet Interaction With Supersonic Flow

FAN Huai-guo, ZHANG Chun-xiao, HE Chuan

2005, 26(10): 1209-1215.

Abstract(2622) PDF(753)

Abstract:
Interaction flow field of the sonic air jet through diamond shaped orifices at different incidence angles (10 degrees, 27.5 degrees, 45 degrees and 90 degrees) and total pressures (0.10 and 0.46 MPa) with a Mach 5.0 freestream was studied experimentally. A 90 degrees circular injector was examined for comparison. Cross-section Mach number contours were acquired by a Pitot-cone five-hole pressure probe. The results indicate that the low Mach semicircular region close to the wall is the wake region. The boundary layer thinning is in the areas adjacent to the wake. For the detached case, the interaction shock extends further into the freestream, and the shock shape has more curvature, also the low-Mach upwash region is larger. The vortices of the plume and the height of the jet interaction shock increase with increasing incidence angle and jet pressure. 90 degrees diamond and circular injector have stronger plume vorticity, and for the circular injector low-Mach region is smaller than that for the diamond injector. Tapered ramp increases the plume vorticity, and the double ramp reduces the level of vorticity. The three-dimensional interaction shock shape was modeled from the surface shock shape, the center plane shock shape, and cross-sectional shock shape. The shock total pressure was estimated with the normal component of the Mach number using normal shock theory. The shock induced total pressure losses decrease with decreasing jet incidence angle and injection pressure, where the largest losses are incurred by the 90 degrees, circular injector.

Adaptive Delaunay Triangulation With Multidimensional Dissipation Scheme for High-Speed Compressible Flow Analysis

P. Dechaumphai, S. Phongthanapanich

2005, 26(10): 1216-1228.

Abstract(2555) PDF(628)

Abstract:
Adaptive Delaunay triangulation is combined with the cell-centered upwinding algorithm to analyze inviscid high-speed compressible flow problems. The multidimensional dissipation scheme was developed and included in the upwinding algorithm for unstructured triangular meshes to improve the computed shock wave resolution. The solution accuracy was further improved by coupling an error estimation procedure to a remeshing algorithm that generates small elements in regions with large change of solution gradients, and at the same time, larger elements in other regions. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accurarcy. Efficiency of the combined procedure was evaluated by analyzing supersonic shocks and shock propagation behaviors for both the steady and unsteady high-speed compressible flows.

Concentration of Coupled Cubic Nonlinear Schrdinger Equations

LI Xiao-guang, ZHANG Jian

2005, 26(10): 1229-1235.

Abstract(2404) PDF(628)

Abstract:
A coupled nonlinear Schr^L dinger equations is considered in 2-D space. Based upon the conservation of mass and energy, local identities was established by the study of the limit behavior of the solutions, and concentration for the blow-up solutions with radially symmetry was obtained.

Lagrangian Mechanics on K hler Manifolds

ZHANG Rong-ye

2005, 26(10): 1236-1246.

Abstract(2844) PDF(656)

Abstract:
Lagrangian mechanics on K hler manifolds were discussed, and the complex mathe matical aspects of Lagrangian operator, Lagrange's equation, the action functional, Hamilton's principle and Hamilton's equation, and so on were given.

A New Efficient Method to the Boundary Value Problem for Ballistic Rocket Guidance

LIU Xin-jian, YUAN Tian-bao

2005, 26(10): 1247-1252.

Abstract(2296) PDF(1281)

Abstract:
The exploitation of rocket guidance technology on the basis of the guidance law of Space Shuttle and Pegasus rocket was performed. A new efficient method of numerical iteration solution to the boundary value problem was put forward. The numerical simulation results have shown that the method features good performance of stability, robustness, high precision, and algebraic formulas in real computation. By virtue of modern digital signal processor(DSP), high speed chip technology, the algorithm can be used in real time and can adapt to the requirements of the big primary bias of rocket guidance.

Mathematical Expectation About Discrete Random Variable With Interval Probability(DRVIP) or Fuzzy Probability(DRVFP)

XIAO Sheng-xie, LÜ En-lin

2005, 26(10): 1253-1260.

Abstract(2822) PDF(1531)

Abstract:
The character and an algorithm about DRVIP(discrete randam variable with interval probability) and the second kind DRVFP (discrete random variable with crisp event-fuzzy probability) are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is typically solving a linear programming problem. A very functional calculating formula solving mathematical expectation of DRVIP was obtained by using the Dantzig's simplex method. The example indicates that the result obtained by using the functional calculate formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.