应用数学和力学

2000 Vol. 21, No. 12

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A Numerical Study for Small Amplitude T-S Waves in a Supersonic Boundary Layer

YUAN Xiang-jiang, ZHOU Heng

2000, 21(12): 1211-1214.

Abstract(2540) PDF(583)

Abstract:
The propagation of the disturbance waves in a boundary layer at Mach number=4.5 is studied by direct numerical simulation(DNS),using NND scheme,and different amplitudes A=0.01,0.001,0.000 1 of the disturbance have been assumed.The numerical result shows that there might be shocklets induced in the boundary layer,even when the amplitude of disturbance wave is still small.

Theoretical Study on the Bifurcation of Vortexes Structure for Flow in Curved Tube

WU Wang-yi, TAN Wen-chang, LI Juan, XIE Wen-jun

2000, 21(12): 1215-1226.

Abstract(2879) PDF(801)

Abstract:
The number and distribution of the singular points of streamlines in the cross section of steady flow through a curved tube are discussed by using the method of topological structure analysis. And a theoretical criterion is obtained for the bifurcation of flow vortexes for the secondary flow turning from two-vortex structure into four-vortex structure.Furthermore,the critical Dean number for bifurcation and the semi-analytical expressions of stream function and axial velocity are given by using Galerkin technique.The result of calculation is consistent with the theoretical criterion.

Superposition About the 3D Vortex Solutions of the Fluid Dynamic Equation

HUANG Yong-nian, HU Xin

2000, 21(12): 1227-1237.

Abstract(2678) PDF(788)

Abstract:
A class of exact general solutions of an axisymmetric flow of the fluid dynamic equations is given.Then some examples are discussed.Some vortex solutions can be superposed to give other exact solutions.It can be used to analyse the generation and evolution of the vortex ring.

Numerical Simulation of Standing Solitons and Their Interaction

ZHOU Xian-chu, Rui Yi

2000, 21(12): 1238-1246.

Abstract(2628) PDF(554)

Abstract:
Standing soliton was studied by numerical simulation of its governing equation,a cubic Schr^Ldiger equation with a complex conjugate term,which was derived by Miles and was accepted. The value of linear damping in Miles equation was studied.Calculations showed that linear damping effects strongly on the formation of a standing soliton and Laedke&Spatschek stable condition is only a necessary condition,but not a sufficient one.The interaction of two standing solitons was simulated.Simulations showed that the interaction pattern depends on system parameters.Calculations for the different initial condition and its development indicated that a stable standing soliton can be formed only for proper initial disturbance,otherwise the disturbance will disappear or develop into several solitons.

Penalty Finite Element Method for Nonlinear Dynamic Response of Viscous Fluid-Saturated Biphasic Porous Media

YAN Bo, ZHANG Ru-qing

2000, 21(12): 1247-1254.

Abstract(2936) PDF(751)

Abstract:
The governing equations as well as boundary and initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphasic porous medium model,based on mixture theory,are presented.With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation,in which the dependencies of volume fraction and permeation coefficients on deformation are included,is obtained.The iteration solution method of the nonlinear system equation is also discussed.As a numerical example,the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program.The numerical results demonstrate the efficiency and correctness of the method.

Research on Stability of Moving Jet Containing Dense Suspended Solid Particles

LIN Jian-zhong, ZHOU Ze-xuan

2000, 21(12): 1255-1264.

Abstract(2432) PDF(481)

Abstract:
The spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model.The stability curves of moving jet for different downstream distances,Reynolds number of flow-field,particle properties and velocities of jetting device are got by the finite difference method based on the asymptotic method and the Eulerian conservative difference scheme.Founded on the analyses of the obtained stability curves it is found that the positive velocity of jetting device widens the unstable frequency range of flow-field but the effect of the negative one is contrary.In addition,particles existing in the flow-field curb the instability of flow-field and the effect enhances with the decrease of Reynolds number of flow-field.These conclusions benefit learning the development of moving two-phase jet.

The Variational Principles and Application of Nonlinear Numerical Manifold Method

LUO Shao-ming, ZHANG Xiang-wei, CAI Yong-chang

2000, 21(12): 1265-1270.

Abstract(2335) PDF(577)

Abstract:
The physical-cover-oriented variational principle of nonlinear numerical manifold method (NNMM)for the analysis of plastical problems is put forward according to the displacement model and the characters of numerical manifold method(NMM).The theoretical calculating formulations and the controlling equation of NNMM are derived.As an example,the plate with a hole in the center is calcaulated and the results show that the solution precision and efficiency of NNMM are agreeable.

Variational Method and Computation for H_∞ Control

ZHONG Wan-xie

2000, 21(12): 1271-1278.

Abstract(2365) PDF(674)

Abstract:
The variational approach is further applied to the measurement feedback H_∞ control problems.Based on the induced norm description of the system Г,the variational functionals J_c and J_p of state feedback H_∞ control for the future time interval(t,t_f],and of H_∞ filter for the past time interval[0,t),respectively,are combined together to generate the variational functional of the measurement feedback for the whole time interval[0,t_f].The connection condition at the present time t is that the estimated state vector x(t) must be continuously extended to be the initial condition of the future state vector estimation.Another connection condition for the dual vector K(t)can be naturally derived from the variational principle.The equations thus derived show that the third condition for the optimal parameter γ_cr^-2 is again a bound of the smallest Rayleigh quotient.Therefore,the precise integration method developed formerly to determine the optimal parameter γ_cr^-2 of H_∞ control and of H_∞ filter respectively can be further applied to the determination of the optimal parameter.

Precise Integration Method for LQG Optimal Measurement Feedback Control Problem

ZHONG Wan-xie, CAI Zhi-qin

2000, 21(12): 1279-1284.

Abstract(2567) PDF(909)

Abstract:
By using the precise integration method,the numerical solution of linear quadratic Gaussian(LQG)optimal control problem was discussed.Based on the separation principle,the LQG control problem decomposes,or separates,into an optimal state-feedback control problem and an optimal state estimation problem.That is the off-line solution of two sets of Riccati differential equations and the on-line integration solution of the state vector from a set of time-variant differential equations. The present algorithms are not only appropriate to solve the two-point boundary-value problem and the corresponding Riccati differential equation,but also can be used to solve the estimated state from the time-variant differential equations.The high precision of precise integration is of advantage for the control and estimation.Numerical examples demonstrate the high precision and effectiveness of the algorithm.

Two Types of New Algorithms for Finding Explicit Analytical Solutions of Nonlinear Differential Equations

ZHANG Hong-qing, YAN Zhen-ya

2000, 21(12): 1285-1292.

Abstract(2677) PDF(925)

Abstract:
The idea of AC=BD was applied to solve the nonlinear differential equations.Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved.If the transformation u=Cv is obtained so that v satisfies Dv=0,then the solutions for Au=0 can be found.In order to illustrate this approach,several examples about the transformation C are given.

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CHEN Da-duan, SHI Wei-hui

2000, 21(12): 1293-1300.

Abstract(2388) PDF(561)

Abstract:
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The C^k Instability of Navier-Stokes Equation Appending Polynomials of Unknown Functions

HE You-hua, SHI Wei-hui

2000, 21(12): 1301-1309.

Abstract(2407) PDF(673)

Abstract:
Applying the theory of stratification,the solution space structure about a class of deformed Navier-Stokes equation is determined.It is proved that such kind of equation has no C^k(k≥2)stable solution by the fact that the strate transversale is a null set.

On the Partially Cavitating Flow Around Two-Dimensional Hydrofoils

CHENG Xiao-jun, LU Chuan-jing

2000, 21(12): 1310-1318.

Abstract(2946) PDF(615)

Abstract:
The steady partially cavitating flow around two-dimensional hydrofoils was simulated numerically by the low-order potential-based boundary integration method.The caviy shape and length are determined for given cavitating numbers in the course of iteration by satisfying the kinematic and dynamic boundary conditions.The re-entrant jet model and the pressure-recovery close model are adopted to replace the high turbulent and two-phase wake forming behind the cavity.The results are compared with the other published numerical ones.