应用数学和力学

2007 Vol. 28, No. 11

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Numerical Simulation of Flow in the Hartmann Resonance Tube and Flow in the Ultrasonic Gas Atomizer

LI Bo, HU Guo-hui, ZHOU Zhe-wei

2007, 28(11): 1261-1271.

Abstract(3323) PDF(802)

Abstract:
The gas flow in the Hartmann resonance tube was numerically investigated by the finite volume method based on the Roe solver. The oscillation of the flow was studied with the presence of a needle actuator set along the nozzle axis. Numerical results agree well with the theoretical and experimental results available. Numerical results indicate that the resonance mode of the resonance tube will switch by means of removing or adding the actuator. The gas flow in the ultrasonic gas atomization (USGA) nozzle was also studied by the same numerical methods. Oscillation caused by the Hartmann resonance tube structure, coupled with a secondary resonator, in the USGA nozzle was investigated. Effects of the variation of parameters on the oscillation were studied. The mechanism of the transition of subsonic flow to supersonic flow in the USGA nozzle was also discussed based on numerical results.

Law of Nonlinear Flow in Saturated Clays and Radial Consolidation

DENG Ying-er, XIE He-ping, HUANG Run-qiu, LIU Ci-qun

2007, 28(11): 1272-1280.

Abstract(2483) PDF(913)

Abstract:
It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with the square root of permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state instead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of Darcy flow are a special case of that of the nonlinear flow.

Blow-up of the Solution for a Generalized Boussinesq Equation

WANG Yan-ping, GUO Bo-ling

2007, 28(11): 1281-1286.

Abstract(2769) PDF(904)

Abstract:
The initial boundary value problem for a generalized Boussinesq equation was studied and the existence and uniqueness of the local generalized solutions of the problem by Galerkin method were proved. Moreover, the sufficient conditions of blow-up of the solution of the problem in finite time by the concavity method were given.

Nanoparticle Coagulation in a Planar Jet via Moment Method

YU Ming-zhou, LIN Jian-zhong, CHEN Li-hua

2007, 28(11): 1287-1295.

Abstract(2551) PDF(733)

Abstract:
Large eddy simulations of nanoparticle coagulation in an incompressible planar jet were performed. The particle is described using a moment method to approximate the particle general dynamics equations. The time-averaged results based on 3 000 time steps for every case were obtained to explore the influence of the Schmidt number and the Damkohler number on the nanoparticle dynamics. The results show that the changes of Schmidt number have the influence on the number concentration of nanoparticles only when the particle diameter is less than 1nm for the fixed gas parameters. The number concentration of particles for small particles decreases more rapidly along the flow direction, and the nanoparticles with larger Schmidt number have a narrower distribution along the transverse direction. The smaller nanoparticles coagulate and disperse easily, grow rapidly hence show a stronger polydispersity. The smaller coagulation time scale can enhance the particle collision and coagulation. Frequent collision and coagulation bring a great increase in particle size. The larger the Damkohler number, the higher the particle polydispersity.

Travelling Wave Solutions for a Hight Order Wave Equation of KdV Type

LONG Yao, LI Ji-bin, RUI Wei-guo, HE Bin

2007, 28(11): 1296-1306.

Abstract(2988) PDF(775)

Abstract:
The theory of planar dynamical systems is used to study the dynamical behaviour of the travelling wave solutions of a nonlinear wave equations of KdV type. In different regions of the parametric space, sufficient conditions to guarantee the existence of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions are given. All possible exact explicit parametric representations are obtained for these waves.

MHD Flow and Heat Transfer From a Continuous Surface in a Uniform Free Stream of a Non-Newtonian Fluid

Bikash Sahoo, H. G. Sharma

2007, 28(11): 1307-1317.

Abstract(2954) PDF(872)

Abstract:
An analysis was carried out to study the steady flow and heat transfer characteristics from a continuous flat surface moving in a parallel free stream of an electrically conducting non-Newtonian viscoelastic fluid. The flow is subjected to a transverse uniform magnetic field. The constitutive equation of the fluid is modeled by that for a second grade fluid. Numerical results were obtained for the distribution of velocity and temperature profiles. The efects of various physical parameters like viscoelastic parameter, magnetic parameter and Prandtl number on various momentum and heat transfer characteristics are discussed in detail and shown graphically.

Nonlinear Analysis of a Structure Loaded by a Stochastic Excitation

GAO Shi-qiao, JIN Lei, M. Kasperski, LIU Hai-peng, LI Ming-hui

2007, 28(11): 1318-1324.

Abstract(2602) PDF(702)

Abstract:
For a non-linear system excited by a stochastic load which is expressed as a time series, a recursive method based on the Z-transform was presented. To identify the obtained response time series, a discrete wavelet transform (DWT) technique was proposed.

Structural First Failure Times Under Non-Gaussian Stochastic Behavior

HE Jun

2007, 28(11): 1325-1332.

Abstract(2403) PDF(811)

Abstract:
An analytical moment-based method for calculating structural first failure times under nonGaussian stochastic behaviour is proposed. In the method, a power series that is constant can be obtained from response moments (skewness, kurtosis, etc.) was used firstly to map a non-Gaussian structural response into a standard Gaussian process, then mean up-crossing rates, mean clump size and the initial passage probability of a critical barrier level by the original structural response were estimated. Finally, the formula for calculating first failure times was established on the assumption that corrected up-crossing rates are independent. An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Gaussian model.

Some New Conditions for Generalized H-matrices

ZHU Li, LIU Jian-zhou

2007, 28(11): 1333-1339.

Abstract(2552) PDF(842)

Abstract:
By using a matrix' continuous transition method and the sub-matrix' estimate of spectral radius methods etc., some decision methods for a generalized H-matrix under positive definite matrix conditions were researched. Some new sufficient conditions for generalized H-matrices are obtained. When a block matrix degenerates a point matrix, these conditions then become H-matrix's sufficient conditions.

Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type

YAO Feng-ping, ZHOU Shu-lin

2007, 28(11): 1340-1352.

Abstract(3143) PDF(916)

Abstract:
Global Schauder estimates for the initial-value parabolic problem of the bi-harmonic type were proved. The existence and uniqueness of the solutions in the suitable space were obtained. Similarly to the second-order case, a fomal expression of solutions by the Fourier transform was obtained. Then the regularity, uniqueness, existence of solutions using the potential theory and approximation argument were got. The approach is simple and straightforward.

Bifurcations of Double Homoclinic Flip Orbits With Resonant Eigenvalues

ZHANG Tian-si, ZHU De-ming

2007, 28(11): 1353-1362.

Abstract(2358) PDF(680)

Abstract:
Concerns double homoclinic loops with or bitflips and two resonant eigenvalues in a fourdimensional system. We use the solution of a normal form system to construct a singular map in some neighborhood of the equilibrium, and the solution of a linear variational system to construct a regular map in some neighborhood of the double homoclinic loops, then compose them to get the important Poincar map. A simple calculation gives explicitly an expression of the associated successor function. By a delicate analysis of the bifurcation equation, we obtain the condition that the original double homoclinic loops are kept, and prove the existence and the existence regions of the large 1-homo clinic orbit bifurcation surface, 2-fold large 1-periodic or bit bifurcation surface, large 2-homoclinic or bit bifur cation surface and their appro ximate expressions. We also locate the large periodic orbits and large homoclinic orbits and their number.

Random Attractors for Asymptotically Upper Semicompact Multivalue Random Semiflows

LI Ting

2007, 28(11): 1363-1369.

Abstract(2431) PDF(863)

Abstract:
The existence of random attractors for multi-value random semiflows was studied. First an abstract result on the existence of limit sets under the assumptions of pullback asymptotically upper semi-compact and absorbing is proved. Then the existence of random attractors is proved.

Instantaneous Spectrum Estimation of Earthquake Ground Motions Based on Unscented Kalman Filter Method

LI Ying-min, DONG Yin-feng, LAI Ming

2007, 28(11): 1370-1378.

Abstract(2673) PDF(951)

Abstract:
Representing earthquake ground motion as time varying ARMA model, the instantaneous spectrum can be determined only by the time varying coefficients of the corresponding ARMA model. Then, unscented Kalman filter was introduced to estimate the time varying coefficients. The comparison between the estimation results of unscented Kalman filter and Kalman filter method shows that unscented Kalman filter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity or abruptness. Moreover, the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power of ARMA model which was usually ignored in former relevant studies has great effect on the estimation precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.

Lagrange-Maxwell Equation and Magnetic Saturation Parametric Resonance of Generator Set

YANG Zhi-an, LI Wen-lan, QIU Jia-jun, XI Xiao-yan

2007, 28(11): 1379-1386.

Abstract(2878) PDF(846)

Abstract:
Lagrange-Maxwell's equation was extended firstly. With the theory of electromechanical analytical dynamics, the magnetic complement energy in air gap of generator was acquired. The torsional viration differential equations with periodic coefficients of rotor shafting of generator that is in the state of magnetic saturation were established. It is shown that the magnetic saturation may cause double frequency electromagnetic moment. By means of the averaging method, the first approximate solution and corresponding solution of the primary parametric resonance was obtained. The characteristics and laws of the primary parametric resonance excited by the electromagnetism were analyzed and some of new phenomena were revealed.