Table of Content

23 July 2010, Volume 31 Issue 8

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Articles

Formation of radially expanding liquid sheet by impinging two round jets

WANG Zhi-Liang;S.P.LIN;ZHOU Zhe-Wei

2010, 31(8):  937-946.  doi:10.1007/s10483-010-1328-x

Abstract ( 459 )   PDF (611KB) ( 1157 )  

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A thin circular liquid sheet can be formed by impinging two identical round jets against each other. The liquid sheet expands to a certain critical radial distance and breaks. The unsteady process of the formation and breakup of the liquid sheet in the ambient gas is simulated numerically. Both liquid and gas are treated as incompressible Newtonian fluids. The flow considered is axisymmetric. The liquid-gas interface is modeled with a level set function. A finite difference scheme is used to solve the governing Navier-Stokes equations with physical boundary conditions. The numerical results show how a thin circular sheet can be formed and break at its circular edge in slow motion. The sheet continues to thin as it expands radially. Hence, the Weber number decreases radially. The Weber number is defined as ρu²h/σ, where ρ and σ are, respectively, the liquid density and the surface tension, and u and h are, respectively, the average velocity and the half sheet thickness at a local radial location in the liquid sheet. The numerical results show that the sheet indeed terminates at a radial location, where the Weber number reaches one as observed in experiments. The spatio-temporal linear theory predicts that the breakup is initiated by the sinuous mode at the critical Weber number W_^ec=1, below which the absolute instability occurs. The other independent mode called the varicose mode grows more slowly than the sinuous mode according to the linear theory. However, our numerical results show that the varicose mode actually overtakes the sinuous mode during the nonlinear evolution, and is responsible for the final breakup. The linear theory predicts the nature of disturbance waves correctly only at the onset of the instability, but cannot predict the exact consequence of the instability.

Hydraulic calculation of steady uniform flows in trapezoidal compound open channels

ZENG Yu-Hong;WANG Yue-Hua;HUAI Wen-Xin

2010, 31(8):  947-954.  doi:10.1007/s10483-010-1329-z

Abstract ( 538 )   PDF (275KB) ( 992 )  

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Hydraulic calculation of steady uniform flows in trapezoidal compound open channels is studied. Based on the force balance of water in each sub-section, the average velocities of the main channel, side slope, and floodplain are derived. The lateral momentum exchanges between the sub-sections are expressed by using the apparent shear stress. To verify the model, seven groups of UK Flood Channel Facility (UK-FCF) measured data with a relative water depth between the floodplain and the main channel varying from 0.057 to 0.4 are used for comparison. The result shows that the calculated velocity is larger than the measured data when the relative water depth is small, while it is less than or close to the measured value in the case of a larger relative water depth. The influence of the apparent shear stress on the calculation of velocity on the floodplain is not obvious, while it is much greater on the main channel. The three-stage model is compared with Liu’s two-stage model, showing that the former can give a better prediction for a three-stage trapezoidal compound channel. Finally, the apparent shear stress is calculated and compared with the measured data. The result shows that the chosen values of the momentum transfer coefficients are appropriate.

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

R.A.DAMSEH;B.A.SHANNAK

2010, 31(8):  955-962.  doi:10.1007/s10483-010-1330-z

Abstract ( 606 )   PDF (337KB) ( 1380 )  

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An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

F.A.SALAMA

2010, 31(8):  963-968.  doi:10.1007/s10483-010-1331-z

Abstract ( 547 )   PDF (252KB) ( 905 )  

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The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.

Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel

S.NADEEM;N.S.AKBAR

2010, 31(8):  969-978.  doi:10.1007/s10483-010-1332-6

Abstract ( 643 )   PDF (393KB) ( 1589 )  

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In this paper, the influence of heat transfer and induced magnetic field on peristaltic flow of a Johnson-Segalman fluid is studied. The purpose of the present investigation is to study the effects of induced magnetic field on the peristaltic flow of non-Newtonian fluid. The two-dimensional equations of a Johnson-Segalman fluid are simplified by assuming a long wavelength and a low Reynolds number. The obtained equations are solved for the stream function, magnetic force function, and axial pressure gradient by using a regular perturbation method. The expressions for the pressure rise, temperature, induced magnetic field, pressure gradient, and stream function are sketched and interpreted for various embedded parameters.

The effects of variable specific heat on the stability of hypersonic boundary layer on a flat plate

JIA Wen-Li;CAO Wei

2010, 31(8):  979-986.  doi:10.1007/s10483-010-1333-7

Abstract ( 478 )   PDF (379KB) ( 1079 )  

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The gas temperature within hypersonic boundary layer flow is so high that the specific heat of gas is no longer a constant but relates to temperature. How variable specific heat influences on boundary layer flow stability is worth researching. The effect of the variable specific heat on the stability of hypersonic boundary layer flows is studied and compared with the case of constant specific heat based on the linear stability theory. It is found that the variable specific heat indeed has some effects on the neutral curves of both the first-mode and the second-mode waves and on the maximum rate of growth also. Therefore, the relationship between specific heat and temperature should be considered in the study of the stability of the boundary layer.

First-order gradient damage theory

ZHAO Bing;ZHENG Ying-Ren;ZENG Meng-Hua;TANG Xue-Song;LI Xiao-Gang

2010, 31(8):  987-994.  doi:10.1007/s10483-010-1334-9

Abstract ( 510 )   PDF (196KB) ( 879 )  

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Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are derived directly from the basic law of irreversible thermodynamics with the constitutive functional expansion method at the natural state. When the damage variable is equal to zero, the expressions can be simplified to the linear elastic constitutive equations. When the damage gradient vanishes, the expressions can be simplified to the classical damage constitutive equations based on the strain equivalence hypothesis. A one-dimensional problem is presented to indicate that the damage field changes from the non-periodic solutions to the spatial periodic-like solutions with stress increment. The peak value region develops a localization band. The onset mechanism of strain localization is proposed. Damage localization emerges after damage occurs for a short time. The width of the localization band is proportional to the internal characteristic length.

Dynamic and quasi-static bending of saturated poroelastic Timoshenko cantilever beam

YANG Xiao;WEN Qun

2010, 31(8):  995-1008.  doi:10.1007/s10483-010-1335-6

Abstract ( 697 )   PDF (820KB) ( 1207 )  

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Based on the three-dimensional Gurtin-type variational principle of the incompressible saturated porous media, a one-dimensional mathematical model for dynamics of the saturated poroelastic Timoshenko cantilever beam is established with two assumptions, i.e., the deformation satisfies the classical single phase Timoshenko beam and the movement of the pore fluid is only in the axial direction of the saturated poroelastic beam. Under some special cases, this mathematical model can be degenerated into the Euler-Bernoulli model, the Rayleigh model, and the shear model of the saturated poroelastic beam, respectively. The dynamic and quasi-static behaviors of a saturated poroelastic Timoshenko cantilever beam with an impermeable fixed end and a permeable free end subjected to a step load at its free end are analyzed by the Laplace transform. The variations of the deflections at the beam free end against time are shown in figures. The influences of the interaction coefficient between the pore fluid and the solid skeleton as well as the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam are examined. It is shown that the quasi-static deflections of the saturated poroelastic beam possess a creep behavior similar to that of viscoelastic beams. In dynamic responses, with the increase of the slenderness ratio, the vibration periods and amplitudes of the deflections at the free end increase, and the time needed for deflections approaching to their stationary values also increases. Moreover, with the increase of the interaction coefficient, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Timoshenko beam.

Generalized passivity-based chaos synchronization

C.K.AHN

2010, 31(8):  1009-1018.  doi:10.1007/s10483-010-1336-6

Abstract ( 481 )   PDF (567KB) ( 1075 )  

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In this paper, a new passivity-based synchronization method for a general class of chaotic systems is proposed. Based on the Lyapunov theory and the linear matrix inequality (LMI) approach, the passivity-based controller is presented to make the synchronization error system not only passive but also asymptotically stable. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation studies for the Genesio-Tesi chaotic system and the Qi chaotic system are presented to demonstrate the effectiveness of the proposed scheme.

Singularity analysis of Duffing-van der Pol system with two bifurcation parameters under multi-frequency excitations

QIN Zhao-Hong;CHEN Yu-Shu

2010, 31(8):  1019-1026.  doi:10.1007/s10483-010-1337-7

Abstract ( 468 )   PDF (622KB) ( 948 )  

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Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed: (1) λ1 is considered as bifurcation parameter, (2) λ2 is considered as bifurcation parameter, and (3) λ1 and λ2 are both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space is divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions are obtained, which provides a theoretical basis for optimal design of the system.

A class of boundary value problems for third-order differential equation with a turning point

MO Jia-Qi;WEN Zhao-Hui

2010, 31(8):  1027-1032.  doi:10.1007/s10483-010-1338-z

Abstract ( 527 )   PDF (142KB) ( 941 )  

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A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed.

Almost sure stability condition of weakly coupled linear nonautonomous random systems

T.W.MA

2010, 31(8):  1033-1038.  doi:10.1007/s10483-010-1339-x

Abstract ( 460 )   PDF (150KB) ( 816 )  

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In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated. The systems considered are assumed to be composed of two weakly coupled subsystems. The driving actions are considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms are used in conjunction with the bounds for the eigenvalues to obtain, in a closed form, the sufficient condition for the almost sure stability of the systems.

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

HUANG Jun-Jie;Alatancang;WANG Hua

2010, 31(8):  1039-1048.  doi:10.1007/s10483-010-1340-x

Abstract ( 414 )   PDF (177KB) ( 1111 )  

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This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.