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2012年 第33卷 第12期    刊出日期：2012-12-10

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论文

Properties of acoustic resonance in double-actuator ultra-sonic gas nozzle: numerical study

祖洪彪;周哲玮;王志亮

2012, 33(12):  1481-1492.  doi:10.1007/s10483-012-1638-x

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The ultra-sonic gas atomization (USGA) nozzle is an important apparatus in the metal liquid air-blast atomization process. It can generate oscillating supersonic gas efflux, which is proved to be effective to enforce the atomization and produce narrow-band particle distributions. A double-actuator ultra-sonic gas nozzle is proposed in the present paper by joining up two active signals at the ends of the resonance tubes. Numerical sim-ulations are adopted to study the effects of the flow development on the acoustic resonant properties inside the Hartmann resonance cavity with/without actuators. Comparisons show that the strength and the onset process of oscillation are enhanced remarkably with the actuators. The multiple oscillating amplitude peaks are found on the response curves, and two kinds of typical behaviors, i.e., the Hartmann mode and the global mode, are discussed for the corresponding frequencies. The results for two driving actuators are also investigated. When the amplitudes, the frequencies, or the phase difference of the input signals of the actuators are changed, the oscillating amplitudes of gas efflux can be altered effectively.

Vibration analysis of foam plates based on cell volume distribution

马宇立;陈继伟;刘咏泉;苏先樾

2012, 33(12):  1493-1504.  doi:10.1007/s10483-012-1639-7

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In this paper, vibration analysis of irregular-closed-cell foam plates is per-formed. A cell volume distribution coefficient is introduced to modify the original Gibson-Ashby equations of effective Young’s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution pa-rameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure.

Phase-plane analysis of conserved higher-order traffic flow model

吴春秀;宋涛;张鹏;S. C. WONG

2012, 33(12):  1505-1512.  doi:10.1007/s10483-012-1640-x

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The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.

Fundamental solution method for inverse source problem of plate equation

顾智杰;谭永基

2012, 33(12):  1513-1532.  doi:10.1007/s10483-012-1641-6

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The elastic plate vibration model is studied under the external force. The size of the source term by the given mode of the source and some observations from the body of the plate is determined over a time interval, which is referred to be an inverse source problem of a plate equation. The uniqueness theorem for this problem is stated, and the fundamental solution to the plate equation is derived. In the case that the plate is driven by the harmonic load, the fundamental solution method (FSM) and the Tikhonov regularization technique are used to calculate the source term. Numerical experiments of the Euler-Bernoulli beam and the Kirchhoff-Love plate show that the FSM can work well for practical use, no matter the source term is smooth or piecewise.

Cross influence of discharge and circulation on head loss of conduit of pump system with low head

陆伟刚;董雷;王兆飞;陆林广

2012, 33(12):  1533-1544.  doi:10.1007/s10483-012-1647-9

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The relationship between the head loss and the discharge and circulation of the conduit of a pump system with low head is an important problem with an obvious influence on the improvement of its hydraulic performance. The velocity circulation from the pump guide vane makes the relationship more complicated, which has to be understood comprehensively. The results indicate that, under the condition of zero circulation, the head loss of the inlet and outlet conduits is in proportion to the square of discharge. Under the condition that the Reynolds number is satisfied with the resistant square area, the conduit loss is in proportion to the square of discharge for the similar working points with different speeds in a certain rotational speed range, indicating that the pump system efficiency is constant. The outlet conduit loss of design discharge for a pump system with low head depends on the velocity circulation from the guide vane exit, and the relationship between the loss and the circulation is an open curve with an upward direction, meaning that there is an optimal circulation for the loss. Under the condition of various working points for a pump system with low head, the head loss of the outlet conduit is under the cross influence of both the discharge and the circulation. As a result, the relationship between the head loss and the discharge is almost linear, and the mechanism needs to be further studied.

Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating

O. D. MAKINDE

2012, 33(12):  1545-1554.  doi:10.1007/s10483-012-1642-8

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The combined effects of viscous dissipation and Newtonian heating on bound-ary layer flow over a moving flat plate are investigated for two types of water-based New-tonian nanofluids containing metallic or nonmetallic nanoparticles such as copper (Cu) and titania (TiO₂). The governing partial differential equations are transformed into ordinary differential equations through a similarity transformation and are solved numer-ically by a Runge-Kutta-Fehlberg method with a shooting technique. The conclusions are that the heat transfer rate at the moving plate surface increases with the increases in the nanoparticle volume fraction and the Newtonian heating, while it decreases with the increase in the Brinkmann number. Moreover, the heat transfer rate at the moving plate surface with Cu-water as the working nanofluid is higher than that with TiO₂-water.

DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

苏晓红;郑连存;张欣欣

2012, 33(12):  1555-1568.  doi:10.1007/s10483-012-1643-9

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An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.

Solving shock wave with discontinuity by enhanced differential transform method (EDTM)

邹丽;王振;宗智;邹东阳;张朔

2012, 33(12):  1569-1582.  doi:10.1007/s10483-012-1644-9

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An enhanced differential transform method (EDTM), which introduces the Padé technique into the standard differential transform method (DTM), is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact power series solution.

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

姚静荪;欧阳成;陈丽华;莫嘉琪

2012, 33(12):  1583-1594.  doi:10.1007/s10483-012-1645-7

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A class of nonlinear disturbed coupled Schrödinger systems is studied. The specific technique is used to relate the exact and approximate solutions. The corresponding typical coupled system is considered. An exact shock travelling solution is obtained by a mapping method. The travelling asymptotic solutions of the disturbed coupled Schrödinger system are then found with an approximate method.

Existence theory for Rosseland equation and its homogenized equation

张乔夫;崔俊芝

2012, 33(12):  1595-1612.  doi:10.1007/s10483-012-1646-6

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The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.