应用数学和力学

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

ZU Hong-biao, ZHOU Zhe-wei, WANG Zhi-liang

2012, 33(12): 1379-1391. doi: 10.3879/j.issn.1000-0887.2012.12.001

Abstract(2874) PDF(1338)

Abstract:
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

MA Yu-li, CHEN Ji-wei, LIU Yong-quan, SU Xian-yue

2012, 33(12): 1392-1402. doi: 10.3879/j.issn.1000-0887.2012.12.002

Abstract(2091) PDF(1182)

Abstract:
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

WU Chun-xiu, SONG Tao, ZHANG Peng, WONG S. C.

2012, 33(12): 1403-1410. doi: 10.3879/j.issn.1000-0887.2012.12.003

Abstract(2229) PDF(1059)

Abstract:
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

GUZhi-jie, TAN Yong-ji

2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004

Abstract(2029) PDF(1208)

Abstract:
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

LU Wei-gang, DONG Lei, WANG Zhao-fei, LU Lin-guang

2012, 33(12): 1431-1441. doi: 10.3879/j.issn.1000-0887.2012.12.005

Abstract(1934) PDF(1025)

Abstract:
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): 1442-1450. doi: 10.3879/j.issn.1000-0887.2012.12.006

Abstract(2179) PDF(1252)

Abstract:
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.

On DTM-BF Method and Dual Solutions for an Unsteady MHD Flow Over a Permeable Shrinking Sheet With Velocity Slip

SU Xiao-hong, ZHENG Lian-cun, ZHANG Xin-xin

2012, 33(12): 1451-1464. doi: 10.3879/j.issn.1000-0887.2012.12.007

Abstract(2335) PDF(1416)

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

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

ZOU Li, WANG Zhen, ZONG Zhi, ZOU Dong-yang, ZHANG Shuo

2012, 33(12): 1465-1476. doi: 10.3879/j.issn.1000-0887.2012.12.008

Abstract(2087) PDF(1077)

Abstract:
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

YAO Jing-sun, OUYANG Cheng, CHEN Li-hua, MO Jia-qi

2012, 33(12): 1477-1486. doi: 10.3879/j.issn.1000-0887.2012.12.009

Abstract(2098) PDF(1153)

Abstract:
A class of the nonlinear disturbed coupled Schrödinger system was studied. Using the specific technique to relate the exact and approximate solutions, firstly, the corresponding typical coupled system was considered. The exact shock travelling solution was obtained by using the mapping method. Then the travelling asymptotic solutions of the disturbed coupled Schrdinger system was found by using an approximate method.

Existence Theory for Rosseland Equation and Its Homogenized Equation

ZHANG Qiao-fu, CUI Jun-zhi

2012, 33(12): 1487-1502. doi: 10.3879/j.issn.1000-0887.2012.12.010

Abstract(1999) PDF(1135)

Abstract:
The global boundness and existence were presented for the kind of Rosseland equation with a general growth condition.A linearized map in a closed convex set was defined. The image set was precompact and this map was continuous, so there existed a fixed point. The Multiple-scale expansion method was used to obtain the homogenized equation.This equation satisfied a similar growth condition.

2012 Vol. 33, No. 12