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2013年 第34卷 第12期    刊出日期：2013-11-29

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论文

Concentration of nitrogen molecules needed by nitrogen nanobubbles existing in bulk water

张萌 涂育松 方海平

2013, 34(12):  1433-1438.  doi:10.1007/s10483-013-1757-x

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This paper investigates the stability of nitrogen nanobubbles under different concentrations of nitrogen molecules by molecular dynamics simulations. It is found that the stability of nanobubbles is very sensitive to the concentration of nitrogen molecules in water. A sharp transition between disperse states and assemble states of nitrogen molecules is observed when the concentration of nitrogen molecules is changed. The relevant critical concentration of nitrogen molecules needed by the existing nitrogen nanobubbles is analyzed.

Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere

K. REGER R. A. VAN GORDER

2013, 34(12):  1439-1452.  doi:10.1007/s10483-013-1758-6

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We study a modified version of the Lane-Emden equation of the second kind modelling a thermal explosion in an infinite cylinder and a sphere. We first show that the solution to the relevant boundary value problem is bounded and that the solutions are monotone decreasing. The upper bound, the value of the solution at zero, can be approximated analytically in terms of the physical parameters. We obtain solutions to the boundary value problem, using both the Taylor series (which work well for weak nonlinearity) and the δ-expansion method (valid for strong nonlinearity). From here, we are able to deduce the qualitative behavior of the solution profiles with a change in any one of the physical parameters.

Shocklets in compressible flows

袁湘江 田俊武 沈清 李筠

2013, 34(12):  1453-1464.  doi:10.1007/s10483-013-1759-7

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The mechanism of shocklets is studied theoretically and numerically for the stationary fluid, uniform compressible flow, and boundary layer flow. The conditions that trigger shock waves for sound wave, weak discontinuity, and Tollmien-Schlichting (T-S) wave in compressible flows are investigated. The relations between the three types of waves and shocklets are further analyzed and discussed. Different stages of the shocklet formation process are simulated. The results show that the three waves in compressible flows will transfer to shocklets only when the initial disturbance amplitudes are greater than the certain threshold values. In compressible boundary layers, the shocklets evolved from T-S wave exist only in a finite region near the surface instead of the whole wavefront.

Blasius flow and heat transfer of fourth-grade fluid with slip

B. SAHOO S.PONCET

2013, 34(12):  1465-1480.  doi:10.1007/s10483-013-1760-6

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This investigation deals with the effects of slip, magnetic field, and non-Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.

Hydromagnetic rotating flow of third grade fluid

T. HAYAT R. NAZ A.ALSAEDI M. M. RASHIDI

2013, 34(12):  1481-1494.  doi:10.1007/s10483-013-1761-7

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This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic (MHD). The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method (HAM). Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.

Numerical simulation of motion and deformation of ring bubble along body surface

倪宝玉 张阿漫 G. X. WU

2013, 34(12):  1495-1512.  doi:10.1007/s10483-013-1762-6

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Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method (BEM). The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.

Non-uniqueness and stability of two-family fiber-reinforced incompressible hyper-elastic sheet under equibiaxial loading

任九生 程昌钧

2013, 34(12):  1513-1520.  doi:10.1007/s10483-013-1763-x

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The problems on the non-uniqueness and stability of a two-family fiberreinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configurations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain critical value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.

Dynamic torsional response of pre-strained end bearing pile embedded in pre-strained isotropic saturated soil medium

胡文韬 夏唐代 张智卿

2013, 34(12):  1521-1534.  doi:10.1007/s10483-013-1764-8

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The influence of initial strain state on the dynamic response of an end bearing pile embedded in isotropic saturated soil is investigated through the linearized theory of small elastic perturbation superposed on largely stressed bodies. The governing equations for soil, based on Biot’s poroelasticity theory, are derived in the cylindrical coordinates, and the pile is modeled by using the one-dimensional elastic theory. The analytical solutions of pile impedance, frequency response of both twist angle and time history of velocity response are obtained by using of separation of variables technique. Finally, a parametric study of the influence of initial strains on the torsional impedance, twist angle, and velocity response at the top of the pile is carried out.

Determination of stress intensity factors in half-plane containing several moving cracks

K. MALEKZADEH FARD M.M.MONFARED K. NOROUZIPOUR

2013, 34(12):  1535-1542.  doi:10.1007/s10483-013-1765-8

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The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a single dislocation and without dislocation. An exact solution in a closed form to the stress fields and displacement is obtained. The Galilean transformation is used to transform between coordinates connected to the cracks. The stress components are of the Cauchy singular kind at the location of dislocation and the point of application of the force. Numerical examples demonstrate the influence of crack length and crack running velocity on the stress intensity factor.

Comprehensive form of solution for Lamb’s dynamic problem expressed by Green’s functions

丁伯阳 徐庭 陈军 欧阳明

2013, 34(12):  1543-1552.  doi:10.1007/s10483-013-1766-8

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By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld’s identity as well as Green’s functions of Stokes’ solution pertaining the conventional elastic dynamic equation, the results of Green’s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a semi-space, the authors obtain the solutions of Green’s function for Lamb’s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb’s previous results, and the solutions of the linear expansion source urr and the linear torsional source uθθ are also given in the paper. The authors reveal that Green’s function of Stokes’ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb’s problem for various situations. It may benefit the investigation of deepening and development of Lamb’s problems and solution for pertinent dynamic problems conveniently.