应用数学和力学

1986 Vol. 7, No. 6

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Fundamental Equations of Turbulent Two-Phase Flow

Tsai Shu-tang, Fan Zheng-qiao, Chen Yue-nan

1986, 7(6): 477-485.

Abstract(2153) PDF(1004)

Abstract:
A new set of Reynolds equations for predicting turbulent two-phase flows has been developed by means of Reynolds averaging method on the unsteady laminar equations of two-phase flow. These equations involve average terms of products of turbulent fluctuations in some physical parameters in a large degree.The interaction forces between two phases, the pressures for dispersed phase, extra stresses except for pressure and the expressions for energy interchange between two phases have been discussed.

An Exact Solution for Incompressible Flow Through a Two-Dimensional Laval Nozzle

Lia Tong-ji, Pu Qun

1986, 7(6): 487-495.

Abstract(1887) PDF(653)

Abstract:
A careful examination of the variation of the velocity along the centerline and the contour of a Laval nozzle in the physical plane shows that either the upper or the lower half of the Laval nozzle assumes the same form of a slitted thick airfoil with tandem trailing edges. These two airfoils lie on different Ricmann sheets in the hodograph plane. The interior of the airfoil is then mapped onto an infinite strip in the complex potential plane. Making use of these results, we obtained an exact solution for the incompressible potential flow through a two-dimensional Laval nozzle. The solution is applicable for nozzles with any given contraction ratio n₁ expansion ratio n₂ and throat wall radius R^*. As examples of the method, various nozzle contours, the velocity distribution of the flow, and the locations of the fluid particles at different time intervals are presented.

The Establishment of Boundary Integral Equations by Generalized Functions

Peng Xiao-lin, He Guang-qian

1986, 7(6): 497-504.

Abstract(1527) PDF(655)

Abstract:
By the theory of generalized functions this paper introduces a specific generalized function δθ_P, by which, together with its various derivatives, the boundary integral equations and its arbitrary derivatives of any sufficiently smooth function can be established. These equations have no non-integral singularities. For a problem defined by linear partial differential operators, the partial differential equations of the problem can always be converted into boundary integral equations so long as the relevant fundamental solutions exist.

An Analysis of the Effects of the Prostatic Hypertropy on the Urinary Flow in Lower-Urinary-Tract

Liu Zhao-rong, Wang Ya-ping

1986, 7(6): 505-516.

Abstract(1664) PDF(632)

Abstract:
In this paper an analytic model corresponding to the collapsible tube for analysing the urinary flow in lower-urinary-tract is set up from physiologic background.By analysing the model it is found that the self-excited oscillations can both occur in the region of negative and positive slope of P_n-Q_n characteristic. So this paper extends the results of Conrad^[1], Griffiths^[2], Conrad, Cohen and McQueen^[3] and others that the self-excited oscillations can only occur in the region of negative slope of P_n-Q_n characteristic. The effects of prostatic hypertropy on the flow parameters in lower-urinary-tract is discussed in detail by numerical calculations. The results show that it is possible to know the conditions of prostatic hypertropy according to the changes of bladder pressure, outlet urinary velocity and other parameters. From these results a theoretical method to detect and diagnose prostatic hypertropy is provided.

Exact Solution of Navier-Stokes Equations——The Theory of Functions of a Complex Variable under Dirac- Pauli Representation and Its Application in Fluid Dynamics (Ⅱ)

Shen Hui-chuan

1986, 7(6): 517-522.

Abstract(1953) PDF(885)

Abstract:
This work is the continuation of the discussion of Ref. [1]. In Ref. [1] we applied the theory of functions of a complex variable under Dirac-Pauli representation, introduced the Kaluza "Ghost" coordinate, and turned Navier-Stokes equations ofviscofluid dynamics of homogeneous and incompressible fluid into nonlinear, equation with only a pair of complex unknown functions. In this paper we again combine the complex independent variable except time, and caust it to decrease in a pair to the number of complex independent variables. Lastly, we turn Navier-Stokes equations into classical Burgers equation. The Cole-Hopf transformation join up with Burgers equation and the diffusion equation is Backlund transformation in fact, and the diffusion equation has the general solution as everyone knows. Thus, we obtain the exact solution of Navier-Stokes equations by Backlund transformation.

Differential Equations of Motion for a Variable-Mass Hoionomic System with a Uniformly Rotating Constraint

Zhao Guang-kang

1986, 7(6): 523-531.

Abstract(1747) PDF(657)

Abstract:
In this paper, the differential equations of motion will be established for variable-mass holonomic mechanical systems constrained to the uniform rotation, including the equations in Lagrangeform, Nielsen form and Appell form. The application of these new equations is illustrated with an example.

Perturbation Initial Parameter Method for Solving the Geometrical Nonlinear Problem of Axisymmetrical Shells

Hwang Chien

1986, 7(6): 533-543.

Abstract(1924) PDF(621)

Abstract:
In the previous paper[7], the author presented a System of First-Order Differential Equations for the problem of axisynrm'trically loaded shells of revolution with small elastic. strains and arbitrarily large axial deflections, and a Method of Variable-Characteristic Nondimensionization with a Scale of Load Parameter. On this basis, by taking the weighted root-mean-square deviation of angular deflection from linearity as perturbation parameter, this paper pressents a perturbation system of nondimensional differential equations for the problem, thus transforms the geometrical nonlinear problem into several linear problems. This paper calculates these linear problems by means of the initial parameter method of numerical integration. The numerical results agree quite well with the experiments^[4].

Stress and Displacement of Ring Shells under Centrifugal Force

Chen Shaa-lin, Wang Dai-yu, Zou Ding-qi

1986, 7(6): 545-552.

Abstract(2546) PDF(765)

Abstract:
Using the results of refs. [1] and [2] about the general axial symmetrical problem, this paper calculates the stress and displacement of ring shells under centrifugal force. The solution is given in Fourier series form.In the paper the examples of open ring shells and close ring shells are given respectively.

Eddy Current Analogy of Torsion Problem

Wang Zhen-min, Zhang Ke-xue

1986, 7(6): 553-564.

Abstract(1982) PDF(641)

Abstract:
In as paper, an eddycurrent analogy and a brief sketch of required equipment are presented. Values oftorsional rigidity and shearing stresses of a prismatic bar under free torsion can be obtained experimentally to a high degree of accuracy in an instant with this equipment whether the cross-section is bounded bv a single boundary or multi-connected boundaries. The error is les than two per cent generally, as shown in Table 3. This new analogy can be used extensively to solve various physical problems expressed by Poisson's (or Laplace's) equation with constant boundary condition.

Oscillatory Correlations between External Force and Damping

Zou Feng-wu

1986, 7(6): 565-569.

Abstract(1607) PDF(540)

Abstract:
In this paper we shall examine the correlations among the external froce, variable damping and variable restoring force. Some new results are obtained.