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61.
The present analysis relates to the study of the full two-dimensional Brinkman equation representing the fluid flow through porous medium. The steady, incompressible fluid flow, with a negligible gravitational force, is constrained to flow in an infinitely long channel in which the height assumes a series of piecewise constant values. The control volume method is used to solve the Brinkman equation which involves the parameter, =/Da, where Da is the Darcy number and is the ratio of the fluid viscosity f to the effective viscosity
. An analytical study in the fully developed section of the composite channel is presented when the channel is of constant height and composed of several layers of porous media, each of uniform porosity. In the fully developed flow regime the analytical and numerical solutions are graphically indistinguishable. A geometrical configuration involving several discontinuities of channel height, and where the entry and exit sections are layered, is considered and the effect of different permeabilities is demonstrated. Further, numerical investigations are performed to evaluate the behaviour of fluid flow through regions which mathematically model some geological structures of various sizes, positions and permeability, for example a fault or a fracture, where the outlet channel is offset at different levels. The effect on the overall pressure gradient is also considered. 相似文献
62.
A one-dimensional approximate analytical model, which preserves the main features of soil-crop-atmospheric hydrodynamics,
has been suggested for plant roots of low soil-root conductivity ratio (SRCR). The proposed approach involves physically based
concepts, such as mass balance equation, Darcy’s law, and related water uptake and plant transpiration functions. Two main
assumptions have been made to derive the analytical solution: (1) gravitational flow is adopted and (2) the uniform soil moisture
distribution within the root water activity zone is supposed. The mass balance equation in its integral form is solved by
the method of characteristics. This leads to the two functional equations for soil pressure head and root potential, which
can be solved simultaneously by using common software. The model has been further verified against the numerical one. The
model represents a reasonable compromise between the complicated mechanism of unsaturated water flow with root water uptake
(RWU) and still insufficient knowledge of the soil-plant-atmospheric continuum. It is able to account for temporal fluctuations
in root activity zone and provides a relatively simple algorithm for investigation of RWU-mechanism. Besides the theoretical
and applicative importance, this flow model yields water and velocity distributions within soil profile, and, thereby, constitutes
a preliminary step toward solution of contaminant transport problems in vadose zone.
Deceased 相似文献
63.
This paper presents an investigation into salt diffusion in new, fully saturated brick under isothermal conditions. A commonly used experiment methodology, diffusion cell method, is adopted. The analytical and numerical solutions are obtained. The analytical solution is simple and straightforward, which determines temporally salt concentrations in the monitored chamber. It enables us to estimate salt diffusion coefficients in a fast and accurate way. 相似文献
64.
According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed. 相似文献
65.
常微分方程技术及其在固体力学计算中的应用 总被引:2,自引:0,他引:2
常微分方程(ODE——Ordinary Differential Equation)边值问题的最新计算求解技术的迅速发展推出了一批高质高效的通用软件,而工程中大量的ODE问题并非呈现为这些求解器(Solver)所接受的标准形式。然而,运用一些简单的ODE变换技巧可以将大量的不同类型的特殊问题转化为标准形式。本文列举了若干常用的变换技巧,并广泛地应用于各种固体力学问题的计算中,使大量的ODE问题在形式上得到统一,得以用标准的ODE Solver方便有效地求解。 相似文献
66.
B. Hinkelmann 《Rheologica Acta》1982,21(4-5):491-493
From literature some representative equations have been compiled describing the influence of filler on the viscosity of polymer melts. By application of these on the experimental results obtained from GF-SAN it was found that the relative viscosity
R
, i.e. the ratio of the viscosities of the filled and unfilled melt, shows a pronounced dependence on the shear rate
but not on the shear stress. Defining
R
with constant and not with constant
(as it is usually done), an analytical approach is possible independent of
Further the influence of pressure, temperature and filler content on the zero-shear viscosity of filled polymer melts may be expressed by a modified Arrhenius equation. 相似文献
67.
68.
In this paper, the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a
computer algebra-perturbation method. The secular terms in the solution from straightforward expansions are eliminated with
the straining of characteristic, coordinates and the use of the renormalization technique, and the four-term uniformly valid
solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic
solution and the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger
ε (e. g., ε=0.25)
Project supported by the National Natural Science Foundation of China and Shanghai Municiple Natural Science Foundation 相似文献
69.
Potential theory and Stokes' stream function techniques are used to investigate the flow structure around the recirculation system developed by Gvirtzman and Gorelick (1992, 1993), which consists of an extraction well and a gallery (trench) for the recharge of treated water to the aquifer. Analytical formulas are derived for the drawdown, velocity, and stream function for a model in which the extraction well is modeled as a uniformly distributed line sink and the gallery is modeled as a uniformly distributed ring source. Travel times are reported for water particles traveling along the streamlines containing 50 and 90% of the flow for various degrees of well penetration and various radii of the ring source. The travel times along the streamline resulting in the shortest travel time (not necessarily the shortest path) are also reported for various degrees of well penetration and various radii of the ring source. The method completely eliminates the use of numerical finite-difference or finite-element methods and can be used for optimization of technological parameters of this remediation system. 相似文献
70.
滑动界面的球形夹杂问题 总被引:3,自引:0,他引:3
滑动界面对多相介质力学性能的影响日益受到重视.但已有的解析结果往往假定界面是自由滑动的.即假设界面上的剪应力为零,这与大多数实际情况并不相符.本文假定界面上剪应力不为零并满足线弹簧型界面条件,在这一前提下,首次获得了球形夹杂本征应变问题的解析解. 相似文献