边界吸收效应对非定常剪切弥散的影响

采用延迟扩散方程［７，９］描述了具有边界吸收条件下，非定常剪切流动中的剪切弥散特性．给出了记忆函数、中心位移函数的控制方程．特例分析结果表明：所采用的模型方程是合理的；边界吸收效应使得纵向浓度分布具有后倾的趋势．这主要是由于边界吸收使得低速强剪切区浓度减少，剪切弥散贡献减少，从而污染物对流速度高于断面的平均速度．     

带形域内裂纹对SH波散射问题的边界元解

采用边界元法研究含裂纹的带形域各向同性弹性体，裂纹对SH波的散射问题，推导出带形域情况下不同边界条件的各种Green函数，导出了以裂纹张开位移为未知数的边界积分方程，计算出表面散射场和总位移．算例表明，利用所提供的格林函数和边界元格式解答带形域的散射问题比较方便．     

R-函数理论及准Green函数方法在正交各向异性板振动问题中的应用

首次将R-函数理论及准Green函数方法应用于求解固支正交各向异性薄板的自由振动问题。首先引入参数变换,将正交各向异性薄板的自由振动微分方程转化为双调和算子的边值问题,并应用R-函数理论,以解析函数形式描述复杂边界形状;利用问题的基本解和边界方程构造了一个准Green函数,该函数满足了问题的齐次边界条件;通过R-函数理论构造适当的边界方程,消除了积分方程核的奇异性;再采用Green公式将其化为第二类Fredholm积分方程。数值算例表明:该方法减少了理论计算量,精度较高。本文还证明了其优越性和正确性,是一种新型的数学方法。     

弹性力学的一种边界无单元法

首先对移动最小二乘副近法进行了研究，针对其容易形成病态方程的缺点，提出了以带权的正交函数作为基函数的方法－改进的移动最小二乘副近法，改进的移动最小二乘逼近法比原方法计算量小，精度高，且不会形成病态方程组，然后，将弹性力学的边界积分方程方法与改进的移动最小二乘逼近法结合，提出了弹性力学的一种边界无单元法，这种边界无单元法法是边界积分方程的无网格方法，与原有的边界积分方程的无网格方法相比，该方法直接采用节点变量的真实解为基本未知量，是边界积分方程无网格方法的直接解法，更容易引入界条件，且具有更高的精度，最后给出了弹性力学的边界无单元法的数值算例，并与原有的边界积分方程的无网格方法进行了较为详细的比较和讨论。     

弹性中厚扁球壳的边界积分方程解法

1.前言近年来,边界元法已成功地求解了薄壳弯曲等问题。经典薄壳理论采用Kirchhoff假设,忽略了剪切变形,转动惯性效应.此理论计算厚壳,带有小孔洞的壳体会带来较大的误差。本文所讨论的球壳平衡方程中,不仅包含薄膜内力项和弯矩项,而且还反映了横向剪切变形。利用假设位移函数法,推导出其基本解。然后由虚功原理导出一组五个边界积分方程。其中含有五个广义位移(两个转角分量和三个位     

紊动流场中悬浮颗粒分布的随机理论

通过分析固体颗粒在紊动流场中的随机运动,建立了二维流场中垂直于时均流动的方向上颗粒随机位移的概率密度分布函数所满足的方程。由该方程解出的分布函数在一定条件下即相当于颗粒浓度分布函数。运用这一方法研究了[1]、[2]中报道的壁面附近颗粒浓度降低的现象。     

简支梯形底扁球壳弯曲问题的准格林函数方法

以简支梯形底扁球壳的弯曲问题为例,详细阐明了准格林函数方法的思想.即利用问题的基本解和边界方程构造一个准格林函数,这个函数满足了问题的齐次边界条件,采用格林公式将简支扁球壳弯曲问题的控制微分方程化为两个互相耦合的第二类Fredholm积分方程.边界方程有多种选择,在选定一种边界方程的基础上,可以通过建立一个新的边界方程...     

梯度介质半空间Rayleigh面波传播性能研究

对剪切弹性模量沿深度以指数函数变化的非均质半空间，本文用摄动法得到了Rayleigh面波的波函数解答及相速度方程。以不同金属与陶瓷复合而成的几种梯度材料为例，用数值方法求解了相速度方程，给出了相应的波的弥散曲线，结果表明，梯度介质半空间自由表面附近的Rayleigh波通常有两种不同的弥散形式，即正常弥散和非正常弥散。     

颗粒增强复合材料的椭圆形刚性夹杂呈双周期分布模型的反平面问题研究

在遵循复合材料中各夹杂相互影响的重要条件下，构造呈双周期分布且相互影响的椭圆形刚性夹杂模型的复应力函数，采用坐标变换和复变函数的依次保角映射方法，达到满足各个夹杂的边界条件，利用围线积分将求解方程化为线性代数方程，推导出了在无穷远双向均匀剪切，椭圆形刚性夹杂呈双周期分布的界面应力解析表达式，最后的算例分析给出了夹杂的形状对界面应力最大值(应力集中系数)的影响规律，并描绘出了曲线。     

非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非     

On diffusion velocity and the mass conservation equation for components

The mass migration velocity(absolute velocity)of component i in a multicomponent flow is equal to the convection velocity(frame velocity)plus the diffusion velocity(relativevelocity).The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow,the mass migration velocity of component i is(?)(mass-weighted time average velocity).The diffusion velocity(-a)consists of turbulent diffusionvelocity(?)and molecular diffusion velocity(?)(?is the simple time average velocity of component i and a is a certain convection velocity).So,the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mass conservation equation for component i,the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes.In turbulent flow,there could be no diffusion terms,or a turbulent diffusion term only,or both the turbulent and molecular diffusion     

Diffusion of macromolecular solutions in the turbulent boundary layer of a cylindrical pipe

A model is presented describing the changes that occur in the diffusion boundary layer upon injection of a macromolecular solution (PEO) into a cylindrical pipe under turbulent flow conditions (Re 40,000). A shape parameter was introduced to describe the shape of the turbulent plume. The value of this parameter was found to be the same for water and various dilute PEO solutions. The proposed model gives a good approximation at low homogeneous concentrations. x downstream distance from the slot - y normal distance from the wall - R radius of the pipe - C concentration - C _w wall concentration - Q _i flow rate injection - Q _t flow rate - C _j =C _i *Q _i /Q _t equivalent homogeneous polymer concentration - L _tf characteristic length of the diffusion plume - characteristic height of the diffusion plume, i.e. the value ofy at whichC/C _w = 0.5 - thickness of the diffusion boundary layer - x ₀ characteristic distance from the slot, i.e. the value ofx at which/R = 1/2 - ⁺ shape parameter of the diffusion boundary layer - ⁺ —/R nondimensionalized variables - x ⁺ —x/L _tf nondimensionalized variables     

Determination of Salt Diffusion Coefficient in Brick: Analytical Methods

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.     

An analysis of species separation in a thermogravitational column filled with a porous medium

In the past, the analysis of species separation in a thermogravitational column filled with porous media has been based on strong dependency of thermal and molecular diffusion to dispersion. In this work, we suggest an alternative and show that the dispersion effect is negligible for the conditions in a packed hermogravitational column and that compositional dependency of the thermal diffusion should be accounted for.     

Monte Carlo Simulations of Observation Time-Dependent Self-Diffusion in Porous Media Models

Observation time-dependent self-diffusion coefficients can be used to obtain microstructural information of porous media. This paper presents two different kinds of Monte Carlo simulations of the self diffusion process of fluids like water in porous systems, a lattice-free method and a lattice-based method. The results for simple porous media model geometries agree well with each other and with published analytical as well as semi-analytical equations. The use of these equations, which are important for the interpretation of Pulsed Field Gradient-Nuclear Magnetic Resonance (PFG-NMR) time-dependent diffusion data with respect to properties of porous media, is discussed.     

Thermal diffusion of dilute polymer solutions

In this paper diffusion of a dilute solution of elastic dumbbell model macromolecules under non-isothermal conditions is studied. Using the center of mass definition for the local polymer concentration, the diffusive flux contains a thermal diffusion dyadic d _T .  To get some idea of thermal diffusion d _T is evaluated for steady state isothermal conditions. Explicit results are presented for some homogeneous flows. It is shown that if the polymeric number density is defined via the beads (of the dumbbell) – termed n _b – then the diffusive flux j contains , where τ ^c is the intramolecular contribution to the bulk stress. Though the form of the diffusion equation for n _b thus differs from the corresponding one for n, it is shown that for essentially unbounded systems differences between n and n _b are small. Since the results involve the translational diffusion coefficient they can readily be taken over for Rouse coils. Received: 23 September 1997 Accepted: 5 June 1998     

The Use of Fick's Law for Modeling Trace Gas Diffusion in Porous Media

Two models for combined gas-phase diffusion and advection in porous media, the advective-diffusive model (ADM) and the dusty-gas model (DGM), are commonly used. The ADM is based on a simple linear addition of advection calculated by Darcy's law and ordinary diffusion using Fick's law with a porosity–tortuosity–gas saturation multiplier to account for the porous medium. The DGM applies the kinetic theory of gases to the gaseous components and the porous media (or dust) to develop an approach for combined transport due to diffusion and advection that includes porous medium effect. The ADM and Fick's law are considered to be generally inferior for gas diffusion in porous media, and the more mechanistic DGM is preferred. Under trace gas diffusion conditions, Fick's law overpredicts the gas diffusion flux compared to the DGM. The difference between the two models increases as the permeability decreases. In addition, the difference decreases as the pressure increases. At atmospheric pressure, the differences are minor (<10%) for permeabilities down to about 10^–13 m². However, for lower permeabilities, the differences are significant and can approach two orders of magnitude at a permeability of 10^–18 m². In contrast, at a pressure of 100 atm, the maximum difference for a permeability of 10^–18 m² is only about a factor of 2. A molecule–wall tortuosity coefficient based on the DGM is proposed for trace gas diffusion using Fick's law. Comparison of the Knudsen diffusion fluxes has also been conducted. For trace gases heavier than the bulk gas, the ADM mass flux is higher than the DGM. Conversely, for trace gases lighter than the bulk gas, the ADM mass flux is lower than the DGM. Similar to the ordinary diffusion variation, the differences increase as the permeability decreases, and get smaller as the pressure increases. At atmospheric pressure, the differences are small for higher permeabilities (>10^–13 m²) but may increase to about 2.7 for He at lower permeabilities of about 10^–18 m². A modified Klinkenberg factor is suggested to account for differences in the models.     

The MHD properties of ambipolar diffusion and quasi—Ambipolar diffusion in a plasma column

In the present paper, based on the conservation law of mass and momentum for ion and electron, the distribution of velocity, density of ions and electrons along radial direction are solved numerically. Furthermore, the comparison between MHD properties of ambipolar and quasi-ambipolar diffusion is made. The numerical calculation is carried out for argon plasma. The results show that the ion density, ratio of ion and electron velocity at the cathode sheath boundary surface increase with the intensity of magnetic induction, meanwhile, the distance between sheaths decreases as well as the radial velocity of ion and electron at the anode sheath boundary. The ion density varies in accord with experiment qualitatively^[1]. All parameters mentioned above are not sensitive to magnetic field in ambipolar diffusion.