存在填隙幂律流体时圆球间切向作用的近似解

在Reynolds润滑理论的基础上，导出了存在填隙幂律流体时，两刚性圆球有相对切向运动时流体压力的近似方程，并进一步求得了圆球所受阻力矩的近似积分表达式，给出了问题的数值解。结果发现幂流体的幂指数、颗粒间最小间隙以及颗粒的大小都是流体压力和颗粒间切向阻力的重要因素。与Godman等人的牛顿流体下圆球平行于平面缓慢运动时圆球所受阻力以及阻力矩的渐近解作的比较表明，本文的数值解优于渐近解。     

填隙幂率流体下两刚性圆球相对错移时的粘性阻力

湿颗粒离散元模型以两球作用时填隙流体定常流动解为基础,其中切向作用是难点,国外仅有Goldman的牛顿流体渐近解.基于Reynolds润滑理论导出了两刚性球切向错动时填隙幂律流体的压力方程,并利用傅立叶级数展开简化,通过数值解法得到相应的压力分布、黏性阻力及阻力矩.该方程的解较之作者先前对速度场附加假定的结果精确,而当幂指数为1时等价于Goldman的牛顿流体渐近解.     

流体晃动时域双协边界元法分析

利用双协边界元法在时域内对流体晃动问题进行分析,推导出边界积分方程及相应的边界条件。分析过程中考虑流体的粘性,自由面上的动力学条件为法向正应力和切向剪应力为零。固壁面上采用流体质点与固壁质点速度相等的条件。时域的离散采用差分法,并利用时间步迭代,逐步追踪流体自由面,在流体的不断变动的边界上考虑其边界条件。数值结果表明本文的双协边界元法是可行的。     

二阶非牛顿流体蠕流精确解

二阶流体是工业界常见的非牛顿流体,因为其本构关系简单而被广泛采用和研究.逆方法预先假定流场满足某类特定的物理的或几何的特性,从而求出流体运动方程的精确解.本文通过假定平面定常二阶非牛顿流体的涡量场与受到扰动的流函数相等这一特定形式,采用求解非线性微分方程常用的逆方法,推导并获得了平面二阶蠕流流场的精确解,由此容易进一步获得流场的压力.所获得的精确解包含了Poiseuille,简单Couette平行流动以及两相向流体的相互作用等流动.这些精确解为实验,数值以及渐进解的检验提供了借鉴和参考.     

注塑成型三维流动的数值模拟

建立了非等温、粘性、不可压缩、非牛顿流体流动的控制方程。为了避免同时求解耦合的压力场、速度场,本文通过修改Galerkin方法的变分方程,导出了关于压力场的拟Poisson方程,用迭代法独立地求解连续性方程、动量方程,并进行速度一粘度迭代求出最终的压力场、速度场。由于直接使用Galerkin方法求解能量方程容易引起温度场的振荡,本文采用隐式格式及“上风”法离散能量方程,用超松驰迭代法求解温度场的代数方程组。比较了模拟结果与等温管道流动的解析解及法兰的实际注射结果,算例表明本文方法可以预测注射成型流动过程中的一些重要特征。与传统Galerkin方法相比,本文方法可以减少内存,提高数值方法的稳定性。     

流体饱和多孔弹性柱体动力响应的微分求积法

基于多孔介质混合物理论,在小变形的假设下,建立了两相不可压流体饱和多孔介质弹性空间轴对称问题的控制方程。在空间域和时间域内分别采用微分求积方法和二阶向后差分格式来离散控制方程,给出了处理对称轴处奇异性条件的方法,并在空间离散后采用消元法来缩减未知量,提高计算速度。作为应用,分析了流体饱和弹性多孔介质圆柱体的动力响应,考察了所布节点数对数值结果的影响。     

低浓度固液两相流的颗粒相动理学模型

用广义Fokker-Planck扩散模型描述液相湍动对颗粒的挟带作用，用修正的BGK模型描述粒间碰撞效应，建立了封闭的颗粒相PDF输运方程．运用Chapman-Enskog迭代法求得方程的二阶近似解，获得颗粒相脉动速度二阶矩和三阶矩闭合关系．模型与颗粒流模型相容，与液相湍流闭合模型是否相容依赖于扩散模型的具体形式，并据此比较了不同的涡一颗粒作用模型．模型与二维明渠流轻质沙和天然沙试验资料符合很好．表明细小粒径颗粒能够充分跟随水流运动；大粒径颗粒的相间平均速度差和壁面滑移速度明显，近壁区内的颗粒沿流向和垂向脉动强度都可能大于水流，并存在一定程度的颗粒碰撞效应．     

一种滞弹簧耗能的新型离散元滚动阻力模型研究

颗粒间滚动阻力对颗粒体系的稳定性起着重要作用. 在传统的离散元法中, 滚动阻力模型通常由转动弹簧、转动黏壶和摩擦元件表达, 颗粒滚动动能由黏滞力(矩)和摩擦力做功耗散. 由于黏滞力(矩)与滚动速度相关, 临近静止状态的颗粒滚动速度变小, 动能耗散减弱, 传统的离散元模拟得到颗粒由滚动到静止耗费的时间比试验观测的结果要长. 为解决这一问题, 基于摩擦学理论分析了滚动阻力产生的材料滞弹性机理, 将其引入离散元滚动阻力模型, 提出了一种速度无关型动能耗散的滞弹簧, 给出了滞弹簧的弹性恢复力计算公式, 建立了一种新型的离散元滞弹性滚动阻力模型(HDEM). 为验证新型滚动阻力模型的正确性, 通过一个光学物理试验对单个圆形颗粒试件的自由滚动过程进行了测量, 将测量数据与新型的滞弹型离散元模型和传统离散元模型计算结果进行了对比. 结果显示, 基于滞弹性滚动阻力模型HDEM计算结果与试验数据吻合程度更高, 而且模拟得到的颗粒摆动频率更符合试验现象.      

二阶流体薄膜润滑研究

针对二阶流体薄膜润滑在润滑方程中引入二阶流体和弹性变形，在考虑薄膜润滑状态下的非牛顿性和类固体性的基础上，建立了薄膜润滑的粘变数学模型，并针对线接触弹流薄膜润滑进行了数值计算．结果表明，在相同载荷下基于粘变模型计算得到的膜厚同牛顿流体相应的膜厚相比大得多，而粘变薄膜厚度同速度的相关性比牛顿流体的小得多，且粘变薄膜能够承受更大的载荷；所建立的粘变模型适用于薄膜润滑的理论计算．     

基于状态空间理论的功能梯度圆球瞬态热传导分析

基于状态空间理论研究功能梯度圆球的球对称瞬态热传导问题。根据热传导方程和热流密度的定义,取温度场和热流密度为系统的状态向量,通过将圆球分层和在时域内应用差分格式对控制方程进行离散,建立了系统的状态方程,给出了功能梯度圆球瞬态热传导问题的半解析解。算例分析表明:本文解不但结果正确、计算效率高,而且适用于材料参数沿径向任意梯度变化的圆球瞬态热传导分析。     

Viscous forces between two spheres colliding through interstitial power-law fluid

Interaction between two spheres with an interstitial fluid is essential in Discrete Element modeling for simulating the behaviors of ‘wet’ particulate materials. In this paper the interaction between two spheres with an interstitial Power-law fluid was approximately resolved as normal and tangential interactive models respectively, for which the governing equations were simplified on the basis of Reynolds approximation. These equations were then solved analytically together with the boundary conditions to obtain the pressure distributions for each individual model, and eventually solutions of the viscous squeeze force and the tangential viscous resistance were obtained, which provide a set of solutions for implementing into DEM code or other purposes.     

Squeeze flow of a second-order fluid between two parallel disks or two spheres

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds‘ lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neelected.     

On unsteady unidirectional flows of a second grade fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows produced by the sudden application of a constant pressure gradient or by the impulsive motion of one or two boundaries. Exact analytical solutions for these flows are obtained and the results are compared with those of a Newtonian fluid. It is found that the stress at the initial time on the stationary boundary for flows generated by the impulsive motion of a boundary is infinite for a Newtonian fluid and is finite for a second grade fluid. Furthermore, it is shown that initially the stress on the stationary boundary, for flows started from rest by sudden application of a constant pressure gradient is zero for a Newtonian fluid and is not zero for a fluid of second grade. The required time to attain the asymptotic value of a second grade fluid is longer than that for a Newtonian fluid. It should be mentioned that the expressions for the flow properties, such as velocity, obtained by the Laplace transform method are exactly the same as the ones obtained for the Couette and Poiseuille flows and those which are constructed by the Fourier method. The solution of the governing equation for flows such as the flow over a plane wall and the Couette flow is in a series form which is slowly convergent for small values of time. To overcome the difficulty in the calculation of the value of the velocity for small values of time, a practical method is given. The other property of unsteady flows of a second grade fluid is that the no-slip boundary condition is sufficient for unsteady flows, but it is not sufficient for steady flows so that an additional condition is needed. In order to discuss the properties of unsteady unidirectional flows of a second grade fluid, some illustrative examples are given.     

Slow motions of a circular cylinder experiencing slip near a plane wall

A theoretical study is presented for the two-dimensional creeping flow caused by a long circular cylindrical particle translating and rotating in a viscous fluid near a large plane wall parallel to its axis. The fluid is allowed to slip at the surface of the particle. The Stokes equations for the fluid velocity field are solved in the quasi-steady limit using cylindrical bipolar coordinates. Semi-analytical solutions for the drag force and torque acting on the particle by the fluid are obtained for various values of the slip coefficient associated with the particle surface and of the relative separation distance between the particle and the wall. The results indicate that the translation and rotation of the confined cylinder are not coupled with each other. For the motion of a no-slip cylinder near a plane wall, our hydrodynamic drag force and torque results reduce to the closed-form solutions available in the literature. The boundary-corrected drag force and torque acting on the particle decrease with an increase in the slip coefficient for an otherwise specified condition. The plane wall exerts the greatest drag on the particle when its migration occurs normal to it, and the least in the case of motion parallel to it. The enhancement in the hydrodynamic drag force and torque on a translating and rotating particle caused by a nearby plane wall is much more significant for a cylinder than for a sphere.     

Flow of an oldroyd fluid in a circular pipe with time dependent pressure gradient

The problem of pulsating flow superimposed on the steady laminar flow in a circular tube is investigated for the fluid characterized by the Oldroyd's constitutive equations. The governing equations are solved in an exact manner and the solution is obtained in terms of two non-dimensional fluid parameters. Several interesting illustrations are provided comparing the behaviour of Newtonian fluid and Oldroyd fluids regarding the velocity field, sectional mean velocity, surface friction and balance of force. The flow for small and large frequencies of vibration are obtained as special cases. For Oldroyd fluids also the flow is basically parabolic for small frequencies while it possesses a boundary layer character at large frequencies. The solution for second order fluids and Maxwell fluids can be obtained by appropriately choosing the two fluid parameters.     

Analysis of Laminar Flow and Forced Convection Heat Transfer in a Porous Medium

The flow of an incompressible Newtonian fluid confined in a planar geometry with different wall temperatures filled with a homogenous and isotropic porous medium is analyzed in terms of determining the unsteady state and steady state velocities, the temperature and the entropy generation rate as function of the pressure drop, the Darcy number, and the Brinkman number. The one-dimensional approximate equation in the rectangular Cartesian coordinates governing the flow of a Newtonian fluid through porous medium is derived by accounting for the order of magnitude of terms as well as accompanying approximations to the full-blown three-dimensional equations by using scaling arguments. The one-dimensional approximate energy and the entropy equations with the viscous dissipation consisting of the velocity gradient and the square of velocity are derived by following the same procedure used in the derivation of velocity expressions. The one-dimensional approximate equations for the velocity, the temperature, and the entropy generation rate are analytically solved to determine the velocity, the temperature, and the entropy distributions in the saturated porous medium as functions of the effective process parameters. It is found that the pressure drop, the Darcy number, and the Brinkman number affect the temperature distribution in the similar way, and besides the above parameters, the irreversibility distribution ratio also affects the entropy generation rate in the similar way.     

非稳态Couette流动阶段的边界位移与黏性能量耗散

本文研究了牛顿流体非稳态Couette流动阶段的边界位移与流体黏性摩擦能耗.在上边界始终保持静止,下边界以恒定速度或恒定内壁剪切应力突然运动的情况下,建立了Couette非稳态流动的数学模型.求解定解问题,获得流体速度分布函数;通过渐近分析,获得不同边界条件下流动充分发展的临界时间,进而获得非稳态过程中的边界位移量.利用边界剪切应力和位移量的结果,计算非稳态过程中移动平板做功;再结合流体动能增加量,计算得出不同边界条件下非稳态流动阶段流体黏性摩擦能耗.     

Extracting inter-particle forces in opaque granular materials: Beyond photoelasticity

This paper presents the first example of inter-particle force inference in real granular materials using an improved version of the methodology known as the Granular Element Method (GEM). GEM combines experimental imaging techniques with equations governing particle behavior to allow force inference in cohesionless materials with grains of arbitrary shape, texture, and opacity. This novel capability serves as a useful tool for experimentally characterizing granular materials, and provides a new means for investigating force networks. In addition to an experimental example, this paper presents a precise mathematical formulation of the inverse problem involving the governing equations and illustrates solution strategies.     

Influence of Heat and Mass Transfer on Newtonian Biomagnetic Fluid of Blood Flow Through a Tapered Porous Arteries with a Stenosis

Heat and mass transfer effects on Newtonian biomagnetic fluid of blood flow through a tapered porous artery with a stenosis is investigated. Governing equations have been modeled by treating blood as Newtonian biomagnetic fluid. The governing equations are simplified under the assumption of mild stenosis. Exact solutions have been evaluated for velocity, temperature, and concentration profiles. The effects of Newtonian nature of blood on velocity, temperature, concentration profile, wall shear stress, shearing stress at the stenosis throat and impedance of the artery are discussed graphically. Stream lines have been presented in last section of the article.