Analysis of Bingham fluid radial flow in smooth fractures

Solutions for radial flow of a Bingham fluid are analyzed in this paper.It aims to eliminate confusions in the literature concerning the plug flow region in different solutions for analysis and design of grouting in rock fractures.The analyses based on the force balance equation reveal that the plug flow region in Bingham radial flow is independent of the fracture radius,and is not a growth function adapted from the solution of one-dimensional(1D)slit flow according to‘similarity’.Based on the shear stress distribution,we analytically proposed that a non-uniform plug flow region cannot exist.The Bingham fluid(grout)penetration and flowrate evolution as functions of grouting time are given using the correct expression for the plug flow region.The radius-independent plug flow region and the presented flowrate evolution equation are also verified numerically.For radial flow,the relative penetration length is equal to the relative width of plug flow region,which is the same as that for 1D channel flow.Discrepancies in analytical solutions for grout penetration and flowrate evolution were also illustrated.The clarification of the plug flow region and evaluation of discrepancies in analytical solutions presented in this work could simplify modeling and design of grouting in rock engineering applications.

A NUMERICAL STUDY OF BINGHAM TURBULENT FLOW IN SUDDEN-EXPANSION STRAIGHT CIRCULAR PIPE

The control equations for the turbulent flow of Bingham fluid are established according to Bingham fluid constitution equation. Pressure field and velocity field are correlted by pressure-correction equation. The numerical computations are performed on Bingham fluid turbulent flow in sudden-expansion straight circular pipe, and the flow mechanisms are discussed.

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

AN IMPLICIT SOLUTION OF BI-PENALTY APPROXIMATION WITH ORTHOGONALITY PROJECTION FOR THE NUMERICAL SIMULATION OF BINGHAM FLUID FLOW

An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial viscosity subjected to the inequality constraint is introduced to approximate the Bingham fluid flow. This approach can effectively simulate the Bingham fluid flow with floating rigid cores or fixing rigid cores.

Bingham型黏性泥石流流体的三维数值模拟

使用CFD软件对泥石流中固体物质以土为主的Bingham型黏性泥石流流体进行了三维数值模拟.首先通过CAD软件AutoCAD和Unigraphics,建立了泥石流沟谷三维地形模型,然后分析了泥石流流体的流变特性,并建立了Bingham计算模型,最后运用CFD软件CFX,对泥石流流体的速度场及压力场的大小与分布进行了三维数值模拟分析,得出了流场的相关力学指标和泥石流速度场及压力场的大小与分布,并实现了泥石流模拟结果的显示.计算结果表明,泥石流流体数值模拟可以在CFD软件环境下完成,计算得出的泥石流流场各种数据有助于更合理地避让和防治泥石流.

精确计算Bingham流体圆管层流压降及速度分布规律的新方法

Bingham(宾汉)模型情况下,多采用通用公式进行圆管层流压降的解析计算,即将Bingham模型本构方程代入粘性流体圆管层流流动通用公式进行计算,仅能得到压降的解析解.新方法结合Bingham流体本构方程与运动方程,建立有关力学平衡方程,并运用代数方程的根式解理论对圆管层流流动时的非线性方程进行求解,可直接求得Bingham流体圆管层流压降及速度流核区半径的解析解,进一步可求得圆管层流速度解析解;Bingham流体圆管层流速度的直接影响因素为流量、塑性粘度和屈服值,研究发现速度流核宽度与屈服值成正比,与流量及塑性粘度成反比,且流核的宽度越大,流核区的速度越小.

Bingham体的连续流和阵性流研究中无量纲参数讨论

本文首先对轴对称管流、二维管流和明渠连续流研究中无量纲参数的选择进行评述 ,通过对这些有分析解的流动的讨论 ,说明采用无量纲表达式的优点、无量纲方法的多样性 ,以及适当选择基本量的重要性。

Bingham流体在定向井眼中层流螺旋流压降公式

正常钻井过程中,环空中上返的钻井液实际上是呈螺旋流运动方式,而不是轴向流,而在定向井、水平井钻进过程中。钻柱由于自身重力的作用常常偏离井眼轴线。致使环空几何流道为偏心环空。为此,将钻井液描绘为Bingham流体,运用柱坐标系下流体质点运动微分方程,结合Bingham流体本构方程,在完成定向井偏心环空中Bingham流体螺旋流层流流动特性研究的基础上,首先建立了Bingham流体在倾斜的同心环空中层流螺旋流流量、压降的计算公式;然后,引入当量间距的概念,简捷地导出了定向并偏心环空中Bingham流体层流螺旋流流量,压降计算公式。为定向井、水平井钻井水力参效设计和计算提供了新的理论基础。

Bingham流体在旋转圆盘上流动的数值解

导出了描述Ｂｉｎｇｈａｍ流体在旋转圆盘上流动的基本方程，用差分方法数值解薄膜厚度分布方程，得到二种类型的厚度分布。数值解分别和计算机磁盘的厚度分布，Ｊｅｎｅｋｈｅ等的实验结果定性一致。

基于Bingham模型的磁流体阻尼器阻尼力研究

介绍了磁流体阻尼器的工作特点,归纳了阻尼力构建使用的不同模型,给出了研究使用磁流体阻尼器的结构示意,指出了阻尼力求解的要点。基于Bingham模型,将磁流体阻尼通道展开为平行平板后,推导了流动模式和剪切模式的磁流体阻尼器的阻尼力公式,构建了相应的阻尼力模型,比较了输入电流差异对阻尼力的影响,并给出了仿真分析的结论。

BINGHAM流体环空管流流动及传热规律研究

结合BINGHAM流体的本构方程、管流运动方程及能量方程 ,推导了BINGHAM流体环空管流速度分布及温度分布。由于BINGHAM流体具有屈服值 ,环空管流流动中会形成流核。流核的宽度与屈服应力成正比 ,与广义压力梯度呈反比。流核中心线偏离环空中心线 ,且偏向环空内侧。环空内外径之比越小 ,相对偏离越远。在其他条件不变的情况下 ,当屈服应力增大时 ,速度分布剖面变得愈扁平。当其他条件不变时 ,流核速度随环空内外径之比减小而增大。流核内温度变化比环空内外侧明显小 ,随屈服应力的增大 ,温度分布剖面愈扁平。

Bingham流体在层流反应器中的停留时间分布

依据Bingham流体在层流反应器中的速度分布，导出流体停留时间分布函数E（θ），F（θ）的数学表达式。

使用GEM求解Bingham流体在非均匀介质中的渗流问题

用GEM(green element method)求解了一维Bingham流体在均匀介质中的渗流问题,并与边界元方法进行了比较,发现两者基本吻合;给出了二维Bingham流体非均匀介质渗流方程使用GEM的求解过程及运算结果,并从Bingham渗流机理方面验证了GEM的可靠性.

基于Polyflow的缓凝砂浆在螺旋槽中的流场模拟

针对缓凝预应力筋包覆装置连续作业的可靠性问题,在包覆试验研究基础上,采用流体力学和流变学理论与计算方法,运用Polyflow等软件,建立了螺旋输送的物理模型、几何模型以及有限元网格模型,结合假设和边界条件,对宾汉姆流体的缓凝砂浆在螺旋槽内的流动和变形进行了计算流体力学(CFD)模拟,并得到了可视化流场。分析结果表明,在不同螺杆转速下,缓凝砂浆在螺槽中出现完全流动状态或"塞流"的固体输送状态,验证了包覆试验现象,同时为机件的优化与设计提供了依据。

Bingham流体偏心环空螺旋流的流函数－轴向速度方程和Newton流体相同条件下的解析解

由偏心环空螺旋流的连续性，引进了流函数，将流体动力学基本方程用流函数来表示。使方程的未知量减少１个；将Ｄｅｓｅａｒｔｅｓ直角坐际变换为双极坐标，使流体动力学基本方程的求解域由偏心环域变换为矩形域，从而建立了双极坐标系下便于解析和数值求解的Ｂｉｎｇｈａｍ流体偏心环空螺旋流的流函数－轴向速度方程及其边界条件、连接条件方程。基于Ｎｅｗｔｏｎ流体是Ｂｉｎｇｈａｍ流体的特殊情形，利用上述的流函数－轴向速度方程及边界条件、连接条件方程，导出了Ｎｅｗｔｏｎ流体偏心环空螺旋流的解析解，绘制了水的偏心环空螺旋流动的流函数和速度分布曲线。分布曲线表明：水在偏心环空螺旋流动时，存在二次流动。

Magnetohydrodynamic approach of non-Newtonian blood flow with magnetic particles in stenosed artery

The non-Newtonian blood flow, together with magnetic particles in a stenosed artery, is studied using a magneto-hydrodynamic approach. The wall slip condition is also considered. Approximate solutions are obtained in series forms under the assumption that the Womersley frequency parameter has small values. Using an integral transform method, analytical solutions for any values of the Womersley parameter are obtained.Numerical simulations are performed using MATHCAD to study the influence of stenosis and magnetic field on the flow parameters. When entering the stenosed area, blood velocity increases slightly, but increases considerably and reaches its maximum value in the stenosis throat. It is concluded that the magnitude of axial velocity varies considerably when the applied magnetic field is strong. The magnitude of maximum fluid velocity is high in the case of weak magnetic fields. This is due to the Lorentz's force that opposes motion of an electrically conducting fluid. The effect of externally transverse magnetic field is to decelerate the flow of blood. The shear stress consistently decreases in the presence of a magnetic field with increasing intensity.

Motion Law of a Sphere in Bingham Fluid with Thixotropy

The thixotropy properties and the motion law of a sphere in the Bingham fluid have been studied. Through observation of the settling motion of a single sphere in the Bingham fluid on the X-ray screen, it has been discovered that the mud in estuaries and along sea bay, and the hyperconcentrated flow all behave as the Bingham fl fluid with thixotropy properties as the large sediment concentration. Through derivation, the theoretical relationship between the yield stress and non-settling maximum sphere supported by the stress for the Bingham fluid has been developed, the equations for calculating the increasing yield stress and the non-settling maximum sphere diameter with the duration at rest of the slurry have been obtained. In consideration of the effect of thixotropy on fluid motion, the Navier-Stokes equation group for the Bingham thixotropy fluid has been developed. Through further study of the flow boundary condition of settling motion of ii single sphere in the Bingham thixotropy fluid, and the solving of the Navier-Stokes equation group, under the small Reynolds number, the theoretical equation of the drag force of the Bingham thixotropy fluid flowing around a sphere has been deduced. The theoretical relationship between drag coefficient and Reynolds number has been derived. By use of the experimental data of rheological test of various slurries measured with viscometer and those of single sphere motion observed on the X-ray screeen, the above equations have been verified. The equations are in good agreement with the experimental data for various slurries.

Bingham流体数值模拟的双罚函数—正交投影的隐式求解方法

本文对Ｂｉｎｇｈａｍ流体给出了双罚函数逼近和正交投影的隐式求解方法·这个方法把Ｂｉｎｇｈａｍ流体处理为承受不等式应力约束的Ｎｅｗｔｏｎ流体的逼近解·有效地模拟了可以出现流动或不流动的“刚性核”的Ｂｉｎｇｈａｍ流体的流动问题·

Bifurcation of Bingham Streamline Topologies in Rectangular Double-Lid-Driven Cavities

Numerical simulation of the bifurcation of Bingham fluid streamline topologies in rectangular double-lid-driven cavity, with varying aspect (height to width) ratio A, is presented. The lids on the top and bottom move at the same speed but in opposite directions so that symmetric flow patterns are generated. Similar to the Newtonian case, bifurcations occur as the aspect ratio decreases. Special to Bingham fluids, the non-Newtonian indicator, Bingham number B, also governs the bifurcation besides the bifurcation parameter A.

蓝宝石光学曲面柱形宽缎带磁流变抛光仿真分析及实验研究

目的针对目前光滑无损伤光学曲面蓝宝石加工成本高、效率低的问题,对加工过程中磁流变抛光缎带进行流体仿真,进而优化抛光轮表面结构。方法设计并提出3种表面结构柱形宽缎带磁流变抛光轮,介绍了磁流变抛光轮加工的基本原理,建立了磁流变抛光垫Bingham流体特性加工仿真模型,分析了3种抛光轮表面结构对工件表面磁通密度模、流场流速、流场压力分布的影响。同时对3种抛光轮的抛光效果进行了实验探究,探究了抛光轮表面结构对材料去除率和抛光后表面粗糙度的影响规律。结果仿真结果表明,抛光轮表面槽型结构具有能增强磁通密度模、增大流体流速和流体压力的特性。实验结果表明,螺旋槽抛光轮的抛光效果最好,在螺旋抛光轮作用下,材料去除率为0.22mg/h,抛光后蓝宝石表面粗糙度为1.08nm。最终抛光轮近壁区总压力和速度的乘积结果与抛光轮实验去除率结果具有较好的一致性。结论槽型结构可以提高抛光液在抛光轮表面的固着效果,影响工件表面流场运动状态,增强工件表面受到抛光垫的作用力。相较于光滑和横条槽抛光轮,螺旋槽抛光轮的抛光效率最高,表面粗糙度最低,可有效提高抛光效果。