Asymmetric vibration effect on the flow of a thin layer of a viscoplastic fluid

The gravity field and vibration effect on the flow of a viscoplastic fluid layer along an inclined solid surface is investigated. The rheological properties of the fluid are described using the Williamson equation. The vibrations are shown to have a considerable effect on the fluid layer flow intensity and direction; in particular, they generate a considerable mean fluid flow even in the cases in which the fluid is at rest in the absence of the vibrations.     

Numerical simulation of time‐dependent hydrodynamic removal of a contaminated fluid from a cavity

The time‐dependent hydrodynamic removal of a contaminated fluid from a rectangular cavity on the floor of a duct is analysed numerically. Laminar duct flows are considered for Reynolds numbers of 50 and 1600 where the characteristic length is the duct height. Two cases are considered where: (1) the fluid density in the cavity is the same as that for the duct fluid and (2) the cavity fluid has a higher density than the duct fluid but the two fluids are miscible. The flow is solved by a numerical solution of the time‐dependent Navier–Stokes equations. Attention is focused on the convective transport of contaminated fluid out from the cavity and the effect of duct flow velocity profile on the cleaning process. Passive markers are used in the numerical simulation for the purpose of identifying the contaminated cavity fluid. The results show that the flow patterns in the cavity are influenced by the type of duct flow. From a cleaning perspective, the results suggest that it is easier for the duct flow to penetrate a cavity and to remove contaminated cavity fluid when the duct flow is of the Poiseuille type and the aspect ratio is large. Copyright © 2003 John Wiley & Sons, Ltd.     

Fluid flow and fluid shear stress in canaliculi induced by external mechanical loading and blood pressure oscillation

The paper studies the problem of fluid flow and fluid shear stress in canaliculi when the osteon is subject to external mechanical loading and blood pressure oscillation. The single osteon is modeled as a saturated poroelastic cylinder. Solid skeleton is regarded as a poroelastic transversely isotropic material. To get near-realistic results, both the interstitial fluid and the solid matrix are regarded as compressible. Blood pressure oscillation in the Haverian canal is considered. Using the poroelasticity theory, an analytical solution of the pore fluid pressure is obtained. Assuming the fluid in canaliculi is incompressible, analytical solutions of fluid flow velocity and fluid shear stress with the Navier-Stokes equations of incompressible fluid are obtained. The effect of various parameters on the fluid flow velocity and fluid shear stress is studied.     

Conical and Quasi-Conical Incompressible Fluid Flows

The solution of the problem of fluid flow inside a cone with a small vertex angle is obtained in closed form. The conditions of occurrence of singular separation are considered within the framework of conical flow theory. A class of conical flows in which the vorticity is transported along streamlines of the potential velocity component is detected.Quasi-conical incompressible fluid flow, i.~e. a flow inside and outside an axisymmetric body with power-law generators is defined by analogy with supersonic compressible fluid flow. The conditions under which the effect of vorticity and swirling is significant are found as a result of an inspection analysis. An approximate solution of the problem of fluid flow inside a zero corner is found.A coordinate expansion representing a plane analog of conical flow is constructed in the neighborhood of the separation point of a creeping flow on a smooth surface.     

The combined effects of inlet fluid flow and temperature nonuniformity in cross flow plate-fin compact heat exchanger using finite element method

An analysis of a crossflow plate-fin heat exchanger accouning for the combined effects of inlet fluid flow nonuniformity and temperature nonuniformity on both hot and cold fluid sides is carried out using a Finite Element Model. A mathematical equation is developed to generate different types of fluid flow/temperature maldistribution models considering the possible deviations in inlet fluid flow. Using these fluid flow maldistribution models, the exchanger effectiveness and its deteriorations due to flow/temperature nonuniformity are calculated for entire range of design and operating conditions. It was found that the performance deteriorations are quite significant in some typical applications due to inlet fluid flow/temperature nonuniformity.     

Studies on the law of laminar helical flow of power-law fluid in eccentric annuli

According to the principle of fluid mechanics,the law of laminar,helical flow of power-law fluid in eccentric annuli is studied extensively in this paper.The apparent viscosity,velocities distribution of laminar helical flow of power-law fluid are discussed and calculating methods of flow rate and pressure loss are presented.The factors influencing flow are also analysed.On the basis of theoretical studies some new results of the present paper are compared with the theories of the helical flow of the power-law fluid in concentric annuli.The test verified that theoretical formulas in this article are proper and general.They can be used for calculating hydraulic parameters in drilling engineering.     

裂隙岩体非稳态渗流数值模型及其应用

为解决裂隙岩体非稳态渗流问题, 发展了一种新的数值模型. 对于单裂隙渗 流求解, 其控制方程是基于一定假设的简化Navier-Stokes方程, 数值方法采用有限差分法 和流体体积法. 在裂隙网络中, 交界处渗流可以由专门的控制方程求解. 计算结果表明, 该 数值模型既可以大幅提高非稳态渗流的计算效率, 还可以避免孤立裂隙所带来的影响. 最后, 通过两个工程算例验证该数值模型的适用性.     

A numerical study of bingham turbulent flow in sudden-expansion straight circular pipe

I.IntroductionBinghamfluidisonebranchofnon-Newtonianfluid,suchascrudeparaffinoil,highsediment--ladenwaterflow,highconcentrationmudandthelikewhicharetransportedinpipelinesinmanyindustries,soit'sofgreatsignificancetostudytheflowmechanismsofBinghamfluid.Tsaietal.II]studiedthelinkagebetweenBinghamfluidandpluggedflow.Wangetal.I2]measuredtheturbulencestructureofBinghammud.Mengetal.[3]researchedthekineticenergycorrectionfactorofBinghamfluidinacircularpipe.However,thestudyofBinghamfluidsofarisn't…     

Wall shape effects on multiphase flow in channels

Two-fluid flow is examined analytically and numerically for increased flow rates through a channel with surface roughness or branching or both. The viscosity and density ratios of the fluids are of order unity. There is much concern in terms of applications as well as fluid dynamical phenomena in configurations where one fluid is present only as a thin layer near an outer wall, leaving the other fluid occupying the channel core and part of a viscous wall layer. The interactive dynamics in both regions is studied and numerical and asymptotic analyses are performed. The major situations examined are: the flow to two symmetrically bifurcating daughters and the flow in a single channel over a rough wall, as well as a combination of the two situations. The principal phenomena of interest are conditions for flow reversal, the presence of upstream influence and the trajectories of the injected fluid as the density or viscosity ratio varies. Special relatively thin or thinning wall layers are produced when the core fluid viscosity increases or when the fluid travels downstream into a daughter vessel.     

一种骨小管中液体流动产生的流量及切应力模型

骨组织受力变形后其内部液体就会流动,同时在其微观结构——骨单元壁中扩散,并进一步产生一系列与骨液流动相关的物理效应,如流体剪切应力、流动电位等,这些物理效应被细胞感知并做出破骨或成骨等反应,来使骨适应外部载荷环境.鉴于骨组织产生的内部液体流动很难实验测定,理论模拟是目前的主要研究手段.基于骨单元的多孔弹性性质建立了骨小管内部液体的流动模型,该模型将骨单元所受的外部载荷与骨小管内部液体的压力、流速、流量和切应力联系起来,并进一步可以研究其力传导与力电传导机制.骨小管模型的建立分别基于中空和考虑哈弗液体的骨单元模型,并考虑了骨单元外壁的弹性约束和刚性位移约束两种边界条件.最终得到骨单元在外部轴向载荷作用下,骨小管内部液体的流量及流体切应力的解析解.结果表明:骨小管中的液体流量与流体切应力都正比于应变载荷幅值和频率,并由载荷的应变率决定.因此应变率可以作为控制流量和流体切应力的一种生理载荷因素.流量随着骨小管半径的增大而非线性增大,而流体切应力则随着骨小管半径的增大而线性增大.此外,在相同的载荷下,含哈弗液体的骨单元的模型中,骨小管中液体的流量和切应力均大于中空骨单元模型.     

Analytic solution for flow of Sisko fluid through a porous medium

This paper presents the analytic solution for flow of a magnetohydrodynamic (MHD) Sisko fluid through a porous medium. The non-linear flow problem in a porous medium is formulated by introducing the modified Darcy’s law for Sisko fluid to discuss the flow in a porous medium. The analytic solutions are obtained using homotopy analysis method (HAM). The obtained analytic solutions are explicitly expressed by the recurrence relations and can give results for all the appropriate values of material parameters of the examined fluid. Moreover, the well-known solutions for a Newtonian fluid in non-porous and porous medium are the limiting cases of our solutions.     

Permanent Waves in Slow Free-Surface Flow of a Herschel–Bulkley fluid

Unsteady flow of a viscoplastic fluid on an inclined plane is examined. The fluid is described by the three-parameter Herschel–Bulkley constitutive equation. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid and steady uniform motion. A permanent wave solution is then derived, and the relation between wave speed and flow depth is discussed. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of flows propagating up a slope. The speed of permanent waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index.     

An investigation on internal thermal flow of non-Newtonian fluid

In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the fiow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied, For the flow into mould cavity the constitutive equation of power-law fluid is used as a rheological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid fiow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting differen     

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.     

Sphere settling in an aging yield stress fluid: link between the induced flows and the rheological behavior

The flow pattern induced by the settling of a non-Brownian sphere in a fluid depends on the rheological properties of that fluid. For instance, at small Reynolds numbers, the pattern presents a fore–aft symmetry in a Newtonian fluid, whereas, in some viscoelastic polymer solutions, it can exhibit a negative wake, i.e., an upward flow in the sphere’s wake. This study is an experimental work on the settling of a sphere in a suspension of a synthetic colloidal clay, laponite. The fluid is a yield stress fluid that ages, i.e., whose rheological properties evolve over time. We show that the settling velocity of a given sphere, as well as the induced flow pattern, are strongly modified as the fluid ages. In particular, the flow pattern asymmetry increases with the age of the fluid, and a negative wake eventually forms. We relate those modifications to rheological measurements and suggest, in line with works dealing with polymer solutions, that it is the increase in the fluid viscoelasticity that is responsible for the formation of a negative wake. The flow field measurements are also compared with flow-induced birefringence measurements, and we show that very slow relaxation processes are involved in the sphere settling.     

Numerical Investigation of Magnetic Nanoparticles Distribution Inside a Cylindrical Porous Tumor Considering the Influences of Interstitial Fluid Flow

A numerical simulation of interstitial fluid flow and blood flow and diffusion of magnetic nanoparticles (MNPs) are developed, based on the governing equations for the fluid flow, i.e., the continuity and momentum and mass diffusion equations, to a tissue containing two-dimensional cylindrical tumor. The tumor is assumed to be rigid porous media with a necrotic core, interstitial fluid and two capillaries with arterial pressure input and venous pressure output. Blood flow through the capillaries and interstitial fluid flow in tumor tissues are carried by extended Poiseuille’s law and Darcy’s law, respectively. Transvascular flows are also described using Starling’s law. MNPs diffuse by interstitial fluid flow in tumor. The finite difference method has been used to simulate interstitial fluid pressure and velocity, blood pressure and velocity and diffusion of MNPs injected inside a biological tissue during magnetic fluid hyperthermia (MFH). Results show that the interstitial pressure has a maximum value at the center of the tumor and decreases toward the first capillary. The reduction continues between two capillaries, and interstitial pressure finally decreases in direction of the tumor perimeter. This study also shows that decreasing in intercapillary distance may cause a decrease in interstitial pressure. Furthermore, multi-site injection of nanoparticles has better effect on MFH.     

Nonlinear fluid flow laws for orthotropic porous media

Nonlinear fluid flow laws for orthotropic porous media are written in invariant tensor form. As usual in the theory of fluid flow through porous media [1, 2], the equations contain the flow velocity up to the second power. Expressions that determine the nonlinear resistances to fluid flow are presented and it is shown that, on going over from linear to nonlinear flow laws, the asymmetry effect may manifest itself, that is, the fluid flow characteristics may differ along the same straight line in the positive and negative directions. It is shown that, as compared with the linear fluid flow law for orthotropic media when for three symmetry groups a single flow law is sufficient, in nonlinear laws the anisotropy manifestations are much more variable and each symmetry group must be described by specific equations. A system of laboratory measurements for finding the nonlinear flow characteristics for orthotropic porous media is considered.     

Stokes Plane-Parallel Vortex Systems in Channels

Plane-parallel vortex systems in a viscous incompressible fluid in channels with parallel walls and in a corner with no-slip conditions on the walls are investigated on the basis of exact solutions of the biharmonic equation. It is found that separation zones and paired (joined) vortices are formed when the fluid flows through these channels and the fluid flow path between these vortex formations is traced. The flow structures are considered in the region of intrusion of the Poiseuille or Hamel flow into the zone of predominance of the intense vortex formations and for outflow of the fluid from this zone.     

Combined effects of rotation and translation on a MHD flow due to compressible viscous fluid

Summary The modification of an axi-symmetric viscous flow due to a relative rotation of a disk or fluid by a translation of the boundary are studied. The fluid is taken to be compressible and electrically conducting. The equations governing the motion are solved iteratively through a central-difference scheme. The effect of an axial magnetic field and disk temperature on the flow and heat transfer are included in the present analysis. The translation of the disk or fluid generates a velocity field at each plane parallel to the disk (secondary flow). The cartesian components of the velocity due to the secondary flow are oscillatory in nature when a rigid body rotation of the free stream along with a translation of the disk is considered. The magnetic field damps out the velocity field, and reduces the thickness of the boundary layer. The cross component of wall shear due to secondary flow acts in a direction opposite to the rotation of the disk or fluid for all cases of the motion. The rise in disk temperature produces an increment in the magnitude of the wall shear associated with the secondary flow.     

Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube

The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability, and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal to the yield stress of the fluid.