Motion Of Fluid Particles Research Articles

Computed Effects of Rotor-Induced Swirl on Brush Seal Performance—Part 1: Leakage Analysis

This paper presents a numerical study of the effects of rotor induced swirl velocity on the performance of brush seals. Such effects have been studied experimentally by Ferguson (1988), but this paper is apparently the first to obtain an enhanced understanding from the detailed flowfield distributions. The analysis involves the solution of the full Navier-Stokes equations in a two-dimensional, idealized configuration using a strongly conservative finite volume method developed by the authors in conjunction with the QUICK differencing scheme. The present computations have demonstrated excellent agreement with measurements for the similar flow across tube banks. An enhanced understanding of decreasing leakage with increasing shaft speed was obtained in terms of the various flow features. Specifically, the cause and effect relationship of certain interactions between the axial and tangential flows was identified. Computer-drawn pathlines show how increased leakage resistance results from large rotor-induced lateral motion of leakage fluid particles. In addition, a first-order streamwise periodic boundary condition treatment which facilitates numerical convergence has been proposed for essentially any flow which is streamwise periodic in two orthogonal directions.

Dielectrophoresis of a deformable fluid particle in a nonuniform electric field.

In nonuniform electric fields, the dielectrophoretic behavior and the interface shape of uncharged fluid particles freely suspended in an immiscible fluid may be significantly influenced by the induced electrohydrodynamic flow. This work presents a theoretical investigation of the primary effects of electrohydrodynamic flow associated with the dielectrophoresis of a deformable fluid particle with a leaky dielectric model. The electrohydrodynamic flow is shown to either enhance or hinder the dielectrophoretic motion of fluid particles. A variety of shapes of deformable fluid particles are predicted. \textcopyright{} 1996 The American Physical Society.

Diffusion of Copper in Polymer During the Metallization of PET

Abstract Thin Cu metal layers were deposited on semicrystalline poly(ethylene terephthalate) PET films by thermal evaporation. RBS measurements revealed that, under our metallization conditions, the Cu layers are buried into the polymer bulk. This has also been confirmed by ToF-SIMS measurements which reveal that some PET remain at the top surface. Since the formation of a diffuse interface has important consequences on the adhesive properties, the Cu diffusion was investigated systematically by means of RBS. After metallization, the samples were annealed under vacuum for times varying between 0 and 120 hours at 80, 90, 100, 120 and 140°C, slightly above the glass transition of the PET (67°C). Since the diffusion profiles exhibit a behavior in accordance with Fick's laws, the diffusion coefficients were evaluted. The results are in agreement with a diffusion model based on the Brownian motion of particles in a viscous fluid.

On the Use of Computational Fluid Dynamics for Simulating Flow and Particle Deposition in the Human Respiratory Tract

Computational fluid dynamics (CFD) can produce erroneous results if not used with adequate thought to several issues, some of which are discussed in the present article. Some of these issues are associated with modeling the physics, particularly the turbulence that occurs in the upper airways. For determining the location of deposition of inhaled aerosols, physical models of particle motion must also be specified and various issues associated with such models should be considered. Numerical modeling issues, including grid resolution and numerical boundary condition effects, can also profoundly affect a numerical simulation. The purpose of the present article is to highlight the importance of some of these issues in the context of modeling the fluid dynamics and particle motion in the human respiratory tract, especially for those researchers whose background is not in a discipline normally associated with CFD.

Bifurcations and pattern formation in a two-dimensional Navier-Stokes fluid.

We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).

Orbital instability and chaos in the Stokes flow between two eccentric cylinders

The motion of fluid particles due to the slow flow between two eccentric cylinders rotating alternately is examined experimentally and numerically. In ‘return experiments’ composed of alternate rotations of the cylinders by N periods and their time reversal, the dye starting from one region almost returns to its initial position even for large N, whereas the deviation of the dye starting from the other region from its initial position is large and rapidly increases with N. These two regions correspond to the regular and chaotic regions in the numerically computed Poincaré plot for the alternate rotations of the cylinders. These results suggest the significance of orbital instability in the chaotic region in the experiments with unavoidable inperfections. A part of the experimental results can be explained qualitatively using a loccl Lyapunov exponent (L.L.E.) for finite evolution time. The importance of the stagnation point of the flow due to the rotation of a cylinder in the orbital instability is also suggested using the L.L.E.

Settling and asymptotic motion of aerosol particles in a cellular flow field

This paper presents a proof that given a dilute concentration of aerosol particles in an infinite, periodic, cellular flow field, arbitrarily small inertial effects are sufficient to induce almost all particles to settle. It is shown that when inertia is taken as a small parameter, the equations of particle motion admit a slow manifold that is globally attracting. The proof proceeds by analyzing the motion on this slow manifold, wherein the flow is a small perturbation of the equation governing the motion of fluid particles. The perturbation is supplied by the inertia, which here occurs as a regular parameter. Further, it is shown that settling particles approach a finite number of attracting periodic paths. The structure of the set of attracting paths, including the nature of possible bifurcations of these paths and the resulting stability changes, is examined via a symmetric one-dimensional map derived from the flow.

Adaptive Singularity Method for Stokes Flow Past Particles

We implement the method of fundamental solutions to compute Stokes flow past or due to the motion of solid particles. The flow is represented in terms of a collection of vectorial fundamental solutions to the governing equations including the point force, the potential dipole, and the couplet. The locations and strengths of the fundamental solutions are computed by minimizing a functional so as to satisfy the required boundary conditions with highest accuracy. The method is applied to compute flow past or due to the motion of spherical and spheroidal particles in an infinite fluid and in a semi-infinite fluid bounded by a plane wall. The computed locations and strengths of the singularities are compared with those corresponding to exact discrete and continuous singularity representations, and the computed force and torque exerted on the particles are compared with exact values available from analytical solutions. It is found that the method yields excellent accuracy with a moderate number of singularities in an extended range of particle aspect ratios up to ten, and for ratios of the particle center to wall separation h and particle radius a as low as h/a = 1.05. The computed singularity solutions are used to establish generalized Faxen laws for the force and torque.

Influence of the surface viscosity on the drag and torque coefficients of a solid particle in a thin liquid layer

The present paper provides a short literature survey of the treatment of particle motion in fluids as a basis of the author's own work in this field. The work relates to the motion of a small solid particle inside a thin liquid film. The particle motion is treated numerically to provide information of interest to thin film liquid coating. The numerical computations yield information on the local velocity and pressure distributions, but also integral information expressed in drag and torque coefficients. The computations are carried out for stationary flows of low Reynolds and capillary numbers and results are presented for different values of surface dilatation and shear viscosities. Translational and rotational motions of the particle are considered by integrating the resultant second-order partial differential equation with an alternating direct implicit method. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid particle in the viscous liquid layer when the radius of the particle is of the same order of magnitude as the thickness of the liquid film or when the particle is close to the liquid-gas interface.

115 水平壁面内のくぼみ列内部および開口部領域の流れの可視化

Flow Visualization on inside and opening region in an Open Cavity Array is experimentally studied under the following conditions: the range of the depth-to-width ratio and Reynolds number are from 0.1 to 3.0 and from 2.0×103 to 5.5×104 repectively. Flow observation is studied by means of the following two technique: one is the scattering method of alminum powder on the water surface of the cavity array model, the other is dye tracer technique in the closed vertical model of the side wall. Flow pattern on inside region of the cavity array is influenced both the depth-to-width ratio and Reynolds number. Flow visualization on the opening region of the open cavity array by tracer technique is as follow: the movement of fluid particles is unsteady with chaotic movement on the different direction superimposed on the external main stream.

Transport coefficients and Lyapunov exponents

After introducing the viscosity of a fluid macroscopically and microscopically as well as the Lyapunov exponents of the fluid, the SLLOD equations of motion with a Gaussian thermostat and Lees-Edwards boundary conditions for the motion of particles in a sheared fluid in a nonequilibrium stationary state are discussed. An explicit expression, due to Posch and Hoover, for the viscosity is then derived in terms of the sum of all Lyapunov exponents, illustrating the direct connection between irreversible entropy production (due to viscous heating) and phase space contraction. A symmetry of the Lyapunov spectrum allows this expression to be reduced to a simple relation between the viscosity and the two maximal Lyapunov exponents of the fluid in the stationary state. A numerical check of this relation for fluids consisting of 108 and 864 particles is presented. Finally, similar relations for other transport coefficients and the connection with other work are discussed.

Predictions of drag and shape of a fluid particle in creeping flow by upper bound approach

Creeping motion of incompressible Newtonian media past axisymmetric fluid and rigid particles has been analysed using the upper bound approach. The variational functional for the problem is identified as the minimum drag principle, in the absence of work against the interfacial tension forces. Extensive theoretical predictions of drag and shape deformation for bubbles rising in liquids and drops moving in another liquid or gas, are obtained by suitable choices of viscosity and density ratios and for wide ranges of kinematic parameters, namely, the Froude number and Weber number. Comparisons are presented with other theoretical analyses available in the literature for the limiting cases.

Numerical nonisothermal flow analysis of non‐Newtonian fluid in a nonintermeshing counter‐rotating twin screw extruder

AbstractA simulation technique for nonisothermal flow analysis of non‐Newtonian fluid in a nonintermeshing counter‐rotating twin screw extruder was developed by modifying the flow analysis network (FAN) method. The local shear viscosity in the flow field was calculated by an iteration method combing the three types of mean shear rate functions. The modified Cross model and an Arrhenius‐type function for temperature dependence were also introduced. Streamlines in the flow field are represented by computing the movements of fluid particles based on the flux fields. The computed residence time from the streamlines led us to solve the energy equation by replacing the coordinate system. The profiles of pressure, shear rate, shear viscosity, temperature, and residence time were simulated. The influence of operating and geometrical parameters on the screw characteristics are discussed. Further, residence time distribution (RTD), strain distribution function (SDF), and interfacial area growth are predicted from the computation of streamlines to analyze the mixing capabilities of the extruder.

Resonant and chaotic advection in a curved pipe

The Lagrangian description is used to study the motion of fluid particles in a curved pipe, when laminar fully developed flow is generated by an oscillatory longitudinal pressure gradient. The (viscous) fluid is assumed to be incompressible, so that the transverse motion is governed by a Hamiltonian dynamical system, which is near-integrable when the flow is quasi-steady. Islands and chaotic regions are seen in a Poincaré section, in accordance wtih Kolmogorov-Arnol'd-Moser (KAM) theory. Resonance between the longitudinal and transverse motion causes ballistic longitudinal transport of particles whose trajectories lie on KAM tori within certain islands. Intermittent longitudinal transport is seen in the chaotic regions bordering such islands, as trajectories are trapped by cantori in the vicinity of both resonant and non-resonant KAM tori. The interaction of advection and molecular diffusion is discussed. When the Péclet number is very large, particles are transported longitudinally in an intermittent manner which resembles transport in chaotic regions. Here the trapping of trajectories is caused by islands, not cantori.

Hamiltonian formulation of the equations of streamlines in three-dimensional steady flows

It is well known that the equations of motion of a fluid particle in a two-dimensional flow can be written in the canonical form with the stream function playing the role of the Hamiltonian. Here we extend this canonical formalism to three-dimensional steady flows. We show how the methods of the theory of Hamiltonian systems can be successfully used to investigate the advection of a passive particle. As an example of the perturbed closed streamline flow we consider a rigid rotation with added small quadratic velocity field and explain the structure of streamlines by averaging the corresponding Hamiltonian. We also show how the Hamiltonian formulation can be used to find the invariants of the fluid particle motion which are then used for non-canonical averaging.

Chaotic Motion of Fluid Particles Due to the Alternate Rotations of Two Eccentric Cylinders

Chaotic or regular motions of the fluid particles by the Stokes flow between two eccentric cylinders counter rotating alternately and of radius ratio 0.3 are investigated numerically and analytically. We examine the dependence of the motions on eccentricity e , focusing on an equilibrium point of the Poincare map of the particle position after every rotations. If both of the winding numbers of the cylinders are small, the area of the chaotic region is small and increases monotonically with e , whereas when at least one of them is not small, this area is relatively large and takes a maximum at a certain e . In the latter case, within a certain region of the winding numbers, the bifurcation of the equilibrium point from elliptic to hyperbolic type occurs at another value of e = e b , resulting in the increase in the area for e around e b . A perturbation analysis can roughly predict this region and the value of e b .

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation

This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.

Motion of fluid particles and stretching of line elements of an ideal fluid

Two-dimensional motion of fluid particles in an ideal fluid is studied in the framework of the differential geometry of a group of diffeomorphisms. First, the influence of small perturbations to the initial velocity field is investigated on the average distance of fluid particles between the original and the perturbed velocity fields. It is found that departure of the average distance from a linear time evolution is determined by the sectional curvature. Some illustrative examples are presented to show influence of the sign of the curvature. Next, stretching of line elements in turbulent flows is investigated, where the curvature is found to be negative on the average in this problem. This gives evidence of the exponential growth of stretching, which is obtained by an approach from a new direction. Numerical calculations have been carried out for comparison with these results. The ratio of the numerically obtained stretching exponent to the theoretical one is found to be around 1.5.

Non-isothermal and Non-Newtonian Flow Analysis for the Non-intermeshing Counter-rotating Twin Screw Extruder Based on FAN Method

On the basis of the flow analysis network (FAN) method, a two-dimensional simulation for the non-isothermal flow of non-Newtonian fluid was developed and applied to the flow of polypropylene (PP) melt in a non-intermeshing counter-rotating twin screw extruder. The constitutive model for the PP melt we used was the Cross model with an Arrhenius-type function for temperature dependence. Calculating the movement of fluid particles permitted us to represent not only streamlines them-selves but internal residence time profiles in the flow field. Then, the energy equation was able to be successfully solved along the streamlines after replacing it in the convected coordinates.Taking into accunt back flow and leakage flow, flux fields and streamlines in the flow field clearly showed the difference of conditions between staggered and matched screw flight configurations. The profiles of pressure, shear rate, shear viscosity, temperature and residence time also told us the mechanism of this complicating flow in the extruder. The non-isothermal flow of non-Newtonian fluid in the extruder was differentiated from the isothermal flow of non-Newtonian fluid and the isothermal flow of Newtonian fluid in terms of screw characteristics. The effects of several geometrical and operating conditions, including staggering angle, helix angle of screw flight, screw rotational speed and set temperature, on the screw characteristics were also investigated. Furthermore, some simulated results were compared with experiments using a model twin screw extruder and they demonstrated good agreements in pressure profiles and screw characteristics.

Nonstirring of an inviscid fluid by a point vortex in a rectangle

Numerical evidence is presented that two-dimensional motion of a large region of incompressible, inviscid fluid due to the motion of a point vortex in a rectangular container leaves does not stir certain finite regions. Such regions are formed by means of the Poincaré mapping in the regular domain for a nonintegrable Hamiltonian system of fluid particle motion.