Variation of fiber orientation in turbulent flow inside a planar contraction with different shapes

In this study, we have investigated the influence of shape of planar contractions on the orientation distribution of stiff fibers suspended in turbulent flow. To do this, we have employed a model for the orientational diffusion coefficient based on the data obtained by high-speed imaging of suspension flow at the centerline of a contraction with flat walls. This orientational diffusion coefficient depends only on the contraction ratio and turbulence intensity. Our measurements show that the turbulence intensity decays exponentially independent of the contraction angle. This implies that the turbulence variation in the contraction is independent of the shape, consistent with the results by the rapid distortion theory and the experimental results of axisymmetric contractions. In order to determine the orientation anisotropy, we have solved a Fokker–Planck type equation governing the orientation distribution of fibers in turbulent flow. Although the turbulence variation and the orientational diffusion are independent of the contraction shape, the results show that the variation of the orientation anisotropy is dependent on shape. This can be explained by the variation of the rotational Péclet number, Pe_r, inside the contractions. This quantity is a measure of the importance of the mean rate of the strain relative to the orientational diffusion. We have shown that when Pe_r < 10 turbulence can significantly influence the evolution of the orientation anisotropy. Since in contractions with identical inlet conditions the streamwise position where Pe_r = 10 depends on the shape, the orientation anisotropy is dependent on the variation of rate of strain in a given contraction. We demonstrate the shape effect by considering contraction with flat walls as well as three contractions with different mean rate of strain variation.     

The effect of two-way coupling and inter-particle collisions on turbulence modulation in a vertical channel flow

Turbulence modulation due to its interaction with dispersed solid particles in a downward fully developed channel flow was studied. The Eulerian framework was used for the gas-phase, whereas the Lagrangian approach was used for the particle-phase. The steady-state equations of conservation of mass and momentum were used for the gas-phase, and the effect of turbulence on the flow-field was included via the standard k–ε model. The particle equation of motion included the drag, the Saffman lift and the gravity forces. Turbulence dispersion effect on the particles was simulated as a continuous Gaussian random field. The effects of particles on the flow were modeled by appropriate source terms in the momentum, k and ε equations. Particle–particle collisions and particle–wall collisions were accounted for in these simulations. Gas-phase velocities and turbulence kinetic energy in the presence of 2–100% mass loadings of two particle classes (50 μm glass and 70 μm copper) were evaluated, and the results were compared with the available experimental data and earlier numerical results. The simulation results showed that when the inter-particle collisions were important and was included in the computational model, the fluid turbulence was attenuated. The level of turbulence attenuation increased with particle mass loading, particle Stokes number, and the distance from the wall. When the inter-particle collisions were negligible and/or was neglected in the model, the fluid turbulence was augmented for the range of particle sizes considered.     

Dynamics of short fiber suspensions in bounded shear flow

We have studied the dynamics of non-colloidal short fiber suspensions in bounded shear flow using the Stokesian dynamics simulation. Such particles make up the microstructure of many suspensions for which the macroscopic dynamics are not well understood. The effect of wall on the fiber dynamics is the main focus of this work. For a single fiber undergoing simple shear flow between plane parallel walls the period of rotation was compared with the Jeffrey’s orbit. A fiber placed close to the wall shows significant deviation from Jeffrey’s orbit. The fiber moving near a solid wall in bounded shear flow follows a pole-vaulting motion, and its centroid location from the wall is also periodic. Simulations were also carried out to study the effect of fiber–fiber interactions on the viscosity of concentrated suspensions.     

Numerical prediction of fiber motion in a branching channel flow of fiber suspensions

Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.The project supported by the National Natural Science Foundation of China (10372090) and Doctoral Program of Higher Education in China (20030335001)The English text was polished by Ron Marshall     

Characteristics of fiber suspension flow in a rectangular channel

Velocity profile of fiber suspension flow in a rectangular channel is measured by pulsed ultrasonic Doppler velocimetry (PUDV), and the effect of fiber concentration and Reynolds number on the shape of the velocity profile is investigated. Five types of flow behavior are observed when fiber concentration increases or flow rate decreases progressively. The turbulent velocity profiles of fiber suspension can be described by a correlation with fiber concentration, nl³, and Reynolds number, Re as the main parameters. The presence of fiber in the suspension will reduce the turbulence intensity and thus reduce the turbulent momentum transfer. On the other hand, fibers in the suspension have the tendency to form fiber networks, which will increase the momentum transfer. The relative contribution of these two types of momentum flux will determine the final shape of the velocity profile.     

Flexible fiber motion in the flow field of a cylinder

In the forming section of a papermachine, a water suspension of pulp fibers is drained through a forming fabric. One canonical test case that incorporates some key features of this process is that which studies the interaction of a single fiber with a cylinder. This article concerns numerical simulations of this interaction.     

EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

IntroductionFlowoffibresuspensionshasbeenveryfamiliarinmanyindustrialfields.Fibreadditivesplayanimportantroleindragreductioninmanytypesofflow[1- 3].Inthesuspensions,somebehavioroftheflowmaybealteredbythefibres.Oneoftheimportantexamplesisthehydrodynamicsta…     

An experimental study of flow-induced fiber orientation and concentration distributions in a concentrated suspension flow through a slit channel containing a cylinder

Flow-induced fiber orientation and concentration distributions were measured in a concentrated fiber suspension (CFS) and a dilute one (DFS). The channel has a thin slit geometry containing a circular cylinder. In the previous work, many researchers have qualitatively studied fiber orientation and concentration distributions in injection-molded products of fiber-reinforced plastics. In the present work, however, they are quantitatively estimated by direct observation of fibers in the concentrated suspension flow. For the CFS, some fibers rotate in an expansion part between the channel wall and the circular cylinder, and the fiber orientation becomes almost random state. On the other hand, fibers are perfectly aligned along the flow direction owing to the elongational flow near the centerline downstream of the cylinder. The fiber concentration has a flat distribution except near the channel wall and the centerline. For the DFS a minimum in the fiber concentration distribution was clearly observed on the centerline, and two peaks beside the centerline and near the channel wall. This characteristic distribution is caused by the fiber-wall and fiber-cylinder interactions. It is found that the obstacle such as the circular cylinder in the channel significantly affects the fiber orientation downstream of the obstacle for the CFD, while it affects the fiber concentration distribution for the DFS.     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

This is the second part of a study examining the mechanical properties and capillary flow of fiber suspensions in Newtonian fluids and in polymer solutions. In part I results for the viscous and elastic properties of the fiber suspensions were presented and it was shown that the fiber suspensions exhibited normal stresses in Newtonian as well as in viscoelastic suspending media. It was thus expected that circulating secondary flows would occur near the entrance to a capillary. Four types of fillers (glass, carbon, nylon and vinylon fibers) suspended in glycerin, HEC solutions and Separan solutions were investigated. The entrance flow patterns were visualized and the pressure fluctuations measured. The visualization enabled the eddies occurring in the fiber suspensions in Newtonian fluids to be analysed and classified into two tpyes. The results from the flow visualization were correlated with the pressure fluctuations. Empirical equations for the tube length correction factor due to the elasticity were obtained.     

Creeping flow of viscoplastic materials through a planar expansion followed by a contraction

In this work, the creeping flow of a viscoplastic fluid through a planar channel with an expansion followed by a contraction is analyzed numerically. The solution of the conservation equations of mass and momentum is obtained via the finite volume method. In order to model the non-Newtonian behavior of the fluid, it was used the generalized Newtonian fluid constitutive equation. The viscosity function was the one proposed by Souza Mendes and Dutra [Souza Mendes, P.R., Dutra, E.S.S., 2004. Viscosity function for yield-stress liquids. Appl. Rheol. 14, 296–302]. The yielded and unyielded regions are obtained for several combinations of rheological parameters. The influence of these parameters on pressure drop through the cavity is also obtained and analyzed.     

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expression, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.     

research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.     

NMR flow imaging of Newtonian liquids and a concentrated suspension through an axisymmetric sudden contraction

Using nuclear magnetic resonance (NMR) flow imaging to examine fluid motions at constant velocities or flows that change relatively slowly has been well-documented in the literature. Application of this technique to accelerative flows, on the other hand, has been limited. This study reports the use of an NMR flow imaging method, for which acceleration is not explicitly compensated in the NMR pulse sequence, to measure axial and radial fluid motions during flow through an axisymmetric sudden contraction. In this flow geometry, both velocity and acceleration are spatially dependent. The flow contraction ratio was 2:1. The method was first applied to examine Newtonian liquids at low and high Reynolds numbers under laminar flow conditions. The measured axial and radial velocity profiles, without accounting for acceleration effects in the data analysis, across the contraction are in excellent qualitative agreement with previous experimental data and theoretical calculations reported in the literature. Quantitative comparison of the axial and radial velocities with numerical results indicates that the maximum error from acceleration effects is about 10%. The method has also been used to examine the flow of a concentrated suspension (50% by volume of solid particles) through the contraction. The flow kinematics of the suspension at creeping flow conditions appear to mimic those of the Newtonian fluid with some slight differences. NMR images taken immediately following the cessation of flow suggest a slight degree of particle migration toward the center of the pipe downstream of the contraction.     

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear‐induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear‐induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse‐flux model. Semi‐implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of polymer–fiber interactions on rheology and flow behavior of suspensions of semi-flexible fibers in polymeric liquids

Rheological properties of suspensions of fibers in polymeric fluids are influenced by fiber–polymer interactions. In this paper, we investigate this influence from both experimental and modeling standpoints. In the experimental part of this investigation, we have changed the fiber–polymer interactions by treating the surface of the fibers. The resulting effects are observed using scanning electron microscopy and dynamic mechanical analysis techniques and quantified from the measurements of the viscosity in the start-up of shear flows and dynamic tests in the linear viscoelastic range region. The results are interpreted with the help of a mesoscopic rheological model developed for suspensions of fibers in viscoelastic fluids.     

Large eddy simulation of gas-particle turbulent channel flow with momentum exchange between the phases

This paper presents results of a large eddy simulation (LES) combined with Lagrangian particle tracking and a point-force approximation for the feedback effect of particles on the downward turbulent gaseous flow in a vertical channel. The LES predictions are compared with the results obtained by direct numerical simulation (DNS) of a finer computational mesh. A parametric study is conducted for particles with two response times in simulations with and without streamwise gravitational settling and elastic, binary interparticle collisions. It is shown that the classical and the dynamic Smagorinsky turbulence models adequately predict the particle-induced changes in the mean streamwise velocity and the Reynolds stresses of the carrier phase for the range of parameters studied. However, the largest discrepancies between the LES and DNS results are found in the cases of particle-laden flows. Conditional sampling of the instantaneous resolved flow fields indicates that the mechanisms by which particles directly oppose the production of momentum and vorticity of the organized fluid motions are also observed in the LES results. However, the geometric features of the near-wall quasistreamwise vortices are overestimated by the use of both turbulence models compared to the DNS predictions.     

Numerical simulation of flow kinematics and fiber orientation for multi-disperse suspension

The development of flow kinematics and fiber orientation distribution from the parabolic velocity profile and isotropic orientation at the channel inlet was computed in multi-disperse suspension flow through a parallel plate channel and their predictions were compared with those of mono- and bi-disperse suspensions. A statistical scheme (orientations of a large number of fibers are evaluated from the solution of the Jeffery equation along the streamlines) was confirmed to be very useful and feasible method to analyze accurately the orientation distribution of fibers in multi-disperse fiber suspension flow as well as mono- and bi-dispersions, instead of direct solutions of the orientation distribution function of fibers or the evolution equation of the orientation tensor which involves a closure equation. It was found that the flow kinematics and the fiber orientation depend completely on both the fiber aspect-ratio and the fiber parameter for multi-disperse suspension when the fiber–fiber and fiber-wall interactions are neglected. Furthermore, the addition of large aspect-ratio fibers as well as an increase in the fiber parameter related to the large aspect-ratio fibers could suppress the complex velocity field and stress distributions which are observed in suspensions containing small aspect-ratio fibers. From a practical point of view, therefore, the mechanical and physical properties of fiber composites should be improved with an increase in the volume fraction of large aspect-ratio fibers.     

Fiber orientation kinetics of a concentrated short glass fiber suspension in startup of simple shear flow

The common approach for simulating the evolution of fiber orientation during flow in concentrated suspensions is to use an empirically modified form of Jeffery's equation referred to as the Folgar–Tucker (F-T) model. Direct measurements of fiber orientation were performed in the startup of shear flow for a 30 wt% short glass fiber-filled polybutylene terephthalate (PBT-30); a matrix that behaves similar to a Newtonian fluid. Comparison between predictions based on the F-T model and the experimental fiber orientation show that the model over predicts the rate of fiber reorientation. Rheological measurements of the stress growth functions show that the stress overshoot phenomenon approaches a steady state at a similar strain as the fiber microstructure, at roughly 50 units. However, fiber orientation measurements suggest that a steady state is not reached as the fiber orientation continues to slowly evolve, even up to 200 strain units. The addition of a “slip” parameter to the F-T model improved the model predictions of the fiber orientation and rheological stress growth functions.     

Investigation of fiber motion near solid boundaries in simple shear flow

In this paper, fiber motion near a planar wall was investigated using a planar shear flow apparatus. Fibers were placed (one at a time) perpendicular to the flow direction at various locations throughout the flow field. The location and orientation of each fiber versus time was measured, using an image processing system, until the fiber aligned with the flow direction. When the centroid of the fiber was located at distances greater than a fiber length from the wall, Jeffery's equations governing particle motion were verified. For distances less than a fiber length and greater than a fiber diameter from the wall, the fiber experienced an increased rate of rotation. In this regime, the motion of the fiber could be described by Jeffery's equations if an increased effective shear rate was used. The effective shear rate was found to increase logarithmically with decreasing separation distance. The wall effect was higher for longer aspect ratio fibers and was also a function of orientation; fibers oriented perpendicular to the wall rotated faster than those oriented parallel to the wall at the same separation distance. Once the fiber aligned with the flow direction, it ceased to rotate within the field of view. In this orientation, the wall had a stabilizing effect on the fiber. In efforts to relate the increase in shear rate to the aspect ratio of the fiber and the separation distance between the fiber and a solid wall, a translation model based on the work of De Mestre and Russel was explored. This model allows one to quantify the increase in shear rate experienced by the fiber due to the presence of a wall or obstruction in the flow field. However, the model has its limitations and care should be taken when applying this model outside its realm of validity. When compared to experimental data, the translation model provides a very good estimate of the increased shear rate experienced by the fiber when it is located less than 2/3 of a fiber length from a planar wall. Received: 20 April 2000 Accepted: 28 September 2000     

Research on the motion of particles in the turbulent pipe flow of fiber suspensions

The motion of fibers in turbulent pipe flow was simulated by 3-D integral method based on the slender body theory and simplified model of turbulence. The orientation distribution of fibers in the computational area for different Re numbers was computed. The results which were consistent with the experimental ones show that the fluctuation velocity of turbulence cause fibers to orient randomly. The orientation distributions become broader as the Re number increases. Then the fluctuation velocity and angular velocity of fibers were obtained. Both are affected by the fluctuation velocity of turbulence. The fluctuation velocity intensity of fiber is stronger at longitudinal than at lateral, while it was opposite for the fluctuation angular velocity intensity of fibers. Finally, the spatial distribution of fiber was given. It is obvious that the fiber dispersion is strenghened with the increase of Re numbers.