Shear influence on fibre orientation

The purpose of this experimental work was to study the influence of shear close to a solid boundary on the fibre orientation in suspensions with different fibre aspect ratios and concentrations. We have studied a laminar suspension flow down an inclined plate. The fibre orientation in different wall parallel planes were measured. We applied an index-of-refraction (IR) matching method together with particle tracking techniques to obtain the fibre motion. The fibre orientation was extracted using a two-dimensional wavelet transform. The shear flow resulted in fibres perpendicularly oriented to the streamwise direction (“rollers”) in the near wall region. These rollers were observed in the experiment to perform a rolling-sliding motion down the inclined plate around a stable perpendicular orientation. As the distance to the wall increased the number of rollers decreased and the fibre orientation was unaffected from its initial streamwise orientation. As the aspect ratio increased the influence of shear on the fibre orientation decreased for all measured wall parallel planes. This was also the case for higher fibre concentrations. The purpose of this study was to contribute to the development of the capacity to control the sheet network structure in papermaking. KTH-Biofibre Materials Centre (BiMaC), FaxenLaboratoriet KTH-Mechanics for supporting this study. Paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Flow of dilute polyacrylamide solutions through a sudden planar contraction

The flow of partially hydrolyzed polyacrylamide solutions through a 10:1.2 sudden planar contraction was investigated by means of laser-Doppler anemometry. The resultant velocity profiles are compared with those for Newtonian water flow. It is shown that velocity profiles of dilute high molecular weight HPAM solutions of concentrations of 25 ppm and 50 ppm exhibit a velocity maximum upstream of the sudden planar contraction. They first appear near the wall and move towards the channel axis as the flow approaches the contraction. Furthermore, it is found that the centreline velocity profiles of the polymer solution show an earlier response to the downstream flow restriction than water. This is associated with enhanced recirculation regions in front of the sudden channel contraction.Streamlines calculated from the experimentally obtained velocity data reveal all the characteristics of a diverging flow field upstream of the contraction. The experiments reveal that, for the volume flow rate investigated, the flow of dilute polymers remains two-dimensional in the centre throughout the major part of the channel.The addition of small amounts of the divalent salt CaCl₂ reduces the polymer effects to pure Newtonian flow behaviour.     

On the orientation probability distribution of flexible fibres in a contracting channel flow

The development of fibre orientation distribution in a plane contracting channel flow is investigated with combining experiments and modelling. A dilute suspension of flexible wood fibres is used in the experiments. The salient feature of the suspension is the flexibility of the fibres. To model the fibre orientation probability distribution (FOPD) a diffusion–convection equation is used. The effect of random motion, in this case turbulence, is considered with translational and rotational diffusion coefficients. In addition to providing the inlet conditions, experiments are used to determine the rotational diffusion coefficient for the model. The work addresses the problems related to the above mentioned modelling method and combines the experiments and modelling in order to understand the mechanisms affecting the development of fibre orientation.     

Fountain flow of pseudoplastic and viscoplastic fluids

Numerical simulations have been undertaken for the benchmark problem of fountain flow present in injection-mold filling. The Finite Element Method (FEM) is used to provide numerical results for both cases of planar and axisymmetric domains under steady-state conditions. The Herschel–Bulkley model of viscoplasticity is used, which reduces with appropriate modifications to the Bingham, power-law and Newtonian models. The present results extend previous ones regarding the shape of the front, which is essential in correctly capturing the flow field. In particular the centreline front position is found as a function of the dimensionless power-law index (in the case of pseudoplasticity) and the dimensionless yield stress (in the case of viscoplasticity). The pressures from the simulations have been used to compute the excess pressure losses in the system (front pressure correction or exit correction). Both shear-thinning and shear-thickening lead to more extended front positions relative to the Newtonian values, which are 0.895 for the planar case and 0.835 for the axisymmetric one. Viscoplasticity leads also to more extended front positions as the dimensionless yield stress goes from zero (Newtonian behaviour) to higher values of the yield stress. In both cases of non-Newtonian behaviour, the front tends to follow the development of the fully developed Poiseuille velocity profile, which tends towards a plug-like profile at the extreme cases of non-Newtonianness. The front pressure (exit) correction increases monotonically with the decrease in the power-law index and the increase in the dimensionless yield stress.     

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.     

The motion of rodlike particles in the pressure-driven flow between two flat plates

The motion of freely suspended rodlike particles has been observed in the pressure-driven flow between the two flat plates of a Hele Shaw flow cell at low Reynolds numbers. Data are reported for rodlike particles with aspect ratios of 12.0 suspended in a Newtonian fluid for gap thickness to particle length ratios of 3, 6, and 20; and for rodlike particles with aspect ratios between 5 and 8 in a non-Newtonian fluid (79.25 wt.% water, 20.2 wt.% glycerine, and 0.55 wt.% polyacrylamide). For the Newtonian fluid, the time-dependent orientation of the particles near and far from walls was shown to be in quantitative agreement with Jeffery's theory for ellipsoids suspended in a simple shear flow if an effective aspect ratio is calculated from the experimental period of rotation. Particles aligned with the flow direction and less than a particle half-length from a wall interacted irreversibly with the wall. For the non-Newtonian fluid, the timedependent orientation far from a wall was shown to be in qualitative agreement with Leal's theory for a second-order fluid; however, particles that were aligned with the flow direction and were near walls did not rotate.     

Mean Flow and Turbulence Measurements in a Turbulent Free Cruciform Jet

The results of measurements of all three components of the mean velocity vector, the Reynolds normal and primary shear stresses and the mean static pressure in a turbulent free jet, issuing from a sharp-edged cruciform orifice, are presented in this paper. The measurements were made with an x-array hot-wire probe and a pitot-static tube in the near flow field of the jet. The Reynolds number, based upon the equivalent diameter of the orifice, was 1.70 × 10⁵. In addition to the quantities measured directly, the mean streamwise centreline velocity decay, the jet half-velocity widths, the jet spreading rate, the mean streamwise vorticity, the mass entrainment rate, the integral momentum flux and the one-dimensional energy spectra have been derived from the measured data. The results show that the mean streamwise centreline velocity decay rate of the cruciform jet is higher than that of a round jet issuing from an orifice with the same exit area as that of the cruciform orifice. The mean streamwise velocity field changed shape continuously from a cruciform close to the orifice exit plane to circular at 12 and half equivalent diameters downstream. The mean streamwise vorticity field, up to about three equivalent diameters downstream of the orifice exit plane, consists of four pairs of counter-rotating cells, which are aligned with the four edges in the centre of the cruciform orifice.     

Experimental Investigation on Turbulent Structure of Drag Reducing Channel Flow with Blowing Polymer Solution from the Wall

Turbulent drag reducing flow with blowing polymer solution from the channel wall was investigated experimentally using particle image velocimetry (PIV). Experiments were carried out with varying conditions of blowing polymer solution (e.g. weight concentration of polymer solution). Reynolds number based on the channel height and mean velocity was set to 20000 and 40000. When the polymer solution was blown from the channel wall, streamwise velocity fluctuation little increased, but wall-normal velocity fluctuation, Reynolds shear stress and correlation coefficient decreased significantly only near the blower wall. This behavior corresponds to the decrease of the ejection and sweep in the near-wall region observed by the investigation of instantaneous velocity map. On the contrary, this characteristic behavior was not observed at a position away from the blower wall (y/(H/2) > 0.4) and the scatter plot was almost the same as that of the water flow in this region. These results suggest that there are two regions in the drag reducing flow with blowing polymer solution from the wall; one is a non-Newtonian region which exists near the blower wall, and the other is a Newtonian region at a distance from the wall. The non-Newtonian region plays a key role in the drag reduction by the blowing polymer solution.     

Time-resolved PIV measurements of the interaction of polystyrene beads with near-wall-coherent structures in a turbulent channel flow

Time-resolved PIV measurements were performed in a dilute particle-laden flow tracking near-neutrally buoyant polystyrene beads and the velocity field of a near wall turbulent boundary layer. Data were taken in a vertical light sheet aligned in the streamwise direction at the center of a horizontal, closed loop, transparent square water channel facility. In addition, low speed measurements were performed characterizing the effects of the dispersed phase on mean and turbulence flow quantities. Reynolds shear stress slightly differed from clear water conditions whereas fluid mean and rms values were not affected. A case study for several beads revealed a clear relation between their movement and near-wall coherent structures. Several structures having 2D vorticity signatures of near-wall hairpin vortices and hairpin packets, directly affected bead movement. A statistical analysis showed that the mean streamwise velocity of ascending beads lagged behind the mean fluid velocity and bead rms values were higher than fluid ones. Particle Reynolds numbers based on the magnitude of the instantaneous relative velocity vector peaked near the wall; values not exceeding 100, too low for vortex shedding to occur. Quadrant analysis showed a clear preference for ascending beads to reside in ejections while for descending beads the preference for sweeps was less.     

Lubricated compression and X-ray microtomography to analyse the rheology of a fibre-reinforced mortar

In this work, the microstructure and the rheology of a glass-fibre-reinforced fresh mortar were studied. Various fibre contents and aspect ratios and two types of fibrous reinforcement, i.e. slender fibre bundles and fibres, were tested. The microstructure was analysed by using X-ray microtomography. It is shown that the non-deformed mortar is a porous granular suspension, the porous microstructure of which is not influenced by the presence of fibres, which in turn display a 2D planar random fibre orientation. The rheology was investigated by subjecting samples to constant axial strain rate and lubricated compression. The roles of the actual strain, the mortar resting time, the fibre content and aspect ratio on recorded stress levels are emphasised. Besides, for the investigated strain rate and material parameters, the mortar flow is quasi-incompressible and does not affect significantly the porous microstructure nor the fibrous one. Lastly, the stress increase which is induced by the addition of fibre bundles is similar to that predicted by Newtonian models of semi-dilute fibre suspensions.     

Characteristic turbulent structure of a modified drag-reduced surfactant solution flow via dosing water from channel wall

The modification of the near-wall structure is very important for the control of wall turbulence. To ascertain the effect of near-wall modulation on the viscoelastic drag-reduced flow, the modified characteristics of a surfactant solution channel flow were investigated experimentally. The modulation was conducted on the boundary of the channel flow by injecting water from the whole surface of one side of the channel wall. The diffusion process of the injected water was observed by using the planar laser-induced fluorescence technique. The velocity statistics and characteristic structure including the spatial distributions of instantaneous streamwise velocity, swirling strength, and Reynolds shear stress were analyzed based on the velocity vectors acquired in the streamwise wall-normal plane by using the particle imaging velocimetry technique. The results indicated that the disturbance of the injected water was constricted within a finite range very near the dosing wall, and the Reynolds shear stress was increased in this region. However, the eventual drag reduction rate was found to be increased due to a relatively large decrement of viscoelastic shear stress in this near-wall region. Moreover, the flow structure under this modulation presented obvious regional characteristics. In the unstable disturbed region, the mixing of high-speed and low-speed fluids and the motions of ejection and sweep occurred actively. Many clockwise vortex cores were also found to be generated. This characteristic structure was similar to that in the ordinary turbulence of Newtonian fluid. Nevertheless, outside this disturbed region, the structure still maintained the characteristics of the drag-reduced flow with non-Newtonian viscoelastic additives. These results proved that the injected Newtonian fluid associated with the modified stress distribution creates a diverse characteristic structure and subsequent enhanced drag reduction. This investigation can provide the experimental basis for further study of turbulence control.     

非球形固体颗粒对弯管内壁的磨损机制

为研究弯管内固体颗粒在液相夹带条件下的运动特性及颗粒对弯管内壁的磨损,采用计算流体动力学与离散元耦合的方法,建立数值模型,考虑固液两相之间的作用,对弯管内的固液两相流动进行数值模拟;通过软件的应用程序编程接口嵌入自编译磨损模型;借助试验结果,验证数值模型的有效性.结果表明,所建立的数值模拟方案可以准确地模拟颗粒在管内的运动特征并能够预测弯管内壁的磨损位置以及磨损程度.弯管内的二次流对颗粒运动有重要影响,弯管外侧壁面中心线附近的磨损较严重,磨损的形式以小角度划擦切削为主.弯管磨损主要与颗粒对壁面的碰撞速度、碰撞角度及碰撞频率有关.运动中的颗粒与壁面发生多次碰撞,碰撞角度逐渐减小.随着颗粒球形度的增大,在相同碰撞条件下引起的磨损量变小,但是会降低颗粒的随流性.颗粒形状影响颗粒在流场中的运动速度以及颗粒与壁面的碰撞.随着颗粒球形度增大,严重磨损区域向弯管进口方向移动,壁面平均磨损量先减小后增大;当输送颗粒的球形度为0.91时,壁面磨损量最小.     

Single-Fluid Model of a Mixture for Laminar Flows of Highly Concentrated Suspensions

A model of laminar flow of a highly concentrated suspension is proposed. The model includes the equation of motion for the mixture as a whole and the transport equation for the particle concentration, taking into account a phase slip velocity. The suspension is treated as a Newtonian fluid with an effective viscosity depending on the local particle concentration. The pressure of the solid phase induced by particle-particle interactions and the hydrodynamic drag force with account of the hindering effect are described using empirical formulas. The partial-slip boundary condition for the mixture velocity on the wall models the formation of a slip layer near the wall. The model is validated against experimental data for rotational Couette flow, a plane-channel flow with neutrally buoyant particles, and a fully developed flow with heavy particles in a horizontal pipe. Based on the comparison with the experimental data, it is shown that the model predicts well the dependence of the pressure difference on the mixture velocity and satisfactorily describes the dependence of the delivered particle concentration on the flow velocity.     

纵向涡对近壁湍流影响的激光测试

用激光测试方法详细地研究了单涡、上洗双涡、下洗双涡对近壁湍流的影响．在涡的下洗区，流体流速高，湍流度低，流体流向壁面；在涡的上洗区，流体流速低，湍流度高，流体远离壁面     

Fibre orientation calculation in injection moulding of reinforced thermoplastics

The orientation of short fibres during the filling with reinforced thermoplastics of a tube and a disk is computed. The flow kinematics is obtained using a finite element method with a moving mesh technique in two dimensions. The orientation is calculated with a decoupled method. Results show the evolution of the orientation of individually tracked fibers, especially in the material front region, for a Newtonian and a shear-thinning matrix behavior, and for different thermal conditions and fiber interactions.     

Study of semidilute fibre suspension rheology with lattice-Boltzmann method

A hybrid lattice-Boltzmann numerical simulation method is undertaken to study the rheology of non-colloidal, rigid fibres in sheared, semidilute Newtonian suspension. The viscosity and the first normal stress difference are calculated with the combined use of numerical fibre orientation information and a corrected form of the slender body theory of Batchelor (J Fluid Mech Digit Arch 46(4):813–829, 1971). The corrections make the theory applicable in semidilute suspension flow (Shaqfeh and Fredrickson, Phys Fluids A: Fluid Dyn 2(1):7–24, 1990) with fibres of finite aspect ratio. The corrected theory within its framework, based on spacing among fibres in semidilute suspension, only considers hydrodynamic interactions among fibres and inferences that the effect of actual fibre–fibre mechanical contacts on rheological properties of such suspension systems remains inconsequential. To investigate this issue, the rheological properties of semidilute suspension were calculated directly from the numerical simulation. This approach accounted for both hydrodynamic and mechanical interactions among fibres. This direct measurement proved that the mechanical interactions increase both the relative shear viscosity and the first normal stress difference in the semidilute suspension to values which are larger than permissible within the framework of Batchelor’s theory.     

基于壁面主动变形的湍流减阻控制研究

采用谱方法, 对反向控制下壁面主动变形的槽道湍流进行了直接数值模 拟研究. 结果表明, 在壁面最大变形量小于5倍黏性尺度条件下, 压差阻力可略, 摩擦阻力 降低7.6%. 施加控制后, 湍流强度和雷诺应力受到明显抑制, 平均速度剖面对数区上移. 受壁面法向运动的影响, 条带结构强度减弱、尺度变大; 流向涡外移且强度减弱, 其倾斜和 抬起的角度均有不同程度的减小. 壁面变形呈现流向拉长的凹槽结构, 其平均间距 为90倍黏性尺度.     

Der Einfluß der elastischen Eigenschaften des Trägermediums auf das Fließverhalten von Kugel- und Fasersuspensionen

The influence of the elastic properties of the suspending medium on the flow of viscoelastic glass bead and glass fibre suspensions through flat orifices was investigated. The results are discussed by contrasting the flow behaviour of the viscoelastic suspensions with that of corresponding suspensions in a Newtonian suspending medium. For the suspensions in a Newtonian oil linear relationships were always found between the pressure loss and the effective velocity gradient in orifice flow. Thus it can be concluded that in this case the influence of the filler on the flow behaviour is independent of the imposed strain. Increasing the filler content or using more anisotropic particles led to higher viscosities and thus to larger pressure losses. It is well known that viscoelastic polyisobutene solutions show strain rate dependent flow behaviour. Due to the increasing influence of elasticity with increasing strain rate, the apparent flow curves can be divided into characteristic regions with different slopes. The addition of filler to such solutions altered the shape of the flow curves and it was found that the onset of “flow hardening” occurred at lower imposed strains. In addition, characteristic changes in the hardening behaviour and flow stability were observed; these were most pronounced for the fibre suspensions, even at low concentrations. For the fibre suspensions, these phenomena could be related to the influence of the fibres on the undisturbed flow field near the orifice, leading, in general, to higher strain velocities between the fibres. On the other hand, enhanced extensional strains are induced at the ends of the fibres and, at the same time, shear flow occurs along the fibres. These two effects counteract each other with respect to the hardening behaviour of the polymer. Similar effects may also occur in the glass bead suspensions, although they would certainly be less pronounced.     

On translational and rotational relative velocities of fibers and fluid in a turbulent channel flow with a backward-facing step

A dilute fiber suspension in a turbulent channel with a backward-facing step is investigated by means of Feature Tracking. Its combination with a phase-discrimination methodology, which is described in detail, allows simultaneous and separate measurement of carrier and dispersed phases velocity fields, the orientation and rotation rate of fibers as well as the fiber–fluid translational and rotational slip velocities. The patterns of fibers concentration, angular velocity and the probability distribution of fibers velocity appear to be dominated by the mechanical interactions with the wall and the local high shear rather than by near-wall turbulent structures. The translational slip velocity obtained from instantaneous data shows that fibers move faster than the surrounding fluid inside the buffer layer, the velocity gap reducing gradually when approaching the channel centerline. On the other hand, the rotational slip profile suggests a gradual decoupling of the translational and rotational dynamics. Downstream of the step, the excess of streamwise velocity displayed by fibers is still observed and extends in the free-shear region, whereas the rotation rate slip decreases at a relatively short distance from the step, as the effect of the wall presence fades away.     

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