Ecoulement de fluides newtoniens et non newtoniens à travers des lits fixes stratifiés

Fixed beds of plate shape particles have been studied in two different “flow-particle” configurations. From pressure drop measurements performed for a Newtonian fluid flow, two characteristic structural parameters have been determined by using a capillary - type model. The differences concerning the hydrodynamic behaviour of the two configurations are discussed and a factor characterizing the bed anisotropy is proposed. A dimensionless equation allowing the pressure drop determination for Newtonian and non-Newtonian purely viscous fluid flow in the two configurations, for a large range of Reynolds numbers, is proposed and tested with experiments.     

Numerical simulation of the flow in an extensional flow mixer. Effect of fluid elasticity on the flow

We discuss the viscoelastic flow of the matrix fluid in an Extensional Flow Mixer (EFM) obtained by a numerical simulation. The effect of the fluid viscoelasticity on the flow state in an EFM was considered by the comparison of the flow states of the purely viscous fluid and the viscoelastic fluid. The mixing performance of the EFM is also considered. The Phan‐Thien Tanner model was used as the constitutive equation of the viscoelastic fluid and the Carreau model was used as that of the purely viscous fluid. Results obtained are as follows: (1) Stagnation flows occur in the converging‐diverging plates (c‐d plates) in the case of viscoelastic fluid. The size of stagnation flow region becomes large when the fluid has a strain‐thickening elongational viscosity. (2) The absolute value of the extensional strain and the pressure drop in the c‐d region increase with fluid elasticity. Meanwhile, the residence time in the c‐d region decreases with that. (3) There is no stagnation region in the c‐d plates for a purely viscous fluid. The stagnation flow has an effect on the estimation value of EFM's performance. The prediction by the purely viscous fluid is not useful for the flow in an EFM because of extremely low accuracy.     

THE DESULFURIZATION OF ORGANIC SULFUR AND THE TRANSFORMATIONS OF ORGANIC SULFUR FUNCTIONAL GROUPS IN COAL PYROLYSIS

The problem of formulation of appropriate boundary conditions for periodic flow fields is investigated. Sufficient conditions are established for the uniqueness of solutions for the creeping flow of Newtonian fluids through periodically constricted tubes. A perturbation solution is developed for the Newtonian periodic flow problem for an arbitrary boundary shape with sufficiently small axial variations in tube radius. The nonuniqueness of solutions to periodic flow problems when an insufficient number of periodic boundary conditions are imposed is illustrated.     

BOUNDARY CONDITIONS FOR PERIODIC FLOW FIELDS

The problem of formulation of appropriate boundary conditions for periodic flow fields is investigated. Sufficient conditions are established for the uniqueness of solutions for the creeping flow of Newtonian fluids through periodically constricted tubes. A perturbation solution is developed for the Newtonian periodic flow problem for an arbitrary boundary shape with sufficiently small axial variations in tube radius. The nonuniqueness of solutions to periodic flow problems when an insufficient number of periodic boundary conditions are imposed is illustrated.     

Mechanics of steady flow in coextrusion fiber spinning

The steady flow of isothermal bicomponent coextrusion fiber spinning has been investigated. A model has been chosen in which a Newtonian fluid and a Phan-Thien/Tanner (PTT) fluid were considered to be the core and the skin layer, respectively. This model was adopted to study the effect on spinline velocity of an interaction between two fluids with quite different extensional rheology. The effects of the hoop stress, gravity, inertia, and surface and interfacial tensions were disregarded. Only viscous and viscoelastic forces were considered. A uniaxial extension was also assumed as the radius variation in the axial direction is small. The Newtonian fluid has been considered prone to fluctuate during melt processing while the viscoelastic skin layer has a stabilizing effect. The velocity profile was affected by the choice of two characteristic parameters: extensional and shear-thinning parameters, as well as the viscoelastic skin flow rate ratio. Both shear-thinning and extensional parameters play important roles in melt flow. The results show that as the draw ratio increases, the system is dominated by the extensional parameters, whereas slow drawing is dominated by shearing, in spite of the thin viscoelastic skin.     

Influence of Rheological Behavior of Purely Viscous Fluids on Analytical Residence Time Distribution in Straight Tubes

In an effort to better understand the homogeneity of heat treatment of foodstuffs in holding tubes, the cumulative residence time distribution function is derived for a Herschel‐Bulkley fluid from fully developed laminar flow in a straight circular tube under isothermal conditions when diffusional effects are negligible. The proposed analytical solution can be reduced to solutions for Newtonian, shear‐thinning, dilatant, Bingham fluids by setting particular rheological parameters, and consequently, it is possible to successfully explain the dependence of residence time distribution on fluid properties for almost all of the rheological models used for time‐independent purely viscous fluids.     

锚式搅拌槽中高粘弹性流体的流速分布及其功率消耗

用照相法测定了锚式搅拌槽中高粘弹性流体的流型和流速分布,另测定了搅拌功率消耗,结果发现:1.与牛顿流体相比,在低Re数下,粘弹性流体的切向速度较大,而径向速度则较小.2.转速相同时,在高剪切率区域,粘弹性流体的剪切率大于牛顿流体.由CEF方程导出功率计算式N_pRe_af_s~(1-n)=k_pf_vf_s~2[1+F_1avf_s~(m-n-3)Wi/K_s~2]用实验数据确定f_(?)和F_(1av),得到可适用于牛顿流体、假塑性流体和粘弹性流体的普适功率计算式,计算结果与实验值比较接近.     

镜像流体法模拟单颗粒沉降和绕凸起物流动

提出一种新的计算流体力学方法,即镜像流体法,通过指定固体区域内的流场参数,使相界面边界条件隐含满足,使得固液两相运动可以在固定的欧拉坐标系中求解。采用SIMPLE算法和控制容积法离散控制微分方程组。利用镜像流体方法数值模拟了单个球形颗粒的自由沉降过程,以及幂律流体、Carreau-Bird流体和粘弹性的Oldroyd-B流体绕半圆环形、三角形和梯形凸起物的二维圆管流动问题,模拟结果与报道的实验数据及计算结果很接近,初步验证了本算法的可靠性。     

Heat transfer in lid driven channels with power law fluids in a hydrodynamic fully developed flow field

We present a finite element numerical study of heat transfer in lid driven channels with fully developed axial flow for non-Newtonian power law fluids. The effect of channel aspect ratio and material properties on temperature distribution and wall heat transfer are studied. The results show that in comparison with Newtonian fluids the shear thinning property of the fluids acts to reduce the local viscous dissipative heating and as a result the axial local fluid temperature is reduced. Applications of the results to scraped-surface heat exchanger design and operation are recommended.     

Fluidization with viscoelastic polymer solutions in the transition flow region

Fluidization of spherical and non-spherical particle beds with shear thinning viscoelastic polymer solutions was investigated experimentally in the transition flow region. It was observed that the influence of elasticity on the anomalous expansion course weakens with the increasing value of Reynolds number. After exceeding a critical value of Reynolds number, which depends on the measure of liquid elasticity, the effect of elasticity vanishes and the expansion curves have the same linear shape as for fluidization with Newtonian (or purely viscous non-Newtonian) fluids. Semi-empirical equations based on the Carreau viscosity model were proposed for predicting the critical value of Reynolds number and the bed expansion in the region of diminishing elasticity effects.     

Thermodynamic and heat transport considerations for viscoelastic fluids

In this paper the application of thermodynamic principles to the mechanics of viscoelastic flow is outlined. Existing theories of heat transfer (for purely viscous fluids) are shown to be equally valid for viscoelastic materials in all steady laminar shearing flow fields provided the temperature-dependency of physical properties may be either neglected or accounted for separately.

In more general flow fields (including boundary layer problems) the additional effects of viscoelastic properties are shown and dimensionless ratios are developed to show under what conditions they are of importance. It is seen that the viscoelastic properties may lead to either increased or decreased heat transfer rates, depending upon the kinematic characteristics of the flow field under consideration and the direction of heat transfer.

Implications of the second law of thermodynamics are discussed and the possibility of negative dissipation functions indicated.     

A STUDY OF SPINLINE DYNAMICS USING ORTHOGONAL COLLOCATION

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

SLOW NON-NEWTONIAN FLOW PAST AN ASSEMBLAGE OF RIGID SPHERES

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

The dispersion of solute in turbulent pipe flow of non-newtonian fluids

The dispersion of solute in turbulent pipe flow of power law fluids is investigated theoretically. Results in terms of the intensity of dispersion are compared for the non-Newtonian and purely viscous Newtonian fluids over a wide range of Schmidt numbers. The computed results indicate that the intensity of dispersion at a constant Schmidt and Reynolds number increases with increasing flow behavior index.     

Analysis of isothermal two-layer blown film coextrusion

The mechanics of a bicomponent two-layer blown film coextrusion is studied theoretically. As a first step for the modeling of this complex process, we adopt a simple system in which the flow is assumed to be isothermal and the two layers are a Newtonian and an upper-convected Maxwell fluid (UCM), respectively. The two fluids are chosen to investigate the relative influence of viscous and viscoelastic forces on the flow mechanics of the process. For a given total flow rate, blow-up ratio, freeze-line height, and film gage, the radius and the melt thickness profiles of the blown film are determined numerically for various values of the flow rate ratio of the two fluids. When the relaxation time of the UCM layer is small, the flow mechanics including the shape of the bubble (or the radius profile) is not much different from that of a Newtonian single-layer flow. With increasing relaxation time, the viscoelasticity effect of the UCM layer becomes more and more pronounced and eventually dominates the bubble dynamics even though its layer thickness may be smaller than that of the Newtonian layer.     

Viscoelastic breakup in a high velocity airstream

Viscoelastic fluids were injected into a high velocity airstream (200 m/s) to investigate how the addition of small polymer quantities to fluids significantly increase the resultant disseminated drop size. For each liquid tested several hundred resultant drops were sampled and measured using an automated image analyzer. The resultant mass median diameter (MMD) for a viscoelastic fluid was an order of magnitude larger than a comparable viscous Newtonian fluid. A relaxation time measured from a die swell experiment correlates the dissemination results suggesting, an elongational rather than shear breakup mechanism.     

Experimental observation on entrance flow inside extrusion dies

A flow visualization technique was employed to observe the flow fields at the entrance region inside extrusion dies. Four types of solutions, i.e., Newtonian, shear-thinning, Boger, and viscoelastic fluids, were used as test fluids. Entrance flows inside center-fed and end-fed dies of different configurations were examined. It was found that, even though the swirling motions appear in the entrance region of center-fed dies, no vortex develops. Shear-thinning behavior tends to enhance swirling, but fluid elasticity suppresses the swirling. On the other hand, vortices exist at certain end-fed die geometries, and vortices will grow if the fluid exhibits shear-thinning, yet fluid elasticity reduces the size of vortices. Several inlet designs effective for eliminating vortices were studied.     

特型螺带桨叶在高粘弹性和非弹性流体中的搅拌功率

本文研究了层流区域有较大叶片截面积的特型双螺带──锚桨叶在高粘弹性和非弹性流体中的搅拌功率，测定了Ｋ_ｐ和Ｋ_ｓ，采用广义二阶流体本构方程导出搅拌功率计算式参数ｆ_ｓ和Ｆ_（１ａｃ）由实验数据确定。该式适用于牛顿型流体、假塑性和粘弹性流体的功率消耗计算。     

不同错列角三角形转子作用下的分布混合数值模拟

以高黏度牛顿流体为研究对象,采用数值模拟方法研究了不同错列角的三角形转子搅拌作用下的腔内的混合过程。根据运动转子的对称性和周期性,用瞬态有限元法(FEM)结合网格叠加技术(MST)计算了三分之一的周期。提出了一种基于周期速度场的四阶Runge-Kutta算法。采用Poincaré截面、拉格朗日相干结构和混合方差指数等对混合进行表征。结果表明,不同错列角对混合和能耗的影响不明显,所有的混合情况都接近于相同的混合方差指数的渐近值,并具有相似的混合机制,属于部分混沌混合,贴近转子各边嵌入了规则的层流KAM(Komogorov-Arnold-Moser)岛。     

Flow pattern variations of viscoelastic fluid flows in three‐dimensional branching channel

Transport phenomena in three‐dimensional branching channel are important because of their relevance in polymer processing. In this article, an experimental study on viscoelastic flow in a three‐dimensional cylindrical branching channel is carried out to investigate variations of flow pattern. Flow visualization in representative symmetric planes is made both for the viscoelastic fluid and Newtonian flow. From the results of the present investigation, the flow field in the three‐dimensional cylindrical branching channel is clarified within the range of laminar flow. It is confirmed that corner vortex, shedding vortex, and secondary vortex flow are all obviously changed with the fluid concentration and the Reynolds number, which are much more three‐dimensional and complex than the Newtonian fluid, and the flow pattern of the viscoelastic fliud flow largely depends on the Reynolds number and fluid concentration. Even for the viscoelastic flow at the low Reynolds number, shedding vortex and secondary vortex and complex three‐dimensional flow occur in the cylinder. The flow field is not symmetric space for the viscoelastic flow and however is fairly symmetric for the Newtonian fluid. The above reasons explain why the flow deflection happens even at the low Reynolds number flow. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers