The influence of the upper wall on the die entry flow of viscoelastic fluids

The influence of the upper wall on the die entry flow of viscoeleastic fluids was investigated experimentally. Aqueous solutions of Separan AP-30 were pushed out by a compressed gas pressure through a capillary attached to the bottom of a reservoir having a height-adjustable upper wall. The driving gas pressure, the flow rate and the pressure at the center of the upper wall were measured and the flow patterns in the entry region above the inlet section of the capillary were observed. Flow rate measurements under the condition of constant driving pressure reveal that the maximum height of the upper wall required to reduce the flow rate is much larger for viscoelastic fluids than for Newtonians, and that this effect of the upper wall becomes more conspicuous with increasing driving pressure. What is curious is that under some conditions the flow rate is larger for a moderate upper wall height than for an infinite. These phenomena are shown to be attributed to the increasing and the reducing effects of the entry pressure loss by the upper wall. The latter effect may be called a new type of pressure-loss reduction phenomenon of viscoelastic fluids. The observation of the flow and the measurement of the pressure at the upper wall center show that typical flow patterns of the die entry flow of viscoelastic fluids are responsible for the far greater pressure loss than for Newtonians, and that the entry pressure loss for a spiralling flow is a little smaller than for the other two types even at an equal driving pressure.     

Driving Potentials of Heat and Mass Transport in Porous Building Materials: A Comparison Between General Linear,Thermodynamic and Micromechanical Derivation Schemes

In systems of coupled transport processes the question of the appropriate driving potentials is a point of discussion. In this article, three different approaches to derive models for transport currents are systematically compared. According to a general linear approach, an arbitrary full set of independent state variables and material properties is sufficient to describe any transport current. This approach is derived here from a symmetry principle. Thermodynamic and micromechanical approaches are more complex and even less general, but they allow additional statements about the transport coefficients and they reduce the number of transport processes. In the thermodynamic approach the additional information stems from the calculation of the entropy production rate; the micromechanical approach involves a microphysical model of the considered porous system. As a practical example, the three derivation schemes are applied to the often-encountered case of non-hysteretic heat and moisture transport in homogeneous building materials. It is shown, how the general state variables of a porous system are reduced to only two. Then from the general linear approach it can be seen, that all equations for the moisture transport current using a main driving potential (e.g. moisture content, vapour pressure, chemical potential) and an independent secondary driving potential (e.g. temperature, liquid pressure) are equivalent, without recurrence to the thermodynamic or micromechanical approach. However, the transport coefficients are arbitrary phenomenological functions depending on the two state variables. Based on a literature survey it is shown, which additional statements can be made in the thermodynamic and in the micromechanical approach. The latter yields the pressure-driven model (vapour and liquid pressure as the two driving potentials). Finally it is shown, what is to be expected, if in more complex systems the number of state variables increases.     

Horizontal Redistribution of Two Fluid Phases in a Porous Medium: Experimental Investigations

Classical models for flow and transport processes in porous media employ the so-called extended Darcy’s Law. Originally, it was proposed empirically for one-dimensional isothermal flow of an incompressible fluid in a rigid, homogeneous, and isotropic porous medium. Nowadays, the extended Darcy’s Law is used for highly complex situations like non-isothermal, multi-phase and multi-component flow and transport, without introducing any additional driving forces. In this work, an alternative approach by Hassanizadeh and Gray identifying additional driving forces were tested in an experimental setup for horizontal redistribution of two fluid phases with an initial saturation discontinuity. Analytical and numerical solutions based on traditional models predict that the saturation discontinuity will persist, but a uniform saturation distribution will be established in each subdomain after an infinite amount of time. The pressure field, however, is predicted to be continuous throughout the domain at all times and is expected to become uniform when there is no flow. In our experiments, we also find that the saturation discontinuity persists. But, gradients in both saturation and pressure remain in both subdomains even when the flow of fluids stops. This indicates that the identified additional driving forces present in the truly extended Darcy’s Law are potentially significant.     

基于应力波动的修正非局部流变模型

基于Pouliquen 提出的非局部流变模型,考虑颗粒流中某个位置重新排列引起的自激发过程,详细分析颗粒介质中应力波动幅值的概率密度分布形式以及剪切速率与体积分数的耦合作用,提出一种修正的非局部流变模型. 采用此修正非局部流变模型对斜面剪切颗粒流的流动特性进行了预测,颗粒流动的临界厚度、平均流动速度及剪切速率廓线的预测结果与实验结果定量吻合. 此修正模型的提出为复杂的密集颗粒流的描述和表征提供了一种新的研究思路.      

A new second‐moment closure approach for turbulent swirling confined flows

An improved anisotropic model for the dissipation rate—ε—of the turbulent kinetic energy (k), to be used together with a non‐linear pressure‐strain correlations model, is proposed. Experimental data from the open literature for two confined turbulent swirling flows are used to assess the performance of the proposed model in comparison to the standard ε transport equation and to a linear approach to model the pressure‐strain term that appears in the exact equations for the Reynolds‐stress tensor. For the less strongly swirling flow the predictions show much more sensitivity to the εtransport equation than to the pressure‐strain model. In opposition, for the more strongly swirling flow, the results show that the predictions are much sensitive to the pressure‐strain model. Nevertheless, the improved εtransport equation together with the non‐linear pressure strain model yield predictions in good agreement with experiments in both studied cases. Copyright © 2003 John Wiley & Sons, Ltd.     

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem

A mathematical model of the human cardiovascular system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a theoretical relation between pressure drop and flow rate based on Lorentz’s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxelbased simulator V-FLOW VOF3 D, where the vessel geometry is expressed by using volume of fluid(VOF) functions, is employed to find the flow distribution in an idealized stenosis vessel and the identity was validated numerically. It is revealed from the correlation that the pressure drop of NS flow in a stenosis vessel can be decomposed into a linear term caused by Stokes flow with the same boundary conditions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication theory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geometric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under different stenosis conditions by using 1D mathematical model.     

Overall softening and anisotropy related with the formation and evolution of dislocation cell structures

In this work, a model, based on a representation of the dislocation cell microstructures by a non-local two-phase material with evolving microstructures, is proposed for the elastic–plastic behavior of metals under monotonic and sequential loading. The first phase represents the cell interior and the second one, the cell walls. The evolution of the microstructure is taken into account considering the cell-wall interfaces as free boundaries. Finally, the accumulation within walls of dislocations crossing the cells defines a non-local hardening process. Assuming a piecewise uniform plastic strain field and assuming ellipsoidal cells, the free energy of the system is calculated. The driving and critical forces associated with the plastic flow of the two-phases and the morphology of the cells are established. In a third part, numerical results are presented for monotonic and sequential loading. The results show an overall softening related to the destabilization of the dislocation microstructures which occurs in sequential as well as monotonic paths.     

Evaluation of a Modified Reynolds Stress Model for Turbulent Dispersed Two-Phase Flows Including Two-Way Coupling

A modified Reynolds stress turbulence model for the pressure rate of strain can be derived for dispersed two-phase flows taking into account gas-particle interaction. The transport equations for the Reynolds stresses as well as the equation for the fluctuating pressure can be derived starting from the multiphase Navier–Stokes equations. The unknown pressure rate of strain correlation in the Reynolds stress equations is then modelled by considering the multiphase equation for the fluctuating pressure. This leads to a multiphase pressure rate of strain model. The extra particle interaction source terms occurring in the model for the pressure rate of strain can be constructed easily, with no noticeable extra computational cost. Eulerian–Lagrangian simulation results of a turbulent dispersed two-phase jet are presented to show the differences in results with and without the new two-way coupling terms.     

Peristaltic transport of a power-law fluid: Application to the ductus efferentes of the reproductive tract

The problem of peristaltic transport of a non-Newtonian (power-law) fluid in uniform and non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. A comparison of the results with those for a Newtonian fluid model shows that the magnitude of pressure rise, under a given set of conditions, is smaller in the case of the non-Newtonian fluid (power-law indexn < 1) at zero flow rate. Further, the pressure rise is smaller asn decreases from 1 at zero flow rate, is independent ofn at a certain value of flow rate and becomes greater if flow rate increases further. Also, at a given flow rate, an increase in wavelength leads to a decrease in pressure rise and increase in the influence of non-Newtonian behaviour. Pressure rise in the case of non-uniform geometry, is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the analysis is applied and compared with observed flow rates in the ductus efferentes of the male reproductive tract.     

Mechanics of the squeeze flow of planar fibre suspensions

This paper discusses the axisymmetric squeeze flow of concentrated transversely isotropic fibre suspensions in a power-law matrix and relates to the processing of composite materials such as sheet moulding compounds (SMCs) and glass mat thermoplastics (GMTs). A solution to the squeeze flow problem for a transversely isotropic power-law fluid is presented first, followed by a more detailed micromechanical analysis. In the first part of the paper a variational approach is applied to the interpretation of squeeze flow behaviour. This gives a simple expression for the total pressure, which enables the contributions due to extension and shear to be separated. Applying the procedure to GMT data suggests that the dissipation is predominantly extensional, except at very low plate separations. In the second part, a non-local constitutive equation is derived based on a simple drag law for hydrodynamic interactions. This is then used to model the pressure distribution when the effective length of the fibres is comparable to or determined by the dimensions of the squeeze flow plates. The model is shown to describe the observed squeeze flow stresses in both long and short fibre systems and to relate behaviour to the underlying resin flow properties.     

Pressure-driven flow of wormlike micellar solutions in rectilinear microchannels

In this paper the inhomogeneous response of the (two species) VCM model (Vasquez et al., A network scission model for wormlike micellar solutions. I. Model formulation and homogeneous flow predictions, J. Non-Newtonian Fluid Mech. 144 (2007) 122–139) is examined in steady rectilinear pressure-driven flow through a planar channel. This microstructural network model incorporates elastically active network connections that break and reform mimicking the behavior of concentrated wormlike micellar solutions. The constitutive model, which includes non-local effects arising from Brownian motion and from the coupling between the stress and the microstructure (finite length worms), consists of a set of coupled nonlinear partial differential equations describing the two micellar species (a long species ‘A’ and a shorter species ‘B’) which relax due to reptative and Rouse-like mechanisms as well as rupture of the long micellar chains. In pressure-driven flow, the velocity profile predicted by the VCM model deviates from the regular parabolic profile expected for a Newtonian fluid and exhibits a complex spatial structure. An apparent slip layer develops near the wall as a consequence of the microstructural boundary conditions and the shear-induced diffusion and rupture of the micellar species. Above a critical pressure drop, the flow exhibits shear banding with a high shear rate band located near the channel walls. This pressure-driven shear banding transition or ‘spurt’ has been observed experimentally in macroscopic and microscopic channel flow experiments. The detailed structure of the shear banding profiles and the resulting flow curves predicted by the model depend on the magnitude of the dimensionless diffusion parameter. For small channel dimensions, the solutions exhibit ‘non-local’ effects that are consistent with very recent experiments in microfluidic geometries (Masselon et al., Influence of boundary conditions and confinement on non local effects in flows of wormlike micellar systems, Phys. Rev. E 81 (2010) 021502).     

Simulation and transport phenomena of a ternary two-phase flow

A chemical flood model for a three-component (petroleum, water, injected chemical) two-phase (aqueous, oleic) system is presented. It is ruled by a system of nonlinear partial differential equations: the continuity equation for the transport of each of its components and Darcy's equation for the two-phase flow. The transport mechanisms considered are ultralow interfacial tension, capillary pressure, dispersion, adsorption, and partition of the components between the fluid phases (including solubilization and swelling).The mathematical model is numerically solved in the one-dimensional case by finite differences using an explicit and direct iterative procedure for the discretization of the conservation equations. Numerical results are compared with Yortsos and Fokas' exact solution for the linear waterflood case including capillary pressure effects and with Larson's model for surfactant flooding. The effects of the above-mentioned transport mechanisms on concentration profiles and on oil recovery are also analyzed.     

明渠层流近床面颗粒拖曳力研究

泥沙颗粒受到的拖曳力是泥沙运动的主要驱动力,而当前应用于计算流体力学-离散颗粒法(CFD-DPM)耦合模型进行水沙运动模拟的泥沙颗粒拖曳力公式均没有考虑明渠流底床边壁作用的影响。求解不可压缩Navier-Stokes方程,对明渠层流不同雷诺数条件下床面附近不同高度处颗粒所受拖曳力进行了模拟,根据模拟结果变化规律,提出了综合考虑床面和水流惯性对标准拖曳力影响的修正拖曳力计算公式。与常用的单颗粒标准拖曳力公式和考虑遮蔽效应的多颗粒拖曳力公式相比,采用本文修正公式得到的水沙作用力更接近高精度数值解,应用于CFD-DPM输沙模拟获得的输沙结果与输沙率公式结果一致,应用分析表明输沙模拟应当采用粗糙底床边界。     

Deformation and damage due to drying-induced salt crystallization in porous limestone

This paper presents a computational model coupling heat, water and salt ion transport, salt crystallization, deformation and damage in porous materials. We focus on crystallization-induced damage. The theory of poromechanics is employed to relate stress, induced by crystallization processes or hygro-thermal origin, to the material's mechanical response. A non-local formulation is developed to describe the crystallization kinetics. The model performance is illustrated by simulating the damage caused by sodium chloride crystallization in a porous limestone. The results are compared with experimental observations based on neutron and X-ray imaging. The simulation results suggest that the crystallization kinetics in porous materials have to be accurately understood in order to be able to control salt damage. The results show that the effective stress caused by salt crystallization depends not only on the crystallization pressure but also on the amount of salt crystals, which is determined by the spreading of crystals in the porous material and the crystallization kinetics.     

Numerical simulation of multiphase cavitating flows around an underwater projectile

The present simulation investigates the multiphase cavitating flow around an underwater projectile. Based on the Homogeneous Equilibrium Flow assumption, a mixture model is applied to simulate the multiphase cavitating flow including ventilated cavitation caused by air injection as well as natural cavitation that forms in a region where the pressure of liquid falls below its vapor pressure. The transport equation cavitating model is applied. The calculations are executed based on a suite of CFD code. The hydrodynamics characteristics of flow field under the interaction of natural cavitation and ventilated cavitation is analyzed. The results indicate that the ventilated cavitation number is under a combined effect of the natural cavitation number and gas flow rate in the multiphase cavitating flows.     

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube

The present theoretical assessment deals with the peristaltic-ciliary transport of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrication approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Furthermore, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.     

Impact of Capillary-Driven Liquid Films on Salt Crystallization

Flow-through drying of ionic liquids in porous media can lead to super saturation and hence crystallization of salts. A model for the evolution of solid and liquid concentrations of salt, in porous media, due to evaporation by gas flow is presented. The model takes into account the impact of capillary-driven liquid film flow on the evaporation rates as well as the rate of transport of salt through those films. It is shown that at high capillary wicking numbers and high dimensionless pressure drops, supersaturation of brine takes place in the higher drying rate regions in the porous medium. This leads to solid salt crystallization and accumulation in the higher drying rate region. In the absence of wicking, there is no transport and accumulation of solid salt. Results from experiments of flow-through drying in rock cores are compared with model prediction of salt crystallization and accumulation.     

Discontinuous bifurcation analysis of thermodynamically consistent gradient poroplastic materials

In this work, analytical and numerical solutions of the condition for discontinuous bifurcation of thermodynamically consistent gradient-based poroplastic materials are obtained and evaluated. The main aim is the analysis of the potentials for localized failure modes in the form of discontinuous bifurcation in partially saturated gradient-based poroplastic materials as well as the dependence of these potentials on the current hydraulic and stress conditions. Also the main differences with the localization conditions of the related local theory for poroplastic materials are evaluated to perfectly understand the regularization capabilities of the non-local gradient-based one. Firstly, the condition for discontinuous bifurcation is formulated from wave propagation analyses in poroplastic media. The material formulation employed in this work for the spectral properties evaluation of the discontinuous bifurcation condition is the thermodynamically consistent, gradient-based modified Cam Clay model for partially saturated porous media previously proposed by the authors. The main and novel feature of this constitutive theory is the inclusion of a gradient internal length of the porous phase which, together with the characteristic length of the solid skeleton, comprehensively defined the non-local characteristics of the represented porous material. After presenting the fundamental equations of the thermodynamically consistent gradient based poroplastic constitutive model, the analytical expressions of the critical hardening/softening modulus for discontinuous bifurcation under both drained and undrained conditions are obtained. As a particular case, the related local constitutive model is also evaluated from the discontinuous bifurcation condition stand point. Then, the localization analysis of the thermodynamically consistent non-local and local poroplastic Cam Clay theories is performed. The results demonstrate, on the one hand and related to the local poroplastic material, the decisive role of the pore pressure and of the volumetric non-associativity degree on the location of the transition point between ductile and brittle failure regimes in the stress space. On the other hand, the results demonstrate as well the regularization capabilities of the non-local gradient-based poroplastic theory, with exception of a particular stress condition which is also evaluated in this work. Finally, it is also shown that, due to dependence of the characteristic lengths for the pore and skeleton phases on the hydraulic and stress conditions, the non-local theory is able to reproduce the strong reduction of failure diffusion that takes place under both, low confinement and low pore pressure of partially saturated porous materials, without loosing, however, the ellipticity of the related differential equations.     

A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow

An overview of present understanding of microstructure in flowing suspensions is provided. An emphasis is placed on how the microstructure leads to observable bulk flow phenomena unique to mixtures. The bridge between the particle and bulk scales is provided by the mixture rheology; one focus of the review is on work that addresses the connection between microstructure and rheology. The non-Newtonian rheology of suspensions includes the well-known rate dependences of shear thinning and thickening, which have influence on bulk processing of suspensions. Shear-induced normal stresses are also measured in concentrated suspensions and include normal stress differences, and the isotropic particle pressure. Normal stresses have been associated with shear-induced migration, and thus have influence on the ultimate spatial distribution of solids, as well as the flow rate during processing; a second focus is on these uniquely two-phase behaviors and how they can be described in terms of the bulk rheology. An important bulk fluid mechanical consequence of normal stresses is their role in driving secondary flows.