A comparison of viscoelastic and empirical rheological models in context of squeeze flows

This work compares the behavior of a Giesekus and Carreau-Yasuda fluid in a squeeze flow between two circular plates. In order to do this the Carreau-Yasuda model is fitted to the shear viscosity curve of the Giesekus model and the squeeze stress is compared over the process time. The investigations are performed numerically with a 2.5 dimensional wedge model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

存在滑移时两圆球间的幂律流体挤压流动

基于Reynolds润滑理论分析了壁面滑移对任意圆球颗粒间幂律流体的挤压流动的影响。研究表明有壁面滑移时挤压流动的粘性力可通过引进本文定义的滑移修正系数分离出无滑移解。推导出的挤压力滑移修正系数是一积分表达式，依赖于滑移参数、幂律指数、球间隙和积分上限。一般地壁面滑移导致粘性力减小，粘性力的减小量随幂律指数的增大而增大，表明壁面滑移对剪切增稠流变材料有更大的影响；粘性力的减小量还随着滑移参数的增大而增加，而这恰与假设相符合；粘性力的减小量又随球间隙减小或积分上限的增大（从液桥情况到完全浸渍）而减小直到趋于常数，这一特性在离散元模拟时可以有效地减少计算量。     

Inertia Effects in Squeeze Flows of Viscoplastic Fluids

A squeeze flow of a viscoplastic fluid through a narrow clearance between two coaxial surfaces of revolution is considered. The problem is described by boundary-layer equations. With the use of the method of integral approaches, formulas for the pressure distribution are obtained. Generally, the flow of viscoplastic fluids given by the nonlinear Shulman model is considered. The flows of viscoplastic fluids given by the Herschel, Bulkley, Bingham, Ostwald-de Waele, and Newton models are discussed in detail. Numerical examples of pressure distributions in the clearance between parallel disks are presented.     

Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell

Summary. The theory of algebraic curves and quadrature domains is used to construct exact solutions to the problem of the squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell. The solutions are exact in that they can be written down in terms of a finite set of time-evolving parameters. The method is very general and applies to fluid domains of any finite connectivity. By way of example, the evolution of fluid domains with two and four air holes are calculated explicitly. For simply connected domains, the squeeze flow problem is well posed. In contrast, the squeeze flow problem for a multiply connected domain is not necessarily well-posed and solutions can break down in finite time by the formation of cusps on the boundaries of the enclosed air holes. Received September 20, 2000; accepted September 10, 2001 Online publication November 5, 2001     

Mathematical modelling of swirling flow in hydraulic turbines for the full operating range

We introduce and validate a novel mathematical model for computing the radial profiles of both axial and circumferential velocity components, respectively, of the swirling flow exiting the runner of hydraulic turbines within the full operating range. We assume an incompressible, inviscid, axisymmetrical, and steady swirling flow, with vanishing radial velocity at runner outlet. First we find the correlation between the flux of moment of momentum downstream the turbine runner and the operating regime given by turbine’s discharge and head. Second, we express the relationship between the axial and circumferential velocity components, corresponding to the fixed pitch runner blades, using the swirl-free velocity instead of the traditional relative flow angle at runner outlet. It is shown that the swirl-free velocity profile practically does not change with the operating regime. Third, we introduce a constrained variational problem corresponding to the minimization of the flow force while maintaining the prescribed discharge and flux of moment of momentum. This formulation also accounts for a possible central stagnant region to develop when operating the turbine far from the best efficiency point. Fourth, we show that by representing the unknown axial velocity profile with a suitable Fourier–Bessel series, the discharge constraint can be automatically satisfied. The resulting numerical algorithm is robust and produces results in good agreement with available data for both axial and circumferential velocity profiles measured on a model Francis turbine at several operating regimes. Our mathematical model is suitable for the early optimization stages of the runner design, as it provides the swirling flow configuration at runner outlet without actually computing the runner. By optimizing the parameterized swirl-free velocity profile one can achieve through the inverse design approaches the most suitable runner blades configuration at the trailing edge.     

On the preliminary design of axial fans: extending the validity of the flow assumptions over the whole hydraulic characteristic and improvement of modeling

In order to carry out a preliminary axial fan design, established assumptions are made onto the flow structure within the fan at the design point. As an example the very common hypothesis of radial equilibrium, states that the radial velocity component downstream the fan is zero, and that the flow in this area is axisymmetric. With the help of this hypothesis, the flow is idealized in order to draw quantitative conclusions. The present communication aims at extending these assumptions on the whole flow regime in order to help fan designers to reduce the try-and-error cycle number. An analytical formulation for axial fan velocity distributions at design and off design conditions is proposed for an arbitrary work distribution. It is shown that the total pressure characteristics can be described by means of hyperbola and straight line. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

两平行圆盘间或两圆球间存在二阶流体时的挤压流动

为了进行湿颗粒群的离散元模拟,研究两圆球颗粒间二阶流体在挤压流动时的法向粘性力．首先用小参数法对两平行圆盘间二阶流体挤压流动的速度场和正应力分布进行了近似分析,然后用类似的方法,分析任意两圆球间二阶流体的挤压流动,得到了压力分布和法向粘性力的解析解．     

Elastoviscoplastic fluid flow in non-circular tubes: Transversal field and interplay of elasticity and plasticity

An analytical study of elastoviscoplastic fluid flow in tubes of non-circular cross section is presented. The constitutive structure of the fluid is described by a linear frame invariant combination of the Phan-Thien−Tanner model of viscoelastic fluids and the Bingham model of plastic fluids. Non-circular tube cross sections are modeled by the shape factor method a one-to-one mapping of the circular base contour into a wide spectrum family of arbitrary tube contours. Field variables are expanded into asymptotic series in terms of the elasticity measure, the Weissenberg number We, coupled with an asymptotic expansion in terms of the geometrical mapping parameter ε leading to a set of hierarchical momentum balance equations which are solved successively up to and including the third order in We when the secondary field appears for the first time. The computational algorithm developed is applied to the study of the non-rectilinear flow in tubes with triangular and square cross sections. We find that the presence of the yield stress dampens the intensity of the purely viscoelastic vortices, the higher the yield stress the lower the intensity of the vortices in the cross-section, and the further away the vortices are from the center of the cross section as compared to the purely viscoelastic vortices. The results also evidence that viscoelasticity increases the axial flow for given viscoplastic conditions and pressure drop, and consequently increases the rate of flow, a phenomenon that may find applications in optimizing material transportation.     

A numerical scheme for unsteady flow of a viscous fluid between elliptic plates

A new continuation method has been developed to solve the nonlinear eigenvalue problem describing the unsteady, squeezing flow of a viscous fluid between elliptic plates. Unlike the numerical schemes previously used (e.g. homotopy algorithm), the present scheme is conceptually simple, noniterative, insensitive to the first approximation and works for all values of squeeze number S characterizing the flow. The numerical results compare extremely well with those obtained with sophisticated schemes. Since existing numerical data are limited to three sparsely spaced values of S, additional data are reported for systematically spaced values of squeeze number S and ellipticity parameter β. Although the scheme has been applied to a specific problem, it appears potentially capable of handling a variety of nonlinear eigenvalue problems.     

Lubrication of porous solids in reference to human joints

A simple mechanical model which has some features in common with load bearing human joints is described. The normal approach of two plane surfaces, one of which is covered with porous material is analysed. The gap between the two surfaces is filled with micropolar fluid to represent a particulate suspension (i.e, synovial fluid) as lubricant. The poresize diameter is so small that only the suspending medium,i.e, the viscous fluid enters into the porous matrix due to the filtration action. The problem has been solved separately in two regions; flow of viscous fluid in the porous matrix and the squeeze film lubrication with micropolar fluid as lubricant in between the two approaching surfaces along with suitable matching conditions at the porous boundary. Several interesting results have been brought out. Agreement with available experimental results and the computational results presented, herein, is quite good.     

Infinite Element Approximation to Axial Symmetric Stokes Flow

We considered in [1] the finite element approximation to axial symmetric Stokes flow in a bounded domain. The problem for the flow passing an obstacle in an unbounded domain is also frequently encountered. In this paper, we are going to give approximate solutions for this problem by an approach stated in [2]. An iterative method is used to calculate the combined stiffness matrix.     

Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects

The vibrational behavior of electrostatically actuated microstructures subjected to nonlinear squeeze film damping and in-plane forces is investigated. First-Order Shear Deformation Theory is used to model dynamical system by means of finite element method, while finite difference method is applied to solve the nonlinear Reynolds equation of squeeze film damping simultaneously. Vibrational analysis of microplates is performed by solving eigenvalue problem, after validating the model by pull-in phenomenon and transient behavior. In addition, considering nonlinear squeeze film damping and step-input actuations, response frequencies of microplates are calculated. Effect of ambient pressure and in-plane forces on dynamic pull-in phenomenon is also studied. Results for simplified models are verified and are in good agreement with the published literature. This investigation can reveal nonlinear vibrational behavior of microstructures.     

非线性边界滑移挤压膜流动

用一种包含初始滑移长度和临界剪切率的非线性边界滑移模型研究了两个球体间的挤压流体膜问题．研究发现初始滑移长度对低剪切率下的滑移行为起主要作用,而临界剪切率决定了高剪切率下的边界滑移程度．球体表面挤压流体膜的边界滑移量是与半径坐标相关的高度非线性函数．在挤压膜的中心点和远离中心点处由于低剪切率滑移量等于初始滑移长度,然而在高剪切率区域滑移长度迅速增加．球体挤压膜的流体动压力随着初始滑移长度的增加和临界剪切率的减小而减小,并且临界剪切率对流体动力的影响要比初始滑移长度大的多,当临界剪切率很小的情况下,流体动压随着最小膜厚的减小几乎不再增加．所用模型给出的理论预报和实验非常吻合．     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.     

Helical flow of a Bingham fluid arising from axial Poiseuille flow between coaxial cylinders

The Bingham fluid model represents viscoplastic materials that display yielding, that is, behave as a solid body at low stresses, but flow as a Newtonian fluid at high stresses. In any Bingham flow, there may be regions of solid material separated from regions of Newtonian flow by so-called yield boundaries. Such materials arise in a range of industrial applications. Here, we consider the helical flow of a Bingham fluid between infinitely long coaxial cylinders, where the flow arises from the imposition of a steady rotation of the inner cylinder (annular Coutte flow) on a steady axial pressure driven flow (Poiseuille flow), where the ratio of the rotational flow compared to the axial flow is small. We apply a perturbation procedure to obtain approximate analytic expressions for the fluid velocity field and such related quantities as the stress and viscosity profiles in the flow. In particular, we examine the location of yield boundaries in the flow and how these vary with the rotation speed of the inner cylinder and other flow parameters. These analytic results are shown to agree very well with the results of numerical computations.     

Uniaxial exchange flows of two Bingham fluids in a cylindrical duct

Buoyancy driven flows of two Bingham fluids in an inclined ductare considered, providing a simplified model for many oilfieldcementing processes. The flows studied are near-uniaxial andstratified, with the heavy fluid moving down the incline, displacingthe lighter fluid upwards. Existence and uniqueness resultsare obtained for quite general flows and for those which satisfyan axial flow rate constraint. Parametric dependence of thesolutions on the axial pressure gradient is studied. Flows whichsatisfy a zero net axial flow constraint result from an axialpressure gradient which minimizes the viscous dissipation, butnot the plastic dissipation. A regularization method is usedto compute solutions to these problems for (more or less) arbitraryfluid-fluid interfaces and duct-cross sections. Examples relatedto a number of practical applications are presented.     

Numerical study of gas–solid flow in a cyclone separator

This paper presents a numerical study of the gas–powder flow in a typical Lapple cyclone. The turbulence of gas flow is obtained by the use of the Reynolds stress model. The resulting pressure and flow fields are verified by comparing with those measured and then used in the determination of powder flow that is simulated by the use of a stochastic Lagrangian model. The separation efficiency and trajectory of particles from simulation are shown to be comparable to those observed experimentally. The effects of particle size and gas velocity on separation efficiency are quantified and the results agree well with experiments. Some factors which affect the performance of cyclone were identified. It is shown that the collision between gas streams after running about a circle and that just entering occurred around the junction of the inlet duct and the cylinder of the cyclone, resulting in a short-circuiting flow. The combination of flow source and sink was distributed near the axis of cyclone, forming a flow dipole at axial section. Particles entering at different positions gave different separation efficiency. A particle with size exceeding a critical diameter, which was condition-dependant, would stagnate on the wall of cyclone cone. This was regarded as one of the main reasons for the deposition on the inner conical surface in such cyclones used in the cement industry.     

Behavior of cylindrical panels made of composite materials subjected to longitudinal impact in a gas flow

The dynamic properties of plates and cylindrical panels made of composite materials subjected to axial impact in a supersonic gas flow are investigated on the basis of a geometrically nonlinear orthotropic model and a linear wave equation for a one-dimensional medium. A solution is obtained by applying the Bubnov—Galerkin procedure with respect to the arc coordinate and a finite-difference method with respect to the axial coordinate and time. The aerodynamic pressure is found by means of an improved variant of linearized piston aerodynamics with a correction for curvature. Numerical results are presented and analyzed.     

Leaders and followers in mutual funds: A dynamic Bayesian approach

This article proposes a dynamic Bayesian framework to analyze the leadership relationships between mutual funds. To this end, a two‐step procedure is proposed. First, a Bayesian rolling window based on the Capital Asset Pricing Model is used to estimate the evolution of mutual funds' market exposure over time. Then, a vector autoregressive (VAR) model is used to analyze the leader‐follower relationship between pair of mutual funds. Several leadership measures are studied. An application to Spanish mutual funds is carried out. In addition, the study examines the determining factors of mutual fund leadership.