Investigation of viscous flow phenomena in a rotating system

In this work we have investigated viscous flow in a rotating system. The system consists of a horizontally oriented cylindrical drum rotating around the center and a fixed plate as a scraping internal tool. By this plate the inner volume is divided into two separate chambers. No mass transport between the chambers can take place. The drum is completely or partially filled with a highly viscous, optically transparent silicon oil. In the second case the remaining space is filled with air as a passive phase. Depending on the settings in the system, which are the rotational speed of the drum, material properties of the liquid and the volume ratio of the two phases, different flow phenomena can be observed [1, 2]. For the characterization of the flow dimensionless ratios given by the Reynolds number Re, the Froude number Fr, the Capillary number Ca and the volumetric filling degree F are used. The system is investigated applying the experimental method of Particle Image Velocimetry (PIV) as well as suitable models of Computational Fluid Dynamics (CFD). The goal of this investigation is to identify the velocity fields in the liquid phase for a better understanding of the observed phenomena. The results obtained by the different methods are presented and discussed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The excitation mechanism of a shear stress induced rotary wave

The free surface flow in a vertical, cylindrical, rotating container will be considered when axis-symmetric angular and radial shear stress distributions are applied on the free surface. It is well known that in the inviscid case a rotary wave which can be described by a flow potential exists. We want to determine the stability limit of the axis-symmetric base state with respect to the rotary wave for small Ekman and Froude numbers. Under the above assumption, the critical flow conditions can be determined analytically. The results can be verified experimentally using a vertical, cylindrical container partially filled with water where the top lid rotates with a given angular velocity. Thus, the induced air flow will exert shear stresses in the angular and radial direction onto the water surface. Above a certain threshold, rotary waves can be observed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of the Free-Surface Flow in Partially Filled Extruders

In this work we present the free-surface flow of high viscous Newtonian liquids in a simplified extruder model, namely the flat-plate model. Due to high density and viscosity ratios, a free-surface approach based on the volume of fluid method is used. The material distribution for different degree of fillings and the resulting power consumption is investigated. In addition, the obtained power characteristic is compared against analytical consideration and numerical simulation of a fully filled case. The investigation shows that the power characteristic of a partially filled extruder can be estimated by a fully filled computation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Curvature and absorption

The problem of finding a distribution of the sources of particles (or radiation) in a bounded domain D by the outputting flow through the boundary δD is considered. It is assumed that the domain D is filled with a medium whose absorption, scattering diagram, and Riemannian metric are known. Under certain assumptions on these characteristics of the medium, the uniqueness of a solution and its stability are proved. Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 187–189.     

Flow characteristics of a metasilicate-filled low-density polyethylene melt

Certain of the flow characteristics of a filled low-density polyethylene melt have been investigated. The results obtained are compared with the results of measurements in the single-frequency vibrational shear regime.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 693–697, July–August, 1969.     

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

This paper presents two contributions to the analysis of three-dimensional slow viscous flows in cylinders of circular section. First the vector axial eigenfunctions for this geometry, namely those that satisfy homogeneous boundary conditions on the flat end walls, are derived. Secondly a method is presented to find particular solutions to the inhomogeneous Stokes equations in this geometry. These new results, together with some results obtained earlier, are used to analyse slow natural convection in a vertical cylinder completely filled with a viscous liquid. The fluid motion is generated by the differential heating of the walls of the cylinder. The natural convection flow field is shown to be a superposition of an inhomogeneous field, the fields generated by the vector eigenfunctions and a Stokes flow field. A by-product of this work has been the identification of constraints on the boundary data that have to be satisfied in order for the eigenfunction expansions to work; this knowledge will be useful when attempts are made to prove the completeness of these Stokes flow eigenfunctions.Received: June 30, 2003; revised: February 26, 2004     

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

This paper presents two contributions to the analysis of three-dimensional slow viscous flows in cylinders of circular section. First the vector axial eigenfunctions for this geometry, namely those that satisfy homogeneous boundary conditions on the flat end walls, are derived. Secondly a method is presented to find particular solutions to the inhomogeneous Stokes equations in this geometry. These new results, together with some results obtained earlier, are used to analyse slow natural convection in a vertical cylinder completely filled with a viscous liquid. The fluid motion is generated by the differential heating of the walls of the cylinder. The natural convection flow field is shown to be a superposition of an inhomogeneous field, the fields generated by the vector eigenfunctions and a Stokes flow field. A by-product of this work has been the identification of constraints on the boundary data that have to be satisfied in order for the eigenfunction expansions to work; this knowledge will be useful when attempts are made to prove the completeness of these Stokes flow eigenfunctions.     

Fluid flows through fractured porous media along Beavers–Joseph interfaces

We study a fluid flow traversing a porous medium and obeying the Darcy's law in the case when this medium is fractured in blocks by an ε  -periodic (ε>0$\epsilon >0$) distribution of fissures filled with a Stokes fluid. These two flows are coupled by a Beavers–Joseph type interface condition. The existence and uniqueness of this flow in our ε-periodic structure are proved. As the small period of the distribution shrinks to zero, we study the asymptotic behaviour of the flow when the permeability and the entire contribution on the interface of the Beavers–Joseph transfer coefficients are of unity order. We find the homogenized problem verified by the two-scale limits of the coupled velocities and pressures. It is well-posed and provides the corresponding classical homogenized problem.     

A circulating gravity wave in a cylindrical tank

A circular cylindrical vertical tank is partially filled with a liquid (Water) and a gas (air) above it. The top lid of the container rotates around the cylinder axis and induces a flow in the gas and the liquid. Above a critical rotational speed a large amplitude circulating gravity wave forms. The two phase flow problem will be reduced to a free surface single phase flow problem and the critical parameters, when the axis-symmetric flow becomes unstable with respect to the circulating gravity wave will be determined. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element and matched asymptotic expansion methods for chemical reactor flow problems

The study of flow behaviour in packed beds is an important part of the development of powerful and economical reactors. The considered averaged flow in the reactor channel filled with pelletes is modelled by the Brinkman-Forchheimer-extended Darcy equation. For the nonlinear problem subjected to Dirichlet boundary conditions we show existence and uniqueness (for small data) of weak solutions. The velocity profiles exhibit boundary layers which have to be resolved numerically. We present error estimates for inf-sup stable finite element pairs. In the case of fully developed flow and high Reynolds number the finite element solution can be compared to the flow profile obtained by using the method of matched asymptotic expansions. Finally, numerical simulations for flows in fixed bed and packed bed membrane reactors are discussed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid polymeric systems and their fillings. 2. Polymers characterized by their molecular mass distribution

Conclusions Much progress has been made in recent years toward understanding the mechanism of anomalous viscosity, elasticity, and the regularities of flow of melts, solutions, and filled systems as well as the mechanisms of periodic shear of finite amplitude. Nonlinear phenomenological models of viscoelastic fluids have been developed. The review does not include the group of problems related to combinations of stationary flow and linear periodic deformations, and combinations of linear periodic deformations with nonlinear ones. Nor have we discussed the development of methods for predicting the effects of extrudate swelling, manifestation of viscoelasticity in systems filled with short fibers, and nonisothermal flow conditions. The review does not contain new data obtained by using laser anemometry and double light refraction. The nature of the resistance in a capillary in the range of nonsteady flow has not been discussed either. The progress in these subjects is dealt with in this journal, "Mekhanika Polimerov." Insufficient attention has been paid to the rheology of viscoelastic biological fluids (blood, synovial fluids, etc.) and their substitutes, to the hydrodynamics of these liquids, and to the problem of pulsed flow. Little work has been done on the rheology of mixtures of melts of different polymers. It is also necessary to investigate the deformation of solutions and melts under superhigh velocities and under high pressures as well as the effect of constant and varying magnetic and electromagnetic fields on the mechanical flow characteristics of polymeric fluids.The second part of a paper by G. V. Vinogradov and L. A. Faitel'son (see [1]), submitted to the Third All-Union Conference on Polymer Mechanics, Riga, 1976.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 113–124, January–February, 1978.     

Influence of heat transfer on a peristaltic transport of Herschel–Bulkley fluid in a non-uniform inclined tube

Peristaltic transport in a two-dimensional non-uniform tube filled with Herschel–Bulkley fluid is studied under the assumptions of long wavelength and low Reynold number. The fluid flow is investigated in the wave frame of reference moving with the velocity of the peristaltic wave. Exact solution for the velocity field, the temperature profile, the stream functions and the pressure gradient are obtained. The physical behavior of τ, n, α and on the pressure rise versus flow rate are discussed through graphs. At the end of the article trapping phenomena for Herschel–Bulkley and also for Newtonian, Bingham and power law (which are the special cases of Herschel–Bulkley fluid) fluid are discussed.     

Optimal use of hub facilities: A two-hub model with fixed arc costs

Summary We introduce a model of a communication network design problem involving the utilization of hub facilities. That is, for a problem with two sets of customers and no intraset demand we seek to determine how the hub node associated with each set should be utilized. We assume that the only costs are the fixed costs associated with creating each of the three types of connecting arcs. A key parameter is the “group” size which is the number of communication circuits which can be bundled together in an arc. The optimal design depends strongly on how closely the arcs can be filled to capacity. The general demand problem is shown to be NP-Hard. However, for unit demand, we derive an almost “all or nothing” result which specifies that all flow should be direct node-to-node or, on the other hand, all or almost all flow should go via the hubs. Research supported in part by Grant SAB-94-0115 from the Spanish Interministerial Commission of Science and Technology while this author was on sabbatical leave at the Polytechnic University of Catalonia in Barcelona.     

Mixed convection of heat generating nanofluid in a lid-driven cavity with uniform and non-uniform heating of bottom wall

Steady state two-dimensional mixed convection in a lid-driven square cavity filled with Cu  –water nanofluid is investigated numerically in the presence of internal heat generation. In the present investigation, bottom wall is uniformly and non-uniformly heated while two vertical walls are fixed and they are thermally insulated. The top wall is moving from left to right at a constant speed. The governing equations are normalized and solved numerically with boundary conditions by finite volume approach using third order accurate upwinding scheme (deferred QUICK). Effects of the pertinent physical parameters are investigated in terms of the flow and temperature fields, as well as Nusselt number distributions. The presented results show that the solid volume fraction plays a significant role on the flow and thermal fields and the Nusselt number distributions for different flow configurations. It is found that Richardson number strongly affect the fluid flow and heat transfer in the cavity. For Ri<1$\mathit{Ri}<1$, the forced convection becomes dominant in the entire cavity, the natural convection relatively weak.     

Boundary element and finite element analysis for the efficient simulation of fluid-structure interaction and its application to mold filling processes

Metal casting and polymer molding are widely used for the economical shape processing of complex geometries. In these manufacturing processes, a liquid melt (metal, mineral or synthetic) is filled into a mold with a cavity of the desired shape. Cooling and solidification of the melt results in a product with almost the same shape as the cavity. Numerical simulations can be employed to increase the accuracy of the process. To this end, boundary element method for Stokes flow and a finite element formulation for liquid membranes are investigated in this work. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

混合微通道中不稳定的广义Couette流

在一个平行板通道中,部分充满了均匀的多孔介质,部分为纯流体的流动区,对其微通道中完全发展的不稳定层流进行了数值分析,流动由其中一块板的运动和压力梯度所引起.多孔介质区域的流动,采用扩展的Brinkman模型,即Darcy模型,纯净流动区域的流动,采用Stokes方程.还对稳定的完全发展流进行了理论分析,给出了分界面速度、边界板处的速度和表面摩擦的闭式解.通过数值计算发现,稳定完全发展流的闭式解,和不稳定流动的数值解,在所有时间点上得到很好地吻合.     

A model for fluid flow in non-fully filled tribological interfaces – Part 1: Basics and Numerics

In literature, most contributions on starved lubrication focus on the occurring pressures in macroscopic devices. Hereby, usually the Reynolds equation is modified in different ways. In contrast to this proceeding, this paper's intention is the general investigation of this tribological regime to get a fundamental comprehension on the transition from boundary lubrication to mixed lubrication. The respective model describes the flow of the fluid through two rough surfaces moving relative to each other. The lack of fluid is regarded by the fact that elements may not be fully filled with the fluid. Only elements where the fluid fully fills the gap, generate a pressure. This effect is considered by a type of unilateral constraint in combination with a penalty function. The fluid flow is computed according to the Navier-Stokes equation. In combination with the continuity equation, a set of implicit nonlinear equations has to be solved. Its potential and basic application fields are finally discussed. A further paper will show applications of the algorithm towards different scenarios. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of a filler on the strength properties of thermosets

The effect of a filler on the strength properties of polymers in tension is investigated. The thermostructural stresses that develop in the composite during cure are taken into account. Relations are given for the strength of the filled polymer as a function of the percentage filler content. In the process of analyzing the thermostructural stresses an analytic expression is obtained for the linear expansion coefficient of the composite with allowance for the structural distribution of the components. Calculated values of the strength and thermostructural stresses are presented for composites with different filler contents. The theoretical determination of the strength of filled polymers is compared with the results of experimental investigations of composites based on epoxy resin filled with quartz dust.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 1, pp. 97–101, January–February, 1973.     

Slow viscous flow near a superhydrophobic surface with trapped gas bubbles

The Boundary Element Method (BEM) is used to solve the problem of Stokes flow of a viscous fluid over a periodic striped texture of a superhydrophobic surface (SHS), partially filled with frictionless gas bubbles. The shape of the bubble surfaces and the position of the meniscus pinning points relative to the cavity walls are taken into account in the study. Two kinds of flows important for practical applications are considered: a pressure-driven flow in a thin channel with a bottom superhydrophobic wall and a shear-driven flow over a periodic texture. We study the flow pattern in the fluid over a single cavity containing a bubble with a curved phase interface shifted into the cavity. A parametric numerical study of the averaged slip length of the SHS is performed as a function of the geometric parameters of the texture. It is shown that the curvature of the phase interface and/or its shift into the cavity both result in the decrease in the average slip length. It is demonstrated that the BEM can be an efficient tool for studying Stokes flows over textured superhydrophobic surfaces with different geometries of microcavities and phase interfaces. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A model describing pressure buildup in rough surfaces with partially filled gaps

Because of an ecological and economical need to reduce the application of lubricants, the tribological regime of starved lubrication in the field of mechanical engineering has gained importance during the last decades. In order to describe the respective processes properly, models should consider that the gap between the bodies is not fully but only partially filled with a fluid. Recently, the authors introduced a model which explicitly describes the fluid flow and its interaction with the buildup of pressures under these conditions [1]. This paper points out that the correlation between the filling ratio and a time- and space-averaged pressure value is highly nonlinear. This is due to the fact that the system's load bearing character changes from being a local effect to a global effect, in particular near the fully filled regime. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)