Unsteady viscometric circular flows of a viscoplastic medium in an annular gap

The time of initiation and cessation of a circular flow of a viscoplastic medium in an annular gap is estimated analytically and is verified numerically.     

Bingham-Il’yushin viscoplastic medium flows in channels with undulating walls

In the present paper, the flow of a Bingham-Il’yushin viscoplastic medium in plane channels with undulating walls is studied numerically. The influence of the region geometry and the yield point on the shape, dimensions, and location of rigid regions are studied. The obtained results are compared with the results of other authors who also used the thin layer approximation. The earlier unknown qualitative characteristics of flows are noted.     

Viscoelastic medium flows in convergent-divergent channels

The problem of viscoelastic fluid flow in a convergent-divergent channel is considered. A mathematical model and the results of numerical investigations are presented. A model of the differential type is used to describe the rheological properties of viscoelastic fluids. A comparative analysis of the flow parameters of generalized Newtonian and viscoelastic fluids in the channels considered is carried out on the basis of the results of numerical calculations.     

Unsteady shear flow of a viscoplastic material

A viscoplastic, or yield-stress, liquid occupies the space between two infinite parallel plates. Initially the whole system is at rest. The lower plate is suddenly jerked into motion with given speed or shear stress, while the upper plate is kept fixed. The flow consists of two regions; (1) a lower sheared region bounded above by the yield surface, (2) an upper unyielded region bounded below by the yield surface. The yield surface propagates to the upper plate as time proceeds. We first consider the equivalent one plate problem of flow over a jerked plate, and find similarity solutions and small time asymptotic solutions for prescribed shear and speed cases respectively. These solutions are used as initial solutions for the two plate case. The motion of the yield surface and the time taken for the entire material to yield are investigated. The problems considered here are two dimensional representations of some control devices, for example the light duty clutch, which consists of two corotating, coaxial discs separated by a layer of electrorheological material. In this application it is useful to know the time taken for all the material to yield.     

Calculating the flows of a viscoplastic medium in tubes using the local variation method

This article considers the problem of the motion of a visco-plastic medium in tubes and channels. The results of [1, 2] are used, which present the variational formulation and the qualitative analysis of this problem. The method of local variations suggested in [3] is used for the numerical solution of the variational problem. A more detailed presentation of the algorithm of this method in application to boundary-value and variational problems is given in [4]. Results of calculations of certain concrete problems on an electronic computer are presented.The author wishes to express his sincere gratitude to F. L. Chernous'ko for the problem formulation and helpful counsel, and G. I. Barenblatt and S. S. Grigoryan for useful discussions.     

Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

We present the results of lattice Boltzmann (LB) simulations for the planar-flow of viscoplastic fluids through complex flow channels. In this study, the Bingham and Casson model fluids are covered as viscoplastic fluid. The Papanastasiou (modified Bingham) model and the modified Casson model are employed in our LB simulations. The Bingham number is an essential physical parameter when considering viscoplastic fluid flows and the modified Bingham number is proposed for modified viscoplastic models. When the value of the modified Bingham number agrees with that of the “normal” Bingham number, viscoplastic fluid flows formulated by modified viscoplastic models strictly reproduce the flow behavior of the ideal viscoplastic fluids. LB simulations are extensively performed for viscoplastic fluid flows through complex flow channels with rectangular and circular obstacles. It is shown that the LB method (LBM) allows us to successfully compute the flow behavior of viscoplastic fluids in various complicated-flow channels with rectangular and circular obstacles. For even low Re and high Bn numbers corresponding to plastic-property dominant condition, it is clearly manifested that the viscosity for both the viscoplastic fluids is largely decreased around solid obstacles. Also, it is shown that the viscosity profile is quite different between both the viscoplastic fluids due to the inherent nature of the models. The viscosity of the Bingham fluid sharply drops down close to the plastic viscosity, whereas the viscosity of the Casson fluid does not rapidly fall. From this study, it is demonstrated that the LBM can be also an effective methodology for computing viscoplastic fluid flows through complex channels including circular obstacles.     

Three-dimensional flows of thin layers of viscoplastic media in deformable channels and cavities

The problem of the three-dimensional flow of a viscoplastic medium in a thin layer bounded by two deformable material surfaces whose points are displaced transversely across the layer is formulated and solved. Expressions for the velocity components and the flow-rate and equations for calculating the pressure and the boundary of the shear flow region are obtained. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 201–205, July–August, 1998.     

Spherical wave propagation in a viscoplastic medium

Summary A study is presented of the problem of spherical wave propagation in an infinite viscoplastic medium. The surface of a spherical cavity is subjected to a uniform impact load which is continuously maintained. The material is elastic/viscoplastic, satisfying Mises condition, isotropic hardening, and viscoplastic incompressibility. A generalized form of Malvern's constitutive relation is used with a bilinear static shear stressshear strain curve, the method of characteristics, and an IBM 7040–7094 digital computer. Particular emphasis is placed on the influence of strain hardening and of the viscosity coefficient. It is shown that changes in the strain hardening coefficient and in the viscosity coefficient have considerable influence on the results, which is to some extent unexpected in view of previous work on this subject.

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Übersicht Eine konkave innere Oberfläche wird durch eine konstante gleichmäßig verteilte Kraft belastet. Das Material wird als elastisch-viscoplastisch angenommen mit isotroper Verfestigung und viscoplastischer Inkompressibilität; es genügt der von Mises'schen Fließbedingung. Es werden eine sinngemäße Erweiterung der Malvernschen Materialgleichung und numerische Lösungen für ein Material mit bilinearer Schubspannungs- and Scherungskennlinie angegeben. Dabei zeigt sich überraschenderweise, daß Änderungen des Verfestigungskoeffizienten und der Viscosität die spherische Wellenausbreitung erheblich beeinflussen.

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This investigation was supported by the National Science Foundation under a grant to Yale University.     

Nonstationary shear flow of a viscoplastic medium

We consider problems involving nonstationary shear flow of a viscoplastic medium between two parallel plates and also in a cylindrical tube under the action of a time-varying shear stress applied to the walls of the passage.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 133–137, July–August, 1972.     

Motion of a viscoplastic liquid in a porous inhomogeneous medium

Equations of motion are derived for a viscoplastic liquid in a nonuniform medium of type 2 (piecewise uniform) or type 3 (with a variable filtration coefficient) [1] on the assumption that the motion is of steady-state type. Solutions are presented for a parallel flow and a flow with axial symmetry.     

Unsteady one-dimensional water and steam flows through a porous medium with allowance for phase transitions

Fluid flow through a porous medium is considered with allowance for heat conduction and phase transition processes. The one-dimensional problem of the breakdown of an arbitrary discontinuity is solved with reference to the processes of combined nonisothermal water and steam flow through the porous medium. It is assumed that there are two-phase zones of water and steam flow through the porous medium to the left and right of the initial discontinuity. Six qualitatively different discontinuous solutions with internal single-phase water or steam zones are constructed and domains corresponding to each of the solutions are found in the determining parameter space. For the parameters considered a solution of the breakdown problem exists and is unique when the requirements for the existence of a discontinuity structure are satisfied [{xc1}].     

Unsteady flows of a third-order viscoelastic fluid

Summary Unsteady third-order viscoelastic flow is examined for the purpose of determining a method by which certain material constants in theRivlin-Ericksen theory can be measured. The concept of an intrinsic pressure hole error is used, and an expression for this error is derived for third-order flow. It is also shown that the velocity field for unsteady creeping motion of a third-order fluid is identical at any time to a corresponding steady third-order flow. The pressure field, however, depends upon the rate of change of the flow with time.

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Zusammenfassung Es wird die instationäre Strömung dritter Ordnung einer viskoelastischen Flüssigkeit untersucht zu dem Zweck, eine Methode anzugeben, mit deren Hilfe gewisse Stoffkonstanten in der Theorie vonRivlin undEricksen gemessen werden können. Dazu wird das Konzept des intrinsic pressure hole error verwendet, und es wird für diesen Fehler im Rahmen der Theorie dritter Ordnung ein Ausdruck abgeleitet. Weiter wird gezeigt, daß das Geschwindigkeitsfeld für die instationäre schleichende Strömung einer Flüssigkeit dritter Ordnung zu jeder Zeit mit der zugeordneten stationären Strömung dritter Ordnung identisch ist. Im Gegensatz dazu hängt das Druckfeld jedoch von der zeitlichen Änderung der Strömungsgeschwindigkeit ab.

     

Unsteady flows in elastico-viscous liquids

Summary Consideration is given to two problems involving the unsteady motion of a sphere in aMaxwell liquid. In both problems the full solutions are obtained and compared in each case to the solution obtained using an approximation procedure. Good agreement is obtained for large values of the elastic parameter. The approximation reduces the mathematics considerably and thus allows experimentalists to determine the elastic parameter involved.With 2 figures     

Natural convection of a viscoplastic fluid in vertical circular channels

In contrast to a Newtonian fluid, a viscoplastic fluid can be in a state of mechanical equilibrium when heat is supplied from the side. Therefore, natural convection in a viscoplastic fluid heated from the side occurs only when the determining parameters exceed certain threshold values. The threshold conditions for the onset of convection for a flat vertical layer have been investigated several times [1–4]. The present paper is an investigation of the conditions of occurrence of plane-parallel natural convection of a viscoplastic fluid in regions with cylindrical symmetry: in a vertical annular layer and in a vertical circular tube.