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  • 1
    Electronic Resource
    Electronic Resource
    Rheological characterization of thixotropic fluids (1979)
    Springer
    Rheologica acta 18 (1979), S. 702-710 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Die Arbeit beschreibt eine phänomenologische Methode zur rheologischen Charakterisierung einer unelastischen thixotropen Flüssigkeit in einer viskometrischen Strömung. Diese Flüssigkeit wurde als Flüssigkeit vom „rate“-Typ behandelt, und es wurde ein Strukturparameterκ definiert, der den inneren Zustand der Flüssigkeit beschreibt. Damit wurde eine Definition der positiven und negativen Thixotropie gegeben. Anschließend wurde eine Prozedur vorgeschlagen, die das Modell der thixotropen Flüssigkeit durch eine Zustandsgleichung und eine Geschwindigkeitsgleichung beschreibt. Unter Benutzung der einfachsten Abhängigkeit, d. h. einer Potenzgleichung, wurde das Modell in expliziter Form konstruiert. Schließlich wurde gezeigt, daß ein Experiment vom Typ einer sprunghaften Änderung der Schergeschwindigkeit die Bestimmung der fünf rheologischen Parameter ermöglicht, die in diesem Modell auftreten.
    Notes: Summary The paper presents a phenomenological method of rheological characterization of inelastic thixotropic fluid in viscometric flow. The fluid was regarded as a material of the rate type and a structural parameterκ was defined as one of the variables describing the fluid state. A definition of positive and negative thixotropy was also given. A procedure leading to the construction of a model of thixotropic fluid in the form of an equation of state and a rate equation was proposed. Using the simplest dependence of power law, the model was constructed in an explicite form. It was proved that the experiment of the type “step-change of the shear rate” enables the determination of the five rheological parameters occurring in this model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01533344
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Laminar flow of some inelastic time-dependent fluids in pipes (1984)
    Springer
    Rheologica acta 23 (1984), S. 261-265 
    Details
    ISSN: 1435-1528
    Keywords: Thixotropy ; fading memory ; pipe flow ; friction factor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The paper presents some modification of the previously published model of thixotropic fluids for the case of fluids with irreversible destruction of the structure. In the second part of the paper the laminar flow of this kind of fluids in pipes is discussed. A simple method of determining the initial value of the structural parameter at the inlet to the pipe is proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01332191
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A generalized rheological model of thixotropic materials (1980)
    Springer
    Rheologica acta 19 (1980), S. 529-538 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Eine früher dargestellte Theorie thixotroper Stoffe wird verallgemeinert, wobei eine von dem Strukturparameter abhängige Fließspannung eingeführt wird. Weiterhin wird der Unterschied zwischen der Zerstörungs-und der Wiederaufbaugeschwindigkeit der Stoffstruktur berücksichtigt. Eine Methode zur Bestimmung der neun benötigten Stoffparameter wird ausgearbeitet. Das Modell wird am Beispiel einer thixotropen Farbe experimentell geprüft.
    Notes: Summary A generalization of the rheological model of thixotropic materials, presented previously, was carried out. In the generalized rheological equation of state the yield stress depending on the structural parameter was introduced. In the generalized rate equation the difference in the destruction and recovery rates of the material structure was taken into account. A procedure leading to the determination of nine rheological parameters of the generalized model was worked out. The model was checked experimentally for a thixotropic paint.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01517508
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  • 4
    Electronic Resource
    Electronic Resource
    Memory effects during the flow of thixotropic fluids in pipes (1981)
    Springer
    Rheologica acta 20 (1981), S. 311-323 
    Details
    ISSN: 1435-1528
    Keywords: Thixotropy ; fading memory ; pipe flow ; friction factor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Die Veröffentlichung behandelt das Phänomen der Thixotropie vom Standpunkt der Theorie der Flüssigkeiten mit schwindendem Gedächtnis. Im ersten Teil wird der Mechanismus der Thixotropie untersucht und die Einführung eines sog. Strukturparameters begründet (dieser Parameter kommt bereits in dem früher behandelten rheologischen Modell eines thixotropen Körpers vor). Im zweiten Teil wird dann eine Formel abgeleitet, welche die Voraussage des mittleren Wertes des Widerstandskoeffizienten bei der Strömung einer thixotropen Flüssigkeit durch ein Rohr ermöglicht. Dieser Formel gemäß ist der Widerstandskoeffizient eine Funktion von drei dimensionslosen Zahlen: einer verallgemeinerten Reynolds-Zahl, einer modifizierten Deborah-Zahl und einer neuen dimensionslosen Zahl, die als Struktur-Kennzahl bezeichnet werden kann. Die vorläufigen Versuchsergebnisse bestätigen die Brauchbarkeit der abgeleiteten Formel.
    Notes: Summary The paper presents the phenomenon of thioxotropy from the point of view of the theory of fluids with fading memory. In the first part of the paper the mechanism of thixotropy was discussed in order to justify the application of the concept of structural parameter (this parameter occurs in the previously presented rheological model of thixotropic materials). In the second part of the paper an equation was derived, which enables the prediction of the mean value of the friction factor during the flow of a thixotropic fluid in a pipe. According to the obtained equation the friction factor is a function of three dimensionless numbers: the generalized Reynolds number, a modified Deborah number and a new dimensionless number which may be called a structural number. The preliminary experimental results confirmed the applicability of the obtained equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01547661
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    A new general-purpose least-squares finite element model for steady incompressible low-viscosity laminar flow using isoparametric C1-continuous Hermite elements (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 215-226 
    Details
    ISSN: 0271-2091
    Keywords: Galerkin method ; Hermite, Lagrange and simplex finite elements ; Mixed UVP ; Continuous and discrete penalty ; Least-squares method ; Low-viscosity laminar flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper deals with a critical evaluation of various finite element models for low-viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least-squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low-viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least-squares method in conjunction with C1-continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping of C1 Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least-squares method in combination with isoparmetric Hermite elements offers a new general-purpose modelling technique which can accurately simulate all types of low-viscosity incompressible laminar flow in complex domains.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180205
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT MODELLING OF FREE SURFACE VISCOELASTIC FLOWS WITH PARTICULAR APPLICATION TO RUBBER MIXING (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 1117-1132 
    Details
    ISSN: 0271-2091
    Keywords: rubber mixing ; free surface flows ; viscoelastic flow ; pseudo-density method ; Lagrangian framework ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Internal mixers are used extensively in industry for mixing the components of rubber compounds. In these operations, in order to achieve effective mixing, the mixer chamber is always partially filled. This inevitably results in the appearance of multiple free surfaces in flow fields inside rubber mixer chambers. Mathematical modelling of such a flow regime is not a simple task and requires a great deal of effort. Traditional free surface flow-modelling techniques, which are mainly based on the use of volume-of-fluid or pseudo-density approaches in an Eulerian framework, are not flexible enough to cope with this problem. In this paper we describe a new method for the numerical modelling of free surface flows. In this method the pseudo-density approach is extended to a special Lagrangian framework along the trajectories of the fluid particles. We show that the developed scheme can very effectively simulate viscoelastic free surface flows encountered in rubber-mixing processes.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 7
    Electronic Resource
    Electronic Resource
    A new least-squares finite element model for combined Navier-Stokes and Darcy flows in geometrically complicated domains with solid and porous boundaries (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1609-1620 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present a novel method for linking Navier-Stokes and Darcy equations along a porous inner boundary in a flow regime which is governed by both types of these equations. The method is based on a least-squares finite element technique and uses isoparametric C1 continuous Hermite elements for domain discretization. We show that our technique is superior to previously developed models for the combined Navier-Stokes/Darcy flows. The previous works use weighted residual finite element procedures in conjunction with C0 elements which are inherently incapable of linking Navier-Stokes and Darcy equations. The paper includes the application of our model to a geometrically complicated axisymmetric slurry filtration system.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370912
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  • 8
    Electronic Resource
    Electronic Resource
    Isoparametric Hermite elements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3489-3519 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Isoparametric Hermite elements are created using Bogner-Fox-Schmit rectangles on a reference domain and mapping these numerically onto the computational domain. The difficulties involved in devising explicit C1 shape functions for isoparametric elements are thus avoided, and the resulting elements have all the benefits of full C1 continuity, the simplicity of the Bogner-Fox-Schmit element and the geometrical flexibility expected from higher-order isoparametric elements. The numerical mapping consists in the finite element solution of a linear boundary value problem, which is inexpensive and is carried out as a preprocessing operation - the required derivatives of the mapping then being supplied to the main analysis as data. Some care is required in defining the differential boundary conditions, and guidance on this is provided. Examples are given showing the success of the mapping procedure, and the use of the resulting elements in the solution of some boundary value problems. The numerical results confirm a convergence analysis provided for the new isoparametric Hermite element.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372006
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    A NEW TWO-DIMENSIONAL FINITE ELEMENT MODEL FOR THE SHALLOW WATER EQUATIONS USING A LAGRANGIAN FRAMEWORK CONSTRUCTED ALONG FLUID PARTICLE TRAJECTORIES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 4159-4182 
    Details
    ISSN: 0029-5981
    Keywords: shallow water equations ; finite element method ; Lagrangian framework ; fluid particle trajectories ; Tay estuary ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we describe a new finite element model for the tidal hydrodynamics in estuaries. The mathematical model is based on the solution of the two-dimensional shallow water equations in a Lagrangian framework which is defined along the trajectories of fluid particles. This method gives a flexible and robust numerical scheme for moving boundary flows encountered in tidal water systems. In order to validate the developed model we have, at first instance, compared our numerical results with analytical solutions obtained for domains with simple geometries. Further tests are then conducted to demonstrate the model's ability to cope with conditions such as hydraulic shock, abrupt changes in the flow domain geometry and gradual changes of water surface breadth. The change in the water surface breadth corresponds to the drying and wetting of the plains along the banks of a typical tidal river/estuary reach. The drying and wetting of flood plains result in the existence of very shallow depth of water at some sections of the flow domain during a tidal cycle. The flow equations under these conditions are strongly convection dominated. Previously published tidal models rely on either, some form of upwinding or the use of extremely fine meshes to give stable results for the convection dominated very shallow depth computations in estuaries. We show that our model can yield stable and accurate results for very shallow depths in the tidal flow domains without using any kind of artifical damping or excessive mesh refinement. Computational costs of simulating hydrodynamical conditions in a natural water course, even using a depth averaged two-dimensional approach, can be very high. The ability of our scheme to cope with convection dominated conditions has enabled us to economize the computational efforts by using coarse meshes in our finite element calculations. After the validation stage, the developed model is applied to simulate the tidal conditions in a real estuary. The comparison of the model results with the field observations shows a close agreement between these sets of data
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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