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Code and accessories for 'Subcritical instabilities in plane Poiseuille flow of an Oldroyd-B fluid'
No full textRecently, detailed experiments on visco-elastic channel flow have provided convincing evidence for a nonlinear instability scenario which we had argued for based on calculations for visco-elastic Couette flow. Motivated by these experiments we extend the previous calculations to the case of visco-elastic Poiseuille flow, using the Oldroyd-B constitutive model. Our results confirm that the subcritical instability scenario is similar for both types of flow, and that the nonlinear transition occurs for Weissenberg numbers somewhat larger than one. We provide detailed results for the convergence of our expansion and for the spatial structure of the mode that drives the instability. This also gives insight into possible similarities with the mechanism of the transition to turbulence in Newtonian pipe flow
Stabilitätsanalyse und Numerische Simulation der Nichtnewtonschen Flüssigkeiten von Oldroyd Art
No full textIn this thesis, a numerical method was introduced for solving non-Newtonian viscoelastic fluid models of Oldroyd type, based on the finite element spatial discretization and on the fractional step theta-scheme time discretization used as operator splitting method. For the velocity and pressure fields, the stable Taylor-Hood element was used, whereas the stress field was discretized using discontinuous elements which satisfy an inf-sup condition in relation to the velocity space. Due to the mixed hyperbolic-parabolic character of the time-dependent system of equations governing the motion of an Oldroyd fluid, the basic idea in the present numerical approach was to decouple the calculation of the velocity and pressure fields from that of the stress field. By the operator splitting algorithm, one reduces the Oldroyd system to three simple subproblems: a Stokes like problem, a Burgers like one and a stress transport problem. A comprehensive stability analysis was given in chapter 5, for the Oldroyd system of equations starting from the continuous case, where already stability limits occurred. Further on, the semi-discretized in time Oldroyd system was analyzed and also the stability of the fractional step theta-scheme coupled with the finite element approximation applied to the linearized Oldroyd problem was investigated. The spectral analysis of the theta-scheme applied to the linearized Oldroyd system, by neglecting the nonlinear terms, was showing good stability properties and second order accuracy of the time discretization scheme. For the linear Oldroyd system no restrictions for the problem parameters were found. Considering the pure stress equation without the stress transport term and with a given stationary velocity field, a stability limit can exist. More precisely, if their exist a point or a region in the computational domain where the determinant of the velocity gradient is negative then for a=1 the stress equation is stable until a critical value of the Weissenberg number. In the case of a=0, no stability limit was found. Considering the stress constitutive equation with given velocity field, the stress will be transported along the characteristics which were the streamlines. Along streamlines which leave the computational domain, no perturbation arise. But, if there exist a stagnation point of the flow in the region with negativedeterminant of the velocity gradient, or if the streamlines are closed curves which intersect such a region, then instability of the stress components along the streamlines arises for Weissenberg numbers over the critical value. For a=0 the pure stress equation was not affected, but in the full Oldroyd system stability limits exists. For the Oldroyd-B system at least the stability limits arising in the pure stress constitutive equation exists. The numerical tests were confirming this stability limits. Two benchmark problems were studied: the lid driven cavity and the four-to-one planar contraction problem. Very good agreement with the results from the literature were obtained in the convergence range of our code. The numerical implementation of the Oldroyd system was based on the Navier-Stokes solver incorporated in the program package Albert. The principal personal contribution was the implementation of the stress tensor field with the corresponding routines for assembling the Oldroyd system and solving the stress transport equation by the discontinuous Galerkin method. Although the author largely focus in this work on the Oldroyd fluid model, the numerical algorithm can readily be extended to other differential and rate type non-Newtonian fluid models.Im Rahmen dieser Arbeit wurden Stabilitäts- und numerische Untersuchungen am Oldroyd- Gleichungssystem durchgeführt. Das numerische Verfahren basiert auf der Finite-Elemente- Raumdiskretisierung und auf dem theta-Zwischenschritt-Verfahren, ausgeführt als Operatoren- Splitting-Methode. Angesichts des gemischten hyperbolisch-parabolischen Charakters des Gleichungsystems besteht die fundamentale Idee des numerischen Verfahrens in der entkoppelten Berechnung des Geschwindigkeits-, Druck- und Spannungsfeldes. In dieser Arbeit wurde auch der nichtlineare konvektive Geschwindigkeitsterm in der Bewegungsgleichung berücksichtigt. Durch die Operatoren-Splitting-Methode wird das Oldroyd-System auf drei Unterprobleme reduziert: ein Stokes-ähnliches Problem, eines von der Art der Burgers-Gleichung und ein Transport-Problem für die Spannungen. Die Stäbilitat des Oldroyd-Gleichungssystems wurde umfassend analysiert, beginnend vom kontinuierlichen Fall, wo schon Stäbilitatsgrenzen auftreten. Weiterhin wurde die Stäbilitat der Zeitapproximation und des theta-Verfahrens gekoppelt mit der Finite-Elemente-Raumdiskretisierung untersucht. Die formale Spektralanalyse des theta-Verfahrens, angewandt auf das linearisierte Oldroyd-System, zeigt gute Stäbilitatseigenschaften und eine Genauigkeit zweiter Ordnung der Zeitdiskretisierung. Für das lineare Oldroyd-System wurden keine Beschränkungen der vier Parameter Weissenberg-Zahl We, Reynolds-Zahl Re, Gleitparameter a und Anteil der viskoelastischen Viskositaten, gefunden. Bei Vernachlässigung des konvektiven Spannungsterms im Materialgesetz kann eine obere Stäbilitatsgrenze für die Weissenberg-Zahl existieren. Im Falle a=1 gibt es zum Beispiel eine Stabilitätsgrenze, falls im Berechnungsgebiet ein Bereich existiert, wo der Determinant des Geschwindigkeitsgradientes negativ ist. Diese Grenze wurde von den numerischen Tests bestätigt. Berücksichtigt man auch den konvektiven Spannungsterm, wird ebenfalls eine Stabilitätsgrenze gefunden. Wenn im Bereich von negativen Determinant des Geschwindigkeitsgradientes (im Falle a=1) ein Staupunkt existiert oder dieser Bereich von geschlossenen Stromlinien durchschnitten wird, dann entsteht bei überkritischen Weissenberg-Zahlen eine Instabilität der Spannungskomponenten, die zeitlich entlang der Stromlinien wächst. Im Falle a=0 bleibt die Spannungsgleichung immer stabil, aber im vollen Oldroyd-System können Instabilitäten vorkommen. Das Programm wurde an zwei Benchmark-Problemen getestet: an der getriebenen Kavitat und an einer Kontraktion. Im Rahmen der Konvergenzgrenzen des Programms zeigen die Ergebnisse dieser Arbeit eine sehr gute Ubereinstimmung mit neuesten Ergebnissen aus der Literatur. Die numerische Implementierung wurde mit Hilfe des Programmpakets Albert realisiert. Der wichtigste personliche Beitrag ist die Implementierung des Spannungstensors mit den entsprechenden Routinen für die Assemblierung des Oldroyd-Systems und für die Lösung des Spannungstransport-Unterproblems mit Hilfe der Discontinuous-Galerkin-Methode
Derivation and Applications of a Generalized Oldroyd Constitutive Model
Full text linkThe search for relevant constitutive models valid for a broad variety of non-Newtonian fluids is an urgent problem in rheology. These constitutive models must accurately capture many of the non-Newtonian behaviors of the fluids and be valid for arbitrary kinematics. Many constitutive models have been proposed, but are sometimes limited in their scope of application. Some constitutive models are only valid for a specific type of fluid, and other models have many material parameters that cannot be readily evaluated. In this work, a generalized Oldroyd model is developed that can be applied to a broad range of complex, non-Newtonian fluids. The generalized Oldroyd model consists of five material parameters, that can be evaluated based on the rheological functions of two base flows--simple shear and planar extension. The material parameters are allowed to be functions of an invariant of the flow, which is chosen to be the energy dissipation rate in this work.The generalized Oldroyd equation is applied to three non-Newtonian suspensions: dilute emulsions, suspensions of rigid spheroids subject to Brownian rotations, and dilute emulsions in the presence of surfactants. A variety of kinematics is explored to validate the effectiveness of the generalized Oldroyd equation, including calculation of the stress components in planar mixed flows and uniaxial extension/compression. A number of Lagrangian-unsteady flows are also explored to test the generalized Oldroyd method in nontrivial time-dependent flows. The Lagrangian-unsteady flows that are explored in this work include: flow in a rectangular cavity with a moving wall; flow around a macroscopic sphere; time-dependent planar extension; flow around a macroscopic sphere at a finite Reynolds number; and flow between two eccentric spheres. For these Lagrangian-unsteady cases, a material fluid element is advected along one of the streamlines in the flow, and the stress is calculated along the streamline. The generalized Oldroyd model is shown in all cases to accurately predict the stresses, with greater accuracy in slower flows. The generalized Oldroyd equation in this work is shown to be a broad constitutive model that can be applied to a variety of complex fluids in arbitrary kinematics
Derivation and Applications of a Generalized Oldroyd Constitutive Model
Full text linkThe search for relevant constitutive models valid for a broad variety of non-Newtonian fluids is an urgent problem in rheology. These constitutive models must accurately capture many of the non-Newtonian behaviors of the fluids and be valid for arbitrary kinematics. Many constitutive models have been proposed, but are sometimes limited in their scope of application. Some constitutive models are only valid for a specific type of fluid, and other models have many material parameters that cannot be readily evaluated. In this work, a generalized Oldroyd model is developed that can be applied to a broad range of complex, non-Newtonian fluids. The generalized Oldroyd model consists of five material parameters, that can be evaluated based on the rheological functions of two base flows--simple shear and planar extension. The material parameters are allowed to be functions of an invariant of the flow, which is chosen to be the energy dissipation rate in this work.The generalized Oldroyd equation is applied to three non-Newtonian suspensions: dilute emulsions, suspensions of rigid spheroids subject to Brownian rotations, and dilute emulsions in the presence of surfactants. A variety of kinematics is explored to validate the effectiveness of the generalized Oldroyd equation, including calculation of the stress components in planar mixed flows and uniaxial extension/compression. A number of Lagrangian-unsteady flows are also explored to test the generalized Oldroyd method in nontrivial time-dependent flows. The Lagrangian-unsteady flows that are explored in this work include: flow in a rectangular cavity with a moving wall; flow around a macroscopic sphere; time-dependent planar extension; flow around a macroscopic sphere at a finite Reynolds number; and flow between two eccentric spheres. For these Lagrangian-unsteady cases, a material fluid element is advected along one of the streamlines in the flow, and the stress is calculated along the streamline. The generalized Oldroyd model is shown in all cases to accurately predict the stresses, with greater accuracy in slower flows. The generalized Oldroyd equation in this work is shown to be a broad constitutive model that can be applied to a variety of complex fluids in arbitrary kinematics
Code and accessories for 'Subcritical instabilities in plane Poiseuille flow of an Oldroyd-B fluid'
No full textRecently, detailed experiments on visco-elastic channel flow have provided convincing evidence for a nonlinear instability scenario which we had argued for based on calculations for visco-elastic Couette flow. Motivated by these experiments we extend the previous calculations to the case of visco-elastic Poiseuille flow, using the Oldroyd-B constitutive model. Our results confirm that the subcritical instability scenario is similar for both types of flow, and that the nonlinear transition occurs for Weissenberg numbers somewhat larger than one. We provide detailed results for the convergence of our expansion and for the spatial structure of the mode that drives the instability. This also gives insight into possible similarities with the mechanism of the transition to turbulence in Newtonian pipe flow.Morozov, Alexander N. (2019). Code and accessories for 'Subcritical instabilities in plane Poiseuille flow of an Oldroyd-B fluid', [dataset]. University of Edinburgh. School of Physics and Astronomy. https://doi.org/10.7488/ds/2510
Douglas Alexander Stewart, poet, author and playwright
No full textDouglas Alexander Stewart, poet, author and playwrigh
Author inscription in William Hazlitt, essayist and critic; selections from his writings, with a memoir, biographical and critical by Alexander Ireland
No full textAuthor's gift inscription, "To W. C. Hazlitt Esq with kind regards, from Alexr Ireland," with tipped-in review of the book.ASU Library edition has inscription from Ireland to Hazlitt [a child of William Hazlitt?].
Hazlitt , William, 1778-1830.
Ireland, Alexander, 1810-1894
The Author of the Alexander Romance
No full textThis paper, which is based on a portion of the introduction of the author’s edition of Il Romanzo di Alessandro (Mondadori: Fondazione Valla 2007), surveys the generic components of the Alexander Romance in an attempt to arrive at a definition of the work. The argument builds on Merkelbach’s categorisation of elements and uses Fusillo’s insight into the novel as an ‘encyclopaedic genre’ to propose that ‘historical novel’ is not, as Hägg contended, a misnomer for the work. The main components I discuss are: ‘life’; praxeis; chreiai; Cynic elements, including choliambic poetry and utopian perspectives; and the Egyptian aspects of the narrative. A concluding jeu d’esprit offers a characterisation of the putative author, his antecedents and his process of composition.Richard Stoneman was for 25 years editor for classics at Croom Helm and then Routledge. In 1997 he was appointed an Honorary Fellow in the department of classics, University of Exeter. After retiring from publishing in 2006 he has been pursuing his researches on the Alexander legends and teaching a course on the subject at Exeter. His Penguin translation of the Alexander Romance was published in 1991, and a volume of translated Legends of Alexander the Great appeared from Everyman in 1994. Also in 1994 he co-edited Greek Fiction with John Morgan. His edition of the Greek recensions of the Alexander Romance was published (volume I) by the Fondazione Valla in 2007 – volumes II and III will follow over the next few years – and his Alexander the Great: A Life in Legend appeared from Yale University Press in spring 2008. He is the author of a number of other books on Greek history and travel, and is writing a book on oracles
Author Correction: The dengue-specific immune response and antibody identification with machine learning
No full textCorrection to: npj Vaccineshttps://doi.org/10.1038/s41541-023-00788-7, published online 20 January 2024 In this article, the affiliation details for author Alexander Horst were incorrectly given as Alexander Horst1,2 but should have been Alexander Horst1 and other affiliations are renumbered. The original article has been corrected
Alexander Woollcott, author and stage actor
No full textAlexander Woollcott, author and stage actorTo order a reproduction, inquire about permissions, or for information about prices see:
http://www.lib.washington.edu/specialcollections/services/reproduction/reproduction
Please cite the Order NumberScanned at 600ppi with an Epson 20000 flatbed scanner. Image then rotated, cropped, level-adjusted, and sharpened using Photoshop CS3. Converted to a JPEG2000 image upon ingest into CONTENTdm
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