Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Ein interaktives Verfahren zur Auswertung von Kaustiken an Trennflächenrissen

Übersicht In diesem Beitrag wird eine auf der interaktiven numerisch/graphischen Bildverarbeitung beruhende Methode zur Ermittlung der Spannungsintensitätsfaktoren, für Trennflächenrisse in Verbundmaterialien vorgestellt. Eine Anzahl von detenpunkten entlang der experimentell aufgezeichneten Kaustik wird als Eingabe verwendet. Das Verfahren überprüft die Genauigkeit und Zuverlässigkeit der Ergebnisse selbst, indem die auf der Basis des Resultats numerisch generierte Kaustik mit der experimentellen verglichen wird.

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An interactive method for data processing from crack tip caustics at interfaces

Summary An interactive numerical-graphical image processing method for the evaluation of stress intensity factors at interface cracks in composites will be presented. Based on a set of experimental data points suitably chosen along the caustic the multipoint overdeterministic data reduction technique provides reliable and rapidly coverging results by cross-checking experimental caustics with numerically generated iterative caustics.

     

Non-Markovian diffusion process in polymers and stretched exponential relaxation

In this contribution, we model the long-time behaviour of the desorption from an LDPE sheet, using non-Markovian random walks. It is shown that the mass of penetrant in the final stage of desorption decays as t ^–m , where m is proportional to the exponent of the probability distribution (t) t ^–(1+u), 0 < v < 1. Furthermore, it is shown that this model may lead to the so-called mechanical stretched exponential relaxation, and that Wagner's memory function can be obtained as a special case.Presented at the second conference Recent Developments in Structured Continua, May 23–25, 1990, in Sherbrooke, Québec, Canada     

Phase Transition with the Line‐Tension Effect

We make the connection between the geometric model for capillarity with line tension and the Cahn‐Hilliard model of two‐phase fluids. To this aim we consider the energies where u is a scalar density function and W and V are double‐well potentials. We show that the behaviour of F _ε in the limit ε→0 and λ→∞ depends on the limit of ε log λ. If this limit is finite and strictly positive, then the singular limit of the energies F _ε leads to a coupled problem of bulk and surface phase transitions, and under certain assumptions agrees with the relaxation of the capillary energy with line tension. These results were announced in [ABS1] and [ABS2]. (Accepted November 5, 1997)     

Entlastungsvorgänge in der durch eine kreisringförmige Wärmequelle plastisch deformierten Scheibe

Übersicht Es wird die instationäre Spannungsverteilung zufolge einer kreisringförmigen Wärmequelle in der elastisch-idealplastischen Scheibe untersucht. Diese stellt ein Modell der rotierenden Anode einer Röntgenröhre dar. Als Kriterium für das Auftreten von plastischem Fließen dient die Trescasche Fließbedingung. Während der Erhitzung bildet sich in der Umgebung der Wärmequelle in plastischer Bereich. Dieser wird nach dem Abschalten von einer entlasteten Zone aufgezehrt.

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Elastic unloading of a disk after plastic deformation by a circular heat source

Summary Subject of the investigation is the transient stress distribution in an elastic-plastic disk acted upon by a circular heat source. The disk serves as a mechanical model of the rotating anode of an x-ray-tube. The calculation is based on Tresca's yield criterion and the flow rule associated to it. During heating, a plastic region spreads around the source, which is absorbed by an unloaded zone after the removal of the source.

     

Nonequilibrium thermodynamics of pseudoelasticity

Solid-solid phase transitions often exhibit hystereses, and a hysteresis indicates energy dissipation. Pseudoelasticity refers to a hysteretic loadingunloading characteristic observed in the stress-induced martensitic transformation of shape memory alloys.This paper describes the thermodynamic model ofideal pseudoelasticity, a largely schematized adaptation of the experimental observations, and it reviews the works of other authors on thermodynamics of pseudoelasticity. Different approaches vary widely and we have chosen to put them into perspective by contrasting their assumptions and predictions against those of ideal pseudoelasticity.Ideal pseudoelasticity receives support from the experimental results of Fu [1] and its thermodynamic properties have been exploited by Huo [2]. The model makes use of an analytical ansatz proposed by Müller [3] in which the hysteresis is assumed to be due to the presence of a coherency energy in solid phase mixtures. This model permits the study of stability of the equilibrium states and the calculation of the energy dissipation or entropy production during the phase transition: The equilibrium states of a phase mixture are found to be unstable in load-controlled processes and the dissipated energy is related to the coherency coefficient.We also discuss some open problems concerning the states inside the hysteresis loop and the formation of interfaces.     

Ein Stoffgruppenmodell für die Berechnung der Diffusion in polynÄren Gasgemischen

A component group model for a simplified calculation of diffusion in multicomponent gaseous mixtures is developed. It is assumed, that the components of the mixture may be classified into groups in such way, that the binary diffusion coefficients between components of a group and also the binary diffusion coefficients between components of different groups may be approximated by averages. The application of the component group model is demonstrated for the mixture of dissociated air and for a 14-component H-C-N-O mixture. For many technically important gaseous mixtures a model with two or three groups of components yields a sufficient accurate approximation.     

Analysis of a method and a system to determine heat transfer and properties of fluids in the absence of temperature measurements and a modified Fourier Equation

The technique to determine by capacitance measurements heat transfer, thermal transport and dielectric properties of fluids introduced recently is now analyzed for a simple system of spherical geometry. The temperature distribution under programmed heat input to a fluid annulus between solid walls is computed by finite difference method for the determination of the capacitance time function of the arrangement. A system of heavy wall structure and heated long enough will produce a capacitance-time curve which is a function of thermal conductivity only. Thermal diffusivity is of influence in thin wall systems. The capacitance change of a heavy wall arrangement is related to the thermal conductivity of the test fluid by a modified Fourier equation. This equation describes the heat flow through the fluid layer but includes the thermal expansion of the solid walls. The change of geometry with T is therefore accounted for. For other multicomposite structures the Fourier equation must be further modified by including the thermal expansion of all materials of the structure and possibly also their compressibilities.

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Zusammenfassung Die kürzlich eingeführte Methode der Bestimmung von Wärmeübergang, thermischen Transport und dielektrischen Größen mittels Kapazitäts-Zeit-Messung wird analysiert für ein einfaches kugeliges System. Die Temperaturverteilung in der Flüssigkeit im Kugelspalt zwischen zwei festen Körpern wird für konstante Wärmezufuhr von außen mittels der Differenzmethode bestimmt und daraus die Kapazitäts-Zeit-Funktion ermittelt. Es wird gezeigt, daß die Kapazitäts-Zeit-Kurve nur eine Funktion der Wärmeleitzahl ist für den Fall dickwandiger Anordnungen. Für dünnwandige Systeme wird sie auch abhängig von der Temperaturleitzahl. Es wird eine modifizierte Fourier-Gleichung eingeführt, die den Wärmetransport durch die Flüssigkeit beschreibt, dabei aber die Änderung der Geometrie der Schicht berücksichtigt, die sich wegen der thermischen Ausdehnung der festen Wände bei der Einstellung der Temperaturdifferenz ergibt. Für andere mehrschichtige Körper muß die Fourier-Gleichung weiterhin modifiziert werden durch Berücksichtigung der thermischen Ausdehnungskoeffizienten aller beteiligten Materialien und möglicherweise auch ihrer Kompressibilitäten.

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Nomenclature A average cross-sectional area of fluid layer - A coefficient matrix - B matrix defined by Eq. (20) - B₀ geometric constant of fluid layer (A/L) at reference temperature - C capacitance of arrangement - C_i, C_r capacitance of layer of fluid i and reference fluid at temperature T - capacitances at reference temperature - C_H, c_l specific heats of outer and inner wall - FA...FE constants defined in Eqs. (13 ... 17) - L thickness of fluid layer - M_H, M_L mass of outer and inner wall - P power input to the system - R constant defined by Eq. (24) - T temperature - T_ref reference temperature - T (O, t), T (L, t) temperatures of outer and inner wall at time t - T _i ⁿ , T _i+0 ^n+m temperatures at location i and time n (m=number of t's; 0=number of x's) - T temperature difference across fluid layer - T apparent temperature difference - t_h, T_l temperature increases of outer and inner wall - T_max temperature change of system from one to another thermal equilibrium condition a thermal diffusivity - k, k_i, k_r thermal qonductivity of fluids and of fluid i and reference fluid - q heat flow through fluid layer - ^rh,^rl inner radius of outer wall and outer radius of inner wall - ^rOH,^rOL radii at reference temperature - t time - t time interval - x coordinate - ¯x vector of unknown T_i ⁿ⁺¹ - x length interval Greek symbols linear thermal expansion coefficient - _H, _L linear thermal expansion coefficient of materials of outer and inner wall - dielectric constant - _i, _ref dielectric constant of fluid i and reference fluid - ₀ permittivity of free space - multiplyer of conduction Eq. (7) in finite difference form - time needed to establish quasi-steady state conditions in the system heated by a constant power input In honor of Prof. Dr. E. Schmidt to his 80th Birthday.     

General solution of the two-dimensional heat equation for two concentric domains of different material

The general solution of the two-dimensional heat equation is given for two concentric domains consisting of different materials; it is represented as integrals over the given source and boundary distribution multiplied by a Green's function. The Green's function in this problem is given for any (linear) boundary condition of Sturm-Liouville type with constant coefficients. Examples are evaluated for source free problems with uniform initial temperature distribution and a boundary condition which corresponds to constant external temperature. Numeric evaluations show the development of the temperature distribution with time in compounds heated from outside and also for an isolated electric conductor which is cooled from outside after it has been heated by a short circuit.

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Allgemeine Lösung der zweidimensionalen Wärmeleitgleichung für zwei konzentrische Kreisbereiche verschiedener Materialien

Zusammenfassung In dieser Arbeit wird die allgemeine Lösung der zweidimensionalen Wärmeleitungsgleichung für zwei konzentrische Kreisbereiche mit unterschiedlichen Materialeigenschaften angegeben. Diese ist als quellenmäßige Darstellung gegeben, d.h. als Integral über die Wärmequellen im Inneren und am Rand und über die Anfangsverteilung, wobei alle mit der zugehörigen Greenschen Funktion multipliziert werden. Die angegebene Greensche Funktion gilt für alle beliebigen (linearen) Randbedingungen vom Sturm-Liouvilleschen Typ mit konstanten Koeffizienten. Es werden für quellenfreie Probleme mit homogener Anfangstemperatur und konstanter Außentemperatur Beispiele berechnet. Numerische Berechnungen zeigen die zeitliche Entwicklung der Temperaturverteilung für Zweischichtenanordnungen, welche von außen erwärmt werden, und für einen isolierten elektrischen Leiter, welcher nach einer Erhitzung durch Kurzschluß von außen gekühlt wird.

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Nomenclature a diffusion constant, m²/s - c specific heat for constant pressure, W_s/kgK - d₁ inner diameter, m - d₂ outer diameter, m - l length of the construction element, m - J_m, Y_m Bessel functions of m-th order - r, polar coordinates; m, rad - t time, s - T₀ initial temperature, K - T_e external temperature of the medium surrounding the compound, K - T(r, , t) temperature field - _n n-th eigenvalue of the characteristic equation - thermal conductivity, W/mK - (r, , t) heat source density, Ws/m⁵ - mass density, kg/m³     

Die Berechnung des Blasenwachstums beim Verdampfen von Flüssigkeiten an Heizflächen als numerische Lösung der Erhaltungsgleichungen

A numerical procedure on the basis of the Marker and Cell-method [1] was developed in order to solve the conservation equations for mass, momentum and energy for the case of bubble growth on a heating surface. This procedure was used to calculate steam bubble growth on a horizontal stainless steel heating surface under saturated pool boiling conditions at a system pressure of 1 bar and different superheatings. The essential results obtained are:

-Good agreement was found between calculations and experiments concerning bubble growth rates, bubble shape and temperature field in the liquid surrounding the bubble.

-During its growth the bubble penetrates the temperature boundary layer formed in the liquid on the heating surface, simultaneously liquid is displaced aside.

-The microlayer evaporation fraction of the total bubble growth increases with growth time from 20 % to 50%.