Nonlinear wave motion in magnetoelasticity

Archive for Rational Mechanics and Analysis -     

Corneal studies by photoelasticity

Freshly enucleated andin vivo eyes of cats were analyzed to determine the detailed distribution of birefringence across the cornea and through its thickness, and to determine the change of birefringence with intraocular pressure. Scattered light and oblique-incidence photoelasticity were used. The experiments are summarized and special considerations are discussed. These include the necessity for a laser-light source; diffraction limitation in producing a narrow ribbon of light; rotation of the plane of polarization; inequalities in reflected components of polarized light.     

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k_W1=1/l (where k_W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k_W1=C_l/l, where C_l is usually lesser than unity and depends on all the new parameters taken into account by the present model.     

Multi-Stage Upscaling: Selection of Suitable Methods

Reservoirs are often composed of an assortment of rock types giving rise to permeability heterogeneities at a variety of length-scales. To predict fluid flow at the full-field scale, it is necessary to be aware of these different types of heterogeneity, to recognise which are likely to have important effects on fluid flow, and to capture them by upscaling. In fact, we may require a series of stages of upscaling to go from small-scales (mm or cm) to a full-field model. When there are two (or more) phases present, we also need to know how these heterogeneities interact with fluid forces (capillary, viscous and gravity). We discuss how these effects may be taken into account by upscaling. This study focusses on the effects of steady-state upscaling for viscous-dominated floods and tests carried out on a range of 2D models are described. Upscaling errors are shown to be reduced slightly by the increase in numerical dispersion at the coarse scale. We select a combination of three different upscaling methods, and apply this approach to a model of a North Sea oil reservoir in a deep marine environment. Six different genetic units (rock types) were identified, including channel sandstone and inter-bedded sandstone and mudstone. These units were modelled using different approaches, depending on the nature of the heterogeneities. Our results show that the importance of small-scale heterogeneity depends on the large-scale distribution of the rock types. Upscaling may not be worthwhile in sparsely distributed genetic units. However, it is important in the dominant rock type, especially if there is good connectivity through the unit between the injector wells (or aquifer) and the producer wells.This revised version was published online in May 2005. In the previous version one of the authors name was missing.     

Dynamics of oblique detonations in ram accelerators

Time-accurate numerical simulations are used to study the dynamic development of oblique detonations on accelerating projectiles in ram accelerators. These simulations show that the oblique detonation can be stabilized on the projectile. The high pressure generated behind the detonation can result in accelerations up to 10⁶G and propel the projectile to velocities higher than 4.0 km/s. The detonation structure on the projectile is sensitive to the projectile geometry. A small change in the projectile shape is sufficient to alter the overall detonation structure and significantly affect the pressure distribution on the projectile. In order to maximize the thrust, an appropriate projectile shape has to be chosen to generate the detonation structure just behind the widest part of the projectile body. The projectile acceleration also has strong effects on the flow field and the detonation structure. During the acceleration, the location of the oblique detonation moves upstream from one reflected shock to another. However, one the detonation is stabilized behind the upstream shock, it remains at the new location until the transition to the next upstream shock occurs. In the simulations, the Non-Inertial-Source (NIS) technique was used to accurately represent of the projectile acceleration. Also, the Virtual-Cell-Embedding (VCE) method was employed to efficiently treat the complex projectile geometry on cartesian grids.     

Torsion pendula with electromagnetic drive and detection system for measuring the complex shear modulus of liquids in the frequency range 80–2500 Hz

An apparatus for the measurement of liquid complex shear viscosity in the frequency range 80–2500 Hz, with the use of a torsion pendulum operating in forced oscillation, is described. The drive and detection system consists of a magnet inside the pendulum, two excitation and two measuring coils. The determination of the complex shear viscosity is based on the measurement of the resonance frequency and the damping of the torsion pendulum.The feasibility of this method is demonstrated with a number of Newtonian liquids in the viscosity range 0.3 to 60 m Pa s. Results for a viscoelastic polymer solution are presented. A comparison is made with other apparatus working in the same frequency range. a coil height - A apparatus constant - B magnetic induction - C ₁,C ₂ apparatus constants - d diameter torsion rod - D pendulum damping - E apparatus constant - F ₀ top frequency - G shear modulus torsion rod - G ^* =G + iG complex shear modulus - h length torsion rod - H transfer function - i - I moment of inertia - J ₀ excitation-current amplitude - J _exc excitation current - K torsion spring constant - l length pendulum mass - M torque - n number of coil turns - p dipole moment - Q = ₀/ mechanical quality - r radius pendulum mass - R Re {Z} - t time - T temperature - U induction voltage - U ₀ induction-voltage amplitude - x distance - X Im {Z} - Z = R + iX liquid impedance - Z _cyl characteristic cylindrical impedance - Z _pl characteristic plane impedance - angle - _M coefficient of linear expansion of the pendulum mass - _R coefficient of linear expansion of the torsion rod - rate of shear - penetration depth - steady-state viscosity - _s solvent viscosity - angular displacement - ₀ angular-displacement amplitude - µ ₀ =4 10^–7 Vs/Am - density - phase angle - angular frequency - ₀ top angular frequency - band-width     

Analysis of buoyancy-aided convection heat transfer from a horizontal cylinder in a vertical duct at low Reynolds number

This paper reports a numerical study on buoyancy-aided steady convection heat transfer from a horizontal cylinder situated in a vertical adiabatic duct. Numerical results have been generated forH ₁/D=2.5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6, 20Re60, andRi up to 4. The placing of a horizontal cylinder in a vertical duct of smaller width results in significantly enhanced pure forced convection due to the blockage effect, but degrades appreciably the extent of buoyancy-aided enhancement in the heat transfer rate. Nevertheless, the presence of a vertical duct leads to an overall enhancement of mixed convection heat transfer coefficient relative to that without the confining duct. Moreover, the average Nusselt number is rather insensitive to the variation of either the position of the cylinder in the duct or the duct height in the investigated ranges of these geometric parameters.Dieser Artikel beschreibt eine numerische Studie über auftriebsunterstützte konvektive Wärmeübertragung von einem horizontalen Zylinder der in einem vertikalen adiabaten Kanal positioniert ist. Die numerischen Ergebnisse sind fürH ₁/D=2, 5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6 sowie 20Re60 undRi bis 4 berechnet worden. Die Anordnung des horizontalen Zylinders in einem schmaleren vertikalen Kanal führt auf Grund des Blockierungs-effektes zu einem deutlichen Anstieg der reinen Zwangskonvektion. Aber sie verschlechtert deutlich den Betrag der auftriebsbedingten Steigerung in der Wärmeübergangsrate. Trotzdem führt die Anwesenheit des vertikalen Kanals insgesamt zu einer Steigerung des Wärmeübergangskoeffizienten bei Mischkonvektion im Vergleich zur Abwesenheit des begrenzenden Kanals. Des weiteren ist die durchschnittliche Nusseltzahl von der Variation der Zylinderposition im Kanal oder der Kanalhöhe abhängig.     

Reflection and transmission of seismic waves at the boundaries of porous media

The mode conversions which occur during the reflection and transmission of seismic waves at the boundaries of porous media are analysed. It is shown how the energy partitioned to the various modes depends on the incident angle and on the physical properties of the fluid and solid components on each side of the boundary. The boundary conditions used here predict the occurrence of bright and dark spots as are currently observed in seismic studies of heavy oil reservoirs. They also give rise to a class of pseudo interface waves which propagate in a direction almost parallel to the surface and which become true interface waves in the limiting case where the porous media degenerate to elastic solids. When thermomechanical coupling is an important attenaution mechanism in one of the media it is also observed to have a substantial effect on the mode conversions which occur at the boundary.     

Simulation und Regelung von Verdunstungskühlern

Zusammenfassung Aus den Bilanzgleichungen für Masse und Energie wurde ein instationäres, eindimensionales Modell für einen Verdunstungskühler mit Wasserumlauf hergeleitet. Die Lösung der Modellgleichungen erfolgte mit Hilfe der Linienmethode. Die Übereinstimmung der berechneten Ergebnisse mit stationären und Instationären Versuchswerten ist gut. Als Anwendungsbeispiel wurden ein 2-Punkt-Regler und ein PI-Regler für die Kühlmittel-Austrittstemperatur verglichen.

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Simulation and control of evaporative coolers

A dynamic, one-dimensional model for an evaporative cooler with water recirculation has been derived from mass and energy balances. The solution of the model equations employs the method of lines. Calculated results are in good agreement with both stationary and non-stationary experimental data. As an application example a comparison of a 2-point-controller and a PI-controller for the cooling medium outlet temperature has been carried out.

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Formelzeichen A Austauschfläche m² - B Breite der Trennwand m - c _p spez. isob. Wärmekapazität J/(kg·K) - g Erdbeschleuningung m/s² - i Zeiger - M Molmasse kg/mol - m Masse kg - m Massenstrom kg/s - P Pumpenleistung W - p Druck, Partialdruck Pa - r Verdampfungsenthalpie J/kg - Re Reynoldszahl - t Temperatur °C - x Wasserdampfbeladung der Luft (kg H₂O)/(kg tr. Luft) Griechische Zeiche Wärmeübergangskoeffizient W/(K·m²) - Differenz - Dicke m - Dynamische Viskosität Pa·s - V Kinematische Viskosität m²/s - P Dischte kg/m³ - Stoffübergangskoeffizient kg/(m²·s) - Zeit s 2|Indizes (tiefgestellt) A Austritt - E Eintritt - F Film - K Kühlmittel - L Luft - S Sättigung - T Trennwand - Umg Umgebung - UW Umlaufwasser - V verdunstet - W Wasser - W, ab Abschlämmwasser - W, zu Zusatzwasser 3|Indizes (hochgestellt) g gasförmig - 0 trocken Wir danken Herrn W. Gohl von der Fa. E. W. Gohl GmbH, Singen/Hohentwiel für seine freundliche Unterstützung und die bereitwillige Überlassung der Meßwerte der Verdunstungskühler.     

Determining reliable edge isopachic data from interior thermoelastic measurements

The maximum stresses in a plane-stressed component typically occur on the boundary. However, it is generally difficult to obtain reliable experimental data at an edge and thermoelastic stress analysis is no exception. The inability to measure reliable edge isopachic stresses has caused many previous thermoelastic stress analyses to be more qualitative than quantitative. This paper develops and implements an effective iterative least-squares method for calculating reliable edge isopachic stresses from measured interior values. The method is based upon the plane-stress isotropic compatibility equation. A regularization scheme is employed to minimize the sensitivity to measurement error and to improve the stability of the algorithm by controlling the rate of convergence. An illustrative example with actual measured thermoelastic data is included. The processes thermoelastically determined results compare well with those obtained using strain gages.Paper was presented at the 1994 SEM Spring Conference held in Baltimore, MD on June 6–8.