Nonlinear wave motion in magnetoelasticity

Archive for Rational Mechanics and Analysis -     

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.     

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.     

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.     

Measurement of the thickness of a fluid layer by light absorption

A method to measure the thickness of a fluid layer and thus the depth of the interface between two layers has been developed. It uses light absorption by dye and quantitative analysis of video images. Its main advantages are that it is not intrusive and that the places and times for which measurements are made can be chosen after the experiment and so be optimally related to particular phenomena.     

Accuracy of thermocouples in radiant-heat testing

Results of an investigation of the accuracy of iron-constantan thermocouples in measuring transient surface temperatures produced by radiant heating on metallic specimens are given. The criterion of thermocouple accuracy was derived from the theory of heat conduction. The thermocouples were tested on metallic specimens of different thicknesses at varying heating rates. Comparison of these results with analytical criteria permitted quantitative determination of thermocouple errors.     

An LDV system for turbulence length scale measurements

An LDV system for making spatial correlation measurements of velocity fluctuations in turbulent nonreacting and reacting flows is presented. The LDV system is the dual beam type and consists of an elongated probe volume and a two-point optical fiber detector. Results are presented of the integral length scale measured in a nonreacting grid generated turbulent flow.A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD, Vol. 66     

Problems of powder flow in tabletting processes

Summary The flow of non-compacted granules in the tablet machine hopper is discussed with relevance to the unit dose of drug, which is required to be dispensed. The various factors used to describe powder flow such as angle of repose, interparticulate cohesion and friction, flow through apertures, bulk density and die fillability are considered. The effects of humidity and of addition of fines or lubricants and the use of commercially available apparatus for induced die feeding are included.During compression powder flows to form a dense compact. Theories of this densification and the effects of entrapped air and die wall friction during the compression and ejection of the tablets are examined.An attempt is made to correlate non-uniformity in the final tablet with problems of powder flow.Paper presented at a meeting of the British Society of Rheology, University of Nottingham, April 6–8, 1965.