Pulsatile flow of an elastico-viscous liquid in a channel of elliptic cross-section

Summary The pulsatile flow of an elastico-viscous liquid through an elliptic tube is considered in this note. The problem is solved as a boundary and initial value problem by using the Laplace Transform method. Explicit expressions for velocity distribution are obtained in the two limiting cases of small and large values of time. The effect of elasticity on the flow is discussed analytically.

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Zusammenfassung In dieser Mitteilung wird die pulsierende Strömung einer viskoelastischen Flüssigkeit durch ein elliptisches Rohr betrachtet. Das Problem wird als Anfangs- und Randwertproblem mit Hilfe der Laplace-Transformation gelöst. Explizite Ausdrücke der Geschwindigkeitsverteilung werden für die beiden Grenzfälle kurzer und langer Zeiten angegeben. Die Wirkung der Elastizität auf die Strömung wird analysiert.

     

Deformation und Stabilität windbeanspruchter Kühlturmschalen

Übersicht Nach der Formulierung des Deformations- und des Stabilitätsproblems auf der Grundlage ursprünglich nicht-konformer, dreiecksförmiger, gekrümmter finiter Elemente wird zunächst das Deformationsproblem für eine ausgeführte Kühlturmschale numerisch gelöst. Die nachfolgende Stabilitätsanalyse dieser Kühlturmschale zeigt gute Übereinstimmung der mittels der Methode der finiten Elemente errechneten Beulsicherheit mit dem aufgrund des Munganschen Beulkriteriums erhaltenen Kleinstwert der Beulsicherheit.

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Summary Following the formulation of the deformation and stability problem on the basis of originally non-conforming triangular curved finite elements with the help of a variational principle with subsidiary conditions, the deformation problem is solved numerically for an existing cooling tower shell. The subsequent stability analysis of this cooling tower shell shows relatively good agreement of the buckling safety computed by means of the finite element method and the minimum of buckling safety obtained with the help of Mungan's stability criterion.

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Diese Arbeit wurde mit Unterstützung der Cooling Tower Division von Zurn Industries, Tampa, Florida, USA, begonnen und mit Unterstützung Seitens des Fonds zur Förderung der wissenschaftlichen Forschung, Wien, zu Ende geführt. Beiden Sponsoren Sei an dieser Stelle aufrichtig gedankt. Der erstgenannte Autor ist darüber hinaus der Max Kade Foundation, New York, N. Y., für die Finanzierung Seines Studienaufenthaltes an der Cornell University, Ithaca, N. Y., im Rahmen dessen er mit der Thematik dieses Aufsatzes konfrontiert wurde, zu Dank verpflichtet. Aus demselben Grund sagt der dritte Autor für ein NATO Fellowship Dank.     

Methods and correlations for the prediction of quenching rates on hot surfaces

A substantial quantity of experimental data on rewetting, much of which has not been previously reported, is analysed using the results of calculations of the two-dimensional conduction processes taking place in the walls of tubes, which have been used to simulate the cladding of nuclear fuel elements. Correlations giving the quenching heat-transfer coefficient and sputtering temperature are proposed as a result of the analysis. These correlations may be combined with the previously reported conduction analysis to predict rewetting rates under a wide range of conditions. The new data include falling film rewetting rates measured for a range of system pressures (1–15 bars), initial wall temperatures (200–650°C), coolant mass flowrates (3–50 g sec^?1) and subcoolings (0–90°C). Measurements have also been made of rewetting rates by bottom flooding of both saturated and subcooled water at atmospheric pressure.     

Development of perturbations in plane shock waves

Investigation of the stability of plane shock waves as regards nonuniform perturbations was first performed by D'yakov [1]. He obtained criteria for stability, and showed that perturbations grow exponentially with time in the case of instability. Iordanskii [2] has shown that in the case of stability, the perturbations are attenuated according to a power law. However, the stability criteria of [2] do not agree with the results of [1], Kontorovich [3] has explained the cause of the apparent discrepancies, and asserts the correctness of the criteria of [2]. A power law for the attenuation of perturbations has also been obtained in [4,5] under a somewhat different formulation of the boundary conditions.The Cauchy problem with perturbations is examined in §1 of this paper, results are obtained for cases of practical interest, and the asymptotic behavior is investigated.In §2 the effect of a low viscosity on the development of perturbations is examined. It is shown that when t the amplitude of perturbations is attenuated mainly as exp(-t), where >0 does not depend on the form of the boundary conditions at the shock wave front. The results of §2 were used in processing the experimental data of [6], which made it possible to determine the viscosity of a number of substances at high pressure.In conclusion, the author expresses his gratitude to A. D. Sakharov for valuable advice, and to A. G. Oleinik and V. N. Mincer for useful discussions. The author also thanks G. I. Barenblatt, L. A. Galin, and others who took part in a seminar at the Institute for Problems in Mechanics, for their interesting discussion and valuable comments.     

Out-of-plane deflections of metallic and composite pin-loaded coupons

The projection shadow moiré technique was employed to determine an out-of-plane contouring history of aluminum, [(+45/–45)]_3S , [(0/90₃,0] _S and [(0/90/+45/–45)]_2S fiberglass epoxy pin-loaded specimens experimentally. The contouring interval was limited to 0.0254 mm by experimental concerns. Qualification of the projection shadow moiré optical arrangement was initially accomplished by the out-of-plane contouring of a clamped, centrally loaded, circular aluminum plate. Experimental results indicate significant out-of-plane displacements in the bearing region of the coupon at load levels well below ultimate. Effects of material anisotropy could be seen in the fiber-oriented shape of the displacement contours. Comparisons with three-dimensional finite-element results indicate that experimental out-of-plane contours were significantly larger than their finite-element counterparts in the region above the pin for the [(+45/–45)]_3S , [(0/90)₃, 0] _S laminates. These deviations increased with increasing pin-load level. These variations could be attributed to linear-elastic through-thickness moduli assumptions as well as through-thickness finite-element mesh coarseness.     

On the receptivity and nonparallel stability of traveling disturbances in rotating-disk flow

The generation and evolution of small amplitude long wavelength traveling disturbances in rotating-disk flow is the subject of this paper. The steady rotational speed of the disk is perturbed so as to introduce high-frequency oscillations in the flow field. Secondly, we introduce surface imperfections on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations which are solved numerically. It is found that, for the class of disturbances considered here (wavelength on the order of Reynolds number), eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are preferentially excited. The width of these roughness elements in the radial direction is about 0.1r ₀ ^* where r ₀ ^* is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wave number than for a positive one. The cumulative wave pattern produced from the roughness site shows that the typical wave angles for these disturbances are about –26° with about seven waves around the circumference. This is in contrast with the wave angles of 10°–14° found for the 30 or so inviscid cross-flow vortices.This work was sponsored by NASA Langley Research Center under Contracts NAS1-18240 (P.B. and M.R.M.) and NAS1-18605 (P.H.).     

Effect of a permeable partition on convective instability in a rectangular cavity

The equilibrium stability of a fluid, heated from below, in a rectangular cavity with a vertical permeable partition is investigated. The small perturbation problem is solved by the Galerkin-Kantorovich method. The relations obtained for the dependence of the critical Rayleigh numbers on the partition parameters and the cavity dimensions make it possible to identify regions in which either even or odd perturbations, sensitive to only the normal or only the tangential resistance of the partition, respectively, are responsible for equilibrium crisis. The effect of a permeable partition on the convective instability of a horizontal layer of fluid under various heating conditions was considered in [1–3], where a significant dependence of the critical Rayleigh numbers on the properties of the partition was established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 6–10, May–June, 1989.     

Vortex structure in laminar boundary layers on a concave wall

Naturally occurring Görtler vortices have been investigated, using laser anemometry, in the laminar concave-surface boundary layers of water channels with 90° bends. Distributions of streamwise and spanwise velocities are presented, supported by flow visualization. Amplification was found to cease at Görtler numbers in the region of 9, followed by increasing distortion and spanwise wandering of the vortices. Development of a vortex system from an imposed disturbance has also been predicted by numerical computations.     

Hydromagnetic flow due to torsional oscillations of an infinite disk about a steady non-zero mean

The present investigation is the study of the laminar hydromagnetic flow due to torsional oscillations of an infinite disk about a steady non-zero mean in an electrically conducting fluid. Separate solutions have been obtained for the limiting cases of low and high frequency oscillations. The low frequency solution is obtained by expressing the flow functions in powers (ik) while for high frequencies, the flow functions are expressed in powers of $\text{(ik)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, where $\text{k =}\text{ω}\text{Ω}$ being the ratio of the frequency of oscillations ω to the mean disk-angular velocity Ω and i² = ?1. It is found that the oscillating part of the transverse shearing stress has a phase-lead while that of the radial shearing stress has a phase lag behind the disk oscillations. The phase-lead in the former case and phase-lag in the latter case decrease with the increase in the strength of the applied magnetic field.     

Energy release rates in a constrained epoxy disc with Hookean and Mooney–Rivlin materials

Assuming that the disc material can be modeled either as Mooney–Rivlin or as Hookean and the steel ring enclosing the disc as Hookean, the energy release rates as a function of the crack length are evaluated and compared. Two loadings are considered––one in which the surface of the star shape hole in the disc is loaded by a uniform pressure and the other in which the temperature of the composite body is uniformly raised. It is found that the linear and the nonlinear analyses give qualitatively similar results for the two loadings. For each load, the energy release rate increases with an increase in the starter crack length, reaches a maximum value and then decreases gradually.