Density distribution in rarefaction wave produced by rupture of diaphragm in a shock tube

The effect of the finite time of opening of the diaphragm in a shock tube on the formation of the rarefaction wave was investigated experimentally. The density distribution in the rarefaction wave was measured in relation to the coordinate and time and was compared with the known self-similar solution.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 130–131, March–April, 1972.     

The effect of random step changes of system parameters on the stability of steady vibration of nonlinear systems

Summary The author proposes a method of analysing the effect of random step changes of system parameters on the stability of steady solution of a nonlinear system in case this steady solution is not the only one. The method is based on the assumption that the time between successive step changes is comparatively long against the period of steady vibration so that transients become stabilized after each parameter change. The parameter is free to vary on a finite interval of values.

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Übersicht Es wird ein Verfahren vorgeschlagen, um die Auswirkung von zufälligen Sprungstörungen der Systemparameter auf die Stabilität von stationären Lösungen nichtlinearer Systeme zu untersuchen. Dabei wird vorausgesetzt, daß es mehrere stationäre Lösungen gibt. Es wird angenommen, daß die Zeit zwischen den nacheinander folgenden Sprungstörungen vergleichsweise lang gegenüber der Periode der stationären Schwingung ist, so daß die Einschwingvorgänge nach jeder Parameteränderung abgeklungen sind. Der Parameter kann sich dabei in einem endlichen Wertcbcreich ändern.

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Herrn Professor Dr. K. Klotter zum 70. Geburtstag gewidmet.     

Unsteady-state temperature distribution in a convecting fin of constant area

A solution for the unsteady-state temperature distribution in a fin of constant area dissipating heat only by convection to an environment of constant temperature, is obtained. The partial differential equation is separated into an ordinary differential equation with position as the independent variable, and a partial differential equation with position and time as the independent variables. The problem is solved for either a step function in temperature or a step function in heat flow rate, for zero time, at one boundary while the other boundary is insulated. The initial condition is taken as an arbitrary constant. The unspecified boundary values (temperature or heat flow rate) are presented for both cases by utilizing dimensionless plots. Experimental verification is presented for the case of constant heat flow rate boundary condition.     

Solution in one-dimensional approximation of the variational problem of constructing a maximum-thrust nozzle for gas-particle flow

In view of the complexity of the exact solution to the variational problem of constructing an optimum nozzle for gas-particle flow (see, for example, [1]) its solution in the one-dimensional approximation is of interest. In certain studies of this sort, by Marble [2] and Sternin [3], in addition to the assumption of one-dimensionality, an important role is also played by additional assumptions of smallness in the differences of the gas and particle velocities (and temperatures), which characterize the dynamic and thermal lag. The resulting linearization, used in [2, 3], not only narrows still further the region of validity of the one-dimensional approximation, but also leads to certain qualitative characteristics which do not correspond to the actual flow. For example, it is found [3] that variation of the contour curvature at only a single point may yield a finite thrust increment.In the following a solution of this problem is obtained without the additional assumptions as to smallness of the lag and the corresponding linearization.The authors wish to thank T. P. Baranova and A. M. Konkina for assistance in this study.     

X-ray diffraction study of residual macrostresses in shot-peened and fatiqued 4130 steel

A study has been made of the effects of shot peening and fatigue cycling on the residual macrostresses determined by X-ray methods in an austenitized and tempered AISI 4130 steel (150–170 ksi). The results show that the effect of shot peening is to produce a residual compressive macrostress layer 0.014-in. deep. The residual-stress profile (stress vs. depth) exhibits a small negative stress gradient at and near the surface and a large positive stress gradient in the interior. Stress relaxation (due to fatique cycling) which occurred early in the fatigue history of the specimen was found greater at the surface than in the subsurface layers. Stress gradients of the stress profile increased with continued cycling and varied with depth. A correlation appears to exist between stress relaxation and stress gradients at the surface.     

Two-layer quasi-one-dimensional model for calculating gas-particle mixture flow in nozzles

The one-dimensional approximation is widely used at the present time to calculate gas-particle (solid or liquid) mixture flows in nozzles within the framework of the two-velocity (or multi-velocity) continuum model. Other studies have been made [1–6] in which the calculations of the two-phase flow in the supersonic part of the nozzle was made by the method of characteristics, and, within the limits of the model adopted, these results may be considered exact. Comparison of the exact and approximate results [6] has shown that even for nozzles of quite simple form (nearly conical) the accuracy of the one-dimensional approximation in the case of mixture flow is considerably lower than for the pure gas, and the computation error increases with increase in the relative particle flow rate. This deterioration of the accuracy is to a considerable degree caused by flow stratification, which arises because of particle lag and leads to the formation of a wall region of pure gas. For high particle content, the wall layer, in which the gas is not subjected to thermal and dynamic input from the particles, has the nature of a low-entropy, low-temperature, high-velocity layer with parameters which differ significantly from the gas parameters in the region occupied by the particles.Therefore, in the present study a modification was made in the one-dimensional theory, based on separate averaging of the flow in the wall layer and in the core, where the gas flows together with the foreign particles. Comparison of the exact results with those obtained with the aid of conventional one-dimensional theory and the proposed two-layer model showed that this modification of one-dimensional theory led to a considerable reduction in the errors of calculation for the flow parameters.In conclusion, the authors wish to thank S. Yu. Krasheninnikov for suggesting this study and also N. S. Galyun, A. M. Konkin, and L. P. Frolov for assistance in the investigation.     

Gas discharge from a tube into a vacuum with unsteady mass and energy addition

We examine the problem of ideal gas discharge from a cylindrical tube closed at one end into a vacuum, with unsteady mass and energy addition. The gas mass is formed by vaporization of the tube wall material due to the thermal flux from the heated gas. Under the assumption of uniform energy addition throughout the volume varying in accordance with the damped oscillation law, we obtain approximate relations for the mass of the discharging gas and the impulse of the pressure forces on the end wall as a function of time and energy.The resulting impulse values are compared with those determined for unsteady expansion into a vacuum of an ideal gas of given mass when energy is added to it. An increase of the impulse calculated by this technique in comparison with the value calculated using the proposed technique is shown.     

Initiation of localized shear bands in plane strain

This study is concerned with the initiation of localized shear bands in plane-strain tension and compression. A theoretical framework which views the initiation of such shear bands as a bifurcation phenomenon from a homogeneous equilibrium field in an elastic-plastic body is first briefly reviewed, and then the predictions of the theory are compared with some experimental observations on an aged maraging steel. The experiments support the physical relevance of the theory within the framework of continuum mechanics.Specifically, the comparison between theory and experiment is concerned with the critical strains to localization and the orientation of the shear bands relative to the load axis. The theoretical predictions are only in qualitative agreement with the experimental observations. A better agreement is obtained with use of the constitutive equations corresponding to the classical deformation theory (a simple vertex model) than with use of the constitutive equations of the classical flow theory. It is concluded that better constitutive equations for elastic-plastic materials are needed before theoretical predictions can be obtained which might be expected to be in closer quantitative accord with experiment.     

The influence of pressure on the capillary flow of poly(methyl methacrylate)

Summary Pressure effects in the capillary flow of a single sample of poly(methyl methacrylate),M _v = 1.33 · 10⁵, were evaluated. The length/diameter ratios of the different capillaries used varied from 4 to 100. The tests were made with an Instron rheometer in the range 160–250 °C. The pressure-viscosity model, derived from the free volume-WLF equation, was used to pressure correct the capillary data. The corrected data agreed well with data obtained at atmospheric pressure using aWeissenberg rheogoniometer. A derived expression to calculate an increase in the flow activation energy with increasing stress predicts the observed increase in activation energy.

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Zusammenfassung Druckeffekte bei der Kapillarströmung einer einzelnen Polymethylmethacrylat-ProbeM _v = 1,33 · 10⁵ werden abgeschätzt. Die Längen/Durchmesserverhältnisse der verschiedenen verwendeten Kapillaren variierten zwischen 4 und 100. Im Temperaturbereich zwischen 160 und 250 °C wurden die Versuche mit einem Instron-Rheometer durchgeführt. Das Druck-Viskositätsmodell, das aus der WLF-Gleichung abgeleitet war, wurde zur Druckkorrektur der Kapillardaten verwendet. Die korrigierten Werte zeigten eine gute Übereinstimmung mit den Werten, die bei Atmosphärendruck mit Hilfe einesWeissenberg-Rheogoniometers gewonnen worden waren. Ein abgeleiteter Ausdruck zur Berechnung des Anstiegs der Strömungs-Aktivierungsenergie mit steigender Spannung sagt den beobachteten Anstieg in der Aktivierungsenergie voraus.

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On leave from Montecatini Edison, Milan (Italy).     

Untersuchungen zur freien Konvektion an ebenen Wänden

Zusammenfassung Es wurde die konvektive Wärmeübertragung durch laminare und turbulente freie Konvektion in Luft an großen waagerechten und lotrechten Flächen untersucht. Insbesondere wurde an einem oberflächenbeheizten Würfel der gegenseitige Einfluß auf die konvektive Wärmeübertragung waagerechter und lotrechter Flächen aufeinander bestimmt. Ferner wurde untersucht, ob Versuche an verkleinerten Modellen in Wasser brauchbare Ergebnisse für die Wärmeübertragung an großen Gegenständen durch laminare und turbulente freie Konvektion in Luft liefern.

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Experiments on free convection at plane surfaces

The convective heat transfer by laminar and turbulent free convection in air was investigated on large horizontal and vertical planes. — Particularly the mutual influence on the convective heat transfer which horizontal and vertical planes exercise versus one another was studied on a cube heated on its outer sides. By means of further suitable experiments on small scale models in water it was investigated if these results are useful to the heat transfer on large objects by laminar and turbulent free convection in air.