Onset of convection regimes with double period in a periodic field of external forces

We investigate the onset of secondary convective flows in the Rayleigh problem (in a horizontal layer of a viscous incompressible liquid with free boundaries) in the presence of a parameter that varies with time and has a period T, namely the temperature gradient or the intensity of the gravitational field.Translated from Zhurnal Prikladnoi Mekhanlki i Tekhnicheskoi Fizlki, No. 6, pp. 65–70, November–December, 1972.     

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.     

Der gerade Stab mit geschlossenem dünnwandigen Profil unter näherungsweiser Berücksichtigung der Schub- und Querschnittsdeformationen

Übersicht Für einen geraden prismatischen Stab mit ein- oder mehrzelligem, dünnwandigem Kastenquerschnitt wird unter näherungsweiser Berücksichtigung der Schub- und Querschnittsdeformationen eine Theorie kleiner Verformungen angegeben. Die entwickelten Differentialgleichungen beschreiben das Verhalten des prismatischen Stabes bei beliebiger Belastung unter Einschluß des Knickproblems sowie die freien und erzwungenen Schwingungen dieses Stabes. Für den einzelligen Kastenträger werden die Differential-gleichungen ausgewertet und auf die freie Torsionsschwingung des beidseitig gabelförmig gelagerten Kastenträgers angewendet.

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Summary The beam theory for infinitesimal deformations of a prismatic singular or multicelled box beam is given using approximations for shear-deformations and for deformations of the cross section. The resulting system of differential equations describes the behaviour of a prismatic beam under a general loading. Furthermore they include the case of stability from collapse as well as the equations of free and forced vibrations. The differential equations are applied to the case of a single celled box beam under free torsion vibration supported at both ends.

     

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.     

Temperature distribution in a thin rotating disk

The problem of heat conduction in a thin rotating disk with heat input at a fixed point is considered. The disk is cooled by forced convection from its lateral surfaces. By defining a complex temperature, the temperature throughout the disk is presented as a series of Bessel functions of complex argument. Results are given for a range of rotational speeds.Nomenclature R radial coordinate - angular coordinate - a radius of disk - b thickness of disk - T temperature - T ambient temperature - rotational speed of disk - q heat flux into disk - k thermal conductivity of disk - density of disk - c specific heat of disk - h coefficient of convective heat transfer - r dimensionless radial coordinate, R/a - T* characteristic temperature, q ₀ a/ k - t dimensionless temperature, (T–T )/T* - C ₁, C ₂ dimensionless parameters defined in (3)     

Calibration and use of the Epprecht Rheomat

Summary This paper deals with the calibration and use of an Epprecht Rheomat with particular reference to non Newtonian liquids. A method of calculating accurate rates of shear for non-Newtonian flow is derived using theEuler-Maclaurin sum formula. Some examples are given of the calculation of shear of poly vinyl chlorideplasticiser suspensions.

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Zusammenfassung Die vorliegende Abhandlung befaßt sich mit der Eichung und dem Gebrauch eines Epprecht-Rheomats mit besonderer Hinsicht auf nicht-Newtonische Flüssigkeiten.Ein Verfahren zur exakten Berechnung von Scherwerten für nicht-Newtonische Flüssigkeiten läßt sich aus derEuler-Maclaurinschen Summenformel ableiten.Einige Beispiele zur Berechnung von Scherwerten für Weichmacher von Polyvinylchlorid sind beigefügt.

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Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968.     

New equipment for cyclic biaxial testing

Methods of achieving biaxial-stress states in fatigue tests are reviewed. A new design of equipment that produces five distinct biaxial-stress states by simultaneous direct pressurization and axial loading of thinwalled cylindrical specimens is described. Four variations of stress state are obtained by the use of two sizes of specimen and by reversal of the pressurizing connections. The fifth state is obtained by direct pressurization without axial load. The actual magnitudes of stress in the specimen are computed from the output of the load cell in the reaction frame in which the biaxial-testing device is mounted. Additional stress ratios are obtained using standard uniaxial and torsional cyclic-testing arrangements. The initial program using this equipment was to investigate the effects of biaxiality on the cyclic properties and low-cycle fatigue behavior of normalized 1018 mild steel, under fully reversed constant-amplitude strain control. Control was achieved using a servo-controlled, electrohydraulic testing system with one of the two clipon strain transducers, that were mounted on the specimen, providing the controlling electrical signal. The system allowed direct recording of the stress-strain hysteresis loops in both principal directions. The behavior of the equipment and the modes of failure of the specimens are described and some test data are presented. The range of application and limitations of the equipment for further cyclic biaxial testing are discussed.     

Calculation of supersonic separation flow in circular nozzles with abrupt expansion

A study is made of the interaction of a circular supersonic jet with a turbulent layer of the near-wake kind formed behind a circular step on the end part of a nozzle with abrupt expansion. The flow in the viscous layer is calculated by the integral method, and in the inviscid flow by a through-computation method using a monotonic implicit difference scheme of first order of accuracy. The interaction between the inviscid and turbulent flows is determined by the displacement thickness of the viscous layer. The initial conditions for the flow in the layer are determined from the integral conditions of its matching to the isobaric mixing flow in the base region behind the step. The computed interaction flows are determined as a function of the length of the end part and the counter pressure simultaneously or separately by the boundary condition that the pressure at the end of the end part be equal to the pressure of the external medium and by a singular solution of the equations passing through a saddle singular point — the throat of the wake. In a conical nozzle with profiled attachments of different lengths, calculations were made of separation flows with open and closed base regions and with allowance for secondary separation. The obtained solutions are multivalued in a certain range of lengths of the end part and values of the counter pressure. The solutions realized in reality are selected by analyzing the regimes of operation of the nozzles, and the calculated regions of hysteresis and associated low-frequency nonstationary separation flows are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 120–128, July–August, 1979.We are grateful to M. Ya. Ivanov for consultation on the use of the program of [6] and to Z. A. Donskovaya for assistance in preparing the paper.