Turbulent jet flows with buoyancy and swirl

Übersicht Das gleichzeitige Auftreten von Auftrieb und Drall in vertikalen, runden, turbulenten Freistrahlen wird mit einer Integralmethode untersucht. Durch Hinzunahme der Bewegungs- und Energiegleichung an der Strahlachse kann auf die Verwendung eines empirischen Entrainmentkoeffizienten verzichtet werden. Es zeigt sich, daß zwischen Druck- und Axialgeschwindigkeitsprofilen eine ganz bestimmte Beziehung bestehen muß, um unrealistische Singularitäten im Strömungsfeld zu vermeiden. Die Beziehung wird durch Meßergebnisse annähernd bestätigt. Der Einfluß des Dralls auf alle Strömungsgrößen ist in der Nähe des Ursprungs am stksten. Eine Zunahme der dimensionslosen Drallzahl bewirkt eine starke Aufwertung des Strahls mit 180° Öffnungswinkel im Ursprung und eine Abnahme der axialen Geschwindigkeit. Im Grenzfall sehr hoher Drallzahlen entsteht eine neue Strahlströmung, die als drallbehafteter, auftriebserzeugter Strahl bezeichnet wird. Stromabwärts klingen die Dralleffekte rasch ab und Auftriebseffekte nehmen an Bedeutung zu. Das asymptotische Verhalten entspricht einem auftriebserzeugten Strahl (plume).

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Turbulent jet flows with buoyancy and swirl

Summary Vertical, round, turbulent jets with combined effects of buoyancy and swirl are investigated by an integral method. The method avoids application of an empirical entrainment coefficient by including the differential equations of motion and energy at the jet axis. It is shown that pressure and velocity profiles have to be related to each other in order to avoid unrealistic singularities in the flow field. This relationship is approximately confirmed by measurements. With respect to all flow quantities, the influence of swirl is felt strongest near the origin. Increasing the dimensionless swirl number strongly increases the width of the jet (with infinite derivative at the origin) and decreases the axial velocity. In the limiting case of very high swirl numbers a new type of jet flow is found which can be called a swirling plume. Further, downstream swirl effects decay rapidly and buoyancy becomes relatively more important. The asymptotic behaviour resembles that of a plume.

     

The displacements solution for steady-state longitudinal vibrations of segment-wise inhomogeneous elastic rods

Summary The Laplace Integral Transform is used to construct the displacements, solution for steady-state vibrations of an inhomogeneous elastic rod made up of n, (n2) homogeneous elastic segments of the same cross section. The method consists in determining the displacements function of the inhomogeneous rod for zero initial conditions and for displacements type superimposed boundary conditions, with the residues calculated for the poles of the Laplace images of the ends boundary conditions. The correctitude of the constructed solution is then proved and several examples are given to illustrate the method (harmonic end excitations are included).

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Sommario Si usa la trasformata integrale di Laplace per costruire gli spostamenti soluzione del problema delle vibrazioni stazionarie di una barra elastica non omogenea fatta di n, (n2) segmenti elastici omogenei di uguale sezione. Il metodo consiste nel determinare la funzione per gli spostamenti della barra non omogenea in corrispondenza di condizioni iniziali nulle e per sovrapposte condizioni al contorno del tipo spostamento, coi residui calcolati per i poli delle immagini di Laplace delle condizioni al contorno agli estremi. Si dimostra poi la correttezza della soluzione costruita e si danno diversi esempi per illustrare il metodo (comprese le armoniche e le eccitazioni).

     

Application of faraday's effect in static and dynamic holographic photoelasticity

The basic principle of applying Faraday's effect to achieve the separation of fringes in static and dynamic holographic photoelasticity, and a study and application of Faraday's light rotator are described in this paper. It is proposed that Faraday's light rotator be used for automating photoelastic instrumentation for measuring isoclinics and the decimal orders of isochromatic fringes.     

Beitrag zur Kenntnis der Wärmeleitfähigkeit poröser Stoffe Teil II

Zusammenfassung Die in einem ersten Teil dieser Untersuchung erhaltenen Ergebnisse werden durch zusätzliche neue Versuche kontrolliert. Der Meßbereich wird auf Rohdichten von 9,5 kg/m³ erweitert; die notwendigen Versuchsdaten für reines Polystyrol werden experimentell neu ermittelt. Ein Vergleich mit den Meßwerten anderer Beobachter ergibt gute Übereinstimmung aller Daten, wenn gleichartige Versuchsbedingungen eingehalten wurden. Der Verlauf der gemessenen (effektiven) Wärmeleitfähigkeit von Polystyrolpartikel-Hartschaumplatten (Styropor) in Abhängigkeit von Rohdichte und Schichtdicke wird aufgezeigt und diskutiert. Zusätzliche Messungen der Absorptionsspektren von Polystyrol und Polystyrol-Schaumstoff ergänzen die Messung der Wärmeleitfähigkeit und mögen zur Klärung des Wärmetransportes in porösen Schaumstoffen beitragen.

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A contribution to the knowledge of heat conductivity of porous materials part II

The results obtained in the first part of this experimental research are controlled by new measurements. The range of apparent over-all density was enlarged till 9.5 kg/m³. The necessary dates for pure polystyrene were experimentally determined. A comparison with the results of other observers shows good agreement, if equal measuring conditions are given. The behaviour of the measured (effective) thermal conductivity of polystyrene foam as function of apparent over-all density and the thickness of the layer may be learned from several diagrams; these are discussed. Additional measurements of some optical absorption spectra of pure polystyrene and polystyrene foam follow the measurement of thermal conductivity; they may contribute to the clearing up of heat transfer through porous materials.

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Herrn Dr.-Ing. F. Stastny, Ludwigshafen/Rh. und der BASF haben wir für sehr entgegenkommende Lieferung der verschiedenartigen Proben zu danken, ferner Herrn Techn. Reg. Amtmann Jugel für sorgfältige Kontrollversuche.     

Poroelasticity-I: Governing Equations of the Mechanics of Fluid-Saturated Porous Materials

We present here the approach to the theory of fluid-filled poroelastics based on consideration of poroelastics as a continuum of “macropoints” (representative elementary volumes), which “internal” states can be described by as a set of internal parameters, such as local relative velocity of fluid and solid, density of fluid, internal strain tensor, specific area, and position of the center of mass of porous space. We use the generalized Cauchy–Born hypothesis and suggest that there is a system of (structural) relationships between external parameters, describing the deformation of the continuum and internal parameters, characterizing the state of representative elementary volumes. We show that in nonhomogenous (and, particularly, nonlinear) poroelastics, an interaction force between solid and fluid appears. Because this force is proportional to the gradient of porosity, absent in homogeneous poroelastics, and one can neglect with dynamics of internal degrees of freedom, this force is equivalent to the interaction force, introduced earlier by Nikolaevskiy from phenomenological reasons. At last, we show that developed theory naturally incorporates three mechanisms of energy absorption: visco-inertial Darcy mechanism, “squirt flow” attenuation, and skeleton attenuation.     

Parametric vibrations of beam with crack

Summary The paper presents a mathematical model of transverse vibrations of a Bernoulli-Euler beam with a closing crack. In damaged cross-sections of the beam there were applied elastic elements of flexibility calculated on the basis of the laws of fracture mechanics. Making use of the elaborated model, an analysis of the effect of magnitude and position of the crack upon the basic instability area of the beam was carried out.

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Parametrische Schwingungen eines Balkens mit Riß

Übersicht Es wird ein mathematisches Modell für die Biegeschwingungen eines Euler-Bernoulli-Balkens mit schließendem Riß vorgestellt. Geschädigte Balkenteile werden ersetzt durch elastische Elemente mit einer Nachgiebigkeit, die nach den Gesetzen der Bruchmechanik berechnet wird. Mit diesem Modell wird der Einfluß von Rißposition und-größe auf den wesentlichen Instabilitätsbereich der Balkenschwingungen untersucht.

     

Analytical simulation as a support tool in the decision process “wheels or tracks”

In the development of a weapon system, the maximization of demands concerning features like fire power, armor and mobility often leads to incompatibilities within the overall systems, to an imbalanced design and excessively high cost. The consequence is a decrease in mission availability. Therefore, system analysis utilizing simulation techniques is being used more and more in the early stages of the development process. This paper describes the application of such simulation techniques to practical cases. First, the development of a system is described by which to select wheeled or tracked running gears for combat vehicles considering the compatibility of fire power, armor, mobility and cost. Secondly, the possible upper weight ranges for wheeled combat vehicles are discussed, using analytical modeling of vehicle mobility as a basis. The methods used in these cases can also be applied to non-military problems.     

General relations of strain-gradient stress analysis

Some particular fields of stress gradients in plates are investigated analytically and experimentally. Carriers of empirical information are light beam deflections caused by stress or strain gradients in homogeneous beams subjected to a particular case of flexure with shear. This study is based on theories and techniques of the strain-gradient method that was recently introduced by the authors. This is a generalization of prior analytical-experimental examination of strain-gradient light deflections produced in stressed plates, which had concentrated on the simplest case where information of interest is collected along a line of symmetry of the stress field and where both the information carrying light beams are deflected in the plane of symmetry only. The developed relations were tested experimentally, by using an S-beam as representative example of general plane stress field. The main purpose of the present investigation is to document the efficacy of the strain-gradient method in analysis of the general case of stress state and to test the ranges of applicability of the accepted mathematical models and of the subsequently derived relations. In this respect, the most interesting stress state is that in a beam subjected to the Saint-Venant bending, where the transversal and longitudinal axes of the beam are in pure shear. The obtained results are compared, at each step, with the predictions of the developed analytical models and with the predictions of Filon's stress function. The results of comparison are satisfactory. The procedures of evaluating the photoelastic and material coefficients using strain-gradient techniques were tested positively. The developed method can yield valuable information on the actual features of stress states in fracture mechanics. Part of the problems and first results of this investigation will be presented in the authors' paper “Strain-gradient stress analysis in Saint-Venant bending”.     

Vibrations of a viscoelastic rod with small non-linearities

Summary A partial differential equation is considered whose dominant linear term involves third order time derivatives and which contains a nonlinear term multiplied by a small parameter. The solutions of initial-boundary-value problems for the equation are investigated using an extension of the Krylov-Bogoliubov-Mitropolskii asymptotic method. The vibrations of a viscoelastic rod lead to an equation of the type considered when the material constitutive relation is that of a standard linear solid together with additional small nonlinearities of behaviour, and this particular physical problem is investigated in detail. It is shown that under appropriate initial conditions only a single mode of vibration is excited to lowest order, and some numerical results are given which illustrate the effects of the nonlinearity on these single mode solutions.

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Sommario Viene considerata una equazione differenziale alle derivate parziali il cui termine lineare dominante implica derivate del terzo ordine del tempo e che contiene un termine non lineare moltiplicato per un parametro di piccola entità. Vengono studiate le soluzioni dell'equazione con le condizioni iniziali e al contorno usando una estensione del metodo asintotico di Krylov-Bogoliubov-Mitropolskii. Le vibrazioni in una sbarra viscoelastica portano ad una equazione del tipo considerato quando la soluzione costitutiva è quella di un normale solido lineare con l'aggiunta di piccole non-linearità di comportamento. Viene studiato nel dettaglio questo particolare problema fisico. Viene mostrato che, con appropriate condizioni iniziali, viene eccitato solo il primo modo di vibrare. Vengono inoltre forniti alcuni risultati numerici che illustrano gli effetti della non linearità per questo particolare modo.

     

Towards the solution of finite plane-strain problems for compressible elastic solids

A new approach to the solution of finite plane-strain problems for compressible Isotropie elastic solids is considered. The general problem is formulated in terms of a pair of deformation invariants different from those normally used, enabling the components of (nominal) stress to be expressed in terms of four functions, two of which are rotations associated with the deformation. Moreover, the inverse constitutive law can be written in a simple form involving the same two rotations, and this allows the problem to be formulated in a dual fashion.For particular choices of strain-energy function of the elastic material solutions are found in which the governing differential equations partially decouple, and the theory is then illustrated by simple examples. It is also shown how this part of the analysis is related to the work of F. John on harmonic materials.Detailed consideration is given to the problem of a circular cylindrical annulus whose inner surface is fixed and whose outer surface is subjected to a circular shear stress. We note, in particular, that material circles concentric with the annulus and near its surface decrease in radius whatever the form of constitutive law within the given class. Whether the volume of the material constituting the annulus increases or decreases depends on the form of law and the magnitude of the applied shear stress.