Optimization of geometry of elastic bodies in the vicinity of singular points on the example of an adhesive lap joint

The stress state in adhesive lap joints with various geometric shapes of spew fillet is studied. It is noted that the applied design models of the considered problem include singular points at which infinite stress values are possible if one uses the linear elasticity theory to calculate the stress state. Based on the conclusions of the solution of the geometry optimization problem in the vicinity of the singular points of elastic bodies, variants of the geometry of spew fillet, which provide the most significant decrease in the concentration of stresses in adhesive lap joints, are proposed.     

The effects of propeller tip vane on flow-field behavior

 This paper investigates the effects of attaching a tip vane to a propeller blade on the development and propagation of a tip vortex. The study employed a two-bladed propeller operating with and without a tip vane. Evaluation of the tip vortex was studied by using both smoke-wire flow visualization, hot wire anemometer, and strain gauge load-cell techniques. The mean velocity distributions and the velocity unsteadiness data as well as thrust, input power and efficiencies were obtained. Experiments were repeated at various rotating speeds ranging from 2000 to 5000 rpm. Received: 26 November 1995/Accepted: 11 April 1997     

The unsteady aerodynamics of a first stage stator vane row

The fundamental unsteady aerodynamics on a vane row of an axial flow research compressor stage are experimentally investigated, demonstrating the effects of airfoil camber and steady loading. In particular, the rotor wake generated unsteady surface pressure distributions on the first stage vane row are quantified over a range of operating conditions. These cambered airfoil unsteady data are correlated with predictions from a flat plate cascade inviscid flow model. At the design point, the unsteady pressure difference coefficient data exhibit good correlation with the nonseparated predictions, with the aerodynamic phase lag data exhibiting fair trendwise correlation. The quantitative phase lag differences are associated with the camber of the airfoil. An aft suction surface flow separation region is indicated by the steady state surface static pressure data as the aerodynamic loading is increased. This separation affects the increased incidence angle unsteady pressure data.List of symbols b airfoil semi-chord - C airfoil chord - C _p dynamic pressure coefficient, - _p static pressure coefficient, - i incidence angle - k reduced frequency, - N number of rotor revolutions - p dynamic pressure difference - static pressure difference, - S stator vane circumferential spacing - U _t rotor blade tip speed - u longitudinal perturbation velocity - V absolute velocity - V _axial absolute axial velocity - v transverse perturbation velocity - x _sep location of separation point - inlet angle - inlet air density - blade passing angular frequency     

The geometry of the orbits of artificial satellites

A novel approach to the study of the orbits of artificial satellites is presented. Emphasis is placed upon the basic geometry and other aspects of satellite motion which are of first importance to satellite engineering. The motion of the orbital plane as a rigid body is introduced and a non-elliptical orbit motion in this plane is defined. The plane orbit so defined possesses the very desirable feature of representing a succession of satellite positions and hence reveals the true motion of the satellite. An analytical treatment yields a completely general second order theory of earth satellite motion which is suitable for engineering purposes. In the latter development, particular attention is paid to the apsidal motion of the orbit and the concomitant resonance effects at the critical orbit inclination. The basic nonlinear features of the apsidal motion, which have not been recognized in earlier theories, are incorporated in the analytical development so as to produce a theory valid at all angles of inclination of the orbit.     

A study on the limitations of a vane rheometer for mineral suspensions using image processing

This study presents the results from the rheological measurement of clay suspensions using vane geometry in a wide gap configuration. It focuses on how measurement of viscosity cannot be effective for two reasons: the limits of the vane geometry itself and the limits of the material depending on its content of solid particles. Image analysis of the flow while shearing the material is carried out to relate the flow behavior. Several approaches to compute the shear flow curve from torque-rotational velocity data are used. The results demonstrate that the applied setpoint while applying a logarithmic shear rate ramp can be very different from the calculated shear rate from existing theories. Depending on the solid volume fraction of the particles in the mixture, we relate the macroscopic behavior using image analysis and the shear flow curves to the rheophysical regime of the flow of the suspensions. Therefore, this paper has two simultaneous goals: the first one is to describe the physical phenomena which control macroscopic behavior and the second one is to highlight the limits of the vane geometry for viscosity measurement of mineral suspensions like kaolinite pastes.     

Interaction of zones of flow separation in a centrifugal impeller-stationary vane system

In a radial flow pump operating in off-design conditions, regions of stall can exist on the rotating impeller blade and on the downstream diffuser blade, vane or tongue. Interaction of these stall zones can generate complex patterns of vorticity concentrations. In turn, these vorticity concentrations are related to sources of unsteady stagnation enthalpy. The form of these patterns is strongly dependent on the instantaneous location of the impeller trailing-edge relative to the leading-edge of the vane.Comparison of instantaneous with ensemble-averaged images shows that the flow structure in the gap region between the impeller and the vane is highly repetitive. Away from this region, in particular in the separated shear layer from the vane, the nonrepetitive nature of the vorticity field is manifested in substantial reduction of peak levels of vorticity in the ensemble-averaged image, relative to the instantaneous image.The three-dimensional flow structure resulting from these separation zone interactions was characterized via end views of the flow patterns. Particularly pronounced concentrations of vorticity can occur in this plane. They tend to be located in the shear layer at the outer edge of the large-scale separation zone. These vorticity concentrations are, however, highly non-stationary for successive passages of the impeller blade. Ensemble-averaging reveals that they persist primarily on the endwalls of the diffuser.The authors are grateful to the Office of Naval Research for support of this research program     

Measurement and calculation of guide vane performance in expanding bends for wind-tunnels

 The design of guide vanes for use in expanding bends was investigated both experimentally and numerically. The primary application in mind is the use of expanding corners in wind-tunnels for the purpose of constructing compact circuits with low losses. To investigate the performance of guide vanes in realistic situations expansion ratios between 1 and 53 were tested in the experiments. These were carried out in an open wind-tunnel specially built for the present purpose. The experimental results demonstrated that suitably designed guide vanes give very low losses and retained flow quality even for quite substantial expansion ratios. For wind-tunnel applications expansion ratios around 1.3 seem appropriate, Optimization of a guide vane design was done using a two-dimensional cascade code, Mises. A new vane optimized for an expansion ratio of 43 gave a two-dimensional total pressure-loss coefficient as low as 0.041 for a chord Reynolds number of 200,000. Received: 7 April 1997/Accepted: 11 August 1997     

On the geometry of nonequilibrium magneto gasdynamic flows

After formulation of the various dynamical and kinematical relations connecting the flow quantities with the geometrical parameters of the stream line trajectories, the expressions for the tangent, principal normal and binormal vectors and the curvature and torsion of the stream line have been obtained in-terms of the velocity components, the pressure, the density, the magnetic field and the relaxation variable. This is followed by expressing the equations governing the flow in the intrinsic forms. It has been shown that the non-equilibrium character of the gas decreases the total pressure gradient along the streamlines, but the total pressure remains constant along the binormals and if the stream lines are straight lines, the trajectories of the principal normals lie on the surface of the constant total pressure. Further, the expressions for vorticity components in terms of curvature of the stream line and the velocity gradients along the stream line and their principal normals and binormals have been obtained. Finally, a class of circular helical flows have been discussed.     

The yield surface of viscoelastic and plastic fluids in a vane viscometer

Vane viscometers are often used to investigate the low shear rate properties of plastic fluids. The shear stress is determined by assuming that the material is held in the space between the vane blades so that it behaves like a rigid cylinder. Experimental evidence supports this assumption and the aim of the present study is to model numerically the yield process in a vane rheometer using viscoelastic and plastic fluids. The finite element method has been used to model the behavior of Herschel-Bulkley (Bingham), Casson and viscoelastic (Maxwell type) fluids. The penalty function approach for the pressure approximation and a rotating reference frame are used together with fine meshes containing more than 1300 elements. The results show that for Herschel-Bulkley (Bingham), and Casson fluids a rotating rigid cylinder of fluid is trapped inside the periphery of the vane, the shear stress is uniformly distributed over the surface of the cylinder. Finally a modified second order fluid is used to simulate the viscoelastic behaviour, anticipated to be an intermediate between the elastic deformation and the plastic flow, to provide a more realistic simulation of the yield process about a vane. In this case, contrast with the concentration of the elastic strain rate at the blade tips, a nearly uniform distribution of the plastic shear rate is still found. This implies that the plastic shear always distributes uniformly during the entire yielding process. Evidently the assumption of uniform shear on a rotating cylinder of material occluded in the blades of a vane is a valid and useful model for many types of fluid possessing a yield stress.     

The differential geometry of bending

Summary The deformation associated with uniform bending has been treated using the techniques of differential geometry. The Burgers circuit as well as various related tensor quantities such as torsion and dislocation density have all been determinated with respect to these various states of deformation.

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Sommario La deformazione associata con la flessione uniforme viene trattata usando le tecniche della geometria differenziale. Il circuito di Burgers e altre quantità tensoriali e la densità di dislocazione, vengono determinate nei vari stati di deformazione.

     

The geometry of the plastic deformation of polycrystalline aggregates

Summary A full geometric analysis of the tensile deformation of cube-texture copper has been carried out by which it has been possible to predict the limit of uniform elongation and associated lattice rotation as well as to account for the plastic anisotropy of cube-texture material. The yield criterion of the oriented material over the whole plastic range is shown to be one of limiting shear energy on particular crystallographic shear systems and this enables the tensile stress-strain relation of the random polycrystalline aggregate to be derived.

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Zusammenfassung Eine vollständige geometrische Analyse der Streckverformung von Kupfer mit Texturen der Kristallite in Würfellage wurde durchgeführt, wodurch es möglich war, die Grenze gleichförmiger Verlängerung und der damit verbundenen Gitterrotation vorauszusagen und auch die plastische Anisotropie dieses Materials zu berechnen. Das Fließgrenzenkriterium (die kritische Fließgrenze) für orientiertes Material über den ganzen Plastizitätsbereich erweist sich als eine der begrenzenden Scherenergien an bestimmten kristallographischen Schersystemen, und so wird es möglich, die Zugspannungs-Dehnungsbeziehung für statistisch polykristallines Material abzuleiten.

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Presented at the conference Flow, Fatigue and Failure held in Leeds on January 8th and 9th, 1959, by the British Society of Rheology.     

Effects of initial geometry on the development of thermals

A series of experiments were performed in a water tank to examine the effects of the initial geometry on the development of buoyant thermals in the near field. The flows were produced by releasing buoyant fluid from cylindrical tubes of aspect ratios 2 to 8 into a uniform density environment. In the near field, a vortical cap forms, followed by a column of buoyant fluid, for the larger aspect ratios. The flow development can be divided into two phases; an initial acceleration phase and a subsequent phase where the flow decelerates and displays thermal-like characteristics. In the first phase, the leading edge of the flow accelerates and the length and time scales are dependent on the initial geometry. In the second phase, the flow attains a constant circulation and the appropriate length and time scales are the cube root of the initial volume and a buoyant time scale. Circulation due to baroclinic torques and the hydrodynamic impulse in the second phase are correlated with the initial buoyant force. The data indicate that the self-similar thermal characteristics are applicable to the buoyant flows in the near field beyond the initial phase, even though the flow may not resemble a spherical thermal.     

Membrane fusion based on the geometry of the stalk model

It is a commonly accepted assumption that membrane fusion involves an hourglass-shaped local contact between two monolayers of opposing membranes, an intermediate structure called a stalk. The shape of the stalk is considered as an axisymmetrical figure of revolution in 3D space, with a planar geometry in the initial configuration. The total energy of the stalk is evaluated from the assumption that the stalk has a constant curvature. Its negative value due to the presence of spontaneous curvature promotes hemifusion. An extension of the original model developed in Markin and Albanesi [23] is proposed, in which any geometrical feature of the stalks can be expressed in explicit form, by considering the stalks as nodoid surfaces. The local stresses and induced internal moments due the membrane bending are evaluated based on the adopted parameterization.     

Pool boiling — And the effect of pool geometry

Simple correlationsh=C·qⁿ for experimental results in nucleate pool boiling often exhibit a wide scatter in the constant and the exponent. Among the many parameters responsible, an effect from confining boundaries causing flow recirculation, cannot be excluded. Heat transfer experiments were performed in a cylindrical and rectangular vessel on finned tubes in a single and twin arrangement. The cylindrical vessel had a smaller fluid cross section area than the rectangular vessel. Although the tubes were identical in geometry (except for length) and surface roughness, they yielded clearly different results. The heat transfer coefficients in the cylindrical vessel were always larger than in the rectangular one.