An experimental study of diabatic spiral vortex flow

In spiral vortex flow, between concentric cylinders with the inner cylinder rotating and the outer stationary, the addition of a thermal gradient across the gap is a known complicating factor. The present diabatic study for narrow and wide gaps (radius ratios N=0.955 and N=0.8), with a heated outer and adiabatic inner cylinder, was undertaken to investigate this problem. The heat transfer characteristics and the modes of transition have been investigated together with the relationship between them. Using standard on-line digital computer techniques, the onset of vortex flow and its higher transitions have been shown to cause a sharp increase in Nusselt number. At higher Taylor numbers, of the order of 10⁶, a marked change in the Nusselt number occurs with the onset of the transition to periodic turbulent vortex flow. Outer wall heating is seen to affect the modes of transition. Diabatic critical Taylor numbers are much higher than those for adiabatic conditions and are found to depend on the close approach of the vortices to the outer wall     

Postbuckling of angle-ply and anisotropic plates

Summary An analysis based on the von Kármán-type large-deflection equations of plates is presented for the postbuckling behavior of homogeneous and symmetrically laminated anisotropic rectangular plates. Boundary conditions for both simply supported and clamped edges are considered. A solution is obtained by expressing the force function and transverse deflection as double series involving the appropriate beam eigen-functions. Numerical results are presented for graphite-epoxy angle-ply laminates and homogeneous anisotropic plates. In the cases of buckling of anisotropic plates and postbuckling of isotropic and orthotropic plates, the present solution is in good agreement with existing solutions.

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Übersicht Es wird das Nachbeulverhalten von homogenen, symmetrisch geschichteten, anisotropen Rechteckplatten auf der Grundlage der von Kármán angegebenen Platten-Gleichungen für große Auslenkungen untersucht. Dabei werden sowohl einfach aufliegende, wie auch eingespannte Ränder als Randbedingungen berücksichtigt. Lösungen werden dadurch gewonnen, daß die Belastungsfunktion und die Querauslenkung als doppelte Reihen von geeigneten Balken-Eigenfunktionen angesetzt werden. Für Graphit-Epoxid-Schichtplatten und anisotrope homogene Platten werden numerische Ergebnisse mitgeteilt. Die erhaltenen Lösungen stimmen in den Fällen des Beulens von anisotropen Platten sowie des Nachbeulens von isotropen und orthotropen Platten gut mit bekannten Lösungen überein.

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The results presented in this paper were obtained in the course of research sponsored by the National Research Council of Canada.     

Profile and departure size of condensation drops on vertical surfaces

The problem of the equilibrium shape and departure size of two-dimensional dropwise condensation drops on a vertical surface is considered. The equation of the surface of the drop is obtained by minimizing (for a given volume) the total energy of the drop, consisting of surface and gravitational energy, using the techniques of variational calculus. The solution is tractable once the advancing contact angle is known, and is taken as an approximation to the axial meridian profile of a three-dimensional drop. The receding contact angle is obtained as part of the solution. The drop size is specified by imposing its vertical length. Upon increasing this vertical length, a point is reached at which no real solution exists, and this is taken as the departure size of the drop. Comparison with measured departure sizes under various body forces from standard to 100 times earth gravity are good.     

On a micromechanical fracture model for cracked reinforced composites

The fracture process of reinforced composite materials is examined. In the outer region of the crack tip anisotropic continuum mechanics is employed, while for the crack tip region a heterogeneous micromechanical model is proposed. A solution is obtained using combined boundary layer — non-linear finite elements.     

Shear flow over a rotating plate

A shear flow interacts with a rotating boundary. The three dimensional Navier-Stokes equations reduce to a set of ninth order, nonlinear, ordinary differential equations which are partially decoupled. Universal similarity velocity profiles are found by numerical integration. If the shear is high enough, reverse flow occurs and the mean drag may be negative. The solution is a rare exact similarity solution of the Navier-Stokes equations.     

Stokes Flow through an Array of Staggered Strips

The Stokes flow through a periodic array of thin staggered strips is studied. The method of eigenfunction expansion and collocation is used to obtain detailed flow and pressure fields. The permeabilities in the three principle directions are found to be different and their characters depend heavily on the geometry. Approximate formulas are also obtained.     

High-intensity turbulence measurements in a Taylor-Couette flow reactor

Turbulence-intensity measurements were made in a Taylor-Couette flow reactor consisting of two counter-rotating concentric cylinders designed for the purpose of studying turbulent premixed-flame propagation. In the annulus separating the two cylinders, a nearly homogeneous turbulent flow is generated. The intensities of turbulent velocity fluctuations in the annulus in both axial and circumferential directions were measured by using laser-Doppler velocimetry for a wide range of cylinder rotation rates, corresponding to low through high (120 cm/s) intensities relative to typical laminar flame speeds for lean methane-air mixtures. The experimental measurements indicate a linear relation between turbulence intensities and average cylinder surface speed and demonstrate the usefulness of the Taylor-Couette apparatus for studies of premixed-flame propagation in high-intensity turbulent flow.     

Influence of load amplitude and uniaxial tensile properties on fatigue crack growth

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., . Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Modified entropic elasticity of rubberlike materials

In the first part of the paper, consisting of Sections 2 and 3, physical grounds are adduced for weakening the concept of strictly entropic elasticity as applied to elastomeric materials. The resulting notion of modified entropic elasticity is shown to provide an alternative formulation of a model of rubberlike thermoelasticity proposed by Chadwick (1974). In the second part (Sections 4 and 5) Chadwick's model is generalized by allowing the deformation-dependent part of the internal energy to be a symmetric function of the principal stretches rather than depending only on their product, as in the original development. Consistently with the molecular theory of polymer networks, and with experimental findings, the extended model predicts that the deviatoric stress is not entirely entropic in origin, but arises in part from changes of internal energy. The energetic fraction of the retractive force in an extended cylinder is calculated and discussed in some detail and the paper concludes with a correlation of theoretical results with measurements on specimens of a lightly cross-linked natural rubber.