Effects of liquid superheat during solidification of pure metals in a square cavity

Numerical investigations on the effects of liquid superheat during solidification of a pure metal (tin) in a square cavity have been performed. Natural convection in the melt is established in a small time compared to the duration of solidification. At high degrees of superheat (ΔT _sup>0.5) the average Nusselt number at the hot wall is practically invariant with time and is correlated by . Multi-cellular flow structure with peaks in the Nusselt number is predicted in the narrow melt for low values of ΔT _sup. A modified superheat parameter, , suggested in the present study for the estimation of solidified volume has been found to be satisfactory. Correlations for the evolution of solid volume with time have been developed.     

Uncertainty in calculating vorticity from 2D velocity fields using circulation and least-squares approaches

The most common method for determining vorticity from planar velocity information is the circulation method. Its performance has been evaluated using a plane of velocity data obtained from a direct numerical simulation (DNS) of a three dimensional plane shear layer. Both the ability to reproduce the vorticity from the exact velocity field and one perturbed by a 5% random uncertainty were assessed. To minimize the sensitivity to velocity uncertainties, a new method was developed using a least-squares approach. The local velocity data is fit to a model velocity field consisting of uniform translation, rigid rotation, a point source, and plane shear. The least-squares method was evaluated in the same manner as the circulation method. The largest differences between the actual and calculated vorticity fields were due to the filter-like nature of the methods. The new method is less sensitive to experimental uncertainty. However the circulation method proved to be slightly better at reproducing the DNS field.The least-squares method provides additional information beyond the circulation method results. Using the correlation and a vorticity threshold criteria to identify regions of rigid rotation (or eddies), the rigid rotation component of the least-squares method indicates these same regions.The authors thank Dr. Michael Rogers of NASA Ames Research Center for supplying the DNS fields. In addition, Professor Ellen Longmire at the University of Minnesota asked how else might one calculate vorticity other than the circulation method and prompted this investigation.     

Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux — an exact solution

An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of a foreign mass and constant mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown on graphs. The skin-friction and the Sherwood number are also shown on graphs. The effects of different parameters likeG (the Grashof number),Gc (the modified Grashof number),Pr (the Prandtl number) andSc (the Schmidt number) are discussed.     

In-cylinder fuel distribution in a port-injected model engine using Rayleigh scattering

The spatial and temporal variation of the fuel concentration (air/fuel ratio) in a model engine was quantified by laser Rayleigh scattering. Fuel was simulated by gaseous Freon-12 injected at various timings and quantities into the intake port. The results showed that the fuel concentration in the engine cylinder was strongly dependent on the injection timing and duration and that the Rayleigh system was able to identify spatial variations of the order of one air/fuel ratio at realistic mixture strengths.     

Stability of a water tower

Summary The stability of a water tower, consisting of a spherical shell rigidly attached to the top of a vertical column, is analyzed. At first, it is shown on a simple conceptual model that problems of this type are imperfection insensitive; thus, the first bifurcation load from the straight state of equilibrium could be considered the buckling load. This is followed by the analysis of the water tower problem taking into consideration the flexibility of the column, the own weight of the structure, the weight of the liquid, and the rotational stiffness of the soil base. Although the differential equation of the resulting eigenvalue problem has a variable coefficient, the problem is solved exactly in closed form. To simplify the utilization of the obtained results, they are presented graphically for a range of water tower and soil stiffness parameters. Model tests were conducted that confirmed the analytical findings. However, nearP _cr , at the smallest disturbance the model underwent large oscillatory motions. This finding suggests that, for water tower design, only a fraction ofP _cr should be used.

---

Stabilität eines Wasserturms

Übersicht Untersucht wird die Stabilität eines Wasserturms aus einer senkrechten Säule mit kugelförmigem Behälter an der Spitze. Zunächst wird anhand einer einfachen Modellabstraktion nachgewiesen, daß Probleme dieser Art unempfindlich sind gegen Imperfektionen; deshalb kann die erste aus dem geraden Gleichgewichtszustand führende Verzweigungslast als Knicklast angesehen werden. Es schließt sich die Untersuchung des Wasserturms mit Nachgiebigkeit und Eigengewicht der Säule, mit Gewicht von Behälter und Inhalt sowie Drehsteifigkeit des Fundaments an. Die Lösung des Eigenwertproblems, dessen Differentialgleichung einen variablen Koeffizienten besitzt, läßt sich geschlossen angeben. Zur bequemen Anwendung werden die Ergebnisse für weite Parameterberciche von Turm und Fundament graphisch dargestellt. Durchgeführte Modellversuche unterstützen die analytischen Ergebnisse. Allerdings vollführte das Modell in der Nähe der kritischen LastP _cr selbst bei kleinsten Störungen große Schwingbewegungen. Deshalb sollte bei einer Auslegung nur ein Bruchteil vonP _cr zugrunde gelegt werden.

     

On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity

Summary A new technique is proposed for the numerical solution of the Cauchy-type singular integral equations, by using the well known Gegenbauer polynomials. A large class of problems of mathematical physics, and especially several plane and antiplane elasticity problems, not possessing closed-form solutions, can be reduced to the solution of certain systems of such a type of singular integral equations. Also by using a certain method the new formula which is used for the numerical solution of the Cauchy-type integral equations can be extended for the general type of the finite-part singular integrals, too.

---

über eine neue, in der Elastizitätstheorie anwendbare Integrationsregel mit Benutzung der Gegenbauer-Polynome zur Lösung singulärer Integralgleichungen

übersicht Es wird eine neue Technik zur numerischen Lösung von Cauchyschen singulÄren Integralgleichungen unter Benutzung der bekannten Gegenbauer-Polynome vorgeschlagen. Eine gro\e Klasse von Problemen der mathematischen Physik und besonders verschiedene ebene und antiplanare Probleme der ElastizitÄtstheorie, welche keine geschlossenen Lösungen besitzen, können zur Lösung auf solche singulÄren Integralgleichungen zurückgeführt werden. Die für die numerische Lösung von Cauchyschen Integralgleichungen hergeleitete Methode kann für den allgemeinen Fall singulÄrer Integrale mit endlichem Anteil erweitert werden.

     

Experimental buckling of internal integral ring-stiffened cylinders

Twenty aluminum cylinders with internal, integral tee-stiffener rings were tested under combinations of axisymmetrical axial load and external lateral pressure to determine buckling characteristics. Seven geometric types were tested; the primary variables were the ratios of cylinder radius to shell thickness, stiffener spacing to shell thickness, and stiffener spacing to stiffener depth. An eighth type, which had variable stiffener spacing and depth, was tested under a lateral pressure varying linearly in the axial direction. Strain-gage data were obtained to aid in evaluation of results. The test results agree well with the theoretical work used for the design.Paper was presented at 1966 SESA Annual Meeting held in Pittsburgh, Pa., on November 6–9.     

Identification of vortex motions in turbulent mixing of choked jets

A specially adapted schlieren system is used to generate fluctuating signals which respond strongly to large scale coherent components of a turbulent mixing jet flow and which have a relatively reduced response to random disturbances. The schlieren signals also provide a direct indication of the presence of vortex-like structures in the turbulent mixing layers by virtue of the phase relationship of the schlieren signals to the pressure field. This system gives a clear resolution of the fluctuating periodic effects associated with vortex structures in the flow from a choked convergent nozzle. It has thus been possible to determine that vortex-like eddies are associated with the feedback screech mechanism, and also generate periodic disturbances due to their passage through the diamond shaped wave structure in the flow. The regular disturbances in the flow move at 0.77 of the fully expanded flow velocity. Phase spectral observations demonstrate clearly the vortex like structure of coherent disturbances in the flow by virtue of the quadrature phase relation between the schlieren and microphone signals. Movement of the sensing microphone in the pressure field external to the flow shows disturbance propagation at the acoustic velocity, and also shows that disturbances at Strouhal numbers above 0.7 emanating from the inner mixing zone can be identified by an additional time delay to reach the microphone and only influence the microphone when it is located downstream of the flow sensing schlieren system due to confinement of pressure disturbances within Mach cones of the flow.     

Dynamic melt flow of nanocomposites based on poly-ɛ-caprolactam

 The dynamic flow behavior of polyamide-6 (PA-6) and a nanocomposite (PNC) based on it was studied. The latter resin contained 2 wt% of organoclay. The two materials were blended in proportions of 0, 25, 50, 75, and 100 wt% PNC. The dynamic shear rheological properties of well-dried specimens were measured under N₂ at T=240 °C, frequency ω=0.1–100 rad/s, and strains γ=10 and 40%. At constant T, γ, and ω the time sweeps resulted in significant increases of the shear moduli. The γ and ω scans showed a complex rheological behavior of all clay-containing specimens. At γ=10% the linear viscoelasticity was observed for all compositions only at ω>1 rad/s, while at γ=40% only for 0 and 25 wt% of PNC. However, the effect was moderate, namely decreasing G′ and G′′ (at ω=6.28 rad/s; γ=50%) by 15 and 7.5%, respectively. For compositions containing >25 wt% PNC two types of non-linearity were detected. At ω≤ω_c=1.4 ± 0.2 rad/s yield stress provided evidence of a 3-D structure. At ω > ω_c, G′ and G′′ were sensitive to shear history – the effect was reversible. From the frequency scans at ω > ω_c the zero-shear relative viscosity vs concentration plot was constructed. The initial slope gave the intrinsic viscosity from which the aspect ratio of organoclay particles, p=287 ± 9 was calculated, in agreement with the value calculated from the reduced permeability data, p=286. Received: 24 May 2001 Accepted: 27 August 2001