Laminar natural convection over a slender vertical frustum of a cone

The problem of laminar, natural convection flow over a slender frustum of a cone is treated in this paper. The governing differential equations are solved by a combination of quasi-linearization and finite-difference methods. Numerical solutions are obtained for Pr=0.7 and for a range of values of the transverse curvature parameter. It is shown that the effect of transverse curvature is of great significance in such flows. In diesem Bericht ist das Problem der laminaren natürlichen Konvektionsströmung an einem dünnen Kegelstumpf behandelt. Die maßgebliche Differentialgleichung ist durch eine Verbindung von Quasilinearisation und Differenzenverfahren gelöst. Eine numerische Lösung für Pr=0.7 wird für verschiedene Werte eines Krümmungsparameters angegeben. Es ist gezeigt, daß in solchen Strömungen dieser Krümmungsparameter eine große Bedeutung besitzt.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46649/1/231_2005_Article_BF01002323.pd

Three-dimensional elastic constitutive relations of aligned carbon nanotube architectures

Tailorable anisotropic intrinsic and scale-dependent properties of carbon nanotubes (CNTs) make them attractive elements in next-generation advanced materials. However, in order to model and predict the behavior of CNTs in macroscopic architectures, mechanical constitutive relations must be evaluated. This study presents the full stiffness tensor for aligned CNT-reinforced polymers as a function of the CNT packing (up to ∼20 vol. %), revealing noticeable anisotropy. Finite element models reveal that the usually neglected CNT waviness dictates the degree of anisotropy and packing dependence of the mechanical behavior, rather than any of the usually cited aggregation or polymer interphase mechanisms. Combined with extensive morphology characterization, this work enables the evaluation of structure-property relations for such materials, enabling design of aligned CNT material architectures.NECST ConsortiumUnited States. Army Research Office (Contract No. W911NF- 07-D-0004)United States. Army Research Office (Contract No. W911NF-13-D-0001)United States. National Aeronautics and Space Administration (NASA Space Technology Research Fellowship Grant No. NNX11AN79H)National Science Foundation (U.S.) (Grant No. CMMI-1130437

Laminar natural convection over a slender vertical frustrum of a cone with constant wall heat flux

The problem of laminar natural convection flow over a slender frustrum of a cone with constant wall heat flux is treated in this paper. The governing differential equations are solved by a combination of quasilinearization and finite-difference methods. Numerical solutions are obtained for Prandtl numbers from 0.1 to 100 for a range of values of transverse curvature parameter. It is found that the effect of transverse curvature is of great significance in such flows. In dieser Arbeit wird das Problem der laminaren, natürlichen Konvektionsströmung öber einem dünnen Kegelstumpf mit konstantem Wandwärmestrom behandelt. Die maßgeblichen Differentialgleichungen werden mit Hilfe einer Kombination von Quasilinearisierung und Differenzenverfahren gelöst. Numerische Lösungen werden für die Prandtl ' sehen Zahlen zwischen 0. l und 100 innerhalb eines Bereiches von Querkrüm mungswerten erhalten. Es wird gezeigt, daß der Einfluß der Querkrümmung in solchen Strömungen von großer Bedeutung ist.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46650/1/231_2005_Article_BF00997635.pd

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We derive the equations of motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B (GPB) complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters

Turbulent natural convection over a slender circular cylinder

The transverse-curvature effect on the heat transfer in the turbulent natural convection flow from the outer surface of a slender vertical circular cylinder is studied by an improved integral method for various values of Prandtl numbers and for various values of a transverse curvature parameter. Der Einfluß der Querkrümmung auf die Wärmeübertragung von der Außenoberfläche eines dünnen senkrechten Kreiszylinders in die turbulente, natürliche Konvektionsströmung wird mittels eines verbesserten Integral-Verfahrens für verschiedene Werte der Prandtl-Zahlen und der Querkrümmungsparameter untersucht.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46651/1/231_2005_Article_BF01637697.pd

Improved perturbation solutions for laminar natural convection on a vertical cylinder

The method of extended perturbation series is applied to solve for laminar natural convection from an isothermal, thin vertical cylinder. The series in terms of the transverse curvature parameter ξ extended to five terms and is subsequently improved by applying the Shanks transformation twice. The validity of the solution is extended up to ξ =10 and possibly even beyond. Up to ξ =10, the results for wall shear as well as the local and average Nusselt numbers agree very closely with those of local nonsimilarity and finite difference solutions. The ease of computation coupled with high accuracy makes the present approach far more attractive than the currently popular local nonsimilarity and finite difference methods. Its success with the present problem should motivate applications to a host of nonsimilar boundary layer flows. Die Methode der erweiterten Störungsserien wird auf die laminare freie Konvektion am isothermen senkrechten dünnen Zylinder angewendet. Die Serien in Ausdrücken des Krümmungsparameters ξ werden auf 5 Terme ausgedehnt und weiter durch doppelte Auswertung der Shank-Transformation verbessert. Die Lösung gilt mindestens bis ξ =10, vielleicht sogar weiter. Bis ξ =10 stimmen die Lösungen für die Wandschubspannung und die örtliche und mittlere Nußelt-Zahl gut überein mit jenen, die auf der örtlichen Nicht-Ähnlichkeit und finiten Differenzen beruhen. Die leichte Berechenbarkeit und die hohe Genauigkeit machen diesen Lösungsweg attraktiver als die heute populären Verfahren der örtlichen Nicht-Ähnlichkeit und der finiten Differenzen. Der hier aufgezeigte Erfolg sollte zur Anwendung auf nicht-ähnliche Grenzschichtströmungen motivieren.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46653/1/231_2005_Article_BF01459764.pd

Instabilities in the wake of an inclined prolate spheroid

We investigate the instabilities, bifurcations and transition in the wake behind a 45-degree inclined 6:1 prolate spheroid, through a series of direct numerical simulations (DNS) over a wide range of Reynolds numbers (Re) from 10 to 3000. We provide a detailed picture of how the originally symmetric and steady laminar wake at low Re gradually looses its symmetry and turns unsteady as Re is gradually increased. Several fascinating flow features have first been revealed and subsequently analysed, e.g. an asymmetric time-averaged flow field, a surprisingly strong side force etc. As the wake partially becomes turbulent, we investigate a dominating coherent wake structure, namely a helical vortex tube, inside of which a helical symmetry alteration scenario was recovered in the intermediate wake, together with self-similarity in the far wake.Comment: Book chapter in "Computational Modeling of Bifurcations and Instabilities in Fluid Dynamics (A. Gelfgat ed.)", Springe

A theoretical and experimental investigation of smooth- and wavy ice layers in laminar and turbulent flow inside an asymmetrically cooled parallel-plate channel

The present paper shows the adaption of the numerical model originally developed by Weigand and Beer [14] for calculating steady-state ice layers inside an asymmetrically cooled parallel-plate channel. The investigation shows the characteristics in ice formation behaviour due to asymmetrically cooled walls. Further, a simple analytical model is presented for calculating smooth ice layers in turbulent flow. The study is supported by own measurements of the freezing fronts inside an asymmetrically cooled channel. A comparison between theoretical calculations and measurements shows generally good agreement.Die vorliegende Arbeit beschreibt die Anwendung des von Weigand und Beer [14] entwickelten, numerischen Modells zur Vorhersage von Eisschichten in einem ebenen, asymmetrisch gekühlten Kanal. Die Studie befaßt sich mit den Unterschieden in der Eisschichtbildung aufgrund der asymmetrisch gekühlten Kanalwände. Weiterhin wird ein einfaches Verfahren angegeben, mit dem sich die Gestalt von glatten Eisschichten bei turbulenter Strömung und asymmetrischer Kühlung sehr einfach berechnen läßt. Die analytisch und numerisch gewonnenen Resultate werden anschließend mit eigenen Messungen von Eisschichten verglichen, wobei eine im allgemeinen gute Übereinstimmung zwischen Theorie und Experiment zu beobachten ist