The effects of streamline curvature and spanwise rotation on near-surface,turbulent boundary layers

A second moment closure model is used to study the mean fields and turbulence structure of spanwise rotating flows and flows with streamline curvature. The effects of flow stabilization and destabilization by rotation and/or curvature and their interpretation in terms of a Rayleigh instability mechanism are discussed in the context of the present model. When applied to the constant flux layer adjacent to a bounding surface, the model provides a similarity theory for flows with spanwise rotation and streamline curvature like that of Monin-Obukhov in the case of density stratified flows. In particular, it is shown that Bradshaw's empirical length scale correction can be derived in terms of the basic constants of the model determined in the absence of rotation and curvature. Also, direct comparisons with experimental data confirm the model predictions. The definitions of strong and mild curvature are discussed and a distinguishing criterion derived.

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Zusammenfassung Gemittelte Strömungsfelder und Turbulenzcharakteristiken werden bestimmt mittels eines numerischen Modelles mit Momenten zweiter Ordnung als Ciosure für lateral rotierende Strömungen und mit gekrümmten Stromlinien. Stabilisierungs- und Destabilisierungseffekte infolge Rotation und/oder Krümmung werden als Raleigh-Instabilitäten im Zusammenhang mit dem Modell diskutiert. Wenn angewandt auf die Konstant-Scherspannungszone in Grenzschichten, liefert das Modell eine Ähnlichkeitstheorie für Strömungen mit lateraler Rotation und Stromlinienkrümmung, vergleichbar dem Falle des Monin-Obukhov Modelles für geschichtete Strömungen. Es wird insbesondere gezeigt, dass Bradshaws empirische Längenkorrektur sich aus den Grundkonstanten des Modelles ergibt für den Grenzfall ohne Rotation und Krümmung. Direkter Vergleich mit experimentellen Daten bestätigt die Rechnungen. Die Definitionen von starker und schwacher Krümmung werden diskutiert und ein Unterscheidungskriterium eingeführt.

     

Turbulent auxiliary functions for symmetric three-dimensional boundary layers

Zusammenfassung Der allgemeine Charakter der dreidimensionalen Grenzschichtströmung in einem Rotationskörper wird mit Hilfe einer verallgemeinerten Impuls-Integral-Methode untersucht. Die notwendigen Hilfsfunktionen und der Ablösungspunkt der turbulenten Grenzschicht werden durch Einführung geeigneter Formfaktoren bestimmt. Die zweidimensionalen Beziehungen werden dabei unter Berücksichtigung neuerer Versuchsergebnisse umgestaltet und so auf den dreidimensionalen Fall übertragen.     

H-bubbles with prescribed large mean curvature

Given a smooth function , we call H-bubble a conformally immersed surface in ³ parametrized on the sphere ² with mean curvature H at every point. We prove that if is a nondegenerate stationary point for H with , then there exists a curve of embedded H-bubbles, defined for large, which become round and concentrate at as . Also the case of topologically stable extremal points for H is considered.Work supported by M.U.R.S.T. progetto di ricerca Metodi variazionali ed equazioni differenziali nonlineari (cofin. 2002) Mathematics Subject Classification (2000):53A10 (49J10)     

An assessment of streamline curvature effects on the mixing region of a turbulent plane jet in crossflow

The flow field of a turbulent plane jet in a weak or moderate crossflow, which is characterised by mild streamline curvature, has been investigated computationally. The values of the jet-to-crossflow velocity ratios chosen are 6, 9 and 10. The time-averaged Navier–Stokes equations are solved on a staggered Cartesian grid using the standard k–ϵ model and the k–ϵ model with streamline curvature modification. The predictions using both the models are compared with available experimental data. It has been shown that by accounting for the effect of streamline curvature in the k–ϵ model results in good prediction of this flow configuration.     

On boundary layers

The concept of boundary layers, introduced by A. Volberg in [7], is generalized from subsets of the unit disk to subsets of general non-tangentially accessible (NTA) domains. Capacitary conditions of Wiener type series of both necessary and sufficient type for boundary layers are presented and the connection between boundary layers and minimally thin sets is studied.     

Turbulent flame propagation with large chemical-heat release

A model is developed to describe the dependence of the turbulent-flame speed on the intensity of an isotropic excitation turbulence prescribed far upstream from the flame for arbitrarily large gas expansion within the flame. For the limit of negligible gas expansion within the flame the new prediction of the present study reduces to an established and recently verified result for isothermal front propagation. It is shown that the turbulent-flame speed varies inversely with the square of the temperature ratio across the flame when the temperature ratio is very large. For typical hydrocarbon flames the results predict generally less substantial rates of decrease of the turbulent-flame speed with increasing heat release. Variations in turbulence kinetic energies and vorticity across the flame and hydrodynamic zones upstream and downstream from the flame are determined as well, accounting for influences of gas expansion and the structure of the excitation turbulence. The results of the present work, which are valid for flame propagation in weakly turbulent flow (where the propagation speed is proportional to the square of the intensity of the excitation turbulence prescribed far upstream from the flame) extend earlier predictions that were limited to relatively small chemical-heat release. The model presented herein does not account for effects of intrinsic flame instability and is appropriate for conditions where influences of buoyancy and flame stretch on flame dynamics are not substantial.     

Stable constant mean curvature surfaces with circular boundary

In this paper we study stable constant mean curvature surfaces in the Euclidean space with circular boundary. We show that in the case of genus zero, the only such surfaces are the spherical caps and the flat discs. We also extend this result to the case of surfaces in the other space forms, namely the sphere and the hyperbolic space .

     

Three-dimensional periodic boundary layers

The method of successive approximations used by Eichelbrenner and A?kovíc¹ for the study of unsteady three-dimensional boundary layer flow has been extended to analyse the periodic boundary layers in three dimensions. The analysis, which is valid for oscillations of small amplitude, shows some special features such as “steady streaming” flow in the first-order cross-flow similar to the one that has been predicted and observed by Schlichting for two-dimensional periodic boundary layers.     

On magneto-aerodynamic boundary layers

Zusammenfassung Der Einfluss eines senkrecht zur Schicht stehenden magnetischen Feldes auf die Geschwindigkeits- und Temperaturverteilung in einer Grenzschicht wird für einen Sonderfall der ?nderung der elektrischen Leitf?higkeit von Luft untersucht. Die Wirkung des magnetischen Feldes auf den Reibungswiderstand und den W?rmeübergang wird bei relativ zur Platte und zur Flüssigkeit in grosser Entfernung von der Platte festgehaltenem Magnetfeld ermittelt.      

Mean curvature flow with linear oblique derivative boundary conditions

Science China Mathematics - In this paper, we study the mean curvature flow with oblique derivative boundary conditions. We prove the longtime existence by choosing a suitable auxiliary function....     

Conformal metrics with prescribed boundary mean curvature on balls

We provide a variety of classes of functions that can be realized as the mean curvature on the boundary of the standard n dimensional ball, n ≥ 3, with respect to some scalar flat metric. Because of the presence of some critical nonlinearity, blow up phenomena occur and existence results are highly nontrivial since one has to overcome topological obstructions. Our approach consists of, on one hand, developing a Morse theoretical approach to this problem through a Morse-type reduction of the associated Euler–Lagrange functional in a neighborhood of its critical points at Infinity and, on the other hand, extending to this problem some topological invariants introduced by A. Bahri in his study of Yamabe type problems on closed manifolds.     

Metrics of positive ricci curvature with large diameter

Examples are constructed of n-manifolds of positive Ricci curvature with almost maximal diameter, consistent with Myer's theorem, which are not homotopy equivalent to the n-sphere. This implies that the topological rigidity associated to the metric rigidity of Myer's theorem, fails in this case. Similar results hold for the estimate of the first eigenvalue of the Laplace operator. Partially supported by an N.S.F. Grant     

Nonsimilar incompressible laminar boundary layers with magnetic field

The solution of the steady laminar incompressible nonsimilar magneto-hydrodynamic boundary layer flow and heat transfer problem with viscous dissipation for electrically conducting fluids over two-dimensional and axisymmetric bodies with pressure gradient and magnetic field has been presented. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for flow over a cylinder and a sphere. The results indicate that the magnetic field tends to delay or prevent separation. The heat transfer strongly depends on the viscous dissipation parameter. When the dissipation parameter is positive (i.e. when the temperature of the wall is greater than the freestream temperature) and exceeds a certain value, the hot wall ceases to be cooled by the stream of cooler air because the ‘heat cushion’ provided by the frictional heat prevents cooling whereas the effect of the magnetic field is to remove the ‘heat cushion’ so that the wall continues to be cooled. The results are found to be in good agreement with those of the local similarity and local nonsimilarity methods except near the point of separation, but they are in excellent agreement with those of the difference-differential technique even near the point of separation.     

Singularly perturbed problems with boundary and internal layers

This paper is an expanded version of the talk given by the authors at the International Conference “Differential Equations and Topology” dedicated to the centenary of the birth of L.S. Pontryagin. We present a brief survey and describe new ideas and methods of analysis in the asymptotic theory of solutions with internal layers, which is one of the topical fields of singular perturbation theory.     

Implementation of near-wall boundary conditions for modeling boundary layers with free-stream turbulence

The paper is devoted to the extension of the near-wall domain decomposition, earlier developed in some previous works by the authors, to modeling flat-plate boundary layers undergoing laminar-to-turbulent bypass transition. The steady-state wall boundary layers at high-intensity free-stream turbulence are studied on the basis of differential turbulence models with the use of non-overlapping domain decomposition. In the approach the near-wall resolution is replaced by the interface boundary conditions of Robin type. In contrast to the previous studies, the main attention is paid to the laminar–turbulent transitional regime. With the use of modified turbulence models we study an effect of free-stream parameters on the development of dynamic processes in the boundary layer including a transitional regime and fully developed turbulent flow. In addition, for the first time a full scale domain decomposition is realized via iterations between the inner and outer subregions until a convergence. The computational profiles of the velocity and intensity of the turbulence kinetic energy are compared with experimental data. A possible range of location of the near-wall interface boundary is found.