The numerical computation of turbulent flows

The standard κ-ϵ equations and other turbulence models are evaluated with respect to their applicability in swirling, recirculating flows. The turbulence models are formulated on the basis of two separate viewpoints. The first perspective assumes that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modeled terms in the κ-ϵ equations. Both stabilizing and destabilizing Richardson number corrections are incorporated to investigate this line of reasoning. A second viewpoint proposes that the eddy viscosity approach is inherently inadequate and that a redistribution of the stress magnitudes is necessary. Investigation of higher-order closure is pursued on the level of an algebraic stress closure. Various turbulence model predictions are compared with experimental data from a variety of isothermal, confined studies. Supportive swirl comparisons are also performed for a laminar flow case, as well as reacting flow cases. Parallel predictions or contributions from other sources are also consulted where appropriate. Predictive accuracy was found to be a partial function of inlet boundary conditions and numerical diffusion. Despite prediction sensitivity to inlet conditions and numerics, the data comparisons delineate the relative advantages and disadvantages of the various modifications. Possible research avenues in the area of computational modeling of strongly swirling, recirculating flows are reviewed and discussed.

Bubbles, Drops, and Particles

This overview of diffusion and separation processes brings unsurpassed, engaging clarity to this complex topic. Diffusion is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering. This spontaneous mixing process is also central to our daily lives, with importance in phenomena as diverse as the dispersal of pollutants to digestion in the small intestine. For students, Diffusion goes from the basics of mass transfer and diffusion itself, with strong support through worked examples and a range of student questions. It also takes the reader right through to the cutting edge of our understanding, and the new examples in this third edition will appeal to professional scientists and engineers. Retaining the trademark enthusiastic style, the broad coverage now extends to biology and medicine.

Diffusion: Mass Transfer in Fluid Systems

Turbulent friction and heat transfer behaviors of dispersed fluids (i.e., uttrafine metallic oxide particles suspended in water) in a circular pipe were investigated experimentally. Viscosity measurements were also conducted using a Brookfield rotating viscometer. Two different metallic oxide particles, γ-alumina (Al2O3) and titanium dioxide (TiO2), with mean diameters of 13 and 27 nm, respectively, were used as suspended particles. The Reynolds and Prandtl numbers varied in the ranges l04-I05 and 6.5-12.3, respectively. The viscosities of the dispersed fluids with γ-Al2O3 and TiO2 particles at a 10% volume concentration were approximately 200 and 3 times greater than that of water, respectively. These viscosity results were significantly larger than the predictions from the classical theory of suspension rheology. Darcy friction factors for the dispersed fluids of the volume concentration ranging from 1% to 3% coincided well with Kays' correlation for turbulent flow of a single-phase fluid. The Nusselt n...

Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles

Boundary conditions for direct simulations of compressible viscous flows

The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

/pdf/boundary-layer-theory-3f5kbgsgov.pdf

Boundary layer theory

In der klassischen Hydrodynamik wird vorwiegend die Bewegung der reibungslosen Flussigkeit behandelt. Von der reibenden Flussigkeit besitzt man die Differentialgleichung der Bewegung, deren Ansatz durch physikalische Beobachtungen wohl bestatigt ist. An Losungen dieser Differentialgleichung hat man auser eindimensionalen Problemen, wie sie u. a. von Lord Rayleigh 1 gegeben wurden, nur solche, bei denen die Tragheit der Flussigkeit vernachlassigt ist oder wenigstens keine Rolle spielt. Das zwei-und dreidimensionale Problem mit Berucksichtigung von Reibung und Tragheit harrt noch der Losung. Der Grund hierfur liegt wohl in den unangenehmen Eigenschaften der Differentialgleichung.

Über Flüssigkeitsbewegung bei sehr kleiner Reibung

Die neuen Versuche von Jakob und Erk 1 uber den Widerstand von stromendem Wasser in glatten Rohren, die mit alteren Messungen von Stanton und Paknell 2 in guter Ubereinstimmung sind, haben mich veranlast, meine bisherige Meinung, das das empirische Blasius-sche Gesetz (Widerstand proportional der 7/4-ten Potenz der mittleren Geschwindigkeit) bis zu beliebig hohen Reynoldsschen Zahlen gelten wurde, zu andern. Nach den neuen Versuchen nahert sich der Exponent mit wachsender Reynoldsscher Zahl immer mehr der Zwei, wobei es noch offen ist, ob ein bestimmter endlicher Grenzwert der Widerstandsziffer λ fur R = ∞ resultiert oder nicht.

Bericht über Untersuchungen zur ausgebildeten Turbulenz

M. H. Was ich Ihnen hier uber die Gesetzmasigkeiten der ausgebildeten turbulenten Flussigkeitsstromung vortragen will, ist, wie ich gleich sagen mochte, noch weit davon entfernt, etwas Abgeschlossenes darzustellen, es handelt sich vielmehr um die ersten Schritte auf einem neuen Weg, denen, wie ich hoffe, noch mancherlei Schritte folgen werden.

Über die ausgebildete Turbulenz

In meinem Bericht gelegentlich des V. Internationalen Mechanik-Kongresses 1938 in Cambridge, USA2 habe ich schon darauf hingewiesen, das bisher die formelmasige Erfassung der Vorgange der ausgebildeten Turbulenz noch sehr unbefriedigend sei, indem man genotigt sei, mehrere Arten von Turbulenz zu unterscheiden, fur die die Rechenregeln jeweils verschieden sind.

Hermann Schlichting

Papers

Boundary layer theory

Über Flüssigkeitsbewegung bei sehr kleiner Reibung

Bericht über Untersuchungen zur ausgebildeten Turbulenz

Über die ausgebildete Turbulenz

Über ein neues Formelsystem für die ausgebildete Turbulenz