Showing papers in "Annual Review of Fluid Mechanics in 1985"

Computing Three-Dimensional Incompressible Flows with Vortex Elements

Abstract: The techniques, capabilities and applicability of numerical models of three-dimensional, unsteady vortical flows with high Re are assessed. Vorticity is calculated only in appropriate regions and the velocity field is derived from the boundary conditions. Vorticity is assumed to take the shape of tubes with uniform core structures in the case of turbulence. The efforts being made to simplify equations for dense collections of vortex filaments in order to make them tractable to computer simulations are described. The effectiveness of vorticity arrow representations for accurately describing vorticity fields near surfaces is discussed, along with Lagrangian vortex elements, which may be of use in modelling the rotational part of flows around bluff bodies, nonuniform density flows and chemically reacting flows.

Sedimentation of noncolloidal particles at low Reynolds numbers

Abstract: Sedimentation, wherein particles fall under the action of gravity through a fluid in which they are suspended, is commonly used in the chemical and petroleum industries as a way of separating particles from fluid, as well as a way of separating particles with different settling speeds from each other. Examples of such separations include dewatering of coal slurries, clarifi­ cation of waste water, and processing of drilling and mining fluids containing rock and mineral particles of various sizes. The separation of different particles by sedimentation is also the basis of some laboratory techniques for determining the distribution of particle sizes in a particulate dispersion. Owing to the significance of the subject, there have been numerous experimental and theoretical investigations of the sedimentation of par­ ticles in a fluid. One of the earliest of these is Stokes' analysis of the translation of a single rigid sphere through an unbounded quiescent Newtonian fluid at zero Reynolds number, which led to his well-known law (0) _ 2a2(p. p )g u 9J.l ' (1.1)

Aerodynamics of Sports Balls

Abstract: Research data on the aerodynamic behavior of baseballs and cricket and golf balls are summarized. Cricket balls and baseballs are roughly the same size and mass but have different stitch patterns. Both are thrown to follow paths that avoid a batter's swing, paths that can curve if aerodynamic forces on the balls' surfaces are asymmetric. Smoke tracer wind tunnel tests and pressure taps have revealed that the unbalanced side forces are induced by tripping the boundary layer on the seam side and producing turbulence. More particularly, the greater pressures are perpendicular to the seam plane and only appear when the balls travel at velocities high enough so that the roughness length matches the seam heigh. The side forces, once tripped, will increase with spin velocity up to a cut-off point. The enhanced lift coefficient is produced by the Magnus effect. The more complex stitching on a baseball permits greater variations in the flight path curve and, in the case of a knuckleball, the unsteady flow effects. For golf balls, the dimples trip the boundary layer and the high spin rate produces a lift coefficient maximum of 0.5, compared to a baseball's maximum of 0.3. Thus, a golf ball travels far enough for gravitational forces to become important.

The Kutta Condition in Unsteady Flow

Abstract: In several papers published in the first decade of this century, Kutta and Joukowsky independently proposed that the lift on an airfoil at incidence in a steady un separated flow is given by potential-flow theory with the unique value of the circulation that removes the inverse-sQuare-root velocity singularity at the trailing edge. This proposal-tantamount to saying (cf. Batchelor 1967) that in the unsteady start-up phase the action of viscosity is such that, in the ultimate steady motion, viscosity can be explicitly ignored but implicitly incorporated in a single edge condition-is known as the Kutta-Joukowsky hypothesis. Subsequently the name "Kutta condition" (no doubt largely for brevity) has come to be used to connote the removal of a velocity singularity at some distinguished point on a body in unsteady flow. 1 The condition has recently been applied to unsteadiness in a variety of mean configurations. These include trailing-edge flows with the same and with different flows on the two sides of the body upstream of the edge, attached leading-edge flows, and grossly separated flows past bluff bodies. Imposition of a Kutta condition on unsteady perturbations to one of these mean flows has a variety of physical ramifications. It represents the mechanism by which both the lift is changed and the amplitude and directivity of a sound field are modified. It is the analytical step that in many cases describes the conversion-almost total-of acoustic energy in an incident sound wave to energy of vortical motion on a shear layer ; on

The response of turbulent boundary layers to sudden perturbations

Abstract: The processes present in a turbulent boundary layer (BL) which experiences a sudden change in the surface roughness are discussed in terms of numerical models in comparison with empirical data. Consideration is limited to flow perturbations which preserve the BL approximation. Generalized continuity, momentum and turbulent energy transport equations are reviewed. The perturbed BL has two regions: one with large velocity gradients and an outer zone with smaller gradients. Expressions are defined for the velocity and temperature profiles and the roughness length after a step change in surface roughness, which causes the disturbance. A pertrurbation could also arise from a heat flux input of a pressure gradient. The effects of the shape of the perturbing step and the presence of several disturbing edges are explored. Finally, it is shown that closure forms and constants for self-preserving flows are worthy of further development because of their demonstrable abilities to describe simple perturbed flows.

Buoyancy-Driven Flows in Crystal-Growth Melts

Abstract: In most of the methods for synthetic production of single crystals, the crystal grows slowly from a fluid nutrient. Several different mechanisms can drive motions in this fluid, and these motions are of concern to the crystal grower because they influence the transport of dopant, impurities, and heat to the growth interface. The seriousness of this concern is reflected by the commissioning of at least seven review articles on the subject during the past decade (Carruthers 1975, 1979, Hurle 1977, Langlois 1981a, Pimputkar & Ostrach 1981, Kobayashi 1981, Jones 1984). The nutrient fluid may be a vapor or a supersaturated solution, but we focus here upon systems in which a crystal is grown from its melt. Actually, . we deal mostly with one specific method of growing crystals, viz. the Czochralski process. There are several reasons for this. The first is its importance. Four of the references cited in this review are from a single issue of PhysicoChemical Hydrodynamics, which was devoted to the role of convection and fluid flow in solidification and crystal growth. In the introductory article of that issue (HurIe & Jakeman 1981), the Czochralski process was described as "the most important and widely used technique." Indeed, Czochralski growth is ideally suited for producing the large quantities of pure crystal required by present technology. For example, single crystals of elemental silicon tens of kilograms in mass, and with diameters exceeding 100 mm, are now routinely produced. The second reason for dwelling on Czochralski growth follows from the first: Because of its importance, it has attracted far more attention from hydrodynamicists than have other melt growth systems. Finally, the flow in Czochralski melts is possessed of a rich structure with regard to both driving mechanisms and streaming patterns. The results obtained for this system provide at least a qualitative understanding of the other systems as well.

Mathematical Models of Dispersion in Rivers and Estuaries

Abstract: Principes sur lesquels reposent les modeles de dispersion: equation fondamentale, moyenne sur un ensemble et moyenne temporelle (la notion d'ensemble est revue en detail); effet des instruments de mesure; mecanisme de dispersion; modele de Taylor (1954) pour la dispersion longitudinale; autres types de modeles de dispersion par des scalaires conservatifs, dispersion des scalaires non conservatifs. Dispersion dans les rivieres: ecart a la solution gaussienne de l'equation de Taylor; dispersion aussitot apres le degagement de scalaire; dispersion a partir de sources stationnaires; complications geometriques. Dispersion dans les estuaires: modeles 1D de dispersion longitudinale; modelisation du flux longitudinal de salinite, relation entre le coefficient de dispersion longitudinale K m et la salinite dans un estuaire

Grid Generation for Fluid Mechanics Computations

Abstract: Fluid mechanics is understood in a descriptive way through experimental observation, mathematical analysis, and numerical simulation. When the understanding is required for flows with complex internal structure and with complicated regional boundaries, insight is gained primarily from experiments and simulations. Numerical simulations are motivated by the prospect of economically obtaining a detailed flow-field description. In each instance, a governing system of flow equations is analytically formulated over the region and is solved in an approximate form on a computer. Various numerical methods have been devised for such ap­ proximations, and most depend upon some representation of the flow-field region by means of finitely many points and the interconnections between them. When each regional boundary is given by a sequence of connected points, the efficiency and accuracy of the various methods are enhanced, since boundary conditions can be applied without interpolation. Further enhancement comes when the connectivity pattern is regular. The most regular and thus preferable patterns are those that result from coordinate transformations. With the application of transformations, regions with topological complexity are consistently treated even when points are in motion. During the course of simulation, motion can be advantageously used to adaptively resolve the significantly varying solution quantities. From a geometric viewpoint, the quantities determine a surface over the physical region. The resolution of the surface as it evolves then determines the adaptive movement.

Modeling Equatorial Ocean Circulation

Abstract: Double objectif de l'article: presenter, aussi succinctement que possible, les principes de la dynamique equatoriale, et passer en revue les recents developpements en la matiere. Les differents chapitres traitent successivement: des modeles suivant leur sophistication dynamique; des solutions non forcees, des solutions forcees par des vents qui s'installent, et des solutions forcees par des vents periodiques; des directions dans lesquelles s'engage la recherche sur l'El Nino; et des solutions lineaires (avec comparaison avec celles non lineaires) vu l'importance des modeles correspondants

Turbulent Diffusion from Sources in Complex Flows

Abstract: The dispersion of matter and heat in turbulent flows is generally analyzed in different ways depending on whether the matter and heat are released from distributed sources, such as heat at the wall of a pipe, or whether (as in this review) they are released from a single source that is small compared with the scale of the flow. There are many examples of such types of dispersion in engineering fluid mechanics, such as the spreading of a flame in a highly turbulent engine flow, the dispersion of one or more species emitted from pipes into large chemical reactors, and the heat released from local overheating in nuclear reactor subassembly channels. There are also many examples where continuous or sudden sources of pollutant or heat are discharged into the atmosphere or into aqueous environments. Usually these discharges occur in complex flows with inhomogeneous turbulence, such as boundary layers over level surfaces, or in flows impinging on surfaces, such as hills in the atmosphere or underwater ridges in the oceans. The aim of this review is primarily to summarize the current ideas and theories about the basic mechanisms for dispersion from localized sources in complex turbulent flows. A brief consideration of the examples already given indicates some of the characteristic features of such flows: inhomogeneity and unsteadiness of the turbulence, the shear and the convergence and divergence of the mean flow, the non-Gaussianity of the turbulence, recirculation of the mean flow, and the presence of surfaces. In most practical dispersion problems, many of these effects occur simultaneously, but in the dispersion from small sources and in the vicinity

Mantle convection and visoelasticity

Abstract: The ongoing revolution in the Earth sciences, which began more than twenty years ago, was originally based upon the increasingly widespread acceptance of the idea that continental masses have moved horizontally with respect to one another throughout geological time. This hypothesis of continental "drift," or at least the form of the hypothesis that came to be called seafloor spreading, now serves as the basic paradigm for the organization of most geological and geophysical research. At the center of this guiding principle is the recognition that the solid outer shell of the planet-its iron-magnesium silicate "mantle," which occupies roughly half Earth's radial extent-must be able to deform as a viscous fluid when it is subjected to an applied shear stress over geological intervals of time. To the extent that this rheological ansatz is correct, it is clear that a thermally induced convective circulation must appear in the mantle in response to a radial temperature gradient that is sufficiently in excess of adiabatic. The observed spreading of the seafloor away from hot mid-oceanic ridges is presumably a surface manifestation of such deep­ seated mantle convection. Likewise, the deep ocean trenches are under­ stood to be regions where cold surface material returns to the mantle to complete the circulation. These and other aspects of the pattern of surface motions associated with mantIe convection have been described kinemati­ cally within the framework of a set of ideas that has come to be called "plate tectonics." The development of this set of ideas has consummated the revolution at a descriptive level and has delivered as its main product a clear view of the velocity field of material at the Earth's surface at the present epoch of geological time. In so doing, it has also contributed in an

Rheometry of Polymer Melts

Abstract: The rheological properties of polymers in the molten state are important for polymer engineering and science for the following reasons: (a) they depend sensitively on the chemical structure of the individual macromolecules and, therefore, are of interest for polymer characterization; (b) they are required for the development of a realistic fluid dynamics of polymer melts as the basis for any theory of polymer processing; and (c) they are responsible for large molecular orientations that are formed in the melt during processing and frozen into the final products. There they create the inhomogeneous anisotropy of all physical quantities and alter the technological end-use properties. In spite of this relevance, the central problem of polymer-melt rheology is not yet solved, viz. the formulation of a workable and correct constitutive equation that describes the stress at any instant for any deformation history. For monographs concerning this subject, see Lodge ( 1964,1974), Truesdell & Noll (1965), Astarita & Maffucci (1974), Bird et al. (1977a,b), and Janeschitz-Kriegl ( 1983). The difficulties are due to the complicated, nonlinear rheological behavior of polymer melts. These melts are not only highly viscous liquids, but in addition they are pseudoplastic (viscosity decreases with increasing shear rate) and viscoelastic (mechanical response is timeand frequency­ dependent), and their viscous flow is often connected with large, rubberlike elastic deformations. Furthermore, polymer melts can be elongated remarkably without rupture. In the following, methods of polymer-melt rheometry are reviewed and discussed. Most of these methods originated in the plastics and rubber industry or were transferred from other areas, like the methods of linear

Fluid Modeling of Pollutant Transport and Diffusion in Stably Stratified Flows over Complex Terrain

Abstract: Investigations of pollutant transport and dispersion in the atmosphere over complex relief are critical for the protection of air quality, because industrial enterprises and other sources of air pollution frequently locate within complex terrain. The ability to predict ground-level concentrations of air pollutants released from sources in or near complex terrain is required in order to determine the environmental impact of existing sources, to evaluate alternative new source locations, designs, and controls, and to estimate the effects of possible modifications to existing sources. Mathematical models that reliably predict concentrations when plumes are affected by complex terrain are not yet available. Field studies are very expensive and time consuming, and their results are not generally transferable to other sites. Wind-tunnel studies on dispersion of effiuents from industrial plants located in complex terrain have been conducted for over 40 years. Usually these studies were designed to answer specific questions, such as the

Mathematical Modeling for Planar, Steady, Subsonic Combustion Waves

Abstract: The propagation of steady combustion waves in a premixed gas has occupied the imagination of scientists since flames were first observed. Fundamental ideas about the possible modes of propagation probably evolved initially from the classical theory of one-dimensional, steady compressible flow with heat addition. The class of discontinuous waves characterized by pressure and density decrease (deflagrations) has a continuous spectrum of propagation speeds, from the ultrasubsonic to an 0(1) value associated with a sonic speed behind the wave. Structural properties of deflagrations and the physical mechanisms controlling their propagation were considered much later. The most enduring and prolific studies are concerned with the steady, isobaric, low-Mach-number flame, which propagates by conductive preheating and forward radical diffusion. Less evident, but of considerable importance, are the structural investi­ gations of subsonic but 0(1) Mach number combustion waves, found initially in the descriptions of idealized planar detonations. Here, the reaction zone behind the thin shock wave propagates like a convecting thermal explosion, basically unaffected by restrictive transport-property effects. Transitional combustion waves, with propagation Mach numbers intermediate to those mentioned previously, have been modeled only recently. Clarke (1983a) finds that an increase in the Mach number causes the influence of transport effects on the flame structure to wane. The entire reaction process is increasingly dominated by a convective-reactive balance.

Sound Transmission in the Ocean

Abstract: Description de l'environnement acoustique de l'ocean. Modeles analytiques: equation parabolique, solutions des raies dependant de la distance, integrales le long d'un chemin, modes, elements finis. Effets a mesoechelle (tourbillons et fronts) et effets des ondes internes. Methodes inverses: acoustique du fond marin, tomographie acoustique