Showing papers in "Annual Review of Fluid Mechanics in 1977"

Bubble Dynamics and Cavitation

Abstract: The first analysis of a problem in cavitation and bubble dynamics was made by Rayleigh (1917), who solved the problem of the collapse of an empty cavity in a large mass of liquid. Rayleigh also considered in this same paper the problem of a gas-filled cavity under the assumption that the gas undergoes isothermal com­ pression. His interest in these problems presumably arose from concern with cavitation and cavitation damage. With neglect of surface tension and liquid viscosity and with the assumption of liquid incompressibility, Rayleigh showed from the momentum equation that the bubble boundary R(t) obeyed the relation RR+W<)2 = p(R)oo, p (1.1)

Fluid Mechanics of Propulsion by Cilia and Flagella

Abstract: Since the Annual Review of Fluid Mechanics first published a review on microorganism locomotion by Jahn & Votta (1972) considerable progress has been made in the understanding of both the biological and the fluid-mechanical processes involved not only in microorganism locomotion but also in other fluid systems utilizing cilia. Much of this knowledge and research, which has been built on the solid foundation of the pioneering work of Sir James Gray (1928, 1968) and Sir Geoffrey Taylor (1951, 1952a,b), has been reported extensively elsewhere, particularly by Gray (1928, 1968), Sleigh (1962), Lighthill (1975), and Wu, Brokaw & Brennen (1975). The subject is now sufficiently broad that it precludes any exhaustive treatment in these few pages. Rather, we restrict this review primarily to a summary of present understanding of the low-Reynolds-number flows associated with microorganism propulsion and the hydromechanics of ciliary systems. In this introductory section we wish to put such fluid-mechanical studies in biological perspective. Section 2 outlines the present status of low-Reynolds-number slender-body theory, and we discuss the application of this theory to biological systems in the final sections.

Compressible Turbulent Shear Layers

Abstract: It is generally accepted that the direct effects of density fluctuations on turbulence are small if the root-mean-square density fluctuation is small compared with the absolute density: this is Morkovin's hypothesis (Favre 1964, p. 367). This means that the turbulence structure of boundary layers and wakes at free-stream Mach numbers Me less than about 5, and of jets at Mach numbers less than about 1.5, is closely the same as in the corrcsponding constant-density flow. By "turbulence structure" we mean dimensionless properties like correlation coefficients and spectrum shapes: the skin-friction coefficient cf == Tw/tPeU; and other ratios of turbulence quantities to mean flow quantities are greatly affected by the influence of mean density changes on the mean motion. The effect of mean density variations in x or y on the turbulence structure is not covered by Morkovin's hypothesis, but is often negligible at the lower Mach numbers if stream wise pressure gradients are small. Therefore assumptions about turbulence structure that give good results in calculation methods for constant-density /low will, if properly scaled, give good results in compressible boundary layers or wakes for Me 5, say. Basic equations for compressible shear layers are given by Howarth (1953) and Lin (1959). More recent treatments (FavJe 1971, Cebeci & Smith 1974, Rubesin & Rose 1973, Bilger 1975) use "mass-weighted" variables, which remove density iluctuations from the time-averaged equations of motion but not from the turbulence or from the response of measuring instruments (although Laufer, in Birch et aI1972, p. 462, suggests that pitot tubes probably yield mass-averaged velocities). It seems probable that the difference between conventional and mass-weighted averages rises more slowly with Mach number than current errors in measuring either. Of problems 1 The author is grateful for a number of helpful comments or contributions, especialIy

Electrokinetic Effects with Small Particles

Abstract: Electrokinetic phenomena is a generic term applied to effects associated with the movement of ionic solutions near charged interfaces. Although a respectable antiquity can be claimed for· the subject, our understanding of the fluid mechanics begins with Smoluchowski's studies in the early part of the twentieth century. Much of the current interest stems from the use of electrokinetic measurements in bio­ chemistry and biophysics. Although electrokinetic phenomena play important roles in many diverse natural and technological processes no attempt is made to deal with their ubiquitous nature here. Instead our understanding of two archetypal problems is reviewed. Other reviews may be consulted for insight into the diversity of the phenomena (see Abramson 1934; Abramson, Moyer & Gorin 1942; Overbeek 1950; Overbeek & Wiersema 1967; Dukhin & Deryagun 1974). Another reason for current interest in these phenomena derives from their roles in the bulk behavior of suspensions. A focus of the work on suspensions is the use of micro scale phenomena, e.g. flow around a single particle, to explain bulk behavior. Considerable attention has been paid to suspensions of uncharged particles but not to charged particles in ionic solutions. Here attention focuses on the description of the two prototypical problems that serve as the basis for an understanding of the bulk behavior. These problems are the motion of a small charged particle in response to an externally applied field and the behavior of a similar particle exposed to some sort of flow without any externally applied field. In both cases the essential complicating feature is the presence of diffuse space charge arising from the response of the ions in solution to the presence of the charged interface. The basis for the description of the phenomena is reviewed first with emphasis on the ways in which electrokinetic effects alter the conservation equations. The current understanding of the two archetypal problems is reviewed in subsequent sections.

Incompressible Boundary-Layer Separation

Abstract: For high-Reynolds-number flow over bodies or in confined channels the effects of viscosity are generally limited to a thin layer, the boundary layer, adjacent to the bounding surface. When the imposed pressure gradient is adverse, however, the thickness of the viscous layer increases as momentum is consumed by both wall shear and pressure gradient, and at some point the viscous layer breaks away from the bounding surface. Downstream of this point (or line) of breakaway the original boundary-layer fluid passes over a region of recirculating flow. The point at which the thin boundary layer breaks away from the surface and which divides the region of downstream-directed flow, in which the viscous effects are quite limited in extent, from the region of recirculating flow is known as the separation point.! Two different types of post-separation behavior are known to exist. In some cases the original boundary layer passes over the region or ' recirculating fluid and reattaches to the body at some point downstream, trapping a bubble of recirculating fluid beneath it. The characteristic length of this separation bubble may be of the same order as the upstream boundary-layer thickness or ma�y times the boundary-layer thickness. In other cases, the original boundary-layer fluid never reattaches to the body but passes downstream, mixing with recirculating fluid, to form a wake. For this wake-type of separation the characteristic dimension of the recirculating region is generally of the same order as the characteristic body dimension. In either case, the recirculating flow alters the effective body shape and hence the inviscid flow about the body.

On the Liquidlike Behavior of Fluidized Beds

Abstract: A bed of particles can be partly or fully supported by an upward flow of fluid through the interstices between the particles; if the bed is fully supported, it is said to be fluidized. This account of the liquidlike behavior of gas-fluidized beds discusses the experimental aspects first. The appearance and properties of gas bubbles in fluidized beds have qualitative similarities to those of gas bubbles in liquids; a brief account of bubble size and shape, formation, rising velocity, and coalescence is given. The role of certain bubble properties, particularly bubble shape, in explaining the viscosity of the particular phase of a fluidized bed is discussed. Then the theory for the motion of a bubble in a viscous liquid is reviewed, and the extent to which this provides an adequate description of a gas bubble in a fluidized bed is examined. Next, the extent to which the motion of particles and the interstitial fluid can be described by treating the particulate phase as an inviscid liquid is considered; the general equations for particle and fluid motion are given. It is concluded, from a comparison of theory and experiment, that particle collisions provide the major contribution to fluidized-bed viscosity. 22 figures,more » 2 tables (RWR)« less

Study of the Unsteady Aerodynamics of Lifting Surfaces Using the Computer

Abstract: 1. Steady processes and those changing slowly with time (aeroelastic, divergence, control reversal, long-period oscillations, auto-oscillations occurring at small values of the dimensionless frequency pj, and so on). Here we require in the first' place aerodynamic derivatives for pj -t O. 2. Flows in which the dependence on time can be considered harmonic, but the dimensionless frequency varies within wide limits (high-frequency flutter, the effect of a turbulent atmosphere). In this case in order to determine the so-called transfer functions it is, generally speaking, necessary to consider the entire range of variation of the dimensionless frequency (0 � pj � 00). 3. Arbitrary dependence on time (violent maneuvers of an aircraft, rapid deflection of control surfaces, envelopment by a gust, effect of a stream past a shock wave).

Flow and transport in plants

Abstract: This review is not a discussion in the language of fluid mechanics about esoteric proper ties of flow in plants, but an attempt by a botanist to explain, with as little technical botanical language as possible, how the life and construction of plants raise problems of flow, some of which are still unresolved. In order to understand these problems it will be necessary to become acquainted with some of the details of plant construction (morphology, anatomy), and some of the conditions of plant life (physiology). At several places in the explanation I have felt that the special knowledge of readers of this Review might illuminate matters that are still obscure to botanists. The symbol (t) indicates such calls for help. Ref erences are scarcely quoted since they are written in a technical jargon that would be barely understood. Rather the names are given of a few works that may serve as entry points into the li terature for any reader who wishes to follow particular lines of thought, and these are grouped in a Bibliography with an indication of their scope. Calculations by plant physiologists about the flows to he discussed are always done in terms of Poiseuille's equation. We are not sensitive to the limitations of this approach or aware of other relations that might be more appropriate in the fluid spaces of the plant (t). Technical botanical terms are italicized at their first appearance.

Optimum Wind Energy Conversion Systems

Abstract: The history of energy-converting machines is the story of consistently increasing specific speed. This is also true for wind-energy converters jf we neglect the step backwards between 1868 and approximately 1910, when comparatively small low­ speed multiblade steel windmills were introduced, as a temporary help mainly for farming in semiarid areas. It was several centuries ago, during the first severe confrontation between Occident and Orient after the decline of the Roman Empire, that the European knights, aside from candied fruits and decimal figures, discerned the importance of those strange windmills, most probably with sail-wing rotors. At all events there does exist a document of 1105, six years after the end of the first crusade, which granted to the Benedictine monastery of Savigny a windmill privilegium ( Bilau 1933 and Golding 1955). From then on up to the end of the eighteenth century a consistently empirical development led finally to those well-known Dutch windmills with four-bladed rotors of from 18 up to 26 m diameter, optimum tangential tip-speed ratios 1.8 � Aw.RTR � 2.4, and maximum speed ratios when idling at zero output of up to 3.2 times the wind velocity VFFL in free flow. We define (1)

Finite-element methods in fluid mechanics

Abstract: The large strides made by the computer industry have continually whetted the appetite of engineers to solve practical problems of higher and higher complexity by numerical simulation. While the utopia of completely dispensing with the expensive full-scale experimental verification may be debatable, it should be no longer controversial to acknowledge the rapidly expanding domain of problems for which answers satisfactory to design engineers can be obtained by numerical studies alone. For both fluid and solid mechanics, important practical applications often involve complex geometrical configurations and nonhomogeneous material proper­ ties. Circumstances, however, have led to a natural contrapuntal development of the solution technique. There is the finite-difference method, time-honored and now superbly honed to deal with many fluid problems, and there is the finite-element method, with a late start but precipitously brought to an omnipresence in solid­ mechanics literature. Not by default alone, however, has the finite-element method established its supremacy in the solid area. It should have the potential to carry over its advantages at least to certain classes of fluid problems. Adaptations of the finite-element method for fluid problems, perhaps not surprisingly, have come mainly from the solid-mechanics community. Beginning with the crude solution of the potential flow of a uniform stream over a circular cylinder by Martin (1968), numerous papers have appeared in diverse applications. From a formal viewpoint, the casting of any set of differential equations of a properly posed problem into an algebraic system, according to a finite-element method, can always be made; the difficulty is primarily one of bookkeeping. But such is also the case if a finite-difference method is used. The difference lies in the flexibility of the finite-element method in permitting a great deal of innovation by the user. The ultimate form of the algebraic system may be thus quite individual. At any rate, reducing the differential equation to an algehraic system is only the first step, and it does not follow that the desired solution can be easily extracted. Most of all, singular behavior abounds in fluid flows, and flow instability and turbulence find little parallel in solid mechanics. It needs no emphasis that an

Hydrodynamics of the Universe

Abstract: After an introduction on the relativistic vs the Newtonian approach, the Friedmann--Robertson--Walker picture of the Universe is considered: isotropic and homogeneous solution, group-theoretic definition of homogeneity, and Friedmann solution are taken up. The paradox of the infinite gravitational potential in Newtonian theory is disposed of. It has long been believed that gravitational instability is the ultimate cause of matter clustering in the Universe. First, the idealized case of a static universe is treated. Then the Newtonian treatment of small perturbation theory is given for an expanding universe. Recent work concerning the extension of the theory to perturbations of finite amplitude is treated. Simple arguments are given showing that the ultimate phase of perturbation growth is the formation of shock waves. Matter compressed by shock wave forms rather flat clumps. Most of the above is written as examples of formal solutions of hydrodynamic equations with gravitational interaction. Finally, the connection of the theory to observational evidence is established. (RWR)

Steady non-viscometric flows of viscoelastic liquids

Abstract: Figure 1 shows a phenomenon that cannot be explained on the basis of material properties measured in standard viscometers. A liquid is being drawn upward into a tube whose orifice is not submerged in the liquid. The liquid is mainly a mixture of glycerin and water, but it contains a small amount of a substance composed of very long-chain molecules, a polymeric material. The mechanical properties of polymer melts and solutions are highly complex. Experimentalists and theoreticians who attempt to characterize these properties often restrict attention to very simple flows, in which limited aspects of the mechanical response of the material can be isolated for study. Steady shearing flows, such as those in the capillary, Couette, cone-and-plate, and other standard viscometers, are particularly simple. The theory of these so-called viscometric flows is the subject of a book by Coleman, Markovitz & Noll (1966), and more recent theoretical and experimental work has been reviewed by Pipkin & Tanner (1972). In the present review we discuss some flows in a category that at first appears to be only slightly broader than visco metric flows. We restrict attention to flows in which the velocity gradient is constant in time, after the motion begins, and uniform in space, throughout the flow region. It might appear that there could hardly be a much simpler class of flows, but the work of Giesekus (1962a,b) has shown that there is a fascinating variety in such motions. We discuss the experimental evidence that by now exists, which shows that the material properties exhibited in some of these motions can differ drastically from anything one might guess from viscometric data. The evident stability of the flow in Figure 1 illustrates this difference. If the shearing viscosity rys(y) as a function of the shear rate y is known, one might suppose

Recollections From an Earlier Period in American Aeronautics

Abstract: The situation of American aeronautics in the year 1929 is examined. In that year manufacturers all over the U.S. were bringing out new aircraft models to capture an assured market. Earlier developments in aviation in the U.S. after World War I are also considered along with the conditions of American aeronautics in the 1930s. Attention is given to the introduction of the Barling NB-3 with its all-metal construction, efforts of NACA to collect and disseminate in a uniform notation aerodynamic characteristics of airfoils from laboratories around the world, and the invention of the variable-density wind tunnel.