Showing papers in "Annual Review of Fluid Mechanics in 1970"

Dynamics of Dusty Gases

Abstract: This review deals with a certain restricted portion of the mechanics of heterogeneous media. The volume fraction of the solid-particle or droplet cloud is considered to be so small that the interaction between individual particles may be neglected or highly simplified. This limitation applies to the individual flow fields about the particles as well as to collisions, and to heat and mass transfer as well as to momentum exchange between phases. Under this circumstance, the problem of detailed transport processes between particles and gas may be treated independently of the complete dynamical problem, and this aspect, being a study of its own, will be suppressed to a considerable extent here. There are problems, such as the impact of particles on walls, the concentration separation in boundary layers or pipe flow, in which the distortion of the particle flow field due to a solid wall or another particle is the central physical issue. These problems therefore lie outside the scope of the review. On the other hand, the structure of shock waves, sound attenuation, and many flow-field problems can be treated within our present restrictions. The basic equations and exchange processes will be introduced first, together with the physical parameters that indicate the relative importance of the particle cloud and the limitations of the dusty-gas concept. Then several different problems will be discussed that lead to some of the significant results in the field and illustrate analytical techniques that have proven useful.

Flow in porous media

Abstract: The problems of flow and transport in porous media present many fascinating challenges to students of mechanics: and it is surprising that, over the years, these questions have received relatively little attention at the Congresses and Symposia of IUTAM and of its predecessors. The 1964 Grenoble Symposium (Kravtchenko and Sirieys 1966) touched on certain special aspects and the 1966 Vienna Symposia (Parkus and Sedov 1968) had some relevance; but the first specific involvement of the Union with flow in porous media was a useful but limited meeting, sponsored jointly by IUTAM and IUGG, at Calgary in 1971.

Rheology of Two-Phase Systems

Abstract: Though much has been written on the dynamics of one, or a few, par­ ticles moving in a viscous fluid (11, 15, 43, 46) , the pragmatic interest in such studies lies more in the realm of polyparticle systems (38, 81) of the type commonly encountered in suspension rheology, sedimentation, flow in porous media, fluidized beds, and the like. Zuber's (86) analysis provides insight into the diversity of engineering applications likely to be encompassed by a satisfactory fundamental theory of such two-phase flows. Under moder­ ately well-defined circumstances these systems may be regarded from a gross view as heterogeneous continua, characterizable by a small set of hetero­ continuum (macrocontinuum) fields. Despite the longevity of this view, dating at least from the work of Darcy [1856] on flow through porous media and of Einstein [1906, 1911] on suspension viscosity, little has been done to formulate a rigorous general theory of the behavior of such systems. That no satisfactory fundamental basis exists is evidenced, for example, by con­ flicting claims as to the legitimacy of various derivations of Darcy's law from first principles, 1 by the innumerable relations (71 , 72) proposed for the higher-order concentration terms in Einstein's (35) viscosity formula, and by the multiplicity of theoretically-derived equations advanced to describe even the first-order concentration corrections to Stokes's law arising in the sedimentation of dilute systems (37) . That divergent views of these elementary problems should exist is symptomatic of a lack of perspective sufficiently general to embrace all such phenomena. The present status of the subject may be likened to that of nonequilibrium molecular statistical mechanics prior to the advent of the work of Kirkwood (53) . What is sorely needed is a comparable statistical mechanics of fluid-particle systems. This promising point of view is currently being pursued by at least several investigators. Clearly, however, an ambi­ tious program of this magnitude must be supplemented by less fundamental, but more tractable, schemes. It is with one such ad hoc scheme that the

The Analogy Between Rotating and Stratified Fluids

Abstract: PART I. GENERAL CONSIDERATIONS

Solar-wind flow past objects in the solar system

Abstract: Solar wind interaction with earth, moon, Venus and Mars, reviewing literature on continuum fluid model, spacecraft observations, plasma characteristics, etc

Critique of Numerical Modeling of Fluid-Mechanics Phenomena

Abstract: Both the fluid-mechanics phenomena numerically modeled to date and the numerical methods used in their calculation are briefly reviewed. I t is shown that oneand two-dimensional problems, both steady and nonsteady, are solvable by various processes, and current work is both developing new methods and determining the potentialities of present methods. Problems of three space dimensions, especially nonsteady ones, are on the edge of present capability both of methods and of computing-machine capacity (or reason­ able running time). Finally, treatment of the phenomena of turbulence by a straightforward approach is well beyond present machine capability; much new work is still required before approximate methods of known and general validity will make such computation feasible, even for academic research.

Applications of Slender-Body Theory in Ship Hydrodynamics

Abstract: The survey reviews the recent applications of slender-body theory to the field of ship hydrodynamics, and thus concerns the motion of a fluid past a slender body, but in the presence of exterior boundaries, and especially near or on a free surface. To make analytical progress viscous effects are ignored which are known to be significant in the steady-state resistance problem, but negligible in most unsteady problems such as that of predicting the heaving and pitching motions of a ship in a seaway. As in other areas of fluid mechanics, progress in this field has been significantly accelerated by the technique of matched asymptotic (or "inner-outer") expansions, although it could be argued that most or all of the problems to be discussed have been or could be successfully treated by other methods. The technique of matched asymptotic expansions is used here, because of the power associated with this method, and because it has become popular and relatively well known to contemporary scientists and engineers. Attention is primarily restricted to the mathematical details of various problems, and to the unity which results from employment of matched asymptotic expansions.

Nonlinear Wave Propagation in Fluids

Abstract: Waves nonlinear propagation in fluids due to convection, reviewing various solution methods