Annual Review of Fluid Mechanics - Volume 29, 1997

Electrohydrodynamics deals with fluid motion induced by electric fields. In the mid 1960s GI Taylor introduced the leaky dielectric model to explain the behavior of droplets deformed by a steady field, and JR Melcher used it extensively to develop electrohydrodynamics. This review deals with the foundations of the leaky dielectric model and experimental tests designed to probe its usefulness. Although the early experimental studies supported the qualitative features of the model, quantitative agreement was poor. Recent studies are in better agreement with the theory. Even though the model was originally intended to deal with sharp interfaces, contemporary studies with suspensions also agree with the theory. Clearly the leaky dielectric model is more general than originally envisioned.

This paper gives an overview of the issues posed by the science and technology of transporting heavy oils in a sheath of lubricating water. It touches on measures of energy efficiency, industrial experience, fouling, stability, models of levitation, and future directions.

As a molten alloy or any multi-component liquid is cooled and solidified the growing solid phase usually forms a porous matrix through which the residual liquid can flow. The reactive two-phase medium comprising the solid matrix and residual liquid is called a mushy layer. Buoyancy forces, owing primarily to compositional depletion as one or more of the components of the alloy are extracted to form the solid phase, can drive convection in the layer. In this review, I present an account of various studies of buoyancy-driven convection in mushy layers, paying particular attention to the complex interactions between solidification and flow that lead to novel styles of convective behavior, including focusing of the flow to produce chimneys: narrow, vertical channels devoid of solid. I define an ‘ideal’ mushy layer and argue that chimneys are an inevitable consequence of convection in ideal mushy layers. The absence of chimneys in certain laboratory experiments is explained in terms of nonideal effects.

This review covers Verification, Validation, Confirmation and related subjects for computational fluid dynamics (CFD), including error taxonomies, error estimation and banding, convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for grid adaptation vs Quantification of Uncertainty.

In contrast to computational aerodynamics, which has advanced to a fairly mature state, computational aeroacoustics (CAA) has only recently emerged as a separate area of study. Following a discussion of the classical field of aeroacoustics as introduced by Lighthill, the paper provides an overview and analysis of the problems associated with utilizing standard computational aerodynamics procedures for acoustic computations. Numerical aspects of computing sound-wave propagation are considered, including assessments of several schemes for spatial and temporal differencing. Issues of particular concern in computing aerodynamically generated noise, such as implementing surface and radiation boundary conditions and algorithms for predicting nonlinear steepening and shocks, are discussed. In addition, the paper briefly reviews alternatives to the conventional finite-difference schemes, such as boundary-element and spectral methods and the uncommon lattice-gas method.

The inertia-dominated dynamics of a single gas or vapor bubble in an incompressible or nearly incompressible liquid has been the subject of intense investigation for many years. Studies prior to 1976 were thoroughly reviewed by Plesset & Prosperetti (1977) in Volume 9 of this series. Our review fills the gap between Plesset & Prosperetti's review and the present. We focus on new understandings of bubble dynamics through a nonlinear dynamical systems approach.

Parabolized stability equations (PSE) have opened new avenues to the analysis of the streamwise growth of linear and nonlinear disturbances in slowly varying shear flows such as boundary layers, jets, and far wakes. Growth mechanisms include both algebraic transient growth and exponential growth through primary and higher instabilities. In contrast to the eigensolutions of traditional linear stability equations, PSE solutions incorporate inhomogeneous initial and boundary conditions as do numerical solutions of the Navier-Stokes equations, but they can be obtained at modest computational expense. PSE codes have developed into a convenient tool to analyze basic mechanisms in boundary-layer flows. The most important area of application, however, is the use of the PSE approach for transition analysis in aerodynamic design. Together with the adjoint linear problem, PSE methods promise improved design capabilities for laminar flow control systems.

The various tools for flow visualization have been significantly expanded over the past several years through the use of molecular scattering and molecular laser-induced fluorescence. These approaches have added the capability of sampling individual small volume elements within a flow, and by using cameras for detection, they are easily extended to sample lines and cross-sectional planes. This localized measurement capability means that these approaches can be made quantitative even in complex and/or unsteady flow fields. If the molecular species is naturally occurring, such as oxygen or nitrogen in air, then no seeding is required.

Furthermore, in these applications, images of the flow can be frozen in time by using a short pulse laser for illumination. The distribution of the molecules reflects the true physics of the flow, so even raw images taken in this manner give an immediate understanding of flow field properties. With proper calibration, the images can be further analyzed to yield quantitative information about the flow. In the case of flow tagging, the analysis gives velocity profiles when lines are written, and deformation, vorticity, and dilation with grid patterns. Molecular scattering can be used to give quantitative values of density, temperature, and two-dimensional velocity.

This paper presents three such molecular-based approaches: laser-induced fluorescence from oxygen, flow tagging by oxygen excitation, and Rayleigh scattering. These three approaches are chosen because all three can be used in naturally occurring air with no seeding. The raw data from each of these approaches gives an immediate appreciation of the flow structure and further analysis yields accurate values of velocity, temperature, and density. These approaches use readily available laser sources; however, they will be greatly enhanced with new source technologies that are currently under development.

Convection into regions with open, or partially-open, lateral boundaries is considered. The products of convectively-driven mixing can flow out from under the source generating a compensating inflow as they do so. The effects of rotation, ambient stratification and the geometry of the region on these flow quantities are considered, since all affect the density and velocity distributions that result. Three typical geometries are considered: convection into a channel or sea with an exit constriction; convection from a patch or strip into stratified and/or rotating surroundings and, finally, into a rotating coastal environment. In each case the simplest possible models are considered in the hope that they can offer some insight into the dynamical processes that affect the overall behaviour of each system. These are supplemented by reference to numerical and laboratory experiments as well as field observations. Finally suggestions for future work in the former two cases are presented in the hope that they will stimulate the reader's interest.

Casting of molten metals against a spinning wheel substrate is considered. Issues of fluid mechanics divide between steady and unsteady behavior (stability). The previous work on steady casting is hung on a framework provided by the long-puddle model of planar flow casting. Heat and fluid flow interact only through the shape of the solidification front in this case. In contrast, there is little previous work concerning stability issues. Stability is discussed in a broad-brush manner using the planar flow process for illustration. Issues range from meniscus motion and resulting ribbon texture to morphological-type instabilities of the solidification front. Fundamental and applied questions arise for both steady and unsteady behavior.

Blood flow in arteries is dominated by unsteady flow phenomena. The cardiovascular system is an internal flow loop with multiple branches in which a complex liquid circulates. A nondimensional frequency parameter, the Womersley number, governs the relationship between the unsteady and viscous forces. Normal arterial flow is laminar with secondary flows generated at curves and branches. The arteries are living organs that can adapt to and change with the varying hemodynamic conditions. In certain circumstances, unusual hemodynamic conditions create an abnormal biological response. Velocity profile skewing can create pockets in which the direction of the wall shear stress oscillates. Atherosclerotic disease tends to be localized in these sites and results in a narrowing of the artery lumen—a stenosis. The stenosis can cause turbulence and reduce flow by means of viscous head losses and flow choking. Very high shear stresses near the throat of the stenosis can activate platelets and thereby induce thrombosis, which can totally block blood flow to the heart or brain. Detection and quantification of stenosis serve as the basis for surgical intervention. In the future, the study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow. This field is rich with challenging problems in fluid mechanics involving three-dimensional, pulsatile flows at the edge of turbulence.

I have sometimes thought that what makes a man's work classic is often just this multiplicity [of interpretations], which invites and at the same time resists our craving for a clear understanding.

Wright (1982, p. 34), on Wittgenstein's philosophy

Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

An overview of the current state of the art in unstructured mesh techniques for computational fluid dynamics is given. The topics of mesh generation and adaptation, spatial discretization, and solution techniques for steady flows are covered. Remaining difficulties in these areas are highlighted, and directions for future work are outlined.

Modern helicopter aerodynamics is challenging because the flow field generated by a helicopter is extremely complicated and difficult to measure, model, and predict; moreover, experiments are expensive and difficult to conduct. In this article we discuss the basic principles of modern helicopter aerodynamics. Many sophisticated experimental and computational techniques have been employed in an effort to predict performance parameters. Of particular interest is the structure of the rotor wake, which is highly three-dimensional and unsteady, and the rotor-blade pressure distribution, which is significantly affected by the strength and position of the wake. We describe the various modern methods of computation and experiment which span the range from vortex techniques to full three-dimensional Navier-Stokes computations, and from classical probe methods to laser velocimetry techniques. Typical results for the structure of the wake and the blade pressure distribution in both hover and forward flight are presented Despite the complexity of the helicopter flow, significant progress has been made within the last ten years and the future will likely bring marked advances.