There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Numerical Heat Transfer And Fluid Flow

Structural features resulting from the interaction of a turbulent jet issuing transversely into a uniform stream are described with the help of flow visualization and hot-wire anemometry. Jet-to-crossflow velocity ratios from 2 to 10 were investigated at crossflow Reynolds numbers from 3800 to 11400. In particular, the origin and formation of the vortices in the wake are described and shown to be fundamentally different from the well-known phenomenon of vortex shedding from solid bluff bodies. The flow around a transverse jet does not separate from the jet and does not shed vorticity into the wake. Instead, the wake vortices have their origins in the laminar boundary layer of the wall from which the jet issues. It is argued that the closed flow around the jet imposes an adverse pressure gradient on the wall, on the downstream lateral sides of the jet, provoking 'separation events’ in the wall boundary layer on each side. These result in eruptions of boundary-layer fluid and formation of wake vortices that are convected downstream. The measured wake Strouhal frequencies, which depend on the jet-crossflow velocity ratio, match the measured frequencies of the separation events. The wake structure is most orderly and the corresponding wake Strouhal number (0.13) is most sharply defined for velocity ratios near the value 4. Measured wake profiles show deficits of both momentum and total pressure.

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Vortical structure in the wake of a transverse jet

Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

The structure of round jets in cross-flow was studied using flow visualization techniques and flying-hot-wire measurements. The study was restricted to jet to freestream velocity ratios ranging from 2.0 to 6.0 and Reynolds numbers based on the jet diameter and free-stream velocity in the range of 440 to 6200.Flow visualization studies, together with time-averaged flying-hot-wire measurements in both vertical and horizontal sectional planes, have allowed the mean topological features of the jet in cross-flow to be identified using critical point theory. These features include the horseshoe (or necklace) vortex system originating just upstream of the jet, a separation region inside the pipe upstream of the pipe exit, the roll-up of the jet shear layer which initiates the counter-rotating vortex pair and the separation of the flat-wall boundary layer leading to the formation of the wake vortex system beneath the downstream side of the jet.The topology of the vortex ring roll-up of the jet shear layer was studied in detail using phase-averaged flying-hot-wire measurements of the velocity field when the roll-up was forced. From these data it is possible to examine the evolution of the shear layer topology. These results are supported by the flow visualization studies which also aid in their interpretation.The study also shows that, for velocity ratios ranging from 4.0 to 6.0, the unsteady upright vortices in the wake may form by different mechanisms, depending on the Reynolds number. It is found that at high Reynolds numbers, the upright vortex orientation in the wake may change intermittently from one configuration of vortex street to another. Three mechanisms are proposed to explain these observations.

An experimental study of round jets in cross-flow

Experiments on turbulent circular jets issuing into cross flow from both heated and unheated jets

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Experiments on a Turbulent Jet in a Cross Flow

Oscillatory thermocapillary convection in a simulated floating-zone configuration

Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients

This paper discusses thermal convection in an enclosure induced by spacecraft vibrations (#-jitter). Under normal circumstances (no maneuvers, no intentional spinning of the spacecraft) the ^-jitter generates predominantly oscillatory velocity and temperature fields with zero time-mean values. The ^-jitter can also generate secondary flows with nonzero mean, but they are of much smaller order. Some implications of the g- jitter on materials processing in space are discussed. NE of the primary advantages foreseen for processing of materials in space is the reduction of natural convection associated with the Earth's gravity. However, there have been some indications (e.g., Apollo 14 experiments 1'2) that spacecraft vibrations might cause appreciable thermal con- vection. Such convection may be important in fluids ex- periments and also affect the quality of crystals grown in space. Therefore, to study the effectiveness of spacecraft vibrations in generating fluid flows, the present work theoretically investigates a case in which a fluid-filled con- tainer with differentially heated walls is subjected to spacecraft vibrations. Implications of the results for space processing are discussed. In an attempt to evaluate the effects of g-jitter on fluid motions Spradley el al. 3 made a numerical analysis for various configurations. They considered three g-jitter profiles, sinusoidal, absolute sinusoidal and saw tooth, and compared the flowfields with that for constant g level. They found that if the g-jitter is decomposed into a time mean part and an oscillatory part, the mean part is more important than the oscillatory part in determining the flowfield and heat- transfer rate. A somewhat related work has been done by Forbes4 where the effect of sinusoidal vibrations on natural convective heat transfer in a rectangular enclosure is studied experimentally as well as numerically under 1-g conditions. The results indicate that the vibrations have very little effect on the heat transfer when the flow is laminar. The present study is more comprehensive than the work by Spradley et al.,3 and is meant to give a better physical insight into the g-jitter in space. Some of the material presented herein is taken from the work by Prasad and Ostrach.5 Formulation of the Problem g-Jitter Consider an experimental setup which is in a spaceship orbiting the Earth (Fig. 1). The coordinates (X0,Y0,Z0) are fixed at the center of the Earth with origin 0 (fixed frame of reference), and the coordinates (X'f Y',Z') are attached to the spacecraft with origin 0' at its center of mass. The coor-

Yasuhiro Kamotani

Papers

Experiments on a Turbulent Jet in a Cross Flow

Oscillatory thermocapillary convection in a simulated floating-zone configuration

Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients

Thermal convection in an enclosure due to vibrations aboard spacecraft

Free surface heat loss effect on oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluids