bluuebunny/crossref_metadata_2025_split huggingface dataset:
Transition in circular Couette flow
Authors: Coles Donald 
Published: March 2006

Two distinct kinds of transition have been identified in Couette flow between concentric rotating cylinders. The first, which will be called transition by spectral evolution, is characteristic of the motion when the inner cylinder has a larger angular velocity than the outer one. As the speed increases, a succession of secondary modes is excited; the first is the Taylor motion (periodic in the axial direction), and the second is a pattern of travelling waves (periodic in the circumferential direction). Higher modes correspond to harmonics of the two fundamental frequencies of the doubly-periodic flow. This kind of transition may be viewed as a cascade process in which energy is transferred by non-linear interactions through a discrete spectrum to progressively higher frequencies in a two-dimensional wave-number space. At sufficiently large Reynolds numbers the discrete spectrum changes gradually and reversibly to a continuous one by broadening of the initially sharp spectral lines.These periodic flows are not uniquely determined by the Reynolds number. For the case of the inner cylinder rotating and the outer cylinder at rest, as many as 20 or 25 different states (each state being defined by the number of Taylor cells and the number of tangential waves) have been observed at a given speed. As the speed changes, theso states replace each other in a repeatable but irreversible pattern of transitions; vortices appear or disappear in pairs, and waves are added or subtracted. More than 70 such transitions have been found in the speed range up to about 10 times the first critical speed. Regardless of the state, however, the angular velocity of the tangential waves is nearly constant at 0.34 times the angular velocity of the inner cylinder.The second kind of transition, which will be called catastrophic transition, is characteristic of the motion when the outer cylinder has a larger angular velocity than the inner one. At a fixed Reynolds number, the fluid is divided into distinct regions of laminar and turbulent flow, and these regions are separated by interfacial surfaces which may be propagating in either direction. Under some conditions the turbulent regions may appear and disappear in a random way; under other conditions they may form quite regular patterns. One common pattern of particular interest is a spiral band of turbulence which rotates at very nearly the mean angular velocity of the two walls without any change in shape except possibly an occasional shift from a right-hand to a left-hand pattern. One example of this spiral turbulence is being studied in some detail in an attempt to clarify the role played in transition by interfaces and intermittency.
On the mathematics of fluidization Part 1. Fundamental equations and wave propagation
Authors: Murray J. D. 
Published: March 2006

When the upward flow of a fluid through a bed of particles of appropriate and almost uniform size is rapid enough so that the drag on each particle is as great as the particles buoyant weight, the particles do not remain close packed and the bed is said to be fluidized. Industrial uses of fluidized beds in the chemical and petroleum industries in particular are already extensive. Uses in the atomicenergy industry are being developed.In this paper a mathematical model which describes the phenomena on a continuum basis is deduced. With this model we find that the system is unstable to small internal disturbances. Alternatively, we find that surface waves can be propagated (with attenuation) in the composite fluid and these waves for fluidized beds with a high ratio of solids density to fluid density are stable. These results are in agreement with experiment. Hot beds, where strongly exothermic reactions may be taking place, centrifugal beds (beds fluidized within a rotating system), and electromagnetic beds (those in which the particulate phase is electrically conducting) are all shown to be unstable to small internal disturbances.The equations derived here may also be used as approximate equations for dispersed particle two-phase flow.
Determination of the sonic line in hypersonic flow past a blunt body
Authors: Bloor M. I. G. 
Published: March 2006

The Newtonian theory of inviscid hypersonic flow is extended to obtain a solution uniformly valid in the subsonic region, and that is used to determine the position and shape of the sonic line. The main modification to the theory has to be made near the body surface and an expansion, essentially in terms of the stream function, is employed.For simplicity the solution is limited to the cases of axially- and plane-symmetric flows. As an illustration of the theory the flows past a sphere and a circular cylinder are treated in some detail. Comparison with the numerical results of Garabedian and Lieberstein gives favourable agreement.
Vorticity amplification in stagnation-point flow and its effect on heat transfer
Authors: Sutera S. P. 
Published: March 2006

Recently a mathematical model was proposed (Sutera, Maeder & Kestin 1963) to demonstrate that vorticity amplification by stretching was an important mechanism underlying the sensitivity of stagnation-point heat transfer on cylinders to free-stream turbulence. According to the model, vorticity of a scale larger than a certain neutral scale and appropriately oriented can undergo amplification as it is convected towards the boundary layer. Such vorticity, present in the oncoming flow with small intensity, can reach the boundary layer with a greatly magnified intensity and induce substantial three-dimensional effects therein. The mean temperature profile was shown to be much more responsive to these effects than the mean velocity profile and very large increases in the wall-heat-transfer rate were calculated for Prandtl numbers 0·74 and 7·0.In this work a second, more general, case is treated in which the approaching flow carries vorticity of scale 1·5 times the neutral. By means of iterative procedures applied on an electronic analogue computer, an approximate solution to the full Navier–Stokes equation is generated. The heat-transfer problem is solved simultaneously for Pr = 0·70, 7·0 and 100. It is found that a vorticity input which increases the wall-shear rate by less than 3% is capable of increasing the wall-heat-transfer rate by as much as 40%. The sensitivity of the thermal boundary layer depends on Prandtl number. In the three cases investigated it is greatest for Pr = 7·0 and least for Pr = 100.
The dispersion and attenuation of helicon waves in a uniform cylindrical plasma
Authors: Klozenberg J. P. , McNamara B. , Thonemann P. C. 
Published: March 2006

A systematic account is given of the derivation of the dispersion relation for helicon waves in a uniform cylindrical plasma bounded by a vacuum. By retaining finite resistivity in the equations, boundary conditions present no difficulties, since the wave magnetic field is continuous through the plasma-vacuum interface. Two unexpected results are found. First, the wave attenuation remains finite in the limit of vanishing resistivity. This is due to the energy dissipated at the interface by the surface currents required to match the plasma wave field to the vacuum wave field. Zero wave attenuation for zero resistivity is recovered if electron inertia is included. Secondly, it is found that waves with azimuthal numbers m of opposite sign propagate differently, but the sense of polarization at the axis of the cylinder is independent of the sign of m.The argument of the dispersion function is complex and numerical results were obtained using a computer. The method of programming is described, and results are given applicable to propagation in metals at low temperatures, or in a typical gas discharge plasma for the m = 0 and m = ± 1 modes.An example of the amplitude of the wave fields as a function of radius is given for the axisymmetric mode, and of amplitude and phase for the m = ± 1 modes.
Shock waves in a gas with several relaxing internal energy modes
Authors: Clarke John F. , Rodgers J. B. 
Published: March 2006

The structure of plane steady shock waves in a gas with several internal energy modes which relax in parallel is investigated. Transport effects are neglected. Conditions for continuity and monotonicity of the velocity profile are discussed; when all modes have constant specific heats and relaxation times it is established that velocity must decrease monotonically. Internal mode energy contents may overshoot their local equilibrium values.Numerical results for waves in a hypothetical gas with two relaxing modes are presented for purposes of illustration.
Space-charge waves carried by a plasma trapped in a potential well
Authors: Kahn F. D. 
Published: March 2006

A mono-energetic electron plasma is trapped in a one-dimensional parabolic potential well. In the undisturbed state a suitable background charge provides space-charge neutrality. It is shown that stationary disturbances of infinitesimal amplitude can exist in the plasma for certain critical values of the parameter $\Lambda = 4\overline{n}e^2|m \omega^2$, where $\overline{n}$ is the mean electron density and ω/2π is the frequency of oscillation of the electrons in the well. The first few critical values are Λ = 0, 4·12, 8·2.The boundary conditions at the end of the plasma are non-linear. As a result stationary disturbances of finite amplitude in a given mode, say the rth, require that Λ shall exceed Λr. Further it can be shown that disturbances of small amplitude in the rth mode are unstable when Λ exceeds Λr. This applies even for Λr = 0; in this case there exist nearby an unstable even and an unstable odd mode.It seems likely that these results can be extended to all cases in which the potential well is symmetrical.
The steady separated flow past a circular cylinder at large Reynolds numbers
Authors: Acrivos Andreas , Snowden D. D. , Grove A. S. , Petersen E. E. 
Published: March 2006

This paper is concerned with deducing the most important features of the steady separated flow past a circular cylinder in the limit of vanishing viscosity. First of all, it is shown that the experimental results reported in an earlier article cannot be reconciled with the notion that, as the Reynolds number Re is increased, the flow becomes inviscid everywhere and that viscous effects remain confined within infinitesimally thin shear layers. In contrast, the limiting solution is visualized as exhibiting three essential features: a viscous, closed ‘wake bubble’ of finite width but with a length increasing linearly with Re in which inertial and viscous effects are everywhere of equal order of magnitude; an outer inviscid flow; and, separating the two regions, a diffuse viscous layer covering large sections of the external field. Further properties of this asymptotic solution include: a finite form drag, a negative rear pressure coefficient at the rear stagnation point of the cylinder, and a Nusselt number for heat transfer which becomes independent of Re along the non-wetted portion of the cylinder surface. This model is shown to be consistent with all the experimental data presently available, including some new heat transfer results that are presented in this paper.An approximate technique is also proposed which takes into account the asymptotic character of the flow in the vicinity of the cylinder and which predicts the pressure distribution around the cylinder in good agreement with the experiments.
The decay of a turbulent swirl in a pipe
Authors: Kreith Frank , Sonju O. K. 
Published: March 2006

This paper presents a linearized theory for the average decay of a tape-induced fully developed turbulent swirl in flow through a pipe. In the Reynolds number range between 104and 105the theoretical analysis was found to be in good agreement with experimental data obtained with water in a 1 in. pipe, provided the eddy diffusivity was chosen appropriately.It was observed that a turbulent swirl decays to about 10–20% of its initial intensity in a distance of about 50 pipe diameters, the decay being more rapid at smaller than at larger Reynolds numbers. The theoretical swirl velocity distribution agreed qualitatively with experimental measurements at distances less than 20 diameters downstream from the outlet of the swirl inducer, but deviated from the experimental results further downstream.
A three-dimensional turbulent boundary layer
Authors: Perry A. E. , Joubert P. N. 
Published: March 2006

The purpose of this paper is to provide some possible explantions for certain observed phenomena associated with the mean-velocity profile of a turbulent boundary layer which undergoes a rapid yawing. For the cases considered the yawing is caused by an obstruction attached to the wall upon which the boundary layer is developing. Only incompressible flow is considered.§1 of the paper is concerned with the outer region of the boundary layer and deals with a phenomenon observed by Johnston (1960) who described it with his triangular model for the polar plot of the velocity distribution. This was also observed by Hornung & Joubert (1963). It is shown here by a first-approximation analysis that such a behaviour is mainly a consequence of the geometry of the apparatus used. The analysis also indicates that, for these geometries, the outer part of the boundary-layer profile can be described by a single vector-similarity defect law rather than the vector ‘wall-wake’ model proposed by Coles (1956). The former model agrees well with the experimental results of Hornung & Joubert.In §2, the flow close to the wall is considered. Treating this region as an equilibrium layer and using similarity arguments, a three-dimensional version of the ‘law of the wall’ is derived. This relates the mean-velocity-vector distribution with the pressure-gradient vector and wall-shear-stress vector and explains how the profile skews near the wall. The theory is compared with Hornung & Joubert's experimental results. However at this stage the results are inconclusive because of the lack of a sufficient number of measured quantities.
The investigation of a standing wave due to gas blowing upwards over a liquid film; its relation to flooding in wetted-wall columns
Authors: Shearer C. J. , Davidson J. F. 
Published: March 2006

A theory is given to predict the shape and amplitude of a standing wave formed on a liquid film running down a vertical surface, and due to an upward flow of gas over the liquid surface. The wave is maintained in position by the pressure gradients induced within the gas stream by acceleration over the windward part of the wave; over the leeward part of the wave, the gas pressure is roughly constant due to breakaway of the gas flow.The wave amplitude is found to be very sensitive to gas velocity so that the theory predicts a critical gas velocity beyond which the wave amplitude becomes very large; this critical velocity is confirmed by experiment, and the experiments confirm the predicted wave shape. The critical gas velocity also agrees reasonably well with published values of the flooding velocity in empty wetted-wall tubes; this velocity is defined as the point at which countercurrent flow of gas and liquid becomes unstable. The phenomenon of flooding, which has puzzled chemical engineers for many years, may thus be due to wave formation on the liquid film.From the theory are derived three dimensionless groups, namely, Weber number $We \equiv \rho_g U_c^2t_0|T$, liquid-film Reynolds number $Re \equiv 4\rho_l Q|\mu, and Z \equiv T(\rho_l|\mu g)^{1/3}|\mu$. Here Uc is the critical gas velocity, Q is the liquid volume flow rate per unit wetted perimeter, ρg and ρl are the gas and liquid densities, μ is the liquid viscosity and T is its surface tension; $t_0 = (3\mu Q|\rho_lg)^{1/3}$ is the liquid film thickness in the absence of gas flow. We, Re and Z are uniquely related at the flooding point, and a diagram is presented to show this relation. This diagram will enable designers to predict flooding in wetted-wall tubes, though more experimental verification is required.
Properties of inviscid, recirculating flows
Authors: Wood W. W. 
Published: March 2006

Integral relations are derived for steady, incompressible recirculating motions with small viscous forces. The circuit time of a fluid particle on a closed streamline in steady, inviscid flow is shown to be the same for all the closed streamlines on a surface of constant total head.The discontinuities of velocity and velocity gradient that occur in the motion of inviscid fluid filling a closed, rotating cylinder set in a rotating support with the two rotation axes slightly misaligned are then investigated.
On the general theory of contained rotating fluid motions
Authors: Greenspan H. P. 
Published: March 2006

A general linear theory is developed to describe the manner in which rigid fluid rotation is established from a prescribed initial state of motion in a container of arbitrary shape. The container rotates with uniform angular velocity and is filled with a viscous incompressible fluid.A new mean circulation theorem is proved and used to separate the flow into geostrophic motion and inertial oscillations. The basic eigenvalue problem is studied and important properties concerning spectrum, orthogonality and completeness are deduced. The effect of viscosity on the inviscid modes is calculated in a manner that maintains the solution uniformly valid through the spin-up time. All modes decay in this time scale which characterizes the entire transition to rigid rotation in all configurations.
On the curvature and torsion of an isolated vortex filament
Authors: Betchov Robert 
Published: March 2006

We consider a very thin vortex filament in an unbounded, incompressible and inviscid fluid. The filament is not necessarily plane. Each portion of the filament moves with a velocity that can be approximated in terms of the local curvature of the filament. This approximation leads to a pair of intrinsic equations giving the curvature and the torsion of the filament, as functions of the time and the arc length along the filament. It is found that helicoidal vortex filaments are elementary solutions, and that they are unstable.The intrisic equations also suggest a linear mechanism that tends to produce concentrated torsion and a non-linear mechanism tending to disperse such singularities.
Shock-shock interaction on a slender supersonic cone
Authors: Blankenship Victor D. 
Published: March 2006

The transient pressure field produced behind a plane shock wave of arbitrary strength, which encounters a slender supersonic cone head on, is theoretically predicted. The analysis is restricted to small cone angles (in order that Mach-reflexion will occur at the surface) and to inviscid flow.A conical-flow technique is utilized to transform the small-perturbation equations of time-dependent rotational motion of the fluid behind the deflected plane shock into time-independent equations. From these equations, a boundary-value problem for pressure alone, in the Mach-reflexion region, is derived which is solved numerically. Results for the small perturbation pressure field of the cone are contrasted with Smyrl's (1963) results, which hold for a moving wedge, for a range of values of cone and plane shock speeds.
The steady motion of a particle of arbitrary shape at small Reynolds numbers
Authors: Cox R. G. 
Published: March 2006

The results given by Brenner & Cox (1963) for the resistance of a particle of arbitrary shape in translation at small Reynolds numbers are generalized. Thus we consider here a single particle of arbitrary shape moving with both translation and rotation in an infinite fluid, the Reynolds number R of the fluid motion being assumed small. With the additional assumption that the motion is steady with respect to some inertial frame of reference, we calculate both the force and couple on the body as an expansion in the Reynolds number to O(R2 In R). This force and couple are expressed entirely in terms of various Stokes flows for the given body in rotation or translation.A discussion is given of the form taken by the formulae for the force and couple for cases in which the body possesses symmetry properties. Quantitative results are obtained for both a spheroid and a dumb-bell-shaped body in pure translation and also for a translating rotating sphere and for a dumb-bell-shaped body in pure rotation.The application of the general results to ‘quasi-steady’ problems is considered, with particular reference to a freely falling spheroid (of small eccentricity) which is shown to orientate itself so that it is broad-side on to its direction of motion.Finally the general results are compared with those that would be obtained by the use of the Oseen equations. By consideration of a particular example it is shown that the Oseen equations do not in general give the correct value of the force on the body to O(R).
Results of an attempt to generate a homogeneous turbulent shear flow
Authors: Rose W. G. 
Published: March 2006

An approximately homogeneous turbulent shear flow is generated in an open-return wind tunnel test-section by a plane parallel-rod grid of uniform rod diameter and non-uniform rod spacing. The grid design is based upon an analysis by Owen & Zienkiewicz (1957). Hot-wire measurements taken in this flow include mean velocities, component turbulence intensities, shear and two-point space correlations, and energy spectra. In addition, microscales, obtained both from instantaneous time derivatives of the hot-wire signal and from two-point space correlations, and integral scales, calculated both from correlations and energy spectra, are reported.Based upon these results, it is concluded that, far enough away from the grid and the test-section wall boundary layers:The turbulence intensities are maintained at uniform values by the nearly constant mean shear.The turbulent shear stress approaches an asymptotic value.Measured two-point space correlation coefficients and one-dimensional energy spectra attain self-preserving forms.When distance downstream of the grid is measured in terms of the number of ‘local’ grid rod spacings, (see discussion of microscales obtained from time derivatives), the Taylor microscale defined by the correlation coefficientRuu(rX, 0, 0) grows linearly with this ‘effective’ distance over most of the region measured.The limited number of integral scale determinations and experimental uncertainty allow only the statements that the magnitude of the longitudinal scale is roughly one-eighth the lateral dimension of the square test-section and tends to increase slightly with ‘effective’ distance from the grid.The lateral integral scales are approximately one-half the longitudinal scales and also increases with distance from the grid.The integral scale which characterizes the size of the eddy primarily responsible for momentum transfer is roughly one-tenth the test-section lateral dimension (measured at one point only).
The three-dimensional structure of the wake of a circular cylinder
Authors: Gerrard J. H. 
Published: March 2006

A critical scrutiny of the nature of the three-dimensional characteristics of the vortex wake of a circular cylinder serves to suggest lines for further investigation and furnishes some ideas on the nature of the growth and development of these non-uniformities. It is suggested that the basic occurrence in the growth of three-dimensionality is the continuation of vortex lines, oriented more or less parallel to the body, into the direction of the free stream. The causes of this vary, as do the details of the development with the particular situation considered.Experiments were performed in a wind tunnel at Reynolds numbers based on cylinder diameter of 85, 235 and 2 × 104, at which stable, transitional and turbulent vortices were investigated.