bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the melting of a semi-infinite body of ice placed in a hot stream of air
Authors: Roberts Leonard 
Published: March 2006

A simple mathematical model is proposed to describe the steady melting of a body of ice which presents a plane surface transverse to a stream of hot air; the temperature of the air is such that vaporization does not occur.The analysis takes into account the convection of heat away from the surface by the water released in melting and the results show that the rate of transfer of heat to the body and thus the rate of melting, is reduced by as much as 46% by this convection.Simple approximate expressions are obtained for the rate of melting, the thickness of the water layer, and the thickness of the thermal boundary layer in the ice, in terms of a basic parameter S which can be calculated in terms of known quantities. These results are compared with those obtained by a separate Pohlhausen calculation and are found to be in good agreement.It is also shown that there exists a thermal boundary layer, in the body, of thickness much greater than that of the boundary layer in the air, in which the temperature changes rapidly from its value at the melting surface to its value in the far interior.
Experimental studies of supercavitating flow about simple two-dimensional bodies in a jet
Authors: Silberman Edward 
Published: March 2006

A two-dimensional free-jet water tunnel developed at the St Anthony Falls Hydraulic Laboratory of the University of Minnesota is described briefly. Results of experimental measurements on a two-dimensional cup, symmetrical wedges, inclined flat plates, and a circular cylinder in the tunnel are given.Measured force coefficients at zero cavitation number are in good agreement with theory. Shapes of the cavities were computed for one of the wedges and for one of the plates at zero cavitation number; the observed shapes are also in good agreement with the theory.For non-zero cavitation numbers, theoretical results for force coefficients were available for comparison in only two cases. For one of these, the cup, agreement between theory and experiment was good up to a cavitation number of about 0.5. For the other, a symmetrical wedge, experimental results were compared with a linear theory with good agreement for cavitation numbers between about 0.1 and 0.3. In the case of the wedge, measured cavity lengths were somewhat shorter than predicted by the linear theory. All other comparisons with theory at non-zero cavitation number had to be made with the theory as developed for infinite fluid. The experimental force coefficients were less than predicted by infinite-fluid theory, but tended to approach the theoretical values as the cavitation number increased. A similar tendency marked the comparison between the experimental data and data taken by others in closed tunnels.
The propagation of small disturbances in hydromagnetics
Authors: Ludford G. S. S. 
Published: March 2006

This paper is concerned with the propagation of small initial disturbances in a conducting gas under the influence of a uniform external magnetic field.For a perfect conductor, there are three types of plane waves, each of which depends strongly on the angle at which the magnetic field is crossed. The modifying effects of finite conductivity are determined and, in the case of these waves, this is done uniformly for all angles. A general disturbance may be resolved into two parts, one of which satisfies a fourth-order equation and the other a fifth; for a perfect conductor these reduce to second-and fourth-order equations, respectively.The free oscillations of the gas are examined when it is contained in a rectangular box, and, in particular, when the external field is very weak or very strong. For vanishingly weak fields the idealization of infinite conductivity proves to be inadequate. Finally, the initial-value problem is discussed.
Ring vortices generated electromagnetically
Authors: Yih Chia-Shun 
Published: March 2006

If an electric current of uniform densityj0is passed axially through a stationary fluid between concentric cylinders of radiir1andr2(>r1), the fluid is stable to axisymmetric disturbances only if the damping provided by viscosity and electrical resistivity is sufficiently large. It is shown herein that the fluid may also be stabilized by passing a line currentJalong the axis, sufficient conditions for stability being$J \le -\pi j _0(r^2_2 - r^2_1)$, or$\ge J\; \pi j _0r^2_1$The values ofJneeded to stabilize the fluid when the fluid has non-zero viscosity and finite conductivity are calculated for the caser2-r1[Lt ]r1. In this latter case, the ring vortices which exist under conditions of neutral stability are exactly the same as those for flow between rotating cylinders ifJandj0have the same sign, and ifJis not very small compared with πj0r2.
Rapid calculations for boundary-layer transfer using wedge solutions and asymptotic expansions
Authors: Merk H. J. 
Published: March 2006

Exact transfer calculations for boundary layers with longitudinal pressure gradients are very complicated, but in the literature several approximate methods are known for the rapid calculation of both the wall friction and the heat transfer. A ‘wedge method’ propounded by Meksyn turns out to be one of the most rapid methods, being no less accurate than other approximate methods. A way of refining this method is proposed.This paper also shows that asymptotic expansions provide convenient relations which are capable of expressing the Nusselt number explicitly in terms of the Prandtl number.It is shown that, together with the asymptotic expansions, Meksyn's method permits rapid calculation of local heat transfer numbers. Some examples of application are given for elliptical cylinders and spheres for several values of the Prandtl number.
On the drag of a flat plate at zero incidence in almost-free-molecule flow
Authors: Liu V. C. 
Published: March 2006

A physical theory is proposed for the skin friction on a flat plate at zero incidence in the transition flow regime, i.e. in the flow of a moderately rarefied gas. The ratio of the molecular mean free path to the characteristic size of the plate is assumed of order unity or larger. A general formula for the perturbation to the well-known friction of the free-molecule theory is given. This perturbation is attributed to the intermolecular collisions which are neglected on the basis of the free-molecule hypothesis. The expected rate of collisions are calculated for rigid spheres, using the classical kinetic theory.Although this is intended as an approximate theory, the theoretical results check surprisingly well with the limited experimental data that are available. The present theory shows that the ratio of the Reynolds number to the Mach number squared is the governing parameter for determining the intermolecular collision effect on skin friction in the transition flow regime.
Atomic recombination in a hypersonic wind-tunnel nozzle
Authors: Bray K. N. C. 
Published: March 2006

The flow of an ideal dissociating gas through a nearly conical nozzle is considered. The equations of one-dimensional motion are solved numerically assuming a simple rate equation together with a number of different values for the rate constant. These calculations suggest that deviations from chemical equilibrium will occur in the nozzle if the rate constant lies within a very wide range of values, and that, once such a deviation has begun, the gas will very rapidly ’freeze’. The dissociation fraction will then remain almost constant if the flow is expanded further, or even if it passes through a constant area section. An approximate method of solution, making use of this property of sudden ’freezing’ of the flow, has been developed and applied to the problem of estimating the deviations from equilibrium under a wide range of conditions. If all the assumptions made in this paper are accepted, then lack of chemical equilibrium may be expected in the working sections of hypersonic wind tunnels and shock tubes. The shape of an optimum nozzle is derived in order to minimize this departure from equilibrium.It is shown that, while the test section conditions are greatly affected by ’freezing’, the flow behind a normal shock wave is only changed slightly. The heat transfer rate and drag of a blunt body are estimated to be reduced by only about 25% even if complete freezing occurs. However, the shock wave shape is shown to be rather more sensitive to departures from equilibrium.
Torsional oscillations of a plane in a viscous fluid
Authors: Rosenblat S. 
Published: March 2006

On the assumption that the rotational oscillations of a rigid plane are small, boundary-layer type solutions of the Navier-Stokes equations are attempted by an expansion of the velocity components in power series of the amplitude. First-and third-order approximations to the transverse velocity are obtained, from which a correction to the moment on a disk of finite radius is found.The first non-vanishing approximation to the radial-axial flow (a second-order term) is seen to have a steady component and a component with frequency twice that of the plate. The former component appears to persist outside the boundary layer, and at large distances from the plate to have the character of an irrotational stagnation flow. A re-examination not involving the series approximation reveals that although steady radial flow does exist outside the boundary layer, it is a viscous flow and is confined within a secondary layer. The ratio of the thicknesses of the two layers is found to be inversely proportional to the amplitude of the oscillations. These results indicate that a second-order flow in a region where the first-order flow field vanishes should not be accepted without further discussion.
Measurements of intermittency of turbulent motion in a boundary layer
Authors: Sandborn V. A. 
Published: March 2006

Previous observations of turbulent motion at large wave-numbers have revealed the existence of an uneven distribution of turbulent energy. The spotty distribution of the turbulent motion at high wave-numbers is here studied experimentally for the turbulent boundary layer. The high wave-number intermittency is observed at all locations through and along the boundary layer from near transition to near separation.The flatness factors for the longitudinal turbulent component at different wave-numbers are measured to give a quantitative value for the intermittency at particular wave-numbers. Upstream of the separation region the flatness factors are found to depend on wave-number and longitudinal distance, but not on the distance from the wall. It appears that the intermittency develops in the transition region and does not diminish very rapidly with distance downstream. Near separation the flatness factors change radically in distribution near the wall, and are there no longer independent of distance from the wall.
An analysis of the vortex street generated in a viscous fluid
Authors: Schaefer John W. , Eskinazi Salamon 
Published: March 2006

An analytic solution for the velocity field of a vortex street generated in a viscous fluid is developed. A method is presented for the determination of the true transverse spacing of vortices. Experimental geometry and velocity data, obtained by hot-wire techniques, are presented.The experimental results verified the validity of the analytic solution. The vortices of a real viscous vortex street were found to resemble very closely the exponential solution of the Navier-Stokes equations for an isolated axisymmetric rectilinear vortex. Three basic regions of vortex street behaviour were apparent at each Reynolds number investigated-a ‘formation region’ in which the vortex street is developed and large dissipation of vorticity occurs, a ‘stable region’ in which the vortices display a stable periodic laminar regularity, and an ‘unstable region’ in which the street disappears and turbulence develops. Geometry and velocities were determined.
The symmetric state of a rotating fluid differentially heated in the horizonal
Authors: Robinson Allan R. 
Published: March 2006

The motion of a fluid inside a rotating annulus of square cross-section, whose dimensions are small compared with the distance from the axis of rotation, is considered. The rigid side walls are held at different constant temperatures and the fluid motions that occur are strongly influenced by Coriolis accelerations. A detailed study is made of the azimuthally independent state, a Hadley cell, in the limit of small thermal Rossby number. It is convenient to employ a boundary layer type analysis, essentially with respect to the Taylor number and all the imposed boundary conditions are rigorously satisfied.An entirely geostrophic thermal wind is found to obtain over the main body of the fluid. The circulation in the plane of the annular cross-section is entirely confined within narrow boundary layers and consists of a superposition of three cellular motions: a cell occupying the cross-section and two additional cells confined to the side-wall boundary layers. These motions are intimately related to the rotational constraint. The temperature distribution and its relation to the conductive and convective processes are determined.
The time-dependent magnetohydrodynamic flow past a flat plate
Authors: Carrier G. F. , Greenspan H. P. 
Published: March 2006

Two time-dependent magnetohydrodynamic flow problems are discussed. In Part I we consider the situation in which a semi-infinite flat plate is moved impulsively in its own plane into an electrically conducting viscous fluid. The ambient magnetic field has the same direction as the motion of the plate; it is found that when $\mu H^2_0| \rho U^2_0 \; \textless \; 1$, the flow pattern approaches asymptotically the steady flow found earlier (Greenspan & Carrier 1959). When $\mu H^2_0| \rho U^2_0 \; \textgreater \; 1$, the asymptotic state is one in which the fluid accompanies the plate in a rigid body motion as was anticipated in the earlier work.In Part II, an infinite plate is moved impulsively in its own plane in the presence of an ambient magnetic field which is perpendicular to the plane of the plate. It is shown that the problem is not uniquely set until one specifies what three-dimensional problem reduces in the limit to the two-dimensional problem so defined. The answers in the conceptually acceptable limit case investigated here (the plate being a pipe of very large radius) have an asymmetry which at first sight is unexpected.
Forced small-amplitude water waves: a comparison of theory and experiment
Authors: Ursell F. , Dean R. G. , Yu Y. S. 
Published: March 2006

This paper describes an attempt to verify experimentally the wavemaker theory for a piston-type wavemaker. The theory is based upon the usual assumptions of classical hydrodynamics, i.e. that the fluid is inviscid, of uniform density, that motion starts from rest, and that non-linear terms are neglected. If the water depth, wavelength, wave period, and wavemaker stroke (of a harmonically oscillating wavemaker) are known, then the wavemaker theory predicts the wave motion everywhere, and in particular the wave height a few depths away from the wavemaker.The experiments were conducted in a 100 ft. wave channel, and the wave-height envelope was measured with a combination hook-and-point gauge. A plane beach (sloping 1:15) to absorb the wave energy was located at the far end of the channel. The amplitude-reflexion coefficient was usually less than 10%. Unless this reflexion effect is corrected for, it imposes one of the most serious limitations upon experimental accuracy. In the analysis of the present set of measurements, the reflexion effect is taken into account.The first series of tests was concerned with verifying the wavemaker theory for waves of small steepness (0.002 ≤ H/L ≤ 0.03). For this range of wave steepnesses, the measured wave heights were found to be on the average 3.4% below the height predicted by theory. The experimental error, as measured by the scatter about aline 3.4% below the theory, was of the order of 3%. The systematic deviation of 3.4% is believed to be partly due to finite-amplitude effects and possibly to imperfections in the wavemaker motion.The second series of tests was concerned with determining the effects of finite amplitude. For therange of wave steepnesses 0.045 ≤ H/L ≤ 0.048, themeasured wave heights were found to be on the average 10% below the heightspredictedfrom the small-amplitude theory. The experimental error was again of the order of 3%.It is considered that these measurements confirm the validity of the small-amplitude wave theory. No confirmation of this accuracy has hitherto been given for forced motions.
The stability and transition of a two-dimensional jet
Authors: Sato Hiroshi 
Published: March 2006

A study was made of the transition of a two-dimensional jet. In the region where laminar flow becomes unstable, two kinds of sinusoidal velocity fluctuation have been found; one is symmetrical and the other is anti-symmetrical with respect to the centre line of the jet. The fluctuations grow exponentially at first and develop into turbulence without being accompanied by abrupt bursts or turbulent spots.The response characteristics of laminar jets to artificial external excitation were investigated in detail by using sound as an exciting agent. The effect of excitation was seen to be most remarkable when the frequency of excitation coincides with that of self-excited sinusoidal fluctuations.Numerical solutions of equation of small disturbances superposed on laminar flow were obtained assuming the Reynolds number as infinity. Theoretical eigenvalues and eigenfunctions are in good agreement with experimental results, thus verifying the existence of a region of linear disturbance in the two-dimensional jet.
A shallow-liquid theory in magnetohydrodynamics
Authors: Fraenkel L. E. 
Published: March 2006

The non-linear and linear ‘shallow-water’ theories, which describe long gravity waves on the free surface of an inviscid liquid, are extended to the case of an electrically conducting liquid on a horizontal bottom, in the presence of a vertical magnetic field. The dish holding the liquid, and the medium outside it, are assumed to be non-conducting. The approximate equations are based on a small ratio of depth to wavelength, on the properties of mercury, and on a moderate magnetic field strength. These equations have a ‘magneto-hydraulic’ character, for in the shallow liquid layer the horizontal fluid velocity and current density are independent of the vertical co-ordinate.Some explicit solutions of the linear equations are obtained for plane flows and for axi-symmetric flows in which the velocity vector lies in a vertical, meridional plane. The amplitudes of waves in a dish, and the amplitudes behind wave fronts progressing into undisturbed liquid, are found to be exponentially damped, the mechanical energy associated with a disturbance being dissipated by Joule heating.The approximate non-linear equations for plane flow are studied by means of characteristic variables, and it appears that, because of the magnetic damping effect, there is less qualitative difference between solutions of the non-linear and linear approximate equations at large times than is the case when the magnetic field is absent. In particular, the characteristic curves depart only a finite distance from their ‘undisturbed positions’.
Free convection in the tilted open thermosyphon
Authors: Leslie F. M. 
Published: March 2006

Approximate solutions are found for the fluid flow and heat transfer in a heated cylinder, closed at the bottom and opening at the top into a reservoir of cool fluid, which has been tilted at a small angle to the vertical.One solution is found for large Rayleigh number when the boundary layer does not fill the tube, and another for small Rayleigh number when the boundary layer fills the tube. In both cases tilting causes a small increase in heat transfer which is proportional to the square of (l/a) tan ϕ, where l/a is the length–radius ratio and ϕ the angle of tilt.
The viscous secondary flow ahead of an infinite cylinder in a uniform parallel shear flow
Authors: Toomre Alar 
Published: March 2006

A simple method is presented in this paper for calculating
the secondary velocities, andthe lateral displacement of total pressure surfaces (i.e. the ‘displacement effect’)
in the plane of symmetry ahead of an infinitely long cylinder situated normal to a steady, incompressible, slightly viscous shear flow; the cylinder is also perpendicular to the vorticity, which is assumed uniform but small. The method is based on lateral gradients of pressure, these being calculated from the primary flow alone. Profiles of the secondary velocities are obtained at several Reynolds numbers ahead of two specific cylindrical shapes: a circular cylinder, and a flat plate normal to the flow. The displacement effect is derived and, rathe surprisingly, is found to be virtually independent of the Reynolds number.
On the motion of thin airfoils in fluids of finite electrical conductivity
Authors: McCune James E. 
Published: March 2006

A two-dimensional, small-perturbation theory for the steady motion of thin lifting airfoils in an incompressible conducting fluid, with the uniform applied magnetic field perpendicular to (and in the plane of) the undisturbed, uniform flow field, is described. The conductivity of the fluid is assumed to be such that the magnetic Reynolds number,Rm, of the flow is large but finite. Within this assumption, a theory based on superposition of sinusoidal modes is constructed and applied to some simple thin airfoil problems.It is shown that with this particular field geometry the Alfvén wave mechanism is important in making possible very deep penetration into the flow field of currents and their associated vorticity. It is also shown that the current penetration for an airfoil is much larger than for a wavy wall of wavelength equal to the airfoil chord.A value ofRm= 5 is found to be a good approximation to infinity in this study; in fact, use of the present technique for values ofRmof the order of unity is permissible. These results provide an indication of what is meant by ‘large’ magnetic Reynolds number in two-dimensional magneto-aerodynamics.
Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell
Authors: Wooding R. A. 
Published: March 2006

Approximate equations of motion, continuity and mass transport are given for a viscous liquid of variable density moving very slowly between vertical and impermeable parallel planes. These equations are used to calculate approximate stability criteria when the liquid is at rest under a vertical density gradient. The results are applicable to the problem of the stability of a viscous liquid of variable density to two-dimensional disturbances in a porous medium.An exact stability analysis for the liquid between parallel planes is also given, and expansions in powers of the disturbance wave-number are obtained for the critical Rayleigh number at neutral stability. The previous approximate results are found to correspond to the leading terms of the series expansions. For the most unstable type of disturbance, the velocity distribution closely resembles plane Poiseuille flow, which was the form assumed in the approximate equations.An asymptotic expansion is derived for the critical Rayleigh number at neutral stability in a long vertical channel, or duct, the cross-section of which is a thin rectangle. The typical neutral disturbance possesses a ‘boundary layer’ at each end of the cell cross-section, and this has a small stabilizing effect.The critical Rayleigh number for a long vertical channel of rectangular cross-section is found experimentally by comparing the density gradient of the liquid in the channel at neutral stability with the corresponding density gradient in a vertical capillary tube. There is better agreement with the exact theory than with the approximate theory, the experimental result being about 4% higher than the value predicted by the ‘exact’ asymptotic expression, and about 10% higher than the value predicted by the simple approximate theory.