bluuebunny/crossref_metadata_2025_split huggingface dataset:
The linearized flow of a dissociating gas
Authors: Clarke J. F. 
Published: March 2006

The equations for planar two-dimensional steady flow of an ideal dissociating gas are linearized, assuming small disturbances to a free stream in chemical equilibrium.As an example of their solution, the flow past a sharp corner in a supersonic stream is evaluated and the variations of flow properties in the relaxation zone are found. Numerical illustrations are provided using an ‘oxygen-like’ ideal gas and comparisons made with a characteristics solution. The flow past a sharp corner can be studied in a conventional shock tube and it may be possible to verify the present theory experimentally. In particular it may prove feasible to use the results to obtain a measure of the reaction rates in the gas mixture.
On the tendency towards hexagonal cells in steady convection
Authors: Palm Enok 
Published: March 2006

This paper attempts to explain theoretically the observed results that (1) the cells in steady convection approach a hexagonal form, and (2) the occurrence of ascent or descent in the middle of the cell depends on how the kinematical viscosity varies with temperature. The theory is based on non-linear equations and, of course, a variable coefficient of viscosity.It is found that, due to the variation of viscosity with temperature, the non-linear terms contain a second-order term which is destabilizing. This second-order term regulates the development and leads to a final motion composed of regular hexagons with ascent or descent in the middle of the cell according as the viscosity decreases or increases with temperature.The influence of a variable viscosity on Rayleigh's result concerning the initiation of convection is obtained as a by-product.
An improved perturbation theory for shock waves propagating through non-uniform regions
Authors: Friedman M. P. 
Published: March 2006

This paper considers the problem of the propagation of a shock wave down a non-uniform tube. Linearized solutions to the problem (Chester 1954) do not hold when the velocity behind the shock is near or at the sonic speed. By retaining appropriate non-linear terms of the flow equations, a solution is obtained which holds for all conditions behind the shock, and reduces to the linearized solution for conditions away from sonic.The behaviour of supersonic or subsonic flow entering regions of expanding or contracting area changes is discussed. It is found that subsidiary shocks may be formed; these can be located and described using the present solution. Explicit solutions are given for the cases of supersonic or subsonic flow entering a region of linearly expanding or contracting area. The point of shock formation as well as the path of the subsidiary shock is obtained for the case in which the area contracts.
Laminar convection in uniformly heated vertical pipes
Authors: Morton B. R. 
Published: March 2006

An exact solution is presented in this paper for the problem of laminar convective flow under a pressure gradient along a vertical pipe, the walls of which are heated or cooled uniformly; the solution is based on the assumption that velocity and buoyancy profiles far from the pipe entrance do not change with height, and entry-lengt effects are ignored. Two different types of behaviour are found accordingly as the pressure gradient and buoyancy forces act together or in opposition near the centre of the pipe.When an upflow is heated (or a downflow cooled) the velocity near the walls is increased relatively and that near the axis decreased until, for sufficiently large Rayleigh numbers, definite velocity and thermal boundary layers are formed.In the case of cooled upflow (or heated downflow) there is an increase in the velocity across the whole profile for small Rayleigh numbers. As the Rayleigh number is increased the velocity and buoyancy increase, slowly at first and then rapidly, and the solution ‘runs away’ at a Rayleigh number of about 33. For higher Rayleigh numbers, laminar Poiseuille flow of an increasingly complicated profile is theoretically possible, but is unlikely to be found in practise.
On the collapse of an empty cavity in water
Authors: Hunter C. 
Published: March 2006

This paper is concerned with the spherically symmetric collapse of an empty cavity in water. The effects of viscosity and surface tension are neglected, but the compressibility of the water is allowed for and a suitable equation of state for the water assumed. The object of this is to clarify the effect of compressibility on the flow by considering it in isolation and thus to describe the formation of a pressure pulse by the collapse and its subsequent propagation.The exact flow equations are integrated numerically and it is found that very high flow speeds develop in the neighbourhood of the collapse point. The radius of the cavity is found to be proportional to (-t)nfor smallt, wheret= 0 is the instant of collapse, andnis some positive number less than unity.The flow in the neighbourhood of the collapse point can be described by means of a similarity solution, and the value ofnis determined by regularity properties of the similarity solution (the value ofndepends on the equation of state assumed for the water). The similarity theory, which is valid only at very high pressures and velocities, can be continued beyond the instant of collapse to describe the formation of a shock wave after the collapse is completed, and the initial propagation of this shock.
Mass transport in the boundary layer at a free oscillating surface
Authors: Longuet-Higgins M. S. 
Published: March 2006

In a previous paper (1953b) it was shown theoretically that just below the boundary layer at the surface of a free wave the mass-transport gradient should be exactly twice that given by Stokes's irrotational theory. The present paper describes careful experiments which confirm the higher value of the gradient.The results have an implication for any oscillatory boundary layer at the free surface of a fluid; such a boundary layer must generate a second-order mean vorticity which diffuses inwards into the interior of the fluid.
Experiments on the effect of suction on the flow due to a rotating disk
Authors: Gregory N. , Walker W. S. 
Published: March 2006

The stability and transition Reynolds numbers for the flow due to a disk rotating in still air were increased by low rates of suction through either a woven wire-cloth or a slitted surface. Observations on the slitted disk at rotational speeds between 550 and 1250 r.p.m. showed that the critical value of the Reynolds number r2ω/ν for instability increased from about 135,000 without suction to nearly 250,000 for a value of the suction parameter a of 0·4. The corresponding values for transition increased from about 275,000 to about 400,000. A given increase in stability Reynolds number required about 75% more suction than that theoretically predicted for uniform distributed suction, a satisfactory result in view of the limitations of the apparatus.At higher rates of suction (0·4 < a < 1·6), the reduction in secondary flow allowed transverse turbulent contamination to spread inwards from the rim. Consequently the vortices associated with secondary-flow instability were not found, though disturbances of larger wavelength appeared. Intermittent turbulent flow was spread over a much larger region of the disk and no laminar flow could be obtained above a Reynolds number of 400,000, Owing to this feature of the flow, it was not possible to extend laminar flow to values of the unit Reynolds number (ratio of stream velocity to kinematic viscosity) corresponding to flight conditions on a swept-back wing. It is concluded that the rotating disk is not a satisfactory tool for the investigation of the effects of suction on secondary-flow instabilities such as arise in the case of a swept-back wing, or for the testing of suction surfaces.
An experimental investigation of turbulent spots and breakdown to turbulence
Authors: Elder J. W. 
Published: March 2006

The theory of hydrodynamic stability and the impact on it of recent work with turbulent spots is discussed. Emmons's (1951) assumptions about the growth and interaction of turbulent spots are found experimentally to be substantially correct. In particular it is shown that the region of turbulent flow on a flat plate is simply the sum of the areas that would be obtained if all spots grew independently.An investigation of the conditions required for breakdown to turbulence near a wall, that is, to initiate a turbulent spot, suggests that regardless of how disturbances are generated in a laminar boundary layer and independent of both the Reynolds number and the spatial extent of the disturbances, breakdown to turbulence occurs by the initiation of a turbulent spot at all points at which the velocity fluctuation exceeds a critical intensity. Over most of the layer this intensity is about 0·2 times the free-stream velocity. The Reynolds number is important merely in respect of the growth of disturbances prior to breakdown.
A note on group velocity
Authors: Whitham G. B. 
Published: March 2006

The kinematic approach to group velocity given in Lighthill & Whitham (1955) for one-dimensional waves is extended to cover the general three-dimensional case. The ideas have particular bearing on the theory developed by Ursell (1960) for treating steady wave patterns on non-uniform steady fluid flows.Although this note was written in ignorance of the fact, all the main ideas presented here are implicit in §§66 and 67 of the book by Landau & Lifshitz (1959). However, these ideas do not seem to be well known to fluid dynamicists, and it was suggested to the author by the editor that a useful purpose would still be served by publishing this note as an expository article amplifying the paragraphs in Landau & Lifshitz. It also serves the original purpose of providing a supplement to Ursell's paper.
On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow
Authors: Stuart J. T. 
Published: March 2006

This paper considers the nature of a non-linear, two-dimensional solution of the Navier-Stokes equations when the rate of amplification of the disturbance, at a given wave-number and Reynolds number, is sufficiently small. Two types of problem arise: (i) to follow the growth of an unstable, infinitesimal disturbance (supercritical problem), possibly to a state of stable equilibrium; (ii) for values of the wave-number and Reynolds number for which no unstable infinitesimal disturbance exists, to follow the decay of a finite disturbance from a possible state of unstable equilibrium down to zero amplitude (subcritical problem). In case (ii) the existence of a state of unstable equilibrium implies the existence of unstable disturbances. Numerical calculations, which are not yet completed, are required to determine which of the two possible behaviours arises in plane Poiseuille flow, in a given range of wave-number and Reynolds number.It is suggested that the method of this paper (and of the generalization described by Part 2 by J. Watson) is valid for a wide range of Reynolds numbers and wave-numbers inside and outside the curve of neutral stability.
An experimental study of the explosion generated by a pressurized sphere
Authors: Boyer D. W. 
Published: March 2006

An experimental investigation of the explosions of 2 in. diameter glass spheres under high internal pressure has been made. The spheres were initially filled with air or helium at 400 and 326 p.s.i., respectively, and were exploded in air at atmospheric pressure. Experiments on the simulation of high-altitude explosions are also described. Schlieren and spark shadowgraph records of explosion phenomena, and pressure records of the reflexion of the spherical shock wave at various radii, are presented.An account of some initial experiments on the implosion of 5 in. diameter glass spheres is given. The results were not very satisfactory because of the failure of the spheres to shatter in a desirable manner while under an external pressure of 65 p.s.i.Numerical solutions to the air and helium sphere explosions are described and the experimental wave phenomena are shown to be in good quantitative agreement with the theoretical predictions, in that they exhibit all the main features that were predicted and are modified only by the physical limitations of the glass diaphragm. A formation process is associated with the spherical shock waves in practice, resulting in initial shock velocities which are lower than the theoretical values.
The influence of radiative transfer on the propagation of a temperature wave in a stratified diffusing atmosphere
Authors: Goody R. M. 
Published: March 2006

An approximate solution is presented to the problem of the propagation of a temperature wave through a stratified medium which both diffuses and radiates heat. The solution is a combination of two waves whose relative amplitudes vary with the distance from the lower boundary. Apparent diffusivities computed from phase lag and attenuation coefficients can differ greatly from each other and can vary with height even if the actual diffusivity does not.An example, using parameters simulating the earth's atmosphere, suggests that analysis of the propagation of the diurnal wave upward from the earth's surface is likely to be inadequate if radiative effects are not considered.
The flow due to a two-dimensional jet issuing parallel to a flat plate
Authors: Sawyer R. A. 
Published: March 2006

An experiment has been performed to determine the cavity pressure and cavity length for the flow under a curved two-dimensional turbulent jet discharging parallel to a flat plate at some distance from the surface. The measurements agree quite closely with the predictions of a simple analysis of the flow when a value is assigned to the spread parameter for the curved jet which is somewhat different from that for the plane jet.Detailed pressure and velocity measurements show that the rate of growth of the curved jet is in fact closely similar to that of the plane jet. This suggests that the adjustment of the spread parameter should be regarded simply as a convenient device for taking into account the quantitative errors of the assumptions made in the analysis.
The method of images in shear flow
Authors: Glauert M. B. 
Published: March 2006

The method of images is used to determine the flow perturbation caused by a small point source of fluid in a stream containing a vortex sheet, a number of vortex sheets, or a continous two-dimensional distribution of vorticity. Calculations are carried out for a variety of such shear flows, to illustrate the range of applicability of the method.The image source distribution provides an alternative approach to that given by Lighthill for calculating small disturbances to a parallel shear flow, and suggests a simple physical picture by which to interpret the complicated effects associated with the distortion and stretching of vortex lines.
Behaviour of small regions of different gases carried in accelerated gas flows
Authors: Rudinger George , Somers Lowell M. 
Published: March 2006

Small regions in a flow where the density is different from that of the surrounding gas do not exactly follow accelerated motions of the latter, but move faster or slower depending on whether their density is smaller or larger than that of the main flow. This behaviour cannot be quantitatively explained by treating a gas ‘bubble’ as a hypothetical solid particle of the same density, because a gas bubble cannot move relative to the surrounding gas without being transformed into a vortex which absorbs part of the energy of the relative motion.To illustrate the acceleration effect, the flow velocity behind known pressure waves in a shock tube is compared with the observed velocity of a bubble produced by a spark discharge. The displacement of such a bubble by a wave exceeds that of a flow element by more than 20%, but the bubble density is not known. If the spark discharge is replaced by a small jet of another gas, a pressure wave cuts off a section of this jet which then represents a bubble of known density.A theory is developed which permits computing the response of such bubbles to accelerations. The ratio of the bubble velocity to the velocity of the surrounding gas depends on the density ratio for the two gases and on the shape of the bubble, but not on the acceleration. Experimental results with H2, He, and SF6bubbles in air, accelerated by shock waves of various strength, are presented and agree well with the theoretical predictions. The results apply regardless of whether accelerations are produced by pressure waves in a non-steady flow or by curvature of streamlines in a steady flow. Various aspects of the experimental observations are discussed.
Wave resistance to vertical motion in a stratified fluid
Authors: Warren F. W. G. 
Published: March 2006

When a body moves through a stratified fluid, i.e. one whose density decreases upwards, gravity waves are set up and this causes a resistance to motion. An axisymmetric case is considered in which a body moves steadily and vertically through a fluid whose density decreases exponentially upwards. The fluid is supposed perfect, incompressible, and unbounded in all directions. The equations of motion are linearized, and with a fairly general initial motion of the surrounding fluid, the limit of the solution as t → ∞ is evaluated. Transform methods are used to solve the equation of motion, and the methods of steepest descents and stationary phase are used to obtain approximate solutions.Streamlines and the distortion of the constant density levels for a spindle-shaped body are shown. The curves of resistance against a function of the velocity for the circular cylinder, the sphere, and a spindle-shaped body are also given. A criterion is given for when the maximum wave resistance for a sphere may be expected, and an estimate of this maximum resistance is made.
The boundary layer near the stagnation point in hypersonic flow past a sphere
Authors: Herring T. K. 
Published: March 2006

When a sphere or other bluff body travels at supersonic speeds, a shock wave is formed close to the front surface. With increase of speed the air behind the shock is further compressed, and the shock wave moves closer to the surface. This paper considers the case where the region close to the stagnation point between the shock and the sphere can be taken to be a steady laminar boundary layer.The approximate solution of the equations of motion follows closely the classical work of Homann (1936), ideas similar to those of Lighthill (1957) being used to apply it to the problem in hand. It consists mainly in reducing the equations to ordinary differential form by assuming forms of the flow variables which satisfy the boundary conditions, notably at the shock wave. In addition, several transformations are employed in order to simplify the equations and to increase the range of solutions, and also to facilitate the use of the ‘Mercury’ electronic computer in solving them.The results give an insight into some aspects of hypersonic flows. Included in this paper are a selection of temperature and transverse velocity profiles across the boundary layer and several graphs relating such quantities as the shock stand-off distance and the skin-friction coefficient with Reynolds number. The last two mentioned are the most interesting. The first set gives the surprising result that the shock stand-off distance increases with increase in Reynolds number, whereas it is known that the skin-friction coefficient is inversely proportional to a decreasing power of the Reynolds number when it is lower than order 103, but the indication is that it tends to the expected constant power of ½ when the Reynolds number is of order 104.
Experiments on power generation from a moving plasma
Authors: Pain H. J. , Smy P. R. 
Published: March 2006

Electrical power of 0·32MW has been extracted for a period of 100 μsec from a plasma of shock-ionized argon travelling at 4×105cm per sec through a magnetic field of 10,000 G. Currents of more than 10,000amp are drawn and the resulting modification of the applied field is considered.Maximum power is obtained when the external load is matched to the plasma generator which has an internal impedance equivalent to its own electrical resistance in series with a resistance arising from its behaviour as a compressible fluid.Values of the electrical conductivity of the plasma obtained in these experiments (about 3 × 103mho per metre) show that the plasma resistance is controlled by electron motion and these values are in good agreement with those found by other methods.
Gaskinetics and gasdynamics of orifice flow
Authors: Liepmann Hans W. 
Published: March 2006

The paper gives the result of a study on the efflux of gases through circular apertures. The problem is considered as an example of a transition from the gasdynamic to the gaskinetic régime.The mass flow of helium, argon and nitrogen was measured for a range of upstream pressures corresponding to (mean free path)/(aperture diameter) from about 50 to 5 × 10−3; within this range the transition from molecular effusion to inviscid, transonic flow takes place. The theory for the two asymptotic limits is discussed and first-order corrections to the free molecular and inviscid limit formulae are given.
On a momentum-mass flux diagram for turbulent jets, plumes and wakes
Authors: Morton B. R. 
Published: March 2006

Many salient features of fully developed turbulent jets, plumes and wakes with steady mean flow are shown clearly by the relationship between the momentum flux and the mass flux in the column of moving fluid. Using a simple model for the flows, this relationship can be found from the solution of a single ordinary differential equation and the character of many related flows can be represented immediately (except for actual distribution in space) on a single momentummass flux diagram.In this note some approximate solutions based on dimensional arguments are outlined briefly for cases of buoyant and non-buoyant wakes and jets directed along the axis of a uniform main stream, and momentum-mass flux curves are presented.