bluuebunny/crossref_metadata_2025_split huggingface dataset:
Flow separation at the upstream edge of a square-edged broad-crested weir
Authors: Moss W. D. 
Published: March 2006

A simple model is suggested to explain the flow mechanism at the upstream edge of a square-edged broad-crested weir. The separation bubble that may be seen to occur at this point is treated as an area of constant static head, while the main flow outside the bubble is deemed to be irrotational and divided from the bubble by a free streamline. If this model is accepted, the flow pattern will be such that energy requirements will be met along the free surface and the streamline bounding the bubble while, within these boundaries, the Laplace equation will be satisfied at every point. Accordingly, a solution satisfying these conditions is established by the use of a relaxation technique.In practice, it is likely that the cavity flow within the bubble will be bounded not by a single streamline but by a turbulent mixing zone and that there will be some increase in pressure near the point of re-attachment. Nevertheless, the surface profile and flow pattern observed in experiments show fair agreement with those predicted using the simple model. Whilst acknowledging, then, that the bubble and the zone bounding it are in fact of a more complex character, we may say that this simplified treatment affords a sound model of the main flow and so permits a better understanding of the action of the square-edged broad-crested weir.
Variational properties of steady fall in Stokes flow
Authors: Weinberger H. F. 
Published: March 2006

It is shown that for a given body and a given orientationgthere is always a position of the centre of mass which produces a stable falling motion in a very viscous fluid withgvertical and, in general, with a spin about the vertical axis. The corresponding terminal settling speed is bounded by means of several variational principles.Relations between the terminal speeds for falls with different downward directions and between the terminal speed and the geometry of the body are deduced. In particular, it is proved that for a large class of slender bodies the first approximation to the drag obtained from the slender-body theory of Burgers (1938) is correct. It follows that the ratio of the terminal speeds for falls with the long axis vertical and horizontal is near two.
Experimental investigations of the stability of channel flows. Part 2. Two-layered co-current flow in a rectangular channel
Authors: Kao Timothy W. , Park Cheol 
Published: March 2006

The stability of the laminar co-current flow of two fluids, oil and water, in a rectangular channel was investigated experimentally, with and without artificial excitation. For the ratio of viscosity explored, only the disturbances in water grew in the beginning stages of transition to turbulence. The critical water Reynolds number, based upon the hydraulic diameter of the channel and the superficial velocity defined by the ratio of flow rate of water to total cross-sectional area of the channel, was found to be 2300. The behaviour of damped and growing shear waves in water was examined in detail using artificial excitation and briefly compared with that observed in Part 1. Mean flow profiles, the amplitude distribution of disturbances in water, the amplification rate, wave speed and wavenumbers were obtained. A neutral stability boundary in the wave-number, water Reynolds number plane was also obtained experimentally.It was found that in natural transition the interfacial mode was not excited. The first appearance of interfacial waves was actually a manifestation of the shear waves in water. The role of the interface in the transition range from laminar to turbulent flow in water was to introduce and enhance spanwise oscillation in the water phase and to hasten the process of breakdown for growing disturbances.
Some effects of intense turbulence on the aerodynamics of a circular cylinder at subcritical Reynolds number
Authors: Surry David 
Published: March 2006

The effect, of high intensity large-scale free-stream turbulence on the flow past a rigid circular cylinder has been studied experimentally a t subcritical Reynolds numbers. Grids were used to produce homogeneous turbulence fields with longitudinal scales ranging from 0·36 to 4·40 cylinder diameters and with longitudinal intensities greater than 10%. Power and cross-spectra of the turbulence components (the ‘system input’) have been measured in order to carefully define the turbulence characteristics.In the response experiments, a special model measured arbitrary two-point pressure correlations. Subsequent integrations yielded the specbral properties of the unsteady lift and drag. Measurements of mean drag and Strouhal frequency indicate that to some extent even severe large-scale turbulence can be considered to be qualitatively equivalent to an increase in the effective Reynolds number. Vortex shedding is not seriously disrupted by severe turbulence, but is affected more by low than by high frequencies. The unsteady lift response is still dominated by the vortex shedding, whereas the unsteady drag becomes primarily a response to turbulence. The cross-spectra of the drag forces for the one turbulence case examined overlay well when plotted against lateral separation divided by wavelength. This has enabled a ‘describing function’ for the drag response to turbulence to be derived. This describing function is the central element needed for the calculation of the structural response of such cylinders in the drag direction.
Conditionally sampled measurements near the outer edge of a turbulent boundary layer
Authors: Antonia R. A. 
Published: March 2006

The conditional sampling technique is used to measure ensemble averages of the longitudinal and normal velocity fluctuations u and v respectively and of the Reynolds shear stress fluctuations uv both within the turbulent and irrotational regions near the outer edge of a turbulent boundary layer. The measurements are made in both a smooth- and a rough-wall boundary layer under zero-pressure-gradient conditions. The smooth- and rough-wall results are qualitatively similar but the magnitude of the rough-wall averages is higher than that of the smooth- wall averages, corresponding with the higher value of wall shear stress on the rough surface. The maximum shear stress value encountered within a burst represents a significant proportion of the wall shear stress.The statistical properties of the turbulence within the burst are close but not quite identical to the nearly Gaussian properties of the inner region of the boundary layer. During an attempt to distinguish between bursts of different ages or strengths at the time of measurement, it was found that bursts of relatively short duration travel at much the same longitudinal velocity as the local mean U and contribute little to the local shear stress. The longer and less frequent bursts have a mean velocity smaller than U and a maximum shear stress comparable to the shear stress at the wall.
Global stability of spiral flow. Part 2
Authors: Hung W. L. , Joseph D. B. , Munson B. R. 
Published: March 2006

The stability of spiral flow between rotating and sliding cylinders is considered. In the limit of narrow gap, a’ modified’ energy theory is constructed. This theory exploits the consequences of assuming the existence of a preferred spiral direction along which disturbances do not vary. The flow is also analyzed from the viewpoint of linearized theory. Both problems depend strongly on the sign of Rayleigh's discriminant, – 2Ωζ. Here Ω is the component of angular velocity, and ζ is the component of total vorticity of the basic flow in the direction perpendicular to the spiral ribbons on which the disturbance is constant. When the discriminant is negative, there is evidently no instability to infinitesimal disturbances, and the spiral disturbance whose energy increases at the smallest R is a roll whose axis is perpendicular to the stream. This restores and generalizes Orr's non-linear results for disturbances having a preferred spiral direction. When the discriminant is positive, the critical disturbances of linear theory and the modified energy theory are spiral vortices. The differences between the energy and linear limits can be made smaller in the restricted class of disturbances with coincidence achieved for axisymmetric disturbances in the rotating cylinder problem in the limit of narrow gap. For the sliding-rotating case, the critical disturbance of the linear theory appears as a periodic wave in a co-ordinate system fixed on the outer cylinder. This wave has a dimensionless frequency equal to - ½ a sin (χ-ψ), where a is the wave-number, χ is the angle between the pipe axis and the direction of motion of the inner cylinder relative to the outer one, and ψ is the disturbance spiral angle.Instability limits, frequencies and wave-numbers are computed numerically when the cylinder gap is not narrow. These are in even closer agreement with Ludwieg's experimental results than the approximate results which were given in part 1.
Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
Authors: Richardson S. 
Published: March 2006

A blob of Newtonian fluid is sandwiched in the narrow gap between two plane parallel surfaces so that, a t some initial instant, its plan-view occupies a simply connected domainD0. Further fluid, with the same material properties, is injected into the gap at some fixed point withinD0, so that the blob begins to grow in size. The domainDoccupied by the fluid at some subsequent time is to be determined.It is shown that the growth is controlled by the existence of an infinite number of invariants of the motion, which are of a purely geometric character. For sufficiently simple initial domainsD0these allow the problem to be reduced to the solution of a finite system of algebraic equations. For more complex initial domains an approximation scheme leads to a similar system of equations to be solved.
The relaxation of stress in a ≠-fluid with reference to the decay of homogeneous turbulence
Authors: Dowden J. M. 
Published: March 2006

It was suggested by Proudman (1970) that many of the phenomena of turbulence at high Reynolds number could be modelled by a suitably chosen member of a class of non-Newtonian fluids, ν-fluids, all of whose properties depend only on a single dimensional constant with the dimensions of viscosity. This paper investigates the relaxation of homogeneous stress in a doubly degenerate third-order ν-fluid (which is the simplest member of the class that can possibly be used to model turbulence) in the limit ν → 0.The equation which governs the stress tensor S is of the form
\[
AS\ddot{S} + B\dot{S}^2 = 0,
\]
where A and B are isotropic tensor constants of the fluid; its differential structure can be of four distinct types. A list of properties required of the solutions of the equation is set out, and it is shown that only one of the four types has all the properties demanded of it. The behaviour of solutions of this equation is found to be consistent with the theoretical and experimental results on the decay of homogeneous turbulence.
Compressible corner flow
Authors: Weinberg Bernard C. , Rubin Stanley G. 
Published: March 2006

The viscous compressible flow in the vicinity of a right-angle corner, formed by the intersection of two perpendicular flat plates and aligned with the free stream, is investigated. In the absence of viscous-inviscid interactions and imbedded shock waves, a theory is developed that is valid throughout the subsonic and supersonic Mach number range. Within this limitation and the additional assumptions of unit Prandtl number and a linear viscosity-temperature law, a consistent set of governing equations and boundary conditions is derived. The method of matched asymptotic expansions is applied in order to distinguish the relevant regions in the flow field.In the corner region the Crocco integral is shown to apply, even for a three-dimensional flow field. The equations governing the flow in the corner layer consist of four coupled nonlinear elliptic partial differential equations of the Poisson variety. Since they do not lend themselves to analytic solution, numerical methods are employed. Two such methods used here are the Gauss-Seidel explicit technique and the alternating direction implicit method. The merits of both techniques are discussed with regard to convergence rate, accuracy and stability. The calculations show that in cases where the Gauss-Seidel method fails to give converged solutions, owing to instability, the alternating direction implicit method does provide converged solutions. However, in cases where both methods are convergent, there is no appreciable difference in convergence rates. The numerical calculations were done on a CDC 6600 computer.Results of calculations are presented for representative compressible-flow conditions. The extent of the corner disturbance is controlled by the Mach number and wall temperature ratio in a manner analogous to the two-dimensional boundary layer. A swirling motion is noted in the corner layer which is influenced to a great extent by the asymptotic cross-flow profiles. The skin-friction coefficient is shown to increase monotonically from zero at the corner point to its asymptotic two-dimensional value. For cold wall cases, this value is approached more rapidly. The asymptotic analysis indicates that for even colder wall cases, not considered here, an overshoot is possible.
Wave mechanics of breakdown
Authors: Landahl M. T. 
Published: March 2006

Kinematic wave theory is used to determine under what conditions breakdown of a steady or unsteady laminar flow into high frequency oscillations should occur. The analysis of a small-scale secondary wave riding on a large-scale inhomogeneity, such as that produced by a finite amplitude primary instability wave, reveals that the breakdown mechanism has three basic ingredients: (i) a self-excited secondary wave with a group velocity near the propagation velocity (phase velocity) of the primary wave, (ii) space-time focusing of the secondary wave train on the primary wave crest and (iii) a nonlinear filtering mechanism leading to rectification of the secondary wave.The theory is applied to a laminar shear flow. Good quantitative agreement with the experiments on boundary-layer transition by Klebanoff, Tidstrom & Sargent (1962) is found for the critical condition leading to breakdown. Also, the theory is able to explain all the main qualitative breakdown features observed by Klebanoff et al. and others, such as the rapid localized onset, and the formation of a hairpin vortex lifting up from the surface downstream of the primary wave crest.
A Reynolds stress model of turbulence and its application to thin shear flows
Authors: Hanjalić K. , Launder B. E. 
Published: March 2006

The paper provides a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor$\overline{u_iu_j}$and for the turbulence energy-dissipation rate ε. In its most general form the model thus entails the solution of seven transport equations for turbulence quantities but contains only six constants to be determined by experiment. It is demonstrated that the proposed approximation to the pressure-rate-of-strain correlations leads to satisfactory predictions of the component stress levels in plane homogeneous turbulence, including the non-equality of the lateral and transverse normal-stress components.For boundary-layer flows a simpler version of the model is derived wherein transport equations are solved only for the shear stress$-\overline{u_1u_2}$the turbulence energy κ and ε. This model has been incorporated in the numerical solution procedure of Patankar & Spalding (1970) and applied to the prediction of a number of boundary-layer flows including examples of flow remote from walls, those developing along one wall and those confined within ducts. Three of the flows are strongly asymmetric with respect to the surface of zero shear stress and here the turbulent shear stress does not vanish where the mean rate of strain goes to zero. In most cases the predicted profiles and other quantities accord with the data within the probable accuracy of the measurements.
The tearing of an adhesive layer between flexible tapes pulled apart
Authors: Williamson A. S. 
Published: March 2006

The tearing of a pressure-sensitive (‘tacky’) adhesive is examined. Two flexible strips bonded by a layer of adhesive are passed between adjacent cylindrical guides and peeled apart, causing the adhesive layer to separate into two about a surface tension membrane. Treating the adhesive as a Newtonian viscous fluid, the slow-flow problem is solved by an iterative numerical scheme in which the surface tension membrane boundary in the vicinity of the region of separation is approximated by a shear-free boundary given by a sixth-degree polynomial expression. The energy dissipation rate, a measure of the ‘strength’ of the adhesive, is obtained from the flow.The solution method is also used to determine the similar flow induced by two counter-rotating rollers partially immersed in a large bath of fluid. The results are in fairly good agreement with available experimental data. The symmetrical eddies observed under the lowest point of the surface tension membrane in the stable flow between the rollers are reproduced in the solution, proving that fluid inertia effects are not essential for their existence.
The motion of a plate in a rotating fluid at an arbitrary angle of attack
Authors: Wilcox David C. 
Published: March 2006

Slow motion of a thin plate at a finite angle of attack in a rotating container filled with a viscous incompressible fluid is analysed. The Rossby and Ekman numbers are assumed to be small. The solution method is developed by studying horizontal translation of an elliptical plate. The plate is shown to carry a stagnant Taylor column with it as it moves. Detailed analysis of the structure of the vertical shear column bounding the Taylor column is circumvented by integrating the equations of motion across the shear column. A jump condition based upon mass conservation in the shear column which relates the geostrophic regions inside and outside the Taylor column results. This jump condition and its method of derivation can be used to analyse arbitrary (slow) motion of any thin plate at any angle of attack.The fluid motion resulting when a disk moves using all six degrees of freedom at an infinitesimal angle of attack is discussed. The forces and moments on the disk are calculated and the streamlines of the geostrophic flow are displayed.
The hydrodynamic interaction of two small freely-moving spheres in a linear flow field
Authors: Batchelor G. K. , Green J. T. 
Published: March 2006

Two rigid spheres of radii a and b are immersed in infinite fluid whose velocity at infinity is a linear function of position. No external force or couple acts on the spheres, and the effect of inertia forces on the motion of the fluid and the spheres is neglected. The purpose of the paper is to provide a systematic and explicit description of those aspects of the interaction between the two spheres that are relevant in a calculation of the mean stress in a suspension of spherical particles subjected to bulk deformation. The most relevant aspects are the relative velocity of the two sphere centres (V) and the force dipole strengths of the two spheres (S′ij, S″ij), as functions of the vector r separating the two centres.It is shown that V, S′ij and S″ij depend linearly on the rate of strain at infinity and can be represented in terms of several scalar parameters which are functions of r/a and b/a alone. These scalar functions provide a framework for the expression of the many results previously obtained for particular linear ambient flows or for particular values of r/a or of b/a. Some new results are established for the asymptotic forms of the functions both for r/(a + b) [Gt ] 1 and for values of r − (a + b) small compared with a and b. A reasonably complete numerical description of the interaction of two rigid spheres of equal size is assembled, the main deficiency being accurate values of the scalar functions describing the force dipole strength of a sphere in the intermediate range of sphere separations.In the case of steady simple shearing motion at infinity, some of the trajectories of one sphere centre relative to another are closed, a fact which has consequences for the rheological problem. These closed forms are described analytically, and also numerically in the case b/a = 1.
Pressure drop due to the motion of a sphere near the wall bounding a Poiseuille flow
Authors: Bungay Peter M. , Brenner Howard 
Published: March 2006

An expression is derived for the (low Reynolds number) additional pressure drop created by a relatively small sphere moving near the wall of a circular tube through which there is a Poiseuille flow. Two specific applications are examined: (i) the sedimentation of a homogeneous non-neutrally buoyant sphere in a quiescent fluid; and (ii) the motion of a neutrally buoyant sphere. In the latter case a pronounced increase in the additional pressure drop is predicted when the separation between the sphere and the tube wall is reduced to zero.This analysis, which includes the behaviour for a sphere in contact with the tube wall, supplements previous ‘method of reflexions’ treatments valid only when the distance from the sphere centre to the wall is large compared with the sphere radius.
Flow past an impulsively started circular cylinder
Authors: Collins W. M. , Dennis S. C. R. 
Published: March 2006

An accurate method is described for integrating the Navier-Stokes equations numerically for the time-dependent flow past an impulsively started circular cylinder. Results of integrations over the range of Reynolds numbers, based on the diameter of the cylinder, from 5 to ∞ are presented and compared with previous numerical, theoretical and experimental results. In particular, the growth of the length of the separated wake behind the cylinder has been calculated forR= 40, 100 and 200 and is found to be in very good agreement with the results of recent experimental measurements. The calculated pressure distribution over the surface of the cylinder forR= 500 is also found to be in reasonable agreement with experimental measurements for the caseR= 560.For Reynolds numbers up to 100 the equations were integrated until most of the features of the flow showed a close approximation to steady-state conditions. The results obtained are in good agreement with previous calculations of the steady flow past a circular cylinder. ForR> 100 the integrations were continued until the implicit method of integration broke down by reason of its failure to converge. A secondary vortex appeared on the surface of the cylinder in the caseR= 500, but for higher Reynolds numbers, including the caseR= ∞, the procedure broke down before the appearance of a secondary vortex. In all cases the flow was assumed to remain symmetrical.
Global stability of time-dependent flows: impulsively heated or cooled fluid layers
Authors: Homsy G. M. 
Published: March 2006

The method of energy is used to discuss the stability of time-dependent diffusive temperature profiles in fluid layers subject to impulsive changes in surface temperature.Bounds for the ratio of disturbance energy production to dissipation are found to be parametric functions of time because the basic temperature develops through diffusion. This time dependence leads to the demarcation of regions of stability in a Rayleigh number-time plane and the interpretation of these regions is given. Numerical results are presented for the cases of impulsive heating and cooling of initialty isothermal fluid layers. New global stability results which give the Rayleigh number below which the diffusive solution to the Boussinesq equations is unique are reported for these cases.