Showing papers on "Reynolds number published in 1979"

Drag coefficient and relative velocity in bubbly, droplet or particulate flows

Abstract: Drag coefficient and relative motion correlations for dispersed two-phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model. The results are compared with a number of experimental data, and satisfactory agreements are obtained at wide ranges of the particle concentration and Reynolds number. Characteristics differences between fluid particle systems and solid particle systems at higher Reynolds numbers or at higher concentration regimes were successfully predicted by the model. Results showed that the drag law in various dispersed two-phase flows could be put on a general and unified base by the present method.

Inception of sediment transport

Abstract: Sediment transport inception curves corresponding to both laminar and turbulent flows are presented. Using these curves one can determine the critical bed shear stress (corresponding to the beginning of sediment transport) depending on the properties of the fluid and of the cohesionless bed material. The laminar flow curve has been revealed on the basis of laboratory measurements carried out by the writers. The curve corresponding to turbulent flows has been established mainly using the available data of previous researchers. It has been found that the laminar flow curve lies in the Shields' plane higher than the turbulent flow curve and thus it yields larger critical values of the dimensionless bed shear stress. Both curves tend to become indistinguishable from each other when the grain size Reynolds number decreases, i.e., when the influence of viscosity on the turbulent flow at the bed increases. For larger values of this number the turbulent flow curve can be identified with the classical Shields' curve.

The dynamics of the head of a gravity current advancing over a horizontal surface

Abstract: The motion behind the head of a gravity current advancing over a no-slip horizontal surface is a complex three-dimensional flow. There is intense mixing between the current and its surroundings and the foremost part of the head is raised above the surface. Experimental results are obtained from (i) an apparatus in which the head is brought to rest by using an opposing flow and a moving floor and (ii) a modified lock exchange flow. The dimensionless velocity of advance, rate of mixing between the two fluids and the depth of the mixed layer left behind the head and above the following gravity current are determined for an extended range of the dimensionless gravity current depth. The mixing between the two fluids is the result of gravitational and shear instabilities at the gravity current head. A semi-empirical analysis is presented to describe the results. The influence of Reynolds number is discussed and comparison with a documented atmospheric flow is presented.

Dynamical instabilities and the transition to chaotic Taylor vortex flow

Abstract: We have used the technique of laser-Doppler velocimetry to study the transition to turbulence in a fluid contained between concentric cylinders with the inner cylinder rotating The experiment was designed to test recent proposals for the number and types of dynamical regimes exhibited by a flow before it becomes turbulent For different Reynolds numbers the radial component of the local velocity was recorded as a function of time in a computer, and the records were then Fourier-transformed to obtain velocity power spectra The first two instabilities in the flow, to time-independent Taylor vortex flow and then to time-dependent wavy vortex flow, are well known, but the present experiment provides the first quantitative information on the subsequent regimes that precede turbulent flow Beyond the onset of wavy vortex flow the velocity spectra contain a single sharp frequency component and its harmonics; the flow is strictly periodic As the Reynolds number is increased, a previously unobserved second sharp frequency component appears at R/Rc = 10·1, where Rc is the critical Reynolds number for the Taylor instability The two frequencies appear to be irrationally related; hence this is a quasi-periodic flow A chaotic element appears in the flow at R/Rc ≃ 12, where a weak broadband component is observed in addition to the sharp components; this flow can be described as weakly turbulent As R is increased further, the component that appeared at R/Rc= 10·1 disappears at R/Rc = 19·3, and the remaining sharp component disappears at R/Rc = 21·9, leaving a spectrum with only the broad component and a background continuum The observance of only two discrete frequencies and then chaotic flow is contrary to Landau's picture of an infinite sequence of instabilities, each adding a new frequency to the motion However, recent studies of nonlinear models with a few degrees of freedom show a behaviour similar in most respects to that observed

Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow

Abstract: Measurements of the three fluctuating components of the velocity and of the two components of the wall shear stress fluctuations have been made in a fully developed turbulent channel flow at Re=7700 using hot‐film probes. These measurements include rms values, skewness and flatness factors, and probability density functions. Although the wall region is emphasized here, information for the whole channel half‐width is also given.

Laminar boundary layer on an impulsively started rotating sphere

Abstract: The problem of determining the development with time of the flow of a viscous incompressible fluid outside a rotating sphere is considered The sphere is started impulsively from rest to rotate with constant angular velocity about a diameter The motion is governed by a coupled set of three nonlinear time‐dependent partial differential equations which are solved by first employing the semi‐analytical method of series truncation to reduce the number of independent variables by one and then solving numerically a finite set of partial differential equations in one space variable and the time The calculations have been carried out on the assumption that the Reynolds number is very large The physical properties of the flow are calculated as functions of the time and compared with existing solutions for large and small times A radial jet is found to develop with time near the equator of the sphere as a consequence of the collision of the boundary layers

On the non-parallel flow stability of the Blasius boundary layer

Abstract: The influence of boundary layer growth on the flow stability of the Blasius boundary layer is analysed on a rational, large Reynolds number, basis, for small disturbances of fixed frequency. The parallel-flow solution forms the leading term and the non-parallel flow effects emerge in a consistent fashion from the asymptotic expansions. Compared with previous, successive approximation, procedures, the theoretical neutral curve obtained here is much more affected by the non-parallel effects and consequently shows somewhat improved agreement with experimental observations, even though the previous and the present approaches (both of which calculate only a finite number of terms) would be identical if taken to infinitely many terms.

Wakes in Stratified Fluids

Abstract: In this article we review research activities concerning wakes generated by moving bodies in stratified fluids. A wake is defined to be the non­ propagating disturbance produced by a moving body, and thus research activities concerning internal waves generated by a moving body are not included. Wakes have been of interest to many fluid dynamicists and engineers because they are a basic flow phenomenon associated with fluid flowing over an obstacle or with the movement of a natural or man-made body. The wake flow depends strongly on the Reynolds number RD == VoDjv, which is defined as the ratio of the inertia force to the viscous force. Here U 0 is the body speed, D is the characteristic length, e.g. the diameter of a cylinder or a sphere, and v is the kinematic viscosity of the fluid. For small Reynolds numbers, the viscous force dominates the inertia force and the wake is laminar. As the Reynolds number increases, the wake becomes unstable and a regular flow pattern, such as Karman's vortex street in the wake of a cylinder, can be observed. At still higher Reynolds numbers, the flow pattern becomes irregular and a turbulent flow is formed. Books written by Townsend (1956), Hinze (1959), and Schlichting ( 1960) can be referred to for further information about wakes. When the fluid is stratified thermally or with foreign additives, such as salt, a gravitational force, in addition to inertia and viscous forces, is exerted on the flow. A stratified fluid occurs very commonly in the

Detailed Study of Attached and Separated Compression Corner Flowfields in High Reynolds Number Supersonic Flow

Abstract: An experimental study has been carried out to detail the interaction of a compressible turbulent boundary layer with shock waves of varying strengths. The interaction was produced by two-dimension al compression corners of 8, 16, 20, and 24 deg angles. The incoming boundary layer had an edge Mach number of 2.85 and a Reynolds number of 1.7 million based on overall thickness. Detailed mean flow and surface measurements are presented for the four corner angles. The 8 deg corner flow was found to be fully attached, while the 16 deg case was near incipient separation. Both the 20 and 24 deg corners produced significant flow separation regions. In the discussion of these results, emphasis is placed on the development of flowfield properties from attached to separated conditions. Comparisons made with a computational solution of the Navier-Stokes equations show good agreement when the corner flow is not separated. Separated corner flows seem to require a more complex turbulence model in the computational solution.

On the theory of unsteady high Reynolds number flow through a circular aperture

Abstract: This paper examines the theory of the unsteady motion caused by fluctuations in the driving pressure of a high Reynolds number mean flow through a circular aperture in a thin rigid plate. A theoretical model is proposed which is amenable to exact analytical treatment, and involves the shedding of vorticity from the rim of the aperture. The theory determines the dependence of the Rayleigh conductivity of the aperture on the Strouhal number, and provides quantitative estimates for the rate of dissipation of large scale ordered structures as a result of the generation of turbulence at the apertures in a perforated liner. The limit of zero Strouhal number yields a description of steady high Reynolds number flow, the contraction ratio of the emerging jet being predicted to be equal to the minimum theoretical value of ½. Application is made to the problem of sound trans­mission through a uniformly perforated screen in the presence of a low Mach number bias flow.

The application of turbulence theory to the formulation of subgrid modelling procedures

Abstract: The problem of subgrid modelling, that is, of representing energy transfers from large to small eddies in terms of the large eddies only, must arise in any large eddy simulation, whether the equations of motion are open or direct (unaveraged) or closed (averaged). Models for closed calculations are derived from classical closures, and these are used to determine the effect of filter shape, grid-scale spectrum and grid-scale anisotropy on the effective eddy viscosity: the Leonard or resolvable-scale stress is calculated separately and is found to account for 14% of the total drain in a typical high Reynolds number case.The validity of using these eddy viscosities in an open calculation is considered. It is concluded that this is not unreasonable, but that the simulation would be much improved if the gross drain could be separated into net drain and backscatter.

Characteristics of Tornado-Like Vortices as a Function of Swirl Ratio: A Laboratory Investigation

Abstract: The investigation of tornado vortex dynamics by means of a laboratory simulation is described. Based on observations from nature and an examination of the Navier-Stokes equations, a laboratory simulator of the Ward type has been constructed. This simulator generates various vortex configurations as a function of swirl ratio, radial Reynolds number and aspect ratio. Configurations which are described are 1) a single laminar vortex; 2) a single vortex with breakdown bubble separating the upper turbulent region from the lower laminar region; 3) a fully developed turbulent core, where the breakdown bubble penetrates to the bottom of the experimental chamber; 4) vortex transition to two intertwined helical vortices; and 5) examples of higher order multiple-vortex configurations that form in the core region. Hot-film anemometry measurements of the magnitude of the velocity vector and inflow (swirl) angle have been obtained in a sequence of flows characterized by progressively increasing values of swirl...

Flying-Hot-wire Study of Flow Past an NACA 4412 Airfoil at Maximum Lift

Abstract: Hot-wire measurements have been made in the boundary layer, the separated region, and the near wake for flow past an NACA 4412 airfoil at mad mum lift. The Reynolds number based on chord was about 1,500,000. Special care was taken to achieve a two-dimensional mean flow. The main instrumentation was a flying hot wire; that is, a hot-wire probe mounted on the end of a rotating arm. The probe velocity was sufficiently high to avoid the usual rectification problem by keeping the relative flow direction always within a range of ± 30 deg from the probe ads. A digital computer was used to control synchronized sampling of hot-wire data at closely spaced points along the probe arc. Ensembles of data were obtained at several thousand locations in the flowfield. The data include Intermittency, two components of mean velocity, and twelve mean values for double, triple, and quadruple products of two velocity fluctuations. No Information was obtained about the third (spanwise) velocity component. An unexpected effect of rotor interference was identified and brought under reasonable control. The data are available on punched cards in raw form and also after use of smoothing and interpolation routines to obtain values on a fine rectangular grid aligned with the airfoil chord. The data are displayed In the paper as contour plots.

Turbulent flow in a depth-limited boundary layer

Abstract: Turbulent flow was investigated at a constant flow Reynolds number in a depth-limited boundary layer. Relative roughness was 0.12. Roughness density (ratio of plan area of elements to total bed area) was varied to cover the range of flow types described by Morris [1955]. The effect of roughness density on velocity profile shape factors, energy dissipation, and streamwise kinetic energy confirmed the existence of three types of roughness density-flow interaction, namely, ‘skimming,’ ‘wake interaction,’ and ‘isolated roughness’ flows. The velocity profiles and kinetic energy measures identified three layers in the vertical profile: an outer layer (y/D > 0.35), a wake layer (0.35 > y/D > 0.10), and an inner region (y/D < 0.10). The wake layer is produced by strong turbulent action accompanying vortex shedding at intermediate roughness densities. Spectral measurements and calculations of the turbulent macroscale indicated that the spectral shape is affected by the free surface but that below y/D = 0.5 a parametric model using the turbulent Reynolds number in the spectral energy equation adequately describes the spectral shape for all roughness densities. Implications of these results are discussed for the study of shallow, natural flows with high relative roughness.

The organized nature of flow impingement upon a corner

Abstract: Oscillations of impinging flows, which date back to the jet-edge phenomenon (Sondhaus 1854), have been observed for a wide variety of impingement configurations. However, alteration of the structure of the shear layer due to insertion of an impingement edge (or surface) and the mechanics of impingement of vortical structures upon an edge have remained largely uninvestigated. In this study, the impingement of a shear layer upon a cavity edge (or corner) is examined in detail. Water is used as a working fluid and laser anemometry and hydrogen bubble flow visualization are used to characterize the flow dynamics. Reynolds numbers (based on momentum thickness at separation) of 106 and 324 are employed. Without the edge, the shear layer produces the same sort of non-stationary (variable) velocity autocorrelations observed by Dimotakis & Brown (1976). When the edge is inserted, the organization of the flow is dramatically enhanced as evidenced by a decrease in variability of autocorrelations and appearance of well-defined peaks in the corresponding spectra. This enhanced organization is not locally confined to the region of the edge but extends along the entire length of the shear layer, thereby reinforcing the concept of disturbance feedback. Comparison of spectra with and without insertion of the edge reveals a remarkable similarity to those of a non-impinging shear layer with and without application of sound at a discrete frequency (Browand 1966; Miksad 1972); with enhanced organization at the fundamental frequency, simultaneous enhancement occurs also at the sub- and higher-harmonics.

Enhanced sedimentation in settling tanks with inclined walls

Abstract: Using the principles of continuum mechanics, a theory is developed for describing quantitatively the sedimentation of small particles in vessels having walls that are inclined to the vertical. The theory assumes that the flow is laminar and that the particle Reynolds number is small, but c0, the concentration in the suspension, and the vessel geometry are left arbitrary. The settling rate S is shown to depend upon two dimensionless groups, in addition to the vessel geometry: a sedimentation Reynolds number R, typically O(1)-O(10); and Λ, the ratio of a sedimentation Grashof number to R, which is typically very large. By means of an asymptotic analysis it is then concluded that, as Λ → ∞ and for a given geometry, S can be predicted from the well-known Ponder-Nakamura-Kuroda formula which was obtained using only kinematic arguments. The present theory also gives an expression for the thickness of the clear-fluid slit that forms underneath the downward-facing segment of the vessel walls, as well as for the velocity profile both in this slit and in the adjoining suspension.The sedimentation rate and thickness of the clear-fluid slit were also measured in a vessel consisting of two parallel plates under the following set of conditions: c0 ≤ 0·1, R ∼ O(1), O(10)5 ≤ Λ ≤ O(107) and 0° ≤ α ≤ 50°, where α is the angle of inclination. Excellent agreement was obtained with the theoretical predictions. This suggests that the deviations from the Ponder-Nakamura-Kuroda formula reported in the literature are probably due to a flow instability which causes the particles to resuspend and thereby reduces the efficiency of the process.

Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus

Abstract: In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up to an error term of O(E^2 ln E), where E is the slenderness parameter (ratio of cross-sectional radius to centre-line radius). This degree of accuracy makes it possible to determine the force per unit length experienced by the torus up to a term of O(E^2). A comparison is made between the force coefficients of the slender torus to those of a straight slender body to illustrate the large differences that may occur as a result of the finite centre-line curvature.

On Stability and Transition in Three-Dimensional Flows

Abstract: The usefulness of the e" method for predicting transition in two-dimensional and axially symmetric flows is well established. In order to extend the method to three-dimensi onal parallel shear flows, it is first necessary to establish a relationship between a and /?, the complex wave numbers in two perpendicular directions in the plane of flow. We suggest that this may be done by making use of group velocity concepts which lead'to the requirement da/dp = - tan<£, where 0 is real and denotes the direction of propagation of centered disturbances. As a paradigm of this approach, the rotating disk is studied. It is established that the critical Reynolds number is 176, that the principal disturbances to the laminar flow travel outwards and at an angle — - 8 deg to the direction of motion of the disk, while the appropriate value of n is —20. The observed direction of propagation of disturbance is at - - 13 deg to the direction of motion of the disk. The generally accepted value of n is -9, much less than that found here.

Vortex ring formation at tube and orifice openings

Abstract: The formation, at tube and orifice openings, of vortex rings generated by a piston moving with velocity proportional to time to some power m, is considered. The expansion of the axisymmetric generating flow about the circular forming edge is used in conjunction with the similarity theory of edge vortex growth to model the ring formation process. For large Reynolds numbers the ring diameter and circulation are not strongly dependent on the piston velocity profile. However, the ring viscous subcore shows peaks in the tangential velocity profile only if m < (π–θ)/(2π–θ), where θ is the edge forming angle.

Rotation of small non-axisymmetric particles in a simple shear flow

Abstract: The equations for the rotation of non-axisymmetric ellipsoids in a simple shear flow at low Reynolds numbers are derived in terms of Euler angles. Numerical solutions of this third-order system of equations show a doubly periodic structure to the rotation, with a change in the general nature of the solutions when a certain planar rotation of the particle becomes unstable. Some analytic progress can be made for nearly spherical ellipsoids and for nearly axisymmetric ellipsoids. The near spheres show the same qualitative behaviour as the general ellipsoids. Quite small deviations from axial symmetry are found to produce large changes in the rotation.

On the perseverance of a quasi-two-dimensional eddy-structure in a turbulent mixing layer

Abstract: Strong external disturbances were introduced into a mixing layer in order to test the formation of the quasi two-dimensional coherent eddies and their survival under less than ideal conditions. Velocity and temperature correlation measurements, flow visualization, and the simultaneous use of a large number of sensors suggest that these eddies are very stable in the range of Reynolds numbers considered and they persevere in spite of the external buffeting imposed. Some measurements were carried out in a mixing layer between two parallel streams and some in a mixing layer entraining quiescent surrounding fluid. In both cases the large eddies could be described. as vortex rolls spanning the test section; these rolls may be contorted and sometimes skewed, but they are basically two-dimensional.

The distortion of turbulence by a circular cylinder

Abstract: The flow of grid-generated turbulence past a circular cylinder is investigated using hot-wire anemometry over a Reynolds number range from 4·25 × 103 to 2·74 × 104 and a range of intensities from 0·025 to 0·062. Measurements of the mean velocity distribution, and r.m.s. intensities and spectral energy densities of the turbulent velocity fluctuations are presented for various radial and circumferential positions relative to the cylinder, and for ratios of the cylinder radius a to the scale of the incident turbulence Lx ranging from 0·05 to 1·42. The influence of upstream conditions on the flow in the cylinder wake and its associated induced velocity fluctuations is discussed.For all measurements, detailed comparison is made with the theoretical predictions of Hunt (1973). We conclude the following. The amplification and reduction of the three components of turbulence (which occur in different senses for the different components) can be explained qualitatively in terms of the distortion by the mean flow of the turbulent vorticity and the ‘blocking’ or ‘source’ effect caused by turbulence impinging on the cylinder surface. The relative importance of the first effect over the second increases as a/Lx increases or the distance from the cylinder surface increases.Over certain ranges of the variables involved, the measurements are in quantitative agreement with the predictions of the asymptotic theory when a/Lx [Lt ] 1, a/Lx [Gt ] 1 or |k| a [Gt ] 1 (where k is the wavenumber).The incident turbulence affects the gross properties of the flow in the cylinder wake, but the associated velocity fluctuations are probably statistically independent of those in the incident flow.The dissipation of turbulent energy is greater in the straining flow near the cylinder than in the approach flow. Some estimates for this effect are proposed.