Showing papers on "Reynolds number published in 1978"

Large-scale structure in the mixing layer of a round jet

Abstract: Late transitional and turbulent flows in the mixing-layer region of a round jet are investigated for a range of Reynolds numbers by using flow-visualization and hotwire techniques. Attention is focused on the vortices in the transition region and the large eddies in the turbulent region. The interaction and coalescence of vortex rings in the transition region are described. The transition region is characterized by a growth of three-dimensional flow due to a wave instability of the cores of the vortex rings. The merging of these distorted vortices produces large eddies which can remain coherent up to the end of the potential-core region of the jet. A conditional sampling technique is used to measure eddies moving near the jet centre-line. These eddies differ significantly from the ring vortices as they are three-dimensional and contain irregular small-scale turbulence. However, when averaged, their structure is similar in cross-section to that of a vortex ring. These sampled eddies contribute greatly to local velocity fluctuations and statistical correlations. The experiments indicate a need for careful consideration of the meanings of terms such as ‘vortex’, ‘eddy’ and ‘turbulent flow’. In particular care must be taken to discriminate between the orderly, easily visualized, vortices in the transition regions of free shear flows and the less clearly visualized, but strong, large eddies in the fully developed turbulent regions.

Flow around a circular cylinder near a plane boundary

Abstract: The flow around a circular cylinder placed at various heights above a plane boundary has been investigated experimentally. The cylinder spanned the test section of a wind tunnel and was aligned with its axis parallel to a long plate and normal to the free stream. It was placed 36 diameters downstream of the leading edge of the plate and its height above the plate was varied from zero, the cylinder lying on the surface, to 3·5 cylinder diameters. The thickness of the turbulent boundary layer on the plate at the cylinder position, but with it removed from the tunnel, was equal to 0·8 of the cylinder diameter. Distributions of mean pressure around the cylinder and along the plate were measured at a Reynolds number, based on cylinder diameter, of 4·5 × 104. Spectral analysis of hot-wire signals demonstrated that regular vortex shedding was suppressed for all gaps less than about 0·3 cylinder diameters. For gaps greater than 0·3 the Strouhal number was found to be remarkably constant and the only influence of the plate on vortex shedding was to make it a more highly tuned process as the gap was reduced. Flow-visualization experiments in a smoke tunnel revealed the wake structure at various gap-to-diameter ratios.

A numerical study of the deformation and burst of a viscous drop in an extensional flow

Abstract: We study the deformation and conditions for breakup of a liquid drop of viscosity λμ freely suspended in another liquid of viscosity μ with which it is immiscible and which is being sheared. The problem at zero Reynolds number is formulated exactly as an integral equation for the unknown surface velocity, which is shown to reduce to a particularly simple form when Δ = 1. This equation is then solved numerically, for the case in which the impressed shear is a radially symmetric extensional flow, by an improved version of the technique used, for Δ = 0, by Youngren & Acrivos (1976) so that we model the time-dependent distortion of an initially spherical drop. It is shown that, for a given Δ, a steady shape is attained only if the dimensionless group Ω ≡4πGμa/γ lies below a critical value Ωc(Δ), where G refers to the strength of the shear field, a is the radius of the initial spherical drop and γ is the interfacial tension. On the other hand, when Ω > Ωc the drop extends indefinitely along its long axis. The numerical results for Δ = 0·3, 0·5, 1, 2, 10 and 100 are in good agreement with the predictions of the small deformation analysis by Taylor (1932) and Barthes-Biesel & Acrivos (1973) and, at the smaller Δ, with those of slender-body theory (Taylor 1964; Acrivos & Lo 1978).

Wind tunnel performance data for two- and three-bucket Savonius rotors

Abstract: Fifteen configurations of a Savonius rotor wind turbine were tested in the Vought Corporation Systems Division 4.9- x 6.1-m Low Speed Wind Tunnel to determine aerodynamic performance. The range of values of the varied parameters was as follows: number of buckets, 2 and 3; nominal freestream velocity, 7 and 14 m/s; Reynolds number per meter, 4.32 x 10/sup 5/ and 8.67 x 10/sup 5/; rotor height, 1 and 1.5 m; rotor diameter (nominal), 1 m; bucket overlap, 0.0 to 0.1 m. The measured test variables were torque, rotational speed, and tunnel conditions. It is concluded that increasing Reynolds number and/or aspect ratio improves performance. The recommended configuration consists of two sets of two-bucket rotors, rotated 90 deg apart, with each rotor having a dimensionless gap width of 0.1 to 0.15.

The Wakes of Cylindrical Bluff Bodies at Low Reynolds Number

Abstract: Experiments on the near wake of a cylinder will be discribed in an attempt to present a coherent picture of the events encountered as the Reynolds number increases from small values up to values of a few thousand. Much work on this subject has already been done, but there are gaps in our description of these flows as well as more fundamental deficiencies in our understanding of them. The subject has been reviewed several times and most recently by Berger & Wille (1972) whose paper covers much of the ground that will be discussed again here. The present work may be regarded as built upon this latest review. I remember with gratitude many helpful discussions with the late Rudolph Wille who contributed so much to this subject. The investigation has concentrated on circular cylinders, but the wakes of bluff cylinders of different cross sectional shapes have also been observed. Bluff cylinders in general are considered in §§4 and 5, together with the effect of splitter plates on circular cylinders in §9. The experiments concern, almost exclusively, flow visualization of the wakes by means of dye washed from the bodies. The patterns of dye observed are, therefore, filament line representations of the flow leaving the separation lines on the body. It must be stressed that the dye does not make visible the vorticity bearing fluid because at low Reynolds number, vorticity diffuses considerably more rapidly than does dye. The ratio of the molecular diffusivity of momentum to that of mass of dye is of the order of 100.

Asymmetric flows and instabilities in symmetric ducts with sudden expansions

Abstract: Flow visualization and laser-Doppler anemometry have been used to provide a detailed description of the velocity characteristics of the asymmetric flows which form in symmetric, two-dimensional, plane, sudden-expansion geometries. The flow and geometry boundary conditions which give rise to asymmetric flow are indicated, and the reason for the phenomenon is shown to lie in disturbances generated at the edge of the expansion and amplified in the shear layers. The spectral distributions of the fluctuations in velocity are quantitatively related to the dimensions of the two unequal regions of flow recirculation. It is also shown that the intensity of fluctuating energy in these low Reynolds number flows can be larger than that in corresponding turbulent flows.

Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles

Abstract: The analysis concerns the alterations produced when small amplitude disturbances, including entropy and vorticity disturbances, are imposed on steady potential flows. For the most general nonacoustic incident distortion field that can be imposed on the uniform upstream flow, it is shown that the perturbation velocity at any point of the resulting unsteady compressible and vortical flow consists of a part that is a known function of the imposed upstream distortion field and the mean flow variables and a potential part that can be found by solving a linear inhomogeneous wave equation with a dipole-type source term whose strength is a known function of the imposed upstream distortion field. The theory is applied to the unsteady flow past a corner, and a closed-form analytical solution is found.

Bifurcation Phenomena in Steady Flows of a Viscous Fluid. I. Theory

Abstract: The investigation deals with questions relating to the existence of multiple solutions to hydrodynamic problems, especially questions about bifurcations of solutions and about stability. Although the aim is to resolve some of these questions generally, particular reference is made to events observed in the Taylor experiment on Couette flow between rotating cylinders, for which a new rationale is developed. In § 2 certain results for the abstract nonlinear problem of steady motion in a bounded fluid are summarized, including a set of generic properties that can be associated with real flows. In § 3 these results are applied to the interpretation of observable phenomena, and several predictions are made which are open to experimental checks. It is shown that new insights into the Taylor experiment are gained by considering its dependence on two parameters, one the Reynolds number R and the other the length l of the flow domain. Attention is paid to the initial development of cells as R is gradually increased from small values (§3.3), to a hysteresis phenomenon accompanying morphogenesis of the cellular structure at critical values of l (§3.4), and to properties of secondary modes possible above respective critical values of R (§ 3.5). In the appendix some corresponding interpretations are noted for the Benard problem of incipient convective motion.

The fine-scale structure of the turbulent velocity field

Abstract: The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated. Recent studies of the fine-scale velocity field for many different flows, e.g. grid flows, wakes, jets and the atmospheric boundary layer, are shown to provide considerable evidence for the existence of Kolmogorov normalized spectral shapes which are universal in the sense that they describe the high wave-number spectral behaviour of all turbulent flow fields with a similar value of the turbulence Reynolds number Rλ. The normalized spectral shapes vary with Rλ in a manner consistent with the later reformulations. The Reynolds number dependence of the normalized spectra is demonstrated for the Rλ range from about 40 to 13 000. Expressions for the Kolmogorov normalized spectral functions are presented for three values of Rλ. Also revealed in this study is the importance of considering effects on spectra caused by deviations from Taylor's approximation in high intensity turbulent flows. Lumley's (1965) model is used to correct the high frequency portion of the measured one-dimensional spectra for these effects. An analytical solution to Lumley's expression is presented and applied to the data.

Visual observations of the flow past a sphere at Reynolds numbers between 10 4 and 10 6

Abstract: The wake configuration of a sphere has been determined by means of the surface oil-flow method, the smoke method and the tuft-grid method in a wind tunnel at Reynolds numbers ranging from 104 to 106. It was found that the wake performs a progressive wave motion at Reynolds numbers between 104 and 3·8 × 105, and that it forms a pair of stream wise line vortices at Reynolds numbers between 3·8 × 105 and 106.

Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges

Abstract: Two complementary procedures were developed to calculate the viscous supersonic flow over conical shapes at large angles of attack, with application to cones and delta wings. In the first approach the flow is assumed to be conical and the governing equations are solved at a given Reynolds number with a time-marching explicit finite-difference algorithm. In the second method the parabolized Navier-Stokes equations are solved with a space-marching implicit noniterative finite-difference algorithm. This latter approach is not restricted to conical shapes and provides a large improvement in computational efficiency over published methods. Results from the two procedures agree very well with each other and with available experimental data.

The number of waves on unstable vortex rings

Abstract: An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory.

Particle motions near the bottom in turbulent flow in an open channel. Part 2

Abstract: This study continues the investigation of particle motions near the bottom in a turbulent open channel flow, reported by Sumer & Oguz (1978; hereafter referred to as part 1). Paths of suspended heavy particles were recorded in three dimensions and in time, employing a stereo-photogrammetric system coupled with a stroboscope. In the case of smooth bottom, the measured kinematical quantities concerning the particle motions were found to be in accord with the available information on the ‘bursting process’. Agreement between the particle motion and the bursting process provided further support for the mechanism of particle suspension near the bottom proposed in part 1. Similar experiments were carried out when the bottom was rough. Comparison between the smooth- and rough-bottom cases could be made on the same basis as the flow Reynolds number as well as the particle properties were kept almost unchanged in both the smooth and rough boundary experiments. The observations showed that particle motions close to the rough bottom are very similar in character to those in the smooth-bottom case. The findings of the present paper suggested that the suspension mechanism given for the smooth-boundary flow could be extended to the rough-boundary case.

Experimental and Computational Steady and Unsteady Transonic Flows about a Thick Airfoil

Abstract: An experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady fiowfieids about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 are predicted and compared with experiment. Results from comparisons with experimental pressure and skin-friction distributions show improved agreement when including test-section wall boundaries in the computations. Steady-flow results were in good quantitative agreement with experimental data for flow conditions which result in relatively small regions of separated flow. For flows with larger regions of separated flow, improvements in turbulence modeling are required before good agreement with experiment will be obtained. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.

Vortex formation at vertical pipe intakes

Abstract: With the object of determining the similarity criterion, experimental studies on vortex formation at pipe intakes were carried out using two geometrically similar circular vortex tanks, circulation in approach flow was generated by means of adjustable guide vanes Transparent pipe intakes of different sizes and liquids of different viscosities and surface tensions were used in a recirculating system Based on the analysis of data, a method has been proposed according to which a geometrically similar model is operated at the same Froude number as in the prototype and the observed critical submergence is corrected for distortion due to change in the model Reynolds number A criterion to determine the type of vortex for known geometric and kinematic conditions has also been proposed

Strongly stratified flow past three-dimensional obstacles

Abstract: An experimental study has been made of the shear flow of stratified fluid of characteristic buoyancy frequency with characteristic speed past a three-dimensional obstacle of height when the Froude number, Fr = , is much smaller than one. It is already known that in the limit Fr→O the inviscid equations of motion may be expanded in powers of Fr2 and that the lowest-order solution is a flow confined to horizontal planes, passing around the obstacle rather than over it. This theory breaks down within a distance / from the level of the top of the obstacle. The experiments were carried out in a closed-circuit stratified water channel with a hemisphere, a cone and a truncated cylinder for Fr between 0.03 and 0.3 at Reynolds numbers between 100 and 1000. The qualitative features have been determined by flow visualization with dye. The flows are found to be nearly in horizontal planes except near the tops of the obstacles. Also there are revealed two other prominent features which the theory cannot predict. In the lee of the obstacles at the level of the top, a cowhorn-shaped eddy with horizontal axis is observed for high enough Fr; it combines the characteristics of rotors and of horseshoe vortices. Below this level, there is a separated wake flow in each horizontal plane. Vortices are shed provided the Reynolds number is large enough and provided Fr is less than about 0.15. The shedding frequency is the same at all heights. Attention is drawn to atmospheric situations of which these features may be ingredients.

Velocity-derivative skewness in small Reynolds number, nearly isotropic turbulence

Abstract: Previous measurements in the moderate to small Reynolds number range of isotropic turbulence have all shown the skewness factor of the streamwise velocity derivative to increase with decreasing Reynolds number. This ‘paradoxical’ trend was found for 150 ≥ Rλ ≥ 4. New data covering the range 4 ≥ Rλ ≥ 1 show a maximum S for Rλ between 4 and 3 and a rapid decrease for Rλ < 2.

Similarity Of Free-Vortex At Horizontal Intake

Abstract: An investigation was conducted to study the onset of air-entraining vortices at a horizontal intake, with and without a bellmouthed entry, when the intake was projected into the experimental flume or mounted flush with the side wall. The basic non-dimensional parameters that govern the onset of vortices at a horizontal intake in model and prototype have been derived and determined experimentally. The results of measurements are given as a set of curves, which can be used for the design of a vortex-free intake and also for the selection of appropriate model scales. The results of the measurement showed that flow conditions in an air-entraining vortex is not affected by surface tension and the viscosity of the test fluid when the radial Reynolds number, and the Weber number are larger than 3x104 and 104 respectively. In this case the formation of vortices depends largely on circulation, submergence head and discharge into the intake. It was found that the bellmouth did not improve the performance of the int...

Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers

Abstract: Two kinds of experiment were made in the wake of a cylinder at Reynolds numbers ranging between 20 and 150. One was a close look at the structure of the vortex street with a stationary cylinder at Reynolds numbers greater than 48. The other experiment was made at lower Reynolds numbers with a cylinder vibrating normal to the flow direction. In this case an artificially induced small-amplitude fluctuation grows exponentially with the rate predicted by the stability theory. Because of the similarity between the two kinds of wake, we postulate that the shedding of the vortex at low Reynolds numbers is initiated by the linear growth, namely, the fluctuation with the frequency of maximum linear growth rate develops into vortex streets. By using the measured width of the wake at the stagnation point in the wake and the result of the stability theory, we could calculate the Strouhal number for Reynolds numbers ranging from 48 to 120. The predicted Strouhal numbers agree well with the values from direct measurements.

The Hydrodynamics of Rheotaxis in the Plaice (Pleuronectes Platessa L.)

Abstract: Plaice resting on the bottom of a flume respond to the current with a clearly defined pattern of behaviour. A simple hydrodynamic model which relates the slip-speed ( U s ) and lift-off speed ( U L ) to the physical forces acting on the fish has been verified experimentally using freshly killed fish and a rigid model. With an asymmetric semi-ellipsoid shape and a fineness ratio of 14 the plaice appears to be morphologically adapted to have minimum drag when heading into the current. As a result of this streamlined shape the lift force experienced by the fish is 10-20 times greater than the drag force, and the rheotactic behaviour therefore appears to be principally adapted to counteract hydrodynamic lift. Values of U s and U L , above which live fish must expend energy against the current, are exceeded for much of each tidal cycle in the southern North Sea. The model is of general application to benthic organisms in flowing water for Reynolds numbers between 10 4 and 10 6 ; outside these limits some modification of the constants is required.

The Linear Stability of Flat Stokes Layers

Abstract: The linear stability of a flat Stokes layer is investigated. The results obtained show that, in the parameter range investigated, the flow is stable. It is shown that the Orr-Sommerfield equation for this flow has a continuous spectrum of damped eigenvalues at all values of the Reynolds number. In addition, a set of discrete eigenvalues exists for certain values of the Reynolds number. The eigenfunctions associated with this set are confined to the Stokes layer while those corresponding to the continuous spectrum persist outside the layer. The effect of introducing a second boundary a long way from the Stokes layer is also considered. It is shown that the least stable disturbance of this flow does not correspond to the least stable discrete eigenvalue of the infinite Stokes layer when this boundary tends to infinity.