Showing papers on "Reynolds number published in 1982"

Numerical investigation of turbulent channel flow

Abstract: Fully developed turbulent channel flow was simulated numerically at Reynolds number 13800, based on centerline velocity and channel halt width. The large-scale flow field was obtained by directly integrating the filtered, three dimensional, time dependent, Navier-Stokes equations. The small-scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC IV computer with up to 516,096 grid points. The computed flow field was used to study the statistical properties of the flow as well as its time dependent features. The agreement of the computed mean velocity profile, turbulence statistics, and detailed flow structures with experimental data is good. The resolvable portion of the statistical correlations appearing in the Reynolds stress equations are calculated. Particular attention is given to the examination of the flow structure in the vicinity of the wall.

Strouhal numbers of rectangular cylinders

Abstract: Experiments on the vortex-shedding frequencies of various rectangular cylinders were conducted in a wind tunnel and in a water tank. The results show how Strouhal number varies with a width-to-height ratio of the cylinders in the range of Reynolds number between 70 and 2 × l04. There is found to exist a certain range of Reynolds number for the cylinders with the width-to-height ratios of 2 and 3 where flow pattern abruptly changes with a sudden discontinuity in Strouhal number. The changes in flow pattern corresponding to the discontinuity of Strouhal number have been confirmed by means of measurements of velocity distribution and flow visualization. These data are compared with those of other investigators. The experimental results have been found to show a good agreement with those of numerical calculations.

The forced mixing layer between parallel streams

Abstract: The effect of periodic two-dimensional excitation on the development of a turbulent mixing region was studied experimentally. Controlled oscillations of variable ampli- tude and frequency were applied at the initiation of mixing between two parallel air streams. The frequency of forcing was at least an order of magnitude lower than the initial instability frequency of the flow in order to test its effect far downstream. The effect of the velocity difference between the streams was also investigated in this experiment. A typical Reynolds number based on the velocity difference and the momentum thickness of the shear layer was l04.It was determined that the spreading rate of the mixing layer is sensitive to periodic surging even if the latter is so small that it does not contribute to the initial energy of the fluctuations. Oscillations at very small amplitudes tend to increase the spreading rate of the flow by enhancing the amalgamation of neighbouring eddies, but at higher amplitudes the flow resonates with the imposed oscillation. The resonance region can extend over a significant fraction of the test section depending on the Strouhal number and a dimensionless velocity-difference parameter. The flow in the resonance region consists of a single array of large, quasi-two-dimensional vortex lumps, which do not interact with one another. The exponential shape of the mean-velocity distribution is not affected in this region, but the spreading rate of the flow with increasing distance downstream is inhibited. The Reynolds stress in this region changes sign, indicating that energy is extracted from the turbulence to the mean motion; the intensity of the spanwise fluctuations is also reduced, suggesting that the flow tends to become more two-dimensional.Amalgamation of large coherent eddies is resumed beyond the resonance region, but the flow is not universally similar. There are many indications suggesting that the large eddies in the turbulent mixing layer at fairly large Re are governed by an inviscid instability.

Strained spiral vortex model for turbulent fine structure

Abstract: A model for the intermittent fine structure of high Reynolds number turbulence is proposed. The model consists of slender axially strained spiral vortex solutions of the Navier–Stokes equation. The tightening of the spiral turns by the differential rotation of the induced swirling velocity produces a cascade of velocity fluctuations to smaller scale. The Kolmogorov energy spectrum is a result of this model.

A numerical study of vortex shedding from rectangles

Abstract: The purpose of this paper is to present numerical solutions for two-dimensional time-dependent flow about rectangles in infinite domains. The numerical method utilizes third-order upwind differencing for convection and a Leith type of temporal differencing. An attempted use of a lower-order scheme and its inadequacies are also described. The Reynolds-number regime investigated is from 100 to 2800. Other parameters that are varied are upstream velocity profile, angle of attack, and rectangle dimensions. The initiation and subsequent development of the vortex-shedding phenomenon is investigated. Passive marker particles provide an exceptional visualization of the evolution of the vortices both during and after they are shed. The properties of these vortices are found to be strongly dependent on Reynolds number, as are lift, drag, and Strouhal number. Computed Strouhal numbers compare well with those obtained from a wind-tunnel test for Reynolds numbers below 1000.

A Simple Model of Mixing and Chemical Reaction in a Turbulent Shear Layer

Abstract: Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale inviscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.

A Numerical Method for Solving the Equations of Compressible Viscous Flow

Abstract: Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.

Experiments on the flow and acoustic properties of a moderate-Reynolds-number supersonic jet

Abstract: Flow and acoustic properties of a jet at Reynolds number of 70,000 were studied at Mach 2.1. Measurements in a free jet test facility were made with pitot tubes and hot-wire anemometry. Center-line Mach number distributions for natural and excited jets were obtained. A slow initial growth rate was in the potential core region of the jet, indicating a transition from laminar to turbulent flow in moderate Reynolds number jets. The transition occurred within the first 2-3 diameters. Spectral components were calculated for the fluctuating flowfield, and sound pressure levels were measured for the overall near-field noise. The centroid of noise was located about 8 nozzle diameters downstream. The growth rates of instabilities were determined to be in agreement with linear stability theory predictions over a broad frequency range.

A Review of Added Mass and Fluid Inertial Forces.

Abstract: This report reviews the existing state of knowledge concerning the evaluation of the forces imposed on a body in a fluid due to acceleration of either the body or the fluid. It concentrates on those fluid inertial forces due to acceleration rather than on the drag/lift forces due to steady motion. The first part of the report presents a survey of the analytical background including the definition of added mass, the structure of the added mass matrix and other effects such as the influence of viscosity, fluid compressibility and the proximity of solid and free surface boundaries. Then the existing data base from experiments and potential flow calculations is reviewed. Approximate empirical methods for bodies of complex geometry are explored in a preliminary way. The possible dramatic effects of the proximity of the ocean bottom are further highlighted. The confused state of affairs regarding the possibly major effects of viscosity in certain regimes of frequency and Reynolds number is discussed. Finally a number of recommendations stemming from ocean engineering problems are put forward.

On the structure of turbulent channel flow

Abstract: Hot-film measurements of the streamwise velocity component were carried out in a fully developed turbulent water-channel flow for three different Reynolds numbers (13800, 34600 and 48900). The results for the first four statistical moments complement and extend the results from previous studies of turbulent channel flow. The VITA variance technique waa employed to detect deterministic events in the streamwise velocity. It waa demonstrated that the VITA technique has a band-pass-filter character. The number of events detected was found to decrerrae exponentially with the threshold level and the events occupy a wide range of timescales. This makes it impossible to define one unique frequency of occurrence or one unique duration of the events. However, by using this technique information was obtained on the amplitude and timescale distributions of the events. The chmacteristic features of the conditional iverages were found to be related to the skewness and flatness factors.

On the effect of torsion on a helical pipe flow

Abstract: An orthogonal coordinate system along a generic spatial curve has been introduced, and the Navier-Stokes equations for a steady incompressible viscous flow have been explicitly written in this frame of reference. As an application the flow in a helical pipe has been studied, and, formdii 5f curvature and torsion small compared with the radius of the pipe, the flow has been considered as a perturbed Poiseuille flow. The result is that for curvatures and torsions of the same order and for low Reynolds number the curvature induces on the flow a first-order effect on the parameter e =κa, where κ is the curvature and a the radius of the pipe, while the effect of the torsion on the flow is of the second order in E. This last result disagrees with those of Wang (1981), who, adopting a non-orthogonal coordinate system, found a first-order effect of torsion on the flow.

A flow-visualization study of transition in plane Poiseuille flow

Abstract: Flow visualization of artificially triggered transition in plane Poiseuille flow in a water channel by means of 10–20 μm diameter tihnium-dioxide-coated mica particles revealed some striking features of turbulent spots. Strong oblique waves were observed both at the front of the arrowhead-shaped spot as well as trailing from the rear tips. Both natural and artificially triggered transition were observed to occur for Reynolds numbers slightly greater than 1000, above which the flow became fully turbulent. The front of the spot moves with a convection speed of about two-thirds of the centreline velocity, while the rear portion moves at about . The spot expands into the flow with a spreading half-angle of about 8°. After growing to a size of some 36 times h (the channel depth) at a downstream distance x/h of about 130, the spot began to split into two spots, accompanied by strong wave activity. The spot(s) was followed visually downstream of its origin a distance x/h of about 300. These results indicate that wave propagation and breakdown play a crucial role in transition to turbulence in Poiseuille flow.

Bubble coalescence in pure liquids

Abstract: Solutions of the flow and deformation during the approach of two bubbles along their centre line are presented for the low Weber number case. When viscosity is absent, Weber number and radius ratio disappear from the equations under suitable transformations of the variables and a universal solution is obtained. This solution indicates the formation of a dimple, after which the thinning rate of the film between the bubbles tends to a constant high value. When liquid viscosity is included the Reynolds number, Re, enters the equations. A retardation of the coalescence process is found for Re <100, while for Re ≤1 dimple formation is suppressed. The influence of gas properties is considered briefly. An extrapolation of the inviscid results to Weber numbers of order unity suggests that the bubbles will bounce apart before coalescence is achieved.

Experimental Studies of Separation on a Two-Dimensional Airfoil at Low Reynolds Numbers

Abstract: The laminar separation, transition, and turbulent reattachment near the leading edge of a two-dimensional NACA 663 -018 airfoil were investigated using a low-speed, smoke visualization wind tunnel. Lift and drag force measurements were made using an external strain gage balance for a chord Reynolds number range of 40,GOO400,000. An extensive flow visualization study was performed and correlated with the force measurements. Experiments were also conducted with distributed surface roughness at the leading edge and external acoustic excitation to influence the development of the airfoil boundary layer. This study delineates the effects of angle of attack and chord Reynolds number on the separation characteristics and airfoil performance. Nomenclature c = model chord cd = section profile drag coefficient (uncorrected) cf = section lift coefficient (uncorrected) Cp = pressure coefficient / = acoustic frequency, Hz R = reattachment location Rc = Reynolds number based on chord length, U^ civ S = separation location T = location of approximate end of transition £/«, = freestream velocity x/c = nondimensional distance along chord a = angle of attack v - kinematic viscosity

Visualization studies of a shear driven three-dimensional recirculating flow

Abstract: A facility has been constructed to study shear-driven, recirculating flows. In this particular study, the circulation cell structure in the lid-driven cavity was studied as a function of the speed of the lid which provides the shearing force to a constant and uniform density fluid. The flow is three-dimensional and exhibits regions where Taylor-type instabilities and Taylor Goertler-like vortices are present. One main circulation cell and three secondary cells are present for the Reynolds number (based on cavity width and lid speed) range considered, viz., 1000-10000. The flows becomes turbulent at Reynolds numbers between 6000 to 8000. The transverse fluid motions (in the direction perpendicular to the lid motion) are significant. In spite of this, some key results from two-dimensional numerical simulations agree well with the results of the present cavity experiments.

Pressures Around an Inclined Ogive Cylinder with Laminar, Transitional, or Turbulent Separation

Abstract: This paper reports results From comprehensive pressure tests on an ogive cylinder in the low-turbulence 12-ft pressure wind tunnel at Ames Research Center. The results consist of detailed pressure distributions over a wide range of Reynolds numbers (0.2 x 10(exp 6) to 4.0 x 10(exp 6)) and angles of attack (20 to 90 deg). Most important, the tests encompassed a complete coverage of different roll orientations. This variation of roll orientation is shown to be essential in order to fully define all the possible flow conditions. When the various roll-angle results are combined, it is possible to interpret correctly the effects of changing angle of attack or Reynolds number. Two basic mechanisms for producing asymmetric flow are identified. One mechanism operates in both the laminar and the fully turbulent separation regimes; this mechanism Is the one qualitatively described by the impulsive flow analogy. The other mechanism occurs only in the transitional separation regime. This asymmetric flow has the same form as that found in the two-dimensional cross flow on a circular cylinder in the transitional flow regime. Finally, these results make it possible to draw up critical Reynolds number boundaries between the laminar, transitional, and fully turbulent separation regimes throughout the angle-of-attack range from 20 to 90 deg.

Active control of laminar-turbulent transition

Abstract: Instability waves, commonly called T-S waves, can be introduced in a laminar boundary layer by periodic heating of flush-mounted heating elements. Experiments have demonstrated that nearly complete cancellation of a T-S wave excited in this way can be achieved by using a second downstream heating element with a suitable phase shift. As one application of the technique, a single element together with a feedback loop activated by measured wall shear stress has been used to reduce the amplitude of naturally occurring laminar instability waves. A significant increase in the transition Reynolds number has been achieved.

The structure of turbulent boundary layers at low Reynolds numbers

Abstract: Conditionally sampled hot-wire and ‘cold-wire’ (resistance-thermometer) measure- ments confirm the general flow picture advanced by Falco (1974, 1977, 1980; see also Smith & Abbott 1978) and by Head & Bandyopadhyay (1981; see also Smith & Abbott) on the basis of smoke observations and more limited hot-wire measurements. The probability density function of turbulent-zone lengths in the intermittent region varies rapidly with Reynolds number, supporting the above authors’ finding that the hairpin-vortex ‘typical eddies’ in the viscous superlayer scale on the viscous length ν/uτ, rather than on boundary-layer thickness. However the average turbulent-zone length, deduced as an integral moment of the probability distribution, tends to a constant fraction of the boundary-layer thickness above a momentum-thickness Reynolds number of 5000, which strongly suggests that at high Reynolds numbers the overall shape of the turbulent irrotational interface is controlled by the classical ‘large eddies’ and not by the viscosity-dependent small eddies. The intermittency profile is practically independent of Reynolds number. The second-order structural parameter increases strongly with increasing Reynolds number but the triple-product parameters, with the exception of the u-component skewness, vary only slowly with Reynolds number. This behaviour of the intermittency and velocity statistics is most simply explained by supposing that the lengthscale of the large eddies is nearly independent of Reynolds number while their intensity is somewhat lower at low Reynolds number. ‘Typical eddies’ evidently contribute to the Reynolds stresses at low Reynolds number, but it is probable that the large eddies carry most of the triple products at any Reynolds number. Our results confirm the usual finding that the mixing length and dissipation length parameter increase, while the wake component of the velocity profile decreases, as Reynolds number decreases.

Use of a Generalized Stokes Number to Determine the Aerodynamic Capture Efficiency of Non-Stokesian Particles from a Compressible Gas Flow

Abstract: The aerodynamic capture efficiency of small but nondiffusing particles suspended in a high-speed stream flowing past a target is known to be influenced by parameters governing small particle inertia, departures from the Stokes drag law, and carrier fluid compressibility. By defining an effective Stokes number in terms of the actual (prevailing) particle stopping distance, local fluid viscosity, and inviscid fluid velocity gradient at the target nose, it is shown that these effects are well correlated in terms of a 'standard' (cylindrical collector, Stokes drag, incompressible flow, sq rt Re much greater than 1) capture efficiency curve. Thus, a correlation follows that simplifies aerosol capture calculations in the parameter range already included in previous numerical solutions, allows rational engineering predictions of deposition in situations not previously specifically calculated, and should facilitate the presentation of performance data for gas cleaning equipment and aerosol instruments.

Numerical study of two-dimensional peristaltic flows

Abstract: The Navier–Stokes equations are solved numerically for two-dimensional peristaltic flows by using the finite-difference technique employing the upwind SOR method, and the velocity, pressure and stress fields for various peristaltic flows are obtained. The influences of the magnitudes of wave amplitude, wavelength and Reynolds number on the flow are investigated through numerical calculations, and the results are compared with those of the perturbation analysis. The paper is mainly concerned with elucidating the characteristics of the peristaltic flow at moderate Reynolds numbers where peristaltic pumping has a possibility of engineering application. As a result, it is found that the validity of the perturbation solutions by Jaffrin (1973) and Zien & Ostrach (1970) are restricted within a narrower range than that which they predicted, and that the reflux phenomenon in the flow does change the whole situation according to Reynolds number.

Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer

Abstract: High-frequency fluctuations of temperature and of longitudinal and vertical velocity components have been measured with high-resolution probes in order to test the local-isotropy assumption. The simultaneous measurements of u’, w’, θ’ and the measurements in two space points with various separations in either the longitudinal or transverse directions were made in the large boundary layer (Rλ = 616) of the I.M.S.T. Air-Sea Interaction Simulation Tunnel. There is consistent evidence that the local-isotropy assumption is satisfied by the velocity field at all scales smaller than twenty times the Kolmogorov microscale (η ≈ 0.27 × 10−3 m), i.e. in the dissipative range of scales but not in the expected inertial subrange. The direct comparisons of the lateral and longitudinal temperature autocorrelation and structure functions show that the temperature field does not verify the isotropy assumption at all scales greater thanor equal to 37 and presumably at even smaller scales. This is confirmed by the study of the temperature-increment skewness and flatness factors. The spectral distribution -of the non-zero derivative skewness (S(θ) = +0.9) shows that it is essentially contributed by those scales for which the dynamic field satisfies isotropy.

Curved Ducts With Strong Secondary Motion: Velocity Measurements of Developing Laminar and Turbulent Flow

Abstract: Two orthogonal components of velocity and associated Reynolds stresses are determined in a square-sectioned, 90 degree bend of 2.3 radius ratio by utilizing laser-Doppler velocimetry for Reynolds numbers of 790 and 40,000. Results show that boundary layers at the bend inlet of 0.25 and 0.15 of the hydraulic diameter create secondary velocity maxima of 0.6 and 0.4 of the bulk flow velocity, respectively. It is concluded that the boundary layer thickness is important to the flow development, mainly in the first half of the bend, especially when it is reduced to 0.15 of the hydraulic diameter. Smaller secondary velocities are found for turbulent flow in an identical duct with a radius ratio of 7.0 than in the strongly curved bend, although their effect is more important to the streamwise flow development because of the smaller pressure gradients. In addition, the detail and accuracy of the measurements make them suitable for evaluation of numerical techniques and turbulence models.

Vortex-flow regimes

Abstract: Analysis of a considerable body of new data, based upon flow-visualization experiments, reveals a simple criterion for the occurrence of vortex breakdown at a fixed location in a tube: ReB ∼ Ω-3 R−1, where Ω is the circulation number, R the ratio of the radial to tangential velocities in the inflow region, and ReB the pipe Reynolds number at which vortex breakdown occurs. The constant of proportionality is found to be practically independent both of the pipe flare angle α and the type of breakdown observed (bubble, spiral, etc.) although the latter is shown to depend on ReB. Theoretical support for the experimental results is derived from the analysis of Benjamin (1962) combined with similarity arguments.

An Experimental Study of Dynamic Stall on Advanced Airfoil Sections. Volume 1. Summary of the Experiment.

Abstract: The static and dynamic characteristics of seven helicopter sections and a fixed-wing supercritical airfoil were investigated over a wide range of nominally two dimensional flow conditions, at Mach numbers up to 0.30 and Reynolds numbers up to 4 x 10 to the 6th power. Details of the experiment, estimates of measurement accuracy, and test conditions are described in this volume (the first of three volumes). Representative results are also presented and comparisons are made with data from other sources. The complete results for pressure distributions, forces, pitching moments, and boundary-layer separation and reattachment characteristics are available in graphical form in volumes 2 and 3. The results of the experiment show important differences between airfoils, which would otherwise tend to be masked by differences in wind tunnels, particularly in steady cases. All of the airfoils tested provide significant advantages over the conventional NACA 0012 profile. In general, however, the parameters of the unsteady motion appear to be more important than airfoil shape in determining the dynamic-stall airloads.