Showing papers on "Reynolds number published in 1989"

XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils

Abstract: Calculation procedures for viscous/inviscid analysis and mixed-inverse design of subcritical airfoils are presented. An inviscid linear-vorticity panel method with a Karman-Tsien compressiblity correction is developed for direct and mixed-inverse modes. Source distributions superimposed on the airfoil and wake permit modeling of viscous layer influence on the potential flow. A two-equation lagged dissipation integral method is used to represent the viscous layers. Both laminar and turbulent layers are treated, with an e 9-type amplification formulation determinining the transition point. The boundary layer and transition equations are solved simultaneously with the inviscid flowfield by a global Newton method. The procedure is especially suitable for rapid analysis of low Reynolds number airfoil flows with transitional separation bubbles. Surface pressure distributions and entire polars are calculated and compared with experimental data. Design procedure examples are also presented.

Oblique and Parallel Modes of Vortex Shedding in the Wake of a Circular Cylinder at Low Reynolds Numbers

Abstract: Two fundamental characteristics of the low-Reynolds-number cylinder wake, which have involved considerable debate, are first the existence of discontinuities in the Strouhal-Reynolds number relationship, and secondly the phenomenon of oblique vortex shedding. The present paper shows that both of these characteristics of the wake are directly related to each other, and that both are influenced by the boundary conditions at the ends of the cylinder, even for spans of hundreds of diameters in length. It is found that a Strouhal discontinuity exists, which is not due to any of the previously proposed mechanisms, but instead is caused by a transition from one oblique shedding mode to another oblique mode. This transition is explained by a change from one mode where the central flow over the span matches the end boundary conditions to one where the central flow is unable to match the end conditions. In the latter case, quasi-periodic spectra of the velocity fluctuations appear; these are due to the presence of spanwise cells of different frequency. During periods when vortices in neighbouring cells move out of phase with each other, ‘vortex dislocations’ are observed, and are associated with rather complex vortex linking between the cells. However, by manipulating the end boundary conditions, parallel shedding can be induced, which then results in a completely continuous Strouhal curve. It is also universal in the sense that the oblique-shedding Strouhal data (S_θ) can be collapsed onto the parallel-shedding Strouhal curve (S_0) by the transformation, S_0 = S_θ/cosθ, where θ is the angle of oblique shedding. Close agreement between measurements in two distinctly different facilities confirms the continuous and universal nature of this Strouhal curve. It is believed that the case of parallel shedding represents truly two-dimensional shedding, and a comparison of Strouhal frequency data is made with several two-dimensional numerical simulations, yielding a large disparity which is not clearly understood. The oblique and parallel modes of vortex shedding are both intrinsic to the flow over a cylinder, and are simply solutions to different problems, because the boundary conditions are different in each case.

Turbulent oscillatory boundary layers at high Reynolds numbers

Abstract: This study deals with turbulent oscillatory boundary-layer flows over both smooth and rough beds. The free-stream flow is a purely oscillating flow with sinusoidal velocity variation. Mean and turbulence properties were measured mainly in two directions, namely in the streamwise direction and in the direction perpendicular to the bed. Some measurements were made also in the transverse direction. The measurements were carried out up to Re = 6 × 106 over a mirror-shine smooth bed and over rough beds with various values of the parameter a/ks covering the range from approximately 400 to 3700, a being the amplitude of the oscillatory free-stream flow and ks the Nikuradse's equivalent sand roughness. For smooth-bed boundary-layer flows, the effect of Re is discussed in greater detail. It is demonstrated that the boundary-layer properties change markedly with Re. For rough-bed boundary-layer flows, the effect of the parameter a/ks is examined, at large values (O(103)) in combination with large Re.

Reynolds-number effects on the structure of a turbulent channel flow

Abstract: A high resolution, two component laser-Doppler anemometer has been used for turbulence measurements at a high data rate in a channel flow of water. Measurements of the velocity components in the stream direction and in a direction normal to the wall are reported over the Reynolds number range of 3000–40000. The combination of high spatial resolution and high data rates enabled accurate reconstruction of time dependent velocity traces. Long-time statistical averages of these signals clearly show that profiles of the dimensionless turbulence quantities such as turbulence intensities and Reynolds stress are strongly Reynolds-number dependent over a large part of the channel flow. For instance, in the Reynolds-number range of this investigation, it is shown that the fluctuating turbulence quantities do not scale with wall variables even as close as 15 viscous lengths from the wall. The velocity traces and associated power spectra exposed two phenomena which may explain the Reynolds number dependencies.

Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid

Abstract: In this paper we examine some general features of the time-dependent dynamics of drop deformation and breakup at low Reynolds numbers. The first aspect of our study is a detailed numerical investigation of the ‘end-pinching’ behaviour reported in a previous experimental study. The numerics illustrate the effects of viscosity ratio and initial drop shape on the relaxation and/or breakup of highly elongated droplets in an otherwise quiescent fluid. In addition, the numerical procedure is used to study the simultaneous development of capillary-wave instabilities at the fluid-fluid interface of a very long, cylindrically shaped droplet with bulbous ends. Initially small disturbances evolve to finite amplitude and produce very regular drop breakup. The formation of satellite droplets, a nonlinear phenomenon, is also observed.

Geometry of self-propulsion at low Reynolds number

Abstract: The problem of swimming at low Reynolds number is formulated in terms of a gauge field on the space of shapes. Effective methods for computing this field, by solving a linear boundary-value problem, are described. We employ conformal-mapping techniques to calculate swimming motions for cylinders with a variety of crosssections. We also determine the net translationl motion due to arbitrary infinitesimal deformations of a sphere.

Molecular Dynamics of Fluid Flow at Solid Surfaces

Abstract: We use molecular dynamics techniques to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids we find the no-slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow-independent slip-length boundary condition. We examine the trajectories of individual molecules in Poiseuille flow, and also find that their average behavior is given by Taylor-Aris hydrodynamic dispersion. An immiscible two-fluid system is simulated by a species-dependent intermolecular interaction. We observe a static meniscus whose contact angle agrees with simple estimates and, when motion occurs, velocity- dependent advancing and receding angles. The local velocity field near a moving contact line shows a breakdown of the no-slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan

Three-Dimensional Flows in Complex Geometries with the Lattice Boltzmann Method

Abstract: It is shown that the lattice Boltzmann equation (LBE) for a lattice gas provides a viable numerical method for the study of three-dimensional flows in complex geometries. Numerical results for low Reynolds number flows in a three-dimensional random medium are reported. The Darcy's law is recovered and a preliminary estimation of the permeability presented.

Inertial migration of a sphere in Poiseuille flow

Abstract: The inertial migration of a small sphere in a Poiseuille flow is calculated for the case when the channel Reynolds number is of order unity. The equilibrium position is found to move towards the wall as the Reynolds number increases. The migration velocity is found to increase more slowly than quadratically. These results are compared with the experiments of Segre & Silberberg (1962 a, b).

Direct numerical simulation of stratified homogeneous turbulent shear flows

Abstract: The exact time-dependent three-dimensional Navier-Stokes and temperature equations are integrated numerically to simulate stably stratified homogeneous turbulent shear flows at moderate Reynolds numbers whose horizontal mean velocity and mean temperature have uniform vertical gradients. The method uses shear-periodic boundary conditions and a combination of finite-difference and pseudospectral approximations. The gradient Richardson number Ri is varied between 0 and 1. The simulations start from isotropic Gaussian fields for velocity and temperature both having the same variances. The simulations represent approximately the conditions of the experiment by Komori et al. (1983) who studied stably stratified flows in a water channel (molecular Prandtl number Pr = 5). In these flows internal gravity waves build up, superposed by hot cells leading to a persistent counter-gradient heat-flux (CGHF) in the vertical direction, i.e. heat is transported from lower-temperature to higher-temperature regions. Further, simulations with Pr = 0.7 for air have been carried out in order to investigate the influence of the molecular Prandtl number. In these cases, no persistent CGHF occurred. This confirms our general conclusion that the counter-gradient heat flux develops for strongly stable flows (Ri [approximate] 0.5–1.0) at sufficiently large Prandtl numbers (Pr = 5). The flux is carried by hot ascending, as well as cold descending turbulent cells which form at places where the highest positive and negative temperature fluctuations initially existed. Buoyancy forces suppress vertical motions so that the cells degenerate to two-dimensional fossil turbulence. The counter-gradient heat flux acts to enforce a quasi-static equilibrium between potential and kinetic energy. Previously derived turbulence closure models for the pressure-strain and pressure-temperature gradients in the equations for the Reynolds stress and turbulent heat flux are tested for moderate-Reynolds-number flows with strongly stable stratification (Ri = 1). These models overestimate the turbulent interactions and underestimate the buoyancy contributions. The dissipative timescale ratio for stably stratified turbulence is a strong function of the Richardson number and is inversely proportional to the molecular Prandtl number of the fluid.

Reynolds number and end‐wall effects on a lid‐driven cavity flow

Abstract: A series of experiments has been conducted in a lid‐driven cavity of square cross section (depth=width=150 mm) for Reynolds numbers (Re, based on lid speed and cavity width) between 3200 and 10 000, and spanwise aspect ratios (SAR) between 0.25:1 and 1:1. Flow visualization using polystyrene beads and two‐dimensional laser‐Doppler anemometer (LDA) measurements have shed new light on the momentum transfer processes within the cavity. This paper focuses on the variation, with Re and SAR, of the mean and the rms velocities profiles, as well as the ∼(U’V’) profile, along the horizontal and vertical centerlines in the symmetry plane. In addition, the contribution of the large‐scale ‘‘organized structures,’’ and the high‐frequency ‘‘turbulent’’ velocity fluctuations to the total rms is examined. At low Re, the organized structures account for most of the energy contained in the flow irrespective of SAR. As the Re increases, however, so does the energy content of the higher frequency fluctuations. This trend is ...

The turbulent flow field around a circular cylinder

Abstract: The flow field around a circular cylinder mounted vertically on a flat bottom has been investigated experimentally. This type of flow occurs in several technical applications, e.g. local scouring around bridge piers. Hydrogen bubble flow visualization was carried out for Reynolds numbers ranging from 6,600 to 65,000. The main flow characteristic upstream of the cylinder is a system of horse-shoe vortices which are shed quasi-periodically. The number of vortices depends on Reynolds number. The vortex system was found to be independent of the vortices that are shed in the wake of the cylinder. The topology of the separated flow contains several separation and attachment lines which are Reynolds number dependent. In the wake region different flow patterns exist for each constant Reynolds number.

The lubrication force between two viscous drops

Abstract: The hydrodynamic force resisting the relative motion of two unequal drops moving along their line of centers is determined for Stokes flow conditions. The drops are assumed to be in near‐contact and to have sufficiently high interfacial tension that they remain spherical. The squeeze flow in the narrow gap between the drops is analyzed using lubrication theory, and the flow within the drops near the axis of symmetry is analyzed using a boundary integral technique. The two flows are coupled through the nonzero tangential stress and velocity at the interface. Depending on the ratio of drop viscosity to that of the continuous phase, and also on the ratio of the distance between the drops to their reduced radius, three possible flow situations arise, corresponding to nearly rigid drops, drops with partially mobile interfaces, and drops with fully mobile interfaces. The results for the resistance functions are in good agreement with an earlier series solution using bispherical coordinates. These results have important implications for droplet collisions and coalescence.

Frequency selection and asymptotic states in laminar wakes

Abstract: A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately.It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.

Time-dependent kinematic dynamos with stationary flows

Abstract: Numerical solutions to the magnetic induction equation in a sphere have been obtained for a number of stationary velocity models. By searching for non-steady magnetic fields and in some circumstances showing that all magnetic field modes decay, the inability of several earlier researchers to find convergent steady solutions is explained. Results of previous authors are generally confirmed, but also extended to cover non-steady fields, different values of magnetic Reynolds number and other parameters, and higher truncation limits. Some non-decaying fields are found where only decaying or non-convergent results have previously been reported. Two flows $\epsilon s^0\_2 + t^0\_2$ and $\epsilon s^0\_2 + t^0\_1$, each consisting of two very simple axisymmetric rolls are seen to sustain growing fields provided that (i) the magnetic Reynolds number R and the poloidal to toroidal flow ratio $\epsilon$ are of appropriate magnitudes, and (ii) the meridional s$^0\_2$ flow is directed inwards along the equatorial plane and out towards the poles. An even simpler axisymmetric single roll flow $\epsilon s^0\_1 + t^0_1$ is also seen to support growing fields for appropriate $\epsilon$ and R. These simple flows dispel the somewhat prevalent belief that dynamo maintenance relies on the supporting flow being complex, and having length scale significantly less than that of the conducting fluid volume.

Lubricated pipelining: Stability of core-annular flow

Abstract: The stability of core-annular flow (CAF) in pipes is analysed using the linear theory of stability. Attention is confined to the potentially stable case of lubricated pipelining with the less viscous liquid, say water, in the annulus. The effects of surface tension and density are included, but gravity is excluded. We find upper and lower branches of the neutral curve in a Reynolds number (ℝ) vs. wavenumber (α) plane. A window of parameters is identified in which CAF is stable to small disturbances. When ℝ is below the lower critical value, CAF is destabilized by surface tension and long waves break up into slugs and bubbles. The sizes of slugs and bubbles of oil in water observed by Charles, Govier & Hodgson (1961) are given by the wavelength of the fastest growing long wave. This long-wave instability is a capillary instability, modified by shear, which reduces to Rayleigh's instability in the appropriate limit. At higher ℝ, the capillary instability is stabilized by shear. At yet higher ℝ, above the upper critical value, the flow is unstable to generally shorter waves which leads to emulsification, water droplets in oil. The theory agrees with experiments. The analysis seems to be applicable to the design of lubricated pipelines; for example, there is an optimum viscosity ratio for stability, greater stability can be obtained by using heavy liquid as a lubricant when the flow is unstable to capillary modes on the lower branch and by using light liquids when the flow is unstable to emulsifying disturbances on the upper branch.

Turbulent free shear layer mixing and combustion

Abstract: : Some experimental data on turbulent free-shear-layer growth, mixing, and chemical reactions are reviewed. The dependence of these phenomena on such fluid and flow parameters as Reynolds number, Schmidt number, and Mach number are discussed, with the aid of some direct consequences deducible from the large-scale organization of the flow as well as from some recent models. The mixing of two or more fluids that are entrained into a turbulent region is an important process from both a scientific and an applications vantage point. Species can be transported by turbulence to produce a more uniform distribution than some initial mean profile. This process is sometimes also referred to as mixing, without regard to whether the transported species are mixed on a molecular scale or not. If the issue of mixing arises in the context of chemical reactions and combustion, however, we recognize that only fluid mixed on a molecular scale can contribute to chemical product formation and associated heat release. The discussion in this paper will be limited to molecular mixing.

Heat transfer in rotating passages with smooth walls and radial outward flow

Abstract: Experiments were conducted to determine the effects of rotation on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a smooth wall, large-scale heat transfer model. The objective was to obtain the heat transfer data base required to develop heat transfer correlations and to assess computational fluid dynamic techniques for rotating coolant passages. An analysis of the governing equations showed that four parameters influence the heat transfer in rotating passages (coolant density ratio, Rossby number, Reynolds number, and radius ratio). These four parameters were varied over ranges that exceed the ranges of current open literature results, but that are typical of current and advanced gas turbine engine operating conditions. Rotation affected the heat transfer coefficients differently for different locations in the coolant passage. For example, heat transfer at some locations increased with rotation, but decreased and then increased again at other locations. Heat transfer coefficients varied by as much as a factor of five between the leading and trailing surfaces for the same test condition and streamwise location. Comparisons with previous results are presented.

Pulsatile flow through constricted tubes: an experimental investigation using photochromic tracer methods

Abstract: A photochromic tracer method has been used to record pulsatile flow velocity profiles simultaneously at three axial locations along a flow channel. Two major advantages of this multiple-trace method are that it enables velocity data to be acquired in an efficient non-invasive manner and that it provides a detailed description of the spatial relationship of the flow field. The latter is found to be particularly useful in the investigation of transitional type flows; for example, in describing coherent flow structures. Studies of the flow patterns in tubes with mild to moderate degrees of vessel constriction were performed using a 2.9 Hz sinusoidal flow superimposed on a steady flow (frequency parameter of 7.5; mean and modulation Reynolds numbers of 575 and 360, respectively). With mild constrictions (< 50% area reduction), isolated regions of vortical and helical structures were observed primarily during the deceleration phase of the flow cycle and in the vicinity of the reattachment point. As expected, these effects were accentuated when the constriction was asymmetric. For moderate constrictions (50%–80%), transition to turbulence was triggered just before peak flow through the breakdown of waves and streamwise vortices that were shed in the high-shear layer. During this vortex generation phase of the flow cycle, the wall shear stress fluctuated quite intensely, especially in the vicinity of the reattachment point, and its instantaneous value increased by at least a factor of eight. Such detailed descriptions of the transition to turbulence and of the spatial and temporal variation of the wall shear stress, particularly near the reattachment point, have not been previously reported for pulsatile flow through constricted tubes. The observed wall shear stress variations support a proposal by Mao & Hanratty (1986) of an interaction of the imposed flow oscillation with the turbulent fluctuations within the viscous sublayer.

The relationship between surface-renewal and bursting motions in an open-channel flow

Abstract: Surface-renewal motions in the interfacial region below a gas-liquid interface were experimentally investigated in relation to bursting motions in the wall region. To estimate the frequency of the appearance of surface-renewal eddies, mass-transport experiments with methylene-blue solution, together with velocity measurements, were done in an open-channel flow. The instantaneous concentration of methylene-blue tracer emitted from a point source positioned in the buffer layer was measured at the free surface downstream from the source by an optical probe. Instantaneous streamwise velocity was measured using a laser-Doppler velocimeter at a position in the buffer region. Frequencies of both surface-renewal and bursting events were computed from these concentration and velocity signals using a conditional-averaging method. In order to clarify whether the surface-renewal eddies actually dominate mass transfer across the gas-liquid interface, gas-absorption experiments were added. Carbon dioxide was absorbed into the water flow across the calm free surface and its mass-transfer coefficient on the liquid side was measured under the same flow conditions as used in the above mass-transport experiments. The results show that the surface-renewal motions originate in the bursting motions which vigorously occur in the buffer region. That is, the decelerated fluid which is strongly lifted towards the outer layer by bursting almost always arrives at the free surface and renews the free surface. The frequency of the surface renewal, as well as the bursting frequency, is uniquely determined by the wall variables or the outer-flow variables and the Reynolds number. Mass transfer across the gas-liquid interface is dominated by the large-scale surface-renewal eddies, and the mass-transfer coefficient on the liquid side is proportional to the square-root of the surface-renewal frequency.

The Dean equations extended to a helical pipe flow

Abstract: In this paper the Dean (1928) equations are extended to the case of a helical pipe flow, and it is shown that they depend not only on the Dean number K but also on a new parameter λ/[Rscr ] where λ is the ratio of the torsion τ to the curvature κ of the pipe axis and [Rscr ] the Reynolds number referred in the usual way to the pipe radius a and to the equivalent maximum speed in a straight pipe under the same axial pressure gradient. The fact that the torsion has no first-order effect on the flow is confirmed, but it is shown that this is peculiar to a circular cross-section. In the case of an elliptical cross-section there is a first-order effect of the torsion on the secondary flow, and in the limit λ/[Rscr ] → ∞ (twisted pipes, provided only with torsion), the first-order ‘displacement’ effect of the walls on the secondary flow, analysed in detail by Choi (1988), is recovered.Different systems of coordinates and different orders of approximations have recently been adopted in the study of the flow in a helical pipe. Thus comparisons between the equations and the results presented in different reports are in some cases difficult and uneasy. In this paper the extended Dean equations for a helical pipe flow recently derived by Kao (1987) are converted to a simpler form by introducing an appropriate modified stream function, and their equivalence with the present set of equations is recovered. Finally, the first-order equivalence of this set of equations with the equations obtained by Murata et al. (1981) is discussed.

Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers

Abstract: Numerical solutions have been obtained for steady streaming flow past an axisymmetric drop over a wide range of Reynolds numbers (0.005 [les ] Re [les ] 250), Weber numbers (0.005 [les ] We [les ] 14), viscosity ratios (0.001 [les ] λ [les ] 1000), and density ratios (0.001 [les ] ζ [les ] 1000). Our results indicate that at lower Reynolds numbers the shape of the drop tends toward a spherical cap with increasing We , but at higher Re the body becomes more disk shaped with increasing We . Unlike the recirculating wake behind an inviscid bubble or solid particle, the eddy behind a drop is detached from the interface. The size of the eddy and the separation distance from the drop depend on the four dimensionless parameters of the problem. The motion of the fluid inside the drop appears to control the behaviour of the external flow near the body, and even for cases when λ and ζ [Lt ] 1 (a ‘real’ bubble), a recirculating wake remains unattached.

Mixing, entrainment and fractal dimensions of surfaces in turbulent flows

Abstract: Some basic thoughts are set down on the relation between the fractal dimension of various surfaces in turbulent flows, and the practically important processes of mixing between two streams (reacting or otherwise) separated by a convoluted surface, as well as of entrainment of irrotational flow by a turbulent stream. An expression based on heuristic arguments is derived for the flux of transportable properties (such as mass, momentum, and energy) across surfaces, and a prediction made on this basis for the fractal dimension of surfaces in fully turbulent flows is shown to be in essential agreement with measurements. It is further shown that this prediction remains robust when corrected for the non-uniform effects along the surface. A related prediction concerning the dependence of mixing on the Reynolds number and the fractal dimension of the surface is substantiated, in the developing as well as the fully developed states, by independent measurements of both the fractal dimension and the amount of mixing between reactants in a temporally evolving countercurrent shear flow.

Particle dispersion in a turbulent, plane, free shear layer

Abstract: The particle dispersion mechanisms in an inhomogeneous, anisotropic, high Reynolds number, turbulent free shear flow are presented. Flow visualization, as well as laser attenuation and diffraction techniques, are used to characterize the evolution of the flow. It is shown that, at each downstream location, the spectral response of the particles to the coherent velocity field that develops in the layer as a result of a Kelvin–Helmholtz type of instability leads to a selective dispersion of the particles across the mixing layer. Furthermore, this particle dispersion layer is shown to be composed of a central core region, characterized by a small mean particle size and two external sublayers with considerably larger mean particle sizes. Finally, the experimental results suggest the dominant role played by the coherent, large scale vortical structure in the dispersion of the particles. Scaling arguments and simplified flow models supporting this hypothesis are also presented.

Numerical simulation of the absolutely and convectively unstable wake

Abstract: The development of the wake behind a flat plate at a supercritical Reynolds number (Re = 200, based on the plate thickness and free-stream velocity) is simulated numerically by solving the two-dimensional unsteady Navier-Stokes equations with a finite-difference Galerkin method. The intermediate quasi-steady state of the wake development is investigated with an Orr-Sommerfeld analysis for complex frequencies and wavenumbers. Based on this linear, local stability analysis it can be shown that the quasi-steady state can be divided into regions of local absolute and local convective instability. One goal of this work is to determine the validity of the linear, local stability theory by comparing the predictions of the Orr-Sommerfeld analysis to the results of a numerical wake simulation. Based on this comparison, for the investigated flow field, the frequency selection mechanisms recently proposed by several authors are discussed. Base bleed is applied in the numerical simulation of the wake as a control parameter, following the well-known experimental result that sufficient base bleed reduces the strength of the vortex street (see e.g. Wood 1964). It can be shown that from a critical base-bleed ratio, disturbances grow no longer in time but only in space, indicating a change of the global stability characteristics. In addition the linear, local stability analysis is used to investigate to what extent this global transition can be described.

On mixing in an elliptic turbulent free jet

Abstract: This paper documents the results of an experimental study of the mean flow and turbulence characteristics of a turbulent free jet of air issuing, into still air surroundings, from a sharp‐edged elliptical slot of aspect ratio 5. The measured quantities, which were obtained with hot‐wire anemometry as a flow diagnostic tool, include the mean streamwise velocity, the turbulence intensities, the Reynolds shear stress, the transport of some of the Reynolds stresses, and the flatness and skewness of the distributions of the streamwise velocity fluctuations. Two switches of the major and minor axes were observed and it was found that the jet attains an axisymmetric shape at about 30 equivalent slot diameters downstream of the exit plane. Also, the jet, compared to a turbulent free jet from a sharp‐edged round slot of the same exit area, was found to entrain ambient fluid faster both in the near and far flow fields.

Renormalization group formulation of large-eddy simulations

Abstract: Perhaps the most distinguishing characteristic of high Reynolds number turbulent flows is their large range of excited space and time scales. In homogeneous turbulence, dissipation-scale eddies are of order R3/4 times smaller than energy-containing eddies, where R is the Reynolds number. In order to solve the Navier-Stokes equations accurately for such a turbulent flow, it is necessary to retain order (R3/4)3 spatial degrees of freedom. Also, since the time scale for significant evolution of homogeneous turbulence is of the order of the turnover time of an energy containing eddy, it is necessary to perform order R3/4 time steps to calculate for a significant evolution time of the flow. Even if these calculations require only O(1) arithmetic operations per degree of freedom per time step, the total computational work involved would be order R3, while the computer storage requirement would be R9/4. In this case, doubling the Reynolds number would require an order of magnitude improvement in computer capability. With this kind of operation and storage count, it is unlikely that forseeable advances in computers will allow the full numerical simulation of turbulent flows at Reynolds numbers much larger than Rλ = 0(100) already achieved (see BRACHET et al. [2]).