Showing papers on "Reynolds number published in 1984"

Vortex shedding from oscillating bluff bodies

Abstract: When placed ih a fluid stream, some bodies generate separated flow over a substantial proportion of their surface and hence can be classified as bluff. On sharp-edged bluff bodies, separation is fixed at the salient edges, whereas on bluff bodies with continuous surface curvature the location of separation depends both on the shape of the body and the state of the boundary layer. At low Reynolds numbers, when separation first occurs, the flow around a bluff body remains stable, but as the Reynolds number is increased a critical value is reached beyond which instabilities develop. These instabilities can lead to organized unsteady wake motion, dis­ organized motion, or a combination of both. Regular vortex shedding, the subject of this article, is a dominant feature of two-dimensional bluff-body wakes and is present irrespective of whether the separating boundary layers are laminar or turbulent. It has been the subject of research for more than a century, and many hundreds of papers have been written. In recent years vortex shedding has been the topic of Euromech meetings reported on by Mair & Maull (1971) and Bearman & Graham (1980), and a comprehensive review has been undertaken by Berger & Wille (1972). Vortex shedding and general wake turbulence induce fluctuating pres­ sures on the surface of the generating bluff body, and if the body is flexible this can cause oscillations. Oscillations excited by vortex shedding are usually in a direction normal to that of the free stream, and amplitudes as large as 1.5 to 2 body diameters may be recorded. In addition to the generating body, any other bodies in its wake may be forced into oscillation. Broad-band force fluctuations, induced by turbulence produced in the flow around a bluff body, rarely lead to oscillations as severe as those caused by vortex shedding. Some form of aerodynamic instability, such that move-

Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow

Abstract: Two unequal rigid spheres are immersed in unbounded fluid and are acted on by externally applied forces and couples. The Reynolds number of the flow around them is assumed to be small, with the consequence that the hydrodynamic interactions between the spheres can be described by a set of linear relations between, on the one hand, the forces and couples exerted by the spheres on the fluid and, on the other, the translational and rotational velocities of the spheres. These relations may be represented completely by either a set of 10 resistance functions or a set of 10 mobility functions. When non-dimensionalized, each function depends on two variables, the non-dimensionalized centre-to-centre separation s and the ratio of the spheres’ radii λ. Two expressions are given for each function, one a power series in s−1 and the other an asymptotic expression valid when the spheres are close to touching.

Numerical calculation of the fluid dynamics of drop-on-demand jets

Abstract: A numerical method that makes use of the complete incompressible flow equations with a free surface is discussed and used to study an impulsively driven laminar jet. Flow behavior dependence upon fluid properties (characterized by a Reynolds number over Weber number nondimensionalization) is compared jor drop integrity purposes. Several variations of square wave pressure history applied at a nozzle inlet are discussed in relation to drop velocities produced and structure of ejected drops. Timewise development of flow both interior and exterior to the nozzle is illustrated through computed contour sequences.

Observations of the flow produced in a cylindrical container by a rotating endwall

Abstract: Observations made using the laser-induced fluorescence technique are presented of the steady swirling flow produced in a closed cylindrical container completely full of fluid (a glycerine/water mixture for the experiments reported here) by rotating one endwall. The flow behaviour is determined by two parameters: the height-to-radius ratioH/R and a rotation Reynolds number ΩR 2/ν. In an earlier study, Vogel (1968) defined the stability limit in the (H/R, Ω R2/ν) plane within which a vortex breakdown bubble occurred on the axis of symmetry. The results of Vogel's investigation are confirmed and extended by the present work. In particular, it is found that asH/R is increased two further stability limits can be determined within which two and ultimately three breakdown bubbles occur in succession. It is also found that there is a Reynolds number boundary above which the flow is oscillatory and at even higher Reynolds number the flow becomes turbulent. Until well into the unsteady-flow domain, the flow shows negligible departure from axisymmetry.

On the scaling of the turbulence energy dissipation rate

Abstract: From an examination of all data to date on the dissipation of turbulent energy in grid turbulence, it is concluded that, for square‐mesh configuration, the ratio of the time scale characteristic of dissipation rate to that characteristic of energy‐containing eddies is a constant independent of Reynolds number, for microscale Reynolds numbers in excess of about 50. Insufficient data available for other grid configurations suggest a possibility that the ratio could assume different numerical values for different configurations. This persistent effect of initial conditions on the time scale ratio is further illustrated by reference to the jet‐grid data of Gad‐el‐Hak and Corrsin.

Heat Transfer and Friction in Channels With Two Opposite Rib-Roughened Walls

Abstract: Etude experimentale d'un ecoulement d'air turbulent dans des conduites carrees avec 2 parois opposees a nervures en vue de determiner l'influence des rapports pas/hauteur des nervures et hauteur nervure/diametre equivalent sur le coefficient de frottement et les coefficients de transfert de chaleur pour un nombre de Reynolds variant de 7000 a 90000

A New Look at Porous Media Fluid Mechanics — Darcy to Turbulent

Abstract: The purpose of this review paper is to present the results of laser anemometry and flow visualization studies of the flow of liquids in porous structures. Three dimensional velocity profiles and movies of dye streaklines will be shown. The porous media consisted of plexiglas spheres in a hexagonal packing and glass and plexiglas rods arranged in a complex, fixed three dimensional geometry. The liquids used were water, silicone oils, Sohio MDI-57 oil and mineral seal oil. The Reynolds number based on average pore size and average pore velocity ranged from 0.16 to 700.

Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid

Abstract: In this paper numerical results are presented for the buoyancy-driven rise of a deformable bubble through an unbounded quiescent fluid. Complete solutions, including the bubble shape, are obtained for Reynolds numbers in the range 1 [less-than-or-equal] R [less-than-or-equal] 200 and for Weber numbers up to 20. For Reynolds numbers R [less-than-or-equal] 20 the shape of the bubble changes from nearly spherical to oblate-ellipsoidal to spherical-cap depending on Weber number; at higher Reynolds numbers ‘disk-like’ and ‘saucer-like’ shapes appear at W = O(10). The present results show clearly that flow separation may occur at a smooth free surface at intermediate Reynolds numbers; this fact suggests a qualitative explanation of the often-observed irregular (zigzag or helical) paths of rising bubbles.

Island wakes in shallow coastal waters

Abstract: Rattray Island, northeast Australia, is 15 km long, 300 m wide, and lies in well-mixed water approximately 25 m deep Its long axis is inclined at about 60° into the direction of the dominant semidiurnal tidal current The length of the wake in the lee of the island, as documented by aerial photographs and satellite imagery, appears to equal that of the wake behind a flat plate in a two-dimensional flow at a Reynolds number of about 10 However, current metering, drogues measurements, and temperature mapping indicate internal wake velocities much greater than would be consistent with such a simple low Reynolds number model Further, estimates of the turbulent eddy coefficient suggest an effective Reynolds number more in the vicinity of 103 To reconcile these observational differences and to explain the observed upwelling in the core of the wake, an Ekman pumping model is proposed It is postulated that the Ekman benthic boundary layer driven by rotation in the wake allows the vertical vorticity introduced into the water at the tip of the island at the point of separation, to be negated by the vorticity of opposite sign introduced at the bottom Further, it is shown that a large fraction of the kinetic energy of the upstream flow facing the island is used to drive the wake eddies, leading to the conclusions that the trapping of water in the lee of islands greatly increases head losses on continental shelves with numerous islands, coral reefs, and rock outcrops

A numerical-experimental study of confined flow around rectangular cylinders

Abstract: A previous numerical study by Davis and Moore of vortex shedding from rectangles in infinite domains is extended to include the effects of confining walls. The major changes to the numerical modeling are the addition of a direct solver for the pressure equation and the use of an infinite‐to‐finite mapping downstream of the rectangle. The parameters in the problem are now Reynolds number, rectangle aspect ratio, blockage ratio, and upstream velocity profile. As each of these is varied, the effects upon the forces acting on the rectangle and the structure of the wake are discussed. Streakline plots composed of multishaped passive marker particles provide a clear visualization of the vortices. These plots are compared with smoke‐wire photographs taken from a wind tunnel test. Strouhal numbers obtained both computationally and experimentally are compared for two values of the blockage ratio. Moving recirculation zones which appear between the wake and the walls are discussed.

The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices

Abstract: … in hydrodynamic turbulence … the fate of vortices extending in the direction of motion is of great importance (J. M. Burgers 1948).We examine an elementary model of the dynamics of streamwise vorticity in a plane mixing layer. We assume that the vorticity is unidirectional and subjected to a two-dimensional spatially uniform strain, positive along the direction of vorticity. The equations of motion are solved numerically with initial conditions corresponding to a strain-viscous-diffusion balance for a layer with a sinusoidal variation of vorticity. The numerical results are interpreted physically and compared to those of an asymptotic analysis of the same problem by Neu. It is found that strained vortex sheets are fundamentally unstable unless their local strength nowhere exceeds a constant (somewhat larger than 2) times the square root of the product of strain and viscosity. The instability manifests itself by the spanwise redistribution of the vorticity towards the regions of maximum strength. This is accompanied by the local rotation of the layer and the intensification of the vorticity. The end result of this evolution is a set of discrete round vortices whose structure is well approximated by that of axially symmetric vortices in an axially symmetric strain. The phenomenon can proceed (possibly simultaneously) on two separate lengthscales and with two correspondingly different timescales. The first lengthscale is the initial spanwise extent of vorticity of a given sign. The second, relevant to initially thin and spanwise slowly varying vortex layers, is proportional to the layer thickness. The two types of vorticity focusing or collapse are studied separately. The effect of the first on the diffusion rate of a scalar across the layer is calculated. The second is examined in detail for a spanwise-uniform layer: First we solve the eigenvalue problem for infinitesimal perturbations and then use the eigenfunctions as initial conditions for a numerical finite-differences solution. We find that the initial instability is similar to that of unstrained layers, in that roll-up and pairings also follow. However, at each stage a strain-diffusion balance eventually imposes the same cross-sectional lengthscale and each of these events leads to an intensification of the local value of the vorticity.The parameters upon which collapse and its timescale depend are related to those which are known to govern a mixing layer. The results suggest that the conditions for collapse of strained vortex sheets into concentrated round vortices are easily met in a mixing layer, even at low Reynolds numbers, so that these structures whose size is the Taylor microscale are far more plausibly typical than are vortex sheets on that scale. We found that they raise significantly the diffusion rate of scalar attributes by enhancing the rate of growth of material surfaces across which diffusion takes place. Finally, experimental methods that rely on the visualization of the gradient of scalar concentration are shown to be unable to reveal the presence of streamwise vorticity unless that vorticity has already gathered into concentrated vortex tubes.

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.

Reduction of Turbulent Skin Friction by Microbubbles

Abstract: Measurements of the effect of microbubbles on a zero pressure gradient turbulent boundary layer generated on the test section wall of a water tunnel are described Microbubbles are created by injecting air through a 05 μm sintered stainless steel plate immediately upstream of a floating element drag balance At the downstream edge of the balance the length Reynolds number is as high as ten million Integrated skin friction reduction of greater than 80% is observed The drag balance results are confirmed by measurements with a surface hot‐film probe For the case in which buoyancy tends to keep the bubbles in the boundary layer, the skin friction data are shown to collapse when plotted against the ratio of air to water volume flow rate The effects of buoyancy on skin friction reduction are also documented

Mixing and combustion with low heat release in a turbulent shear layer

Abstract: Turbulent mixing and combustion are investigated in a gaseous shear layer formed between two streams: one containing a low concentration of hydrogen in nitrogen and the other containing a low concentration of fluorine in nitrogen. The resulting temperature field is measured simultaneously at eight points across the width of the layer using fast-response cold-wire thermometry. The results show the presence of large, hot structures separated by tongues of cool fluid that enter the layer from either side. The usual bell-shaped mean-temperature profiles therefore result from a duty cycle whereby a fixed probe sees alternating hot and cool fluid, which results in the local mean. The adiabatic flame temperature is not achieved in the mean, at any location across the layer. For fixed velocities, it is found that, in general, two different mean-temperature profiles result from a given pair of reactant compositions if the sides of the layer on which they are carried are exchanged (‘flipped’). This finding is a direct consequence of the asymmetric entrainment of fluid into the layer. Results are compared with the predictions of Konrad and discussed in the context of the Broadwell–Breidenthal model. By comparison with the liquid result of Breidenthal, the amount of product formed in the layer at high Reynolds number is found to be dependent upon the Schmidt number. Results for a helium–nitrogen layer are discussed briefly.

Turbulent Burning Velocities and Flame Straining in Explosions

Abstract: Turbulent burning velocities have been measured in an explosion bomb equipped with four high speed fans. Turbulent parameters were measured by laser doppler anemometry. The turbulent Reynolds numbers were significantly higher than in most previous measurements and high rates of strain were achieved until, ultimately, several of the flames quenched. Results are presented in terms of previously used dimensionless parameters plus a Lewis number and a dimensionless activation energy. The two-eddy theory of burning can allow for flame straining reductions in laminar burning velocity and experimental values of u t / u 1 were compared with those from such a theory.

High Marangoni number convection in a square cavity

Abstract: Steady thermocapillary flow is examined in a square two‐dimensional cavity with a single free surface and differentially heated side walls. The numerical solutions are obtained with a finite difference method applied to a streamfunction‐temperature formulation. This work investigates the Prandtl number dependence, structure, and stability of high Marangoni number flow. It is found that the character of thermocapillary flow is highly sensitive to the value of the Prandtl number over a range of Marangoni numbers exceeding 1×105 for 1≤Pr≤50, the magnitude of the flow showing nonmonotonic dependence on the Marangoni number for Pr≤∼10. A complete structural analogy is observed between flow in a cavity driven by a moving lid and thermocapillary flow in the boundary layer limit, and it is found that all the solutions, spanning a wide range of Marangoni and Prandtl numbers, are linearly stable to a restricted class of disturbances.

Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave

Abstract: We use a numerical method that was described in Part 1 (Marcus 1984 a ) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow. We compute several stable axisymmetric Taylor-vortex equilibria and several stable non-axisymmetric wavy-vortex flows that correspond to one travelling wave. For each flow we compute the energy, angular momentum, torque, wave speed, energy dissipation rate, enstrophy, and energy and enstrophy spectra. We also plot several 2-dimensional projections of the velocity field. Using the results of the numerical calculations, we conjecture that the travelling waves are a secondary instability caused by the strong radial motion in the outflow boundaries of the Taylor vortices and are not shear instabilities associated with inflection points of the azimuthal flow. We demonstrate numerically that, at the critical Reynolds number where Taylor-vortex flow becomes unstable to wavy-vortex flow, the speed of the travelling wave is equal to the azimuthal angular velocity of the fluid at the centre of the Taylor vortices. For Reynolds numbers larger than the critical value, the travelling waves have their maximum amplitude at the comoving surface, where the comoving surface is defined to be the surface of fluid that has the same azimuthal velocity as the velocity of the travelling wave. We propose a model that explains the numerically discovered fact that both Taylor-vortex flow and the one-travelling-wave flow have exponential energy spectra such that In [E(k)] ∝ k 1 , where k is the Fourier harmonic number in the axial direction.

A comparison of vaporization models in spray calculations

Abstract: : The effects of different gas- and liquid-phase models on the vaporization behavior of a single-component isolated droplet are studied for both stagnant and convection situations in a high-temperature gas environment. In conjunction with four different liquid-phase models, namely, d2 law, infinite conductivity, diffusion limit, and internal vortex circulation, the different gas-phase models include a spherically symmetric model in the stagnant case and Ranz-Marshall correlation plus two other axisymmetric models in the convective case. A critical comparison of all these models is made. The use of these models in a spray situation is examined. A transient one-dimensional flow of an air- fuel droplet mixture is considered. It is shown that the fuel vapor mass fraction can be very sensitive to the particular liquid- and gas-phase models. The spherically symmetric conduction or diffusion limit model is recommended when the droplet Reynolds number is negligible compared to unity, while the simplified vortex model accounting for internal circulation is suggested when the droplet Reynolds number is large compared to unity. Keywords include: Spray; Droplet; Evaporation; Combustion; Modeling.

Small-scale structure of the Taylor-Green vortex

Abstract: The dynamics of both the inviscid and viscous Taylor-Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier-Stokes equations (with up to 2563 modes) and by power-series analysis in time. The inviscid dynamics are strongly influenced by symmetries which confine the flow to an impermeable box with stress-free boundaries. There is an early stage during which the flow is strongly anisotropic with well-organized (laminar) small-scale excitation in the form of vortex sheets located near the walls of this box. The flow is smooth but has complex-space singularities within a distance cf(ct) of real (physical) space which give rise to an exponential tail in the energy spectrum. It is found that b(t) decreases exponentially in time to the limit of our resolution. Indirect evidence is presented that more violent vortex stretching takes place at later times, possibly leading to a real singularity (6 = 0) at a finite time. These direct integration results are consistent with new temporal power-series results that extend the Morf, Orszag Rr. Frisch (1980) analysis from order t4* to order Po. Still, convincing evidence for or against the existence of a real singularity will require even more sophisticated analysis. The viscous dynamics (decay) have been studied for Reynolds numbers R (based on an integral scale) up to 3000 and beyond the time t,,, at which the maximum energy dissipation is achieved. Early-time, high-R dynamics are essentially inviscid and laminar. The inviscidly formed vortex sheets are observed to roll up and are then subject to instabilities accompanied by reconnection processes which make the flow increasingly chaotic (turbulent) with extended high-vorticity patches appearing away from the impermeable walls. Near t,,, the small scales of the flow are nearly isotropic provided that R 1000. Various features characteristic of fully developed turbulence are observed near t,,, when R = 3000 and R, = 110: (i) a k-n inertial range in the energy spectrum is obtained with n z 1.G2.2 (in contrast with a much steeper spectrum at earlier times) ;

The formation and expansion of a toroidal drop moving in a viscous fluid

Abstract: The deformation of an initially spherical liquid drop moving under the action of gravity in another fluid with which it is completely miscible is investigated under conditions of small values of the drop Reynolds number. It is found experimentally that such a drop evolves into an open torus which subsequently expands, and this phenomenon is examined theoretically for two limiting drop geometries: (i) a slightly deformed spherical drop, and (ii) a highly expanded, slender open torus. Under the assumptions of zero interfacial tension and creeping flow, the theory provides a qualitative description for the initial stages of the drop evolution [case (i)], but is unable to account for the observed drop expansion during latter stages of deformation [case (ii)]. On the other hand, if small inertial effects are retained in the analysis, the theory predicts that a slender open fluid torus possessing an arbitrary cross‐sectional geometry will expand without change of shape to first order in Reynolds number. Quantitative comparisons of theoretically predicted rates of expansion with experimental measurements suggest the possible existence of a small, time‐dependent interfacial tension across the drop interface.

Wave speeds in wavy Taylor-vortex flow

Abstract: The speed of travelling azimuthal waves on Taylor vortices in a circular Couette system (with the inner cylinder rotating and the outer cylinder at rest) has been determined in laboratory experiments conducted as a function of Reynolds number R, radius ratio of the cylinders η, average axial wavelength , η and m1) the wave speeds have been measured, extrapolated to infinite aspect ratio, and compared with the numerically computed values. For each of these three cases the agreement is within 0.1 %.