Showing papers on "Turbulence published in 1982"

An Album of Fluid Motion

Abstract: Keywords: visualisation de l'ecoulement ; tourbillon ; dynamique des : fluides ; aubes ; cylindre ; instabilite ; ecoulement : secondaire Note: moult photos Reference Record created on 2005-11-18, modified on 2016-08-08

Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model

Abstract: 2~5 However, the effects of the kinematic viscosity on the turbulence structure were ignored in many of these treatments. Consequently, the exact boundary conditions at the wall cannot be used when the turbulence Reynolds number is not high as, e.g., in flows with rapid expansions or near the transition/turbulence interface. The general goal of the present investigation was to develop a single transport model from the Navier-Stokes equation for accurate predictions of skin friction, heat transfer, and fluctuating kinetic energy distributions in transitional and turbulent flow regimes. As a first step toward this general goal, a new turbulence model valid down to the solid wall is formulated in this paper. Turbulence model equations which provide predictions of the flow within the viscous layer adjacent to the wall have been proposed by several investigators.3'4'6'7 Although the general approach of the present model is the same as that of Jones and Launder,3 the detailed proposals are substantially different. In the present study, the Taylor series expansion technique was used to systematically investigate the proper behavior of the turbulent shear stress and the kinetic energy and its rate of dissipation near a solid wall. The results were used in developing a new turbulence model which retains the proper physical behavior of the balance between the dissipation and the molecular diffusion of the turbulent kinetic energy at the solid wall. The model was applied to the problems of a fully developed turbulent channel flow and of a turbulent boundary-layer flow over a flat plate. Results on skin friction, the distribution of mean velocity, turbulent shear stress, and turbulent kinetic energy will be presented and compared with available experimental data and with the theory of Jones and Launder.

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.

On the mechanism of wall turbulence

Abstract: In this paper an attempt is made to formulate a model for the mechanism of wall turbulence that links recent flow-visualization observations with the various quantitative measurements and scaling laws established from anemometry studies. Various mechanisms are proposed, all of which use the concept of the horse-shoe, hairpin or ‘A’ vortex. It is shown that these models give a connection between the mean-velocity distribution, the broad-band turbulence-intensity distributions and the turbulence spectra. Temperature distributions above a heated surface are also considered. Although this aspect of the work is not yet complete, the analysis for this shows promise.

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.

Movable bed roughness in unsteady oscillatory flow

Abstract: A model to predict the roughness in unsteady oscillatory flows over movable, noncohesive beds is presented. The roughness over movable beds is shown to be a function of the boundary shear stress, rather than a fixed geometrical scale as is the case for fully rough turbulent boundary shear flows over immobile beds. The model partitions the roughness into two distinct contributions. These two contributions are due to the form drag around individual bed forms and to the near-bed sediment transport. The form drag over the bed forms is treated explicitly as a function of the boundary geometry and shear stress. The ripples are predicted as a function of the local skin friction, and a semiempirical expression is derived using standard law-of-the-wall arguments, which gives the ripple or form roughness as a function of the boundary geometry. The ripple roughness is found to be proportional to the product of the ripple steepness and height. Favorable comparison of the form drag model with the results of Bagnold's (1946) fixed ripple study is found. The value of z0 associated with intense sediment transport in oscillatory flow over a flat bed is determined from Carstens et al.'s (1969) experiments. This value is found to be 7 or 8 grain diameters. An expression is derived for the roughness associated with the maximum thickness of a near-bottom sediment-transporting layer consistent with Owen's (1964) roughness hypothesis for saltation of uniform grains in air. At large values of the boundary shear stress relative to the critical value for initial sediment motion, the derived expression is similar to the results of Smith and McLean's (1977) unidirectional flow approach modified for oscillatory flow. The total roughness model is found to compare favorably with Carstens et al.'s (1969) data. In contrast to Smith and McLean's (1977) steady flow findings, the results here show that when ripples are present, they account for a significant portion of the boundary roughness.

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.

Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity

Abstract: To study effects of flow inhomogeneities on the dynamics of laminar flamelets in turbulent flames, with account taken of influences of the gas expansion produced by heat release, a previously developed theory of premixed flames in turbulent flows, that was based on a diffusive-thermal model in which thermal expansion was neglected, and that applied to turbulence having scales large compared with the laminar flame-thickness, is extended by eliminating the hypothesis of negligible expansion and by adding the postulate of weak-intensity turbulence. The consideration of thermal expansion motivates the formal introduction of multiple-scale methods, which should be useful in subsequent investigations. Although the hydrodynamic-instability mechanism of Landau is not considered, no restriction is imposed on the density change across the flame front, and the additional transverse convection correspondingly induced by the tilted front is described. By allowing the heat-to-reactant diffusivity ratio to differ slightly from unity, clarification is achieved of effects of phenomena such as flame stretch and the flame-relaxation mechanism traceable to transverse diffusive processes associated with flame-front curvature. By carrying the analysis to second order in the ratio of the laminar flame thickness to the turbulence scale, an equation for evolution of the flame front is derived, containing influences of transverse convection, flame relaxation and stretch. This equation explains anomalies recently observed at low frequencies in experimental data on power spectra of velocity fluctuations in turbulent flames. It also shows that, concerning the diffusive-stability properties of the laminar flame, the density change across the flame thickness produces a shift of the stability limits from those obtained in the purely diffusive-thermal model. At this second order, the turbulent correction to the flame speed involves only the mean area increase produced by wrinkling. The analysis is carried to the fourth order to demonstrate the mean-stretch and mean-curvature effects on the flame speed that occur if the diffusivity ratio differs from unity.

Homogenization of potential vorticity in planetary gyres

Abstract: The mean circulation of planetary fluids tends to develop uniform potential vorticity q in regions where closed time-mean streamlines or closed isolines of mean potential vorticity exist. This state is established in statistically steady flows by geostrophic turbulence or by wave-induced potential-vorticity flux. At the outer edge of the closed contours the expelled gradients of q are concentrated. Beyond this transition lies motionless fluid, or a different flow regime in which the planetary gradient of q may be dominant. The homogenized regions occur where direct forcing by external stress or heating within the closed isoline is negligible, upon the potential-density surface under consideration. In the stably stratified ocean such regions are found at depths greater than those of direct wind-induced stress or penetrative cooling. In ‘channel’ models of the atmosphere we again find constant q when mesoscale eddies cause the dominant potential-vorticity flux. In the real atmosphere the results here can apply only where internal heating is negligible. The derivations given here build upon the Prandtl–Batchelor theorem, which applies to non-rotating, steady two-dimensional flow. Supporting evidence is found in numerical circulation models and oceanic observations.

Turbulence and waves in a rotating tank

Abstract: A turbulent field is produced with an oscillating grid in a deep, rotating tank. Near the grid, the Rossby number is kept large, 0(3-33), and the turbulence is locally unaffected by rotation. Away from the grid, the scale of the turbulence increases, the r.m.s. turbulent velocity decreases, and rotation becomes increasingly important. The flow field changes dramatically at a local Rossby number of about 0.20, and thereafter remains independent of depth. The flow consists of concentrated vortices having axes approximately parallel to the rotation axis, and extending throughout the depth of the fluid above the turbulent Ekman layer. The number of vortices per unit area is a function of the grid Rossby number. The local vorticity within cores can be a factor of 50 larger than the tank vorticity 2Ω. The total relative circulation contained in the vortices remains, however, a small fraction of the tank circulation.The concentrated vortex cores support waves consisting of helical distortions, which travel along the axes of individual vortices. Isolated, travelling waves seem well-described by the vortex-soliton theory of Hasimoto (1972). The nonlinear waves transport mass, momentum and energy from the vigorously turbulent region near the grid to the rotation-dominated flow above. Interactions between waves, which are frequent occurrences, almost always result in a local breakdown of the vortex core, and small-scale turbulence production. Usually the portions of broken core reform within ½−1 rotation periods, but occasionally cores are destroyed and reformed on a much longer timescale.

Why, how, and when, MHD turbulence becomes two-dimensional

Abstract: A description of MHD turbulence at low magnetic Reynolds number and large interaction parameter is proposed, in which attention is focussed on the role of insulating walls perpendicular to a uniform applied magnetic field. The flow is divided in two regions: the thin Hartmann layers near the walls, and the bulk of the flow. In the latter region, a kind of electromagnetic diffusion along the magnetic field lines (a degenerate form of Alfv6n waves) is displayed, which elongates the turbulent eddies in the field direction, but is not sufficient to generate a two-dimensional dynamics. However the normal derivative of velocity must be zero (to leading order) at the boundaries of the bulk region (as at a free surface), so that when the length scale 1, perpendicular to the magnetic field is large enough, the corresponding eddies are necessarily two-dimensional. Furthermore, if I, is not larger than a second limit, the Hartmann braking effect is negligible and the dynamics of these eddies is described by the ordinary Navier-Stokes equations without electromagnetic forces. MHD then appears to offer a means of achieving experiments on two-dimensional turbulence, and of deducing velocity and vorticity from measurements of electric field.

LDV measurements of an air–-solid two-phase flow in a horizontal pipe

Abstract: Measurements of air and solid velocities were made in an air-solid two-phase flow in a horizontal pipe by the use of a laser-Doppler velocimeter (LDV). The pipe was 30 mm inner diameter, and two kinds of plastic particles, 0.2 and 3.4 mm in diameter, were conveyed in addition to fine particles (ammonium chloride) for air-flow detection. The air velocities averaged over the pipe cross section ranged from 6 to 20m/s and the solid-to-air mass-flow ratio was up to 6. Simultaneous measurements of both air and 0.2 mm particle velocities were found possible by setting threshold values against the pedestal and Doppler components of the photomultiplier signal. As the loading ratio increased and the air velocity decreased, mean-velocity distributions of both phases increased asymmetrical tendency. I n the presence of 0.2mm particles, a flattening of the velocity profile was remarkable. The effects of the solid particles on air-flow turbulence varied greatly with particle size. That is, 3.4 mm particles increased the turbulence markedly, while 0-2 mm ones reduced it. The probability-density function of the air flow deviated from the normal distribution (Gaussian) in the presence of particles. Finally, the frequency spectra of air-flow turbulence were obtained in the presence of 0.2 mm particles by using a fast Fourier transform (FFT). As a result, it was found that t,he higher-frequency components increased with increasing loading ratio.

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.

Markov-chain simulation of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerian velocity variance

Abstract: The Langevin equation is used to derive the Markov equation for the vertical velocity of a fluid particle moving in turbulent flow. It is shown that if the Eulerian velocity variance Σ wE is not constant with height, there is an associated vertical pressure gradient which appears as a force-like term in the Markov equation. The correct form of the Markov equation is: w(t + δt) = aw(t) + bΣ wEζ + (1 − a)T L ∂(Σ wE 2)/∂z, where w(t) is the vertical velocity at time t, ζ a random number from a Gaussian distribution with zero mean and unit variance, T L the Lagrangian integral time scale for vertical velocity, a = exp(−δt/T L), and b = (1 − a 2)1/2. This equation can be used for inhomogeneous turbulence in which the mean wind speed, Σ wE and T L vary with height. A two-dimensional numerical simulation shows that when this equation is used, an initially uniform distribution of tracer remains uniform.

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.

Calculation of Secondary Currents in Channel Flow

Abstract: A model is presented for calculating the flow in channels with turbulence-driven secondary motion, with an emphasis on open channel flow. Algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying modelled Reynolds stress equations. A simple eddy viscosity model is used for the shear stresses in the logitudinal momentum equation. The kinetic energy k, and the dissipation rate ϵ of the turbulent motion appearing in the algebraic and eddy viscosity expressions are determined from transport equations for these quantities. The restricting influence of a free surface on the length scale of turbulence is accounted for by a special free surface boundary condition for ϵ. The resulting set of equations is solved with a marching forward numerical procedure for three-dimensional boundary layers. The model is tested by application to developed two-dimensional closed and open channel flow, closed square duct flow, and flow in open channels of various width-to-depth-ratios. Most features of these flows are simulated well by the model, including the reduction of the eddy viscosity near the free surface and the depression of the velocity maximum below the surface.

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.

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.

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.

Dissipation Within the Surface Mixed Layer

Abstract: Observations of turbulent energy dissipation, ϵ, measured during a week-long mixed-layer study on the continental shelf off Nova Scotia are presented. This time series of dissipation measurements at a fixed site and with a wide range of wind speeds indicates that a constant fraction of the energy flux in the atmospheric boundary layer appears as dissipation in the mixed layer. Our measured velocity-shear spectra are consistent in shape with an isotropic-turbulence spectral form and simultaneous determinations of spectral level from two mutually perpendicular sensors are consistent with isotropy. Significant changes in turbulence levels between two profiles a few minutes apart are observed. These changes (often a factor of 10) emphasize the necessity of adequate space-time averaging to obtain good mean values of ϵ. Including data from measurements of the large-scale density and velocity fields, the generation of the observed turbulence is thought to be Richardson-number instabilities in the mixed ...

On the inviscid instability of a circular jet with external flow

Abstract: The influence of an external flow velocity on the instability of a circular jet has been investigated by means of the inviscid linearized stability theory. The instability properties of spatially growing axisymmetric and first-order azimuthal disturbances show that the external flow inhibits the instability of the circular jet, but increases the unstable frequency range. Similarity considerations lead to the result that, in a first approximation, the disturbed flow field is independent of the external flow velocity, if the axial co-ordinate is contracted by a suitably chosen stretching factor and if the disturbance frequency is reduced by the same factor. It is concluded that the large-scale structure of jet turbulence is modified in the same manner by the external flow.

Large volume limit of the distribution of characteristic exponents in turbulence

Abstract: For spatially extended conservative or dissipative physical systems, it appears natural that a density of characteristic exponents per unit volume should exist when the volume tends to infinity. In the case of a turbulent viscous fluid, however, this simple idea is complicated by the phenomenon of intermittency. In the present paper we obtain rigorous upper bounds on the distribution of characteristic exponents in terms of dissipation. These bounds have a reasonable large volume behavior. For two-dimensional fluids a particularly striking result is obtained: the total information creation is bounded above by a fixed multiple of the total energy dissipation (at fixed viscosity). The distribution of characteristic exponents is estimated in an intermittent model of turbulence (see [7]), and it is found that a change of behavior occurs at the valueD=2.6 of the self-similarity dimension.

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.