Showing papers on "Turbulence published in 1987"

Turbulence statistics in fully developed channel flow at low reynolds number

Abstract: A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

Spectral Methods in Fluid Dynamics

Abstract: Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields

Abstract: The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, is shown to depend on the particle inertia and the free-fall terminal velocity in still fluid. With no inertia the particle settles on average at the same rate as in still fluid, assuming there is no mean flow. Particle inertia produces a bias in each trajectory towards regions of high strain rate or low vorticity, which affects the mean settling velocity. Results from a Gaussian random velocity field show that this produces an increased settling velocity.

On nonlinear K-l and K-ε models of turbulence

Abstract: The commonly used linear K-l and K-e models of turbulence are shown to be incapable of accurately predicting turbulent flows where the normal Reynolds stresses play an important role. By means of an asymptotic expansion, nonlinear K-l and K-e models are obtained which, unlike all such previous nonlinear models, satisfy both realizability and the necessary invariance requirements. Calculations are presented which demonstrate that this nonlinear model is able to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model. Furthermore, the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts - a phenomenon which the linear models are fundamentally unable to describe. An additional application of this model to the improved prediction of separated flows is discussed briefly along with other possible avenues of future research.

On the parameters influencing air-water gas exchange

Abstract: Detailed gas exchange measurements from two circular and one linear wind/wave tunnels are presented. Heat, He, CH4, CO2, Kr, and Xe have been used as tracers. The experiments show the central importance of waves for the water-side transfer process. With the onset of waves the Schmidt number dependence of the transfer velocity k changes from k ∝ Sc−⅔ to k ∝ Sc−½indicating a change in the boundary conditions at the surface. Moreover, energy put into the wave field by wind is transferred to near-surface turbulence enhancing gas transfer. The data show that the mean square slope of the waves is the best parameter to characterize the free wavy surface with respect to water-side transfer processes.

A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance

Abstract: It has been suggested that hairpin vortices may play a key role in developing and sustaining the turbulence process in the near-wall region of turbulent boundary layers. To examine this suggestion, a study was done of the hairpin vortices generated by the interaction of a hemisphere protuberancee within a developing laminar boundary layer. Under the proper conditions, hairpin vortices are shed extremely periodically, which allows detailed examination of their behaviour. Shedding characteristics of the hemispheres were determined using hot-film-anemometry techniques. The flow patterns created by the presence of the hairpin vortices have been documented using flow visualization and hot-film-anemometry techniques, and cross-compared with the patterns observed in the near-wall of a fully turbulent boundary layer. In general, it has been observed that many of the visual patterns observed in the near-wall region of a turbulent boundary layer can also be observed in the wake of the hairpin-shedding hemisphere, which appears supportive of the importance of hairpin vortices in the near-wall turbulence production process. Furthermore, velocity measurements indicate the presence of strong inflexional profiles just downstream of the hairpin-vortex generation region which evolve into fuller profiles with downstream distance, eventually developing a remarkable similarity to a turbulent-boundary-layer velocity profile.

The growth and breakdown of streamwise vortices in the presence of a wall

Abstract: The growth and breakdown of counter-rotating streamwise vortices, generated on a concave wall via the Goertler instability mechanism, were experimentally studied as a model for comparable eddy structures that exist in transitional and turbulent flat-plate boundary layers. The experiments were conducted in a low-speed open-return wind tunnel, using smoke-wire visualization and multiple-probe hot wires to study the vortices. As low-momentum fluid was removed from the wall, low-speed regions formed between the vortices; these regions grew in the normal direction faster than a nominally Blasius boundary layer and created strongly inflexional normal and spanwise profiles of the streamwise velocity component. Instability oscillations developed on these unstable profiles that scaled with the local shear-layer thickness and velocity difference. The spatial scales of the temporal velocity fluctuations were found to correlate with the velocity gradient in the spanwise (rather than in the normal) direction.

Numerical simulation of compressible homogeneous flows in the turbulent regime

Abstract: Compressible flows with r.m.8. velocities of the order of the speed of sound are studied with direct numerical simulations using a pseudospectral method. We concentrate on turbulent homogeneous flows in the two-dimensional case. The fluid obeys the Navier-Stokes equations for a perfect gas, and viscous terms are included explicitly. No modelling of small scales is used. We show that the behaviour of the flow differs sharply at low compared with high r.m.9. Mach number Ma, with a transition at Mu = 0.3. In the large scales, temporal exchanges between longitudinal and solenoidal modes of energy retain an acoustical character; they lead to a slowing down of the decrease of the Mach number with time, which occurs with interspersed plateaux corresponding to quiescent periods. When the flow is initially supersonic, the small scales are dominated by shocks behind which vortices form. This vortex production is particularly prominent, when two strong shocks collide, with the onset of shear turbulence in the region downstream of the collision. However, at the resolutions reached by our code on a 256 x 256 uniform grid, this mechanism proves insufficient to bring vortices into equipartition with shocks in the small-scale tail of the energy spectrum.

Turbulent secondary flows

Abstract: Revue des connaissances concernant les couches limites tridimensionnelles et autres couches de cisaillement ainsi que les ecoulements a tourbillons dans les turbomachines

Turbulent burning velocities: a general correlation in terms of straining rates

Abstract: All known experimental values of turbulent burning velocity have been scrutinized. These number 1650, a significant proportion of which at the higher turbulent Reynolds numbers we measured in a fan-stirred bomb. Dimensionless correlations which have a theoretical basis are presented. These are in terms of flame straining rates and the effective r.m.s. turbulent velocity, as well as the laminar burning velocity of the mixture. When a flame develops from an ignition source it is not initially exposed to the lower frequencies of the turbulent spectrum. As the kernel grows the flame is affected by ever-lower frequencies and the turbulent burning velocity increases towards a fully developed value. An experimental dimensionless power spectral density function is presented, and used to show how both effective r.m.s. turbulent velocity and flame straining rate develop in an explosion. The results are relevant to a variety of practical devices, including gasoline engines, as well as atmospheric explosions.

Turbulent oscillatory flow over rough beds

Abstract: Velocity measurements are presented for turbulent oscillatory flow over rough beds. Two components of velocity were measured with a laser-Doppler anemometer and the rough beds consisted of a single layer of sand, gravel or pebbles on a flat surface. Turbulence intensities showed significant variation during the course of the cycle. Maximum turbulence intensity propagated out from the bed at a more or less constant velocity for all beds. Variation of time-mean turbulence intensity with height was qualitatively similar to that observed in steady flows. Reynolds stress showed several interesting features. Near the bed, maximum Reynolds stress was in phase with one of the two peaks of turbulence intensity but further out it was in phase with the other, i.e. the phase of maximum Reynolds stress showed a 180° phase shift at a certain height above the bed. A related effect was seen in the time-mean eddy viscosity which was negative near the bed but positive further out. It is suggested that these effects are caused by the jets of fluid associated with vortex formation and ejection in oscillatory flow over rough beds. Maximum Reynolds stress was also significantly less than the horizontal force per unit area of bed obtained from the momentum integral. Eddy viscosity and mixing length were found to vary significantly during the course of the cycle. Variation with height of time-mean values of these variables showed similar trends, except in the near-bed region, to those observed in steady flow but derived values of the Karman constant were significantly lower. Non-dimensional defect velocity appeared to show dependence on a/ks as well as on y/δ in the outer layer away from the bed, even at high Reynolds numbers.

The structure of the vorticity field in homogeneous turbulent flows

Abstract: The structures of the vorticity fields in several homogeneous irrotational straining flows and a homogeneous turbulent shear flow were examined using a database generated by direct numerical simulation of the unsteady Navier-Stokes equations. In all cases, strong evidence was found for the presence of coherent vortical structures. The initially isotropic vorticity fields were rapidly affected by imposed mean strain and the rotational component of mean shear and developed accordingly. In the homogeneous turbulent shear-flow cases, the roll-up of mean vorticity into characteristic hairpin vortices was clearly observed, supporting the view that hairpin vortices are an important vortical structure in all turbulent shear flows; the absence of mean shear in the homogeneous irrotational straining flows precludes the presence of hairpin-like vortices.

Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes

Abstract: Measurements in the viscous sublayer of a flat-plate turbulent boundary layer in air, using single hot-wire sensors with lengths from 1–60 viscous length scales show that, at a given distance from the surface, the turbulence intensity, flatness factor, and skewness factor of the longitudinal velocity fluctuation are nearly independent of wire length when the latter is less than 20–25 times the viscous length scale (i.e. 20–25 “wall units”), and decrease significantly and abruptly for larger wire lengths. This conclusion is consistent with other workers' probability density functions of streak spacing: the lateral spacing of “streaks” in the viscous sublayer is 80–100 wall units on average with minimum spacing of 20–25 wall units, which implies that signals would be strongly attenuated by wires whose length exceeds 20–25 wall units. To achieve wire lengths of less than 20–25 wall units, subminiature hot wire probes like those described by Ligrani and Bradshaw (1987), having lengths as small as 150 μm, are necessary for sublayer measurements in typical laboratory wind tunnels. As well as the measurements mentioned above, dissipation spectra are presented, to show the effect of spanwise averaging on the high-frequency motions, which is necessarily more severe than the effect on overall intensities.

The impact of a vortex ring on a wall

Abstract: The flow induced by a vortex ring approaching a plane wall on a trajectory normal to the wall is investigated for an incompressible fluid which is otherwise stagnant. The detailed characteristics of the interaction of the ring with the flow near the surface have been observed experimentally for a wide variety of laminar rings, using dye in water to visualize the flow in the ring as well as near the plane surface. Numerical solutions are obtained for the trajectory of the ring as well as for the unsteady boundary-layer flow that develops on the wall. The experimental and theoretical results show that an unsteady separation develops in the boundary-layer flow, in the form of a secondary ring attached to the wall. A period of explosive boundary-layer growth then ensues and a strong viscous-inviscid interaction occurs in the form of the ejection of the secondary vortex ring from the boundary layer. The primary ring then interacts with the secondary ring and in some cases was observed to induce the formation of a third, tertiary, ring near the wall. The details of this process are investigated over a wide Reynolds number range. The results clearly show how one vortex ring can produce another, through an unsteady interaction with a viscous flow near the wall.

A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection

Abstract: It has been suggested that hairpin vortices are a major sustaining flow structure involved in the perpetuation of turbulent boundary layers, although their origin within the boundary layer is unclear. One hypothesis is that hairpin structures are formed by the breakdown of the low-speed streak structures which develop adjacent to the surface beneath turbulent boundary layers. To examine this hypothesis, a water-channel study has been done which utilizes injection through surface slots in a flat plate to create artificial low-speed streak-type regions beneath a laminar boundary layer. Under appropriate conditions, these synthesized low-speed streaks develop a three-dimensional, shear-layer instability which breaks down to form a hairpin-vortex street. Employing both flow visualization and anemometry measurements, the characteristics of these hairpin structures and the parameters influencing their generation have been examined. The hairpin streets were determined to develop in a very periodic and repeatable manner within a definite range of flow parameters. Detailed flow patterns obtained using dye and hydrogen bubbles, both individually and collectively, indicate a remarkable similarity with previously observed patterns in the near-wall region of turbulent boundary layers. In addition, the development of the hairpin structures is observed to be quite sensitive to external forcing, as well as exhibiting a tendency for organized development of larger, more complex structures through a pairing-type process. Velocity measurements indicate the initial presence of strong inflexional profiles which evolve rapidly to velocity and turbulence-intensity profiles commensurate with those associated with turbulent boundary layers, but which do not exhibit the marked spreading associated with turbulence.

Time-dependent behavior of a reattaching shear layer

Abstract: Conditionally sampled velocities have been measured in a reattaching turbulent shear layer behind a rearward facing step in an effort to understand unsteady behaviour of reattaching flows. Laser-Doppler velocimeter measurements were conditionally sampled on the basis of instantaneous flow direction near reattachment. Conditions of abnormally short reattachment and abnormally long reattachment were considered. Ensemble-averages of measurements made during these conditions were used to obtain mean velocities and Reynolds stresses. In the mean flow, conditional streamlines show a global change in flow pattern which correlates with wall-flow direction. This motion can loosely be described as a "flapping" of the shear layer. Stresses shown also vary with the change in flow pattern. Yet, the global "flapping" motion does not appear to contribute much to the fluctuating energy in the flow. A second type of fluctuating motion (vortical) was observed. Spectral analysis of both wall static pressure and streamwise velocity show that the majority of energy in the flow resides in frequencies characteristic of roll-up and pairing of vortical structure seen in free shear layers (St = 0.2). Two-point velocity correlations also indicate a vortical behaviour of the flow. It is conjectured that the "flapping" is a disorder of the roll-up and pairing process occurring in the shear layer.

Laminar separation bubble characteristics on an airfoil at low Reynolds numbers

Abstract: An experimental investigation was conducted in order to document the structure and behavior of laminar separation bubbles at low Reynolds numbers. Data of this type are necessary if the currently insufficient analytical and numerical models are to be improved. The laminar separation bubble that forms on a NACA 663-018 airfoil model was surveyed at chord Reynolds numbers of 50,000-200,000 at angles of attack of 8-12 deg. The effects of the various testing conditions on the separation bubble were isolated and the data were analyzed in relation to existing separation bubble correlations in order to test their low Reynolds number applicability. This analysis indicated that the chord Reynolds number and the disturbance environment strongly influence the experimental pressure distributions. These effects must be included in any analytic prediction technique applied to the low Reynolds number flight regime.

Self-organization of electrostatic turbulence in a cylindrical plasma.

Abstract: On the basis of theory and computer simulations we show that electrostatic turbulence in a cylindrical plasma with magnetic shear and curvature self-organizes to form a macroscopic potential \ensuremath{\varphi} which depends only on the radial coordinate r and is given by \ensuremath{\varphi}(r)\ensuremath{\simeq}${\mathrm{J}}_{0}$(pr)+${\mathrm{C}}_{1}$${\mathrm{r}}^{2}$+${\mathrm{C}}_{2}$ where ${\mathrm{C}}_{1}$ and ${\mathrm{C}}_{2}$ are functions of a constant p. A unique feature of the potential is the existence of a coaxial \ensuremath{\varphi}(${\mathrm{r}}_{0}$)=0 surface at ${\mathrm{r}}_{0}$\ensuremath{\simeq}0.7a, where a is the radius of the cylinder. This surface is found to be fairly rigid and is considered to inhibit radial particle transport.

Stratified flow in pyroclastic surges

Abstract: Stratified flow theory is applied to pyroclatic surges in an effort to gain insight into transport dynamics during explosive eruptions. Particle transport is assumed to be by turbulent suspension, and calculations contained herein show that this is likely for many cases including the 18 May 1980 blast at mount St. Helens. The discussion centers on the Rouse number (Pn), which represents a ratio of particle settling velocity to scale of turbulence; the Brunt-Vaisala frequency (N), which is the maximum possible frequency of internal waves; the Froude number (Fr), representing the ratio of inertial forces to gravitational forces; and the Richardson number (Ri), a ratio of buoyant restoring forces to turbulent mixing forces. The velocity or flow power dependence of bed-form wavelength in surge deposits is related to a velocity dependence of wavelength of internal waves in the turbulent surge. This produces a decrease in dune wavelength with increasing distance from vent. Migration direction of bed forms is related toFr as it is defined for a continuously stratified flow. Proximal to distal facies variations in surge deposits reflect increasingPn andRi as the flows move away from their sources. This produces the progression from sandwave to massive to planar facies with increasing distance from vent. Where the long axis of topography is at low angles to the flow direction, massive facies in topographic lows may from concurrently with sandwave facies on highs, due to the higher particle concentration in the lows. Where long axis of topography is at high angles to flow direction, denser lower parts of the surge may be dammed or “blocked”. Blocked material tends to form massive flows that may move down slope independent of the overriding surge. A model incorporating turbulent transport, stratified flow, and time evolution of pyroclastic surges is proposed for deposits which have been attributed to both pyroclastic flow and pyroclastic surge transport by various workers. During the initial high energy (waxing) phase of the eruptive event,Pn is sufficiently low that only coarse, but poorly sorted, material is deposited to form relatively coarse bottom layers. As the event wanes, remaining finer material is deposited through a thin bed load to produce overlying bedded and cross-bedded veneer deposits. Throughout most of the event, blocking occurs to produce relatively thick and massive deposits in valley bottoms.

Experimental Study of Particle Deposition in Bends of Circular Cross Section

Abstract: The deposition efficiency of liquid particles in tube bends of circular cross section has been measured for flow Reynolds numbers of 100, 1000, 6000, and 10,000. The particle Reynolds number, Re p, was in the range 0.6–3.9 for the laminar flow cases (i.e., Re = 100 and 1000), whereas for the turbulent flow cases (i.e., Re = 6000 and 10,000) Re p was in the range 1.3–12.7. Bends constructed of stainless steel and glass tubes of different diameters were used. The experiments were performed using monodisperse aerosols generated by the vibrating orifice aerosol generator. The results were in good agreement with the theory of Cheng and Wang for Re = 1000, but differed from theory for Re = 100. For the turbulent cases, no dependence was found on the flow Reynolds number and an exponential curve of deposition efficiency versus Stokes number was fitted to the experimental results. A theoretical justification of the form of the curve is given in the paper.

Analysis of surf zone turbulence

Abstract: Measurements of turbulent kinetic energy k under surf zone waves are analyzed to show how k varies over depth, between breaker point and shoreline, and how k depends on the beach slope. It is found that the variation of k over depth is remarkably weak, large values being measured a few percent of the depth above the bottom. A simple model for the dissipation mechanism makes it possible to derive an empirical formula for the time-averaged k that accurately describes all the data considered reliable.