Scales Of Turbulent Motion Research Articles

Experimental investigation of a blunt trailing edge flow field with application to sound generation

The unsteady lift generated by turbulence at the trailing edge of an airfoil is a source of radiated sound. The objective of the present research was to measure the velocity field in the near wake region of an asymmetric beveled trailing edge in order to determine the flow mechanisms responsible for the generation of trailing edge noise. Two component velocity measurements were acquired using particle image velocimetry. The chord Reynolds number was 1.9 × 106. The data show velocity field realizations that were typical of a wake flow containing an asymmetric periodic vortex shedding. A phase average decomposition of the velocity field with respect to this shedding process was utilized to separate the large scale turbulent motions that occurred at the vortex shedding frequency (i.e., those responsible for the production of tonal noise) from the smaller scale turbulent motions, which were interpreted to be responsible for the production of broadband sound. The small scale turbulence was found to be dependent on the phase of the vortex shedding process implying a dependence of the broadband sound generated by the trailing edge on the phase of the vortex shedding process.

Statistics of Absolute and Relative Dispersion in the Atmospheric Convective Boundary Layer: A Large-Eddy Simulation Study

Abstract The influence of the different scales of turbulent motion on plume dispersion in the atmospheric convective boundary layer (CBL) is studied by means of a large-eddy simulation (LES). In particular, the large-scale (meandering) and small-scale (relative diffusion) contributions are separated by analyzing dispersion in two reference systems: the absolute (fixed) coordinate system and the coordinate system relative to the plume’s instantaneous center of mass. In the relative coordinate system, the (vertically) inhomogeneous meandering motion is removed, and only the small-scale, homogeneous turbulent motion contributes to the dispersion process. First, mean plume position, dispersion parameters (variance), and skewness of the plume position are discussed. The analysis of the third-order moments shows how the structure and the symmetry of scalar distribution are affected with respect to the turbulent characteristics of the CBL (inhomogeneity of the large-scale vertical motion) and the presence of the boundary conditions (surface and top of the CBL). In fact, the reflection of the plume by the CBL boundaries generates the presence of nonlinear cross-correlation terms in the balance equation for the third-order moments of the plume position. As a result, the third-order moment of the absolute position is not balanced by the sum of the third-order moments of the meandering and relative plume position. Second, mean concentration and concentration fluctuations are calculated and discussed in both coordinate systems. The intensity of relative concentration fluctuation icr, which quantifies the internal (in plume) mixing, is explicitly calculated. Based on these results, a parameterization for the probability distribution function (PDF) of the relative concentration is proposed, showing very good agreement with the LES results. Finally, the validity of Gifford’s formula, which relates the absolute concentration’s high-order moments to the relative concentration and the PDF of the plume centerline, is studied. It is found that due to the presence of the CBL boundaries, Gifford’s formula is not able to reproduce correctly the value of the absolute mean concentration near the ground. This result is analyzed by showing that, when the plume is reflected by the CBL boundaries, the instantaneous relative plume width z′2r(t) departs from its mean value σ2r. By introducing the skewness of the relative plume position into a parameterization for the relative mean concentration, the results for the calculated mean concentration are improved.

Leaking method approach to surface transport in the Mediterranean Sea from a numerical ocean model

We use Lagrangian diagnostics (the leaking and the exchange methods) to characterize surface transport out of and between selected regions in the Western Mediterranean. Velocity fields are obtained from a numerical model. Residence times of water of Atlantic origin in the Algerian subbasin, with a strong seasonal dependence, are calculated. Exchange rates between these waters and the ones occupying the northern basin are also evaluated. At surface, northward transport is dominant, and involves filamental features and eddy structures that can be identified with the Algerian eddies. The impact on these results of the presence of small scale turbulent motions is evaluated by adding Lagrangian diffusion.

Turbulent vortex dipoles in a shallow water layer

This paper describes an experimental study on turbulent dipolar vortices in a shallow water layer. Dipoles are generated by an impulsive horizontal jet, by which a localized three-dimensional turbulent flow region is created. Dipole emergence is only controlled by the confinement number C=Q/H2tinj whereas the jet Reynolds number Re=Q/v has no influence in the studied range 50 000<Re<75 000 (H is the water depth, v is the kinematical viscosity, Q the injected momentum flux and tinj the injection duration). When C>2, the flow becomes quasi-two-dimensional and a single vortex dipole emerges in most cases. By qualitative observations and application of particle image velocimetry, the main dipole features have been determined. The shallow water dipoles are characterized by the simultaneous presence of several scales of turbulence: A quasi-two-dimensional main flow at large scale and three-dimensional turbulent motions at small scale. A vertical circulation takes place in the dipole front. A theoretical model is presented and compared to experimental results. The three-dimensional turbulence production occurs mainly in the frontal circulation. A good agreement has been found between the model prediction and the measurements for the velocity evolution.

A two-scale PBM for modeling turbulent flocculation in water treatment processes

A population balance model (PBM) that incorporates two scales of turbulent motion in the breakup frequency function has been presented. The breakup frequency function is designed such that particles smaller than the impeller-region Kolmogoroff microscale will erode according to a critical velocity related to the local energy dissipation rate. Particles larger than the impeller-region Kolmogoroff microscale will fracture according to a critical velocity related to the impeller tip speed. The two-scale model was found to better predict the experimental steady-state particle size distribution in 5, 28, and 560 l tank sizes and with a Rushton turbine and A310 fluid foil impellers. The two-scale PBM was also used to investigate the most appropriate scale-up law for drinking water flocculation processes. In addition, the impact of higher tank average energy dissipation rate, primary particle concentration, and coagulant concentration on the volume mean particle size with increasing tank size and different impeller types was also presented.

Wave Number Frequency Spectra of a Lifting Wake for Broadband Noise Prediction

Measurements of wave number frequency spectra of velocity fluctuations have been made using two three-component hot-wire probes in the wake of a rectangular NACA 0012 half-wing at a 5-deg angle of attack. Spectra were measured along spanwise lines in the near two-dimensional part of the wake, in the stretched region where the wake begins to wind around the vortex, directly above the vortex core, and radially from the core center. Dominated by the large-scale organized motions present in the wake, the spectra show little similarity with the von Karman isotropic turbulence spectrum. Outside the core, upwash spectra contain a single maximum at the passage frequency of these large structures. Motions associated with this peak are highly anisotropic, both in terms of velocity components and length scales. Similar anisotropy is also seen at higher wave numbers, suggesting either that the smaller scale turbulent motions are organized by the large eddies or that the nonsinusoidal components of those eddies contribute significantly to the spectrum at higher wave numbers. The implications of these results for broadband noise prediction have been assessed by considering the sound radiation from this turbulent flow over a semi-infinite flat plate. The major conclusion is that the correlation length scales of the flow are small compared to the acoustic wavelength and so are well represented by their values at zero spanwise wave number. However, the blade response function has a variation with spanwise wave number that cannot be ignored and significantly influences the spanwise directionality.

Wave number frequency spectra of a lifting wake for broadband noise prediction

Measurements of wave number frequency spectra of velocity fluctuations have been made using two three-component hot-wire probes in the wake of a rectangular NACA 0012 half-wing at a 5-deg angle of attack. Spectra were measured along spanwise lines in the near two-dimensional part of the wake, in the stretched region where the wake begins to wind around the vortex, directly above the vortex core, and radially from the core center. Dominated by the large-scale organized motions present in the wake, the spectra show little similarity with the von Karman isotropic turbulence spectrum. Outside the core, upwash spectra contain a single maximum at the passage frequency of these large structures. Motions associated with this peak are highly anisotropic, both in terms of velocity components and length scales. Similar anisotropy is also seen at higher wave numbers, suggesting either that the smaller scale turbulent motions are organized by the large eddies or that the nonsinusoidal components of those eddies contribute significantly to the spectrum at higher wave numbers. The implications of these results for broadband noise prediction have been assessed by considering the sound radiation from this turbulent flow over a semi-infinite flat plate. The major conclusion is that the correlation length scales of the flow are small compared to the acoustic wavelength and so are well represented by their values at zero spanwise wave number. However, the blade response function has a variation with spanwise wave number that cannot be ignored and significantly influences the spanwise directionality.

Multiscaling properties of concentration fluctuations in dispersing plumes revealed using an orthonormal wavelet decomposition

The dynamical characteristics of concentration fluctuations in a dispersing plume over the energetic and inertial-convective range of scales of turbulent motion are studied using a multiscale analysis technique that is based on an orthonormal wavelet representation. It is shown that the Haar wavelet concentration spectrum is similar to the Fourier concentration spectrum in that both spectra exhibit an extensive inertial-convective subrange spanning about two decades in frequency, with a scaling exponent of -5/3. Analysis of the statistical properties (e.g., fluctuation intensity, skewness, and kurtosis) of the concentration wavelet coefficients (i.e., the concentration discrete detailed signal) suggests that the small scales are always more intermittent than the large scales. The degree of intermittency increases monotonically with decreasing scale within the inertial-convective subrange, reaching a plateau at the very small scales associated with the beginning of the near-dissipation subrange. The probability density function (pdf) of the concentration discrete detailed signal displays stretched exponential tails with an intermittency exponent (tail slope) q that increases as Τa, where Τ is the scale or dilation and a is a power-law exponent that is dependent on downwind distance, plume height, and stratification strength with typical values in the range from about 0.25 to 0.35. It is shown that the concentration variance cascade process requires a phase coherency of eddies between different scales at the small-scale end of the inertial-convective subrange.

High-frequency propagation in a turbulent flow

As part of the new ONR-initiative in moderate-to-high-frequency acoustics, a pilot experiment will be carried out in a shallow tidally forced channel in September 1994 to compare acoustic variability with direct measurements of turbulent velocity and sound-speed fluctuations. The acoustic configuration will consist of a linear array of four sources on one side, and four receivers on the other (f=67.5 kHz, L≊700 m), together with a single source and receiver for reciprocal transmission. Separation of reciprocal transmission from reception of the other four sources allows a repetition rate for all sources of 5 Hz. The spatial filter will be applied to the acoustic data so as to focus the measurement on the central portion of the channel, at which location a moored turbulence sensor (R. Lueck) will be deployed at the same depth as the acoustic path. Supplementary measurements will be acquired with a multiple frequency backscatter sonar, moored current meters, and pressure gauges, and a neutrally buoyant float to measure the larger scale turbulent motions (E. D’Asaro, APL-UW and D. Veenstra, IOS). The experimental work will be discussed in the context of prior studies of forward scattering from turbulence and preliminary results will be presented.

The velocity field beneath wind-waves — observations and inferences

An extensive set of measurements taken from a fixed tower is used to study the velocity field under wind waves. Velocity measurements, made with miniature drag spheres, are compared with linear theory estimates of the orbital velocities obtained from measured surface elevation. Results are presented in the context of how well linear theory is able to predict wave-induced forces on cylindrical structural members. Linear theory is seen to predict the flow velocities to within about 7%. Furthermore, both the inertial and drag forces are generally well predicted by linear theory, although small scale turbulent motions not accounted for by linear theory can result in significantly higher inertial forces on smaller structural members.

Particle dispersion in the developing free shear layer. Part 2. Forced flow

An experimental investigation of the dispersion of small particles in a developing, high-Reynolds-number, turbulent, plane mixing layer is presented. Flow visualizations, laser attenuation and diffraction techniques as well as hot-wire anemometry are used to describe the evolution of the mean and instantaneous particle and gas flow fields. It is shown that the large scale turbulent motion existing in the mixing layer plays a central role in the dispersion of the particles. The mean particle concentration field is shown to be the result of a statistical distribution of streaks produced by the large-scale coherent component of the turbulent motion in the mixing layer. Furthermore, for every particle size, the spreading of the particle concentration thickness is found to occur at a smaller rate than the one characterizing the momentum of the turbulent carrier gas. Large particles are shown to initially disperse into the mixing layer less effectively than the small ones. However, when both downstream and cross-stream coordinates are non-dimensionalized with a characteristic length proportional to the square of the droplet diameter, a universal, particle-size independent dispersion field is found to exist.

The production of uniformly sheared streams by means of double gauzes in wind tunnels: a mathematical analysis

The methods which have been used to design gauzes for the production of uniformly sheared streams in wind tunnels are analysed. The analysis of the results which have been obtained with single gauzes show that the poor theoretical evaluations of the shear rate that have been reported in the literature seem to be related to the different empirical expressions which have been assumed for the lift coefficient. This analysis indicates that the empirical relation established by Dryden and Schubauer (1947) gives satisfactory results, as long as mean mean angle of inclination of the gauze is taken into account in evaluating the resistance coefficient. The theoretical analysis of these flows shows that streams with “high” shear rates can only be obtained with single gauzes when “high” drag screens are used. This has the disadvantage of producing large scale turbulent motion downstream from the gauze. As an alternative to this single gauze approach, and to the semi-empirical technique used by Woo et al. (1981) of building a double gauze with non-uniform porosity, a theoretical analysis of the flow through double gauzes of uniform porosity leads to a useful method of designing gauzes for specific shear rates of high intensity. The method was used in the design of a double gauze that produced a stream with a non-dimensional shear rate of 1.73 (Woo et al. obtained 1.8), which is quite uniform and shows close agreement with the theoretical value. The results of this analysis indicate that the most appropriate method of producing high shear rates with low turbulence intensities is to use a set of several gauzes of low resistance. Modifications to the theoretical expressions obtained that take into account the presence of the additional gauzes might be a valuable improvement in the designing of gauzes for highly sheared streams with low turbulence intensities.

Drag reduction caused by the injection of polymer thread into a turbulent pipe flow

Drag reduction caused by the injection of concentrated polymer solutions into a turbulent pipe flow was studied. Measurements were made of the radial distribution of fluctuating velocities by means of video image analysis. The results showed that a higher velocity was observed for injected polymer threads and both the radial fluctuation and the Reynolds stress were significantly suppressed. It was suggested that the wall turbulence structure might be controlled by suppressing the large scale turbulent motion in the turbulent core region.

Large and small scale motions in Kinematic dynamos

Abstract Kinematic, axisymmetric mean field dynamos are examined for a number of models in order to study the cooperation between small scale turbulent motions (α-affect) and the large scale motions (ω-effect and meridional flow). For a spherical dynamo we show that it is more difficult to excite an α2-dynamo with dipolar parity in the presence of differential rotation, which increases with increasing depth, when the magnitude of the toroidal shearing effect is too small. Meridional streaming in the absence of differential rotation has an inhibitory effect on α2-dynamos. For dynamos in spheres the ease with which a dynamo is excited when the combined effects of differential rotation and meridional flow are present depends on the model for ω(r,θ). For a model where the maximum in the toroidal shearing is towards the edge of the region enclosing the streamlines a small amount of meridional flow enhances dynamo action. For dynamos confined to a spherical shell the effect of a small amount of single cell meri...

Studies on Oxygen Transfer Models

The liquid film coefficient of the oxygen transfer at air-water surfaces is dependent on turbulence characteristics of the flow. There are two methods for evaluating the liquid film coefficient with relation to turbulence; One is based on the root mean square velocity fluctuation and the larger scale movement and the other is based on the energy dissipation rate and the smaller scale movement. Conclusions obtained from some experimental and dimensional analyses imply that, for the mass transfer mechanism at the air-water surfaces, larger scale turbulent motion is dominated over smaller scale eddies represented by Kolmogoroff's micro-scale.

On the coherent structure of the axisymmetric mixing layer: a flow-visualization study

In an effort to resolve some controversies regarding the turbulent mixing-layer structure, the near field of a large (18 cm diameter) air jet has been investigated for the jet exit speed of 30 m s−1. The smoke-laden axisymmetric mixing layer has been illuminated by a thin sheet of laser light in an azimuthal plane passing through the jet axis. High-speed visualization films of the mixing layer in the region of its self-preservation (of which a few picture sequences depicting space-time evolutions of the structure of the layer are presented) reveal that most of the time the mixing layer is in a state of disorganization, consisting of relatively smaller scale, random and diffuse turbulent motions; only occasionally are organized distinct large-scale coherent structures formed. The survival distances of the large-scale structures are found to be comparable to their average sizes. The survival time of these structures is about one ‘turnover’ time, each being roughly about five times the local characteristic time scale of the mixing layer. It is seen that tearing is as dominant a mode of large-scale interaction as pairing is; large-scale structures are continually sheared and typically fragmented due to a segment on the high-speed side being torn and swept away from the slower-moving outer portion. Evolution of the large structures occur not primarily through complete pairing as widely believed but quite frequently through ‘fractional pairing’ between segments which have been torn from different upstream large-scale coherent structures or through ‘partial pairing’ when one structure captures only a part of another. The movies show that along with entrainment of non-vortical ambient fluid, radially outward ejection of vortical fluid into the ambient is an important aspect of jet mixing. From aligned displays of ciné film frame sequences, space-time trajectories of identifiable vortical fluid elements have been traced. The convection velocity variation across the shear layer and even the overall structure convection velocity measured from these trajectories agree with those determined from the wave-number-celerity spectra, obtained from double-Fourier transformation of longitudinal velocity space-time correlation measurements with hot-wires.The visualization films do not bear out the two-street vortex ring model recently propounded by Lau. Based on our observations, we propose that tearing, ‘slippage’ and fractional and partial pairings are responsible for the observed radial variation of structure passage frequency, and the causes of the different coherent structures educed by Bruun on the high- and low-speed sides of the mixing layer and for Yule's failure in educing a coherent structure on the low-speed side of the layer.

Further development of the three-region model of a premixed turbulent flame III. Eddy entrainment, combustion in depth process of region 3

An experimental study of the turbulent kinetic energy balance for the eddy entrainment, combustion in depth process of region 3 has been carried out. The influence of approach turbulence scale, intensity and laminar burning velocity on each term in the balance equation has been examined for propane-air and acetylene-air flames and the important role of small scale turbulent motion is highlighted. It is observed that either an increase in intensity or a reduction in scale of approach turbulence increases the magnitude of all terms except that for convection. The core region of the flame shows jet-like behaviour. The entrainment, combustion in depth process produces a very high level of fluctuating vorticity. Therefore, the dominant terms appear to be those of viscous dissipation and advection. Finally, a large increase in laminar burning velocity enhances the contribution of the advection term at the expense of a reduction in the convection term.

On the Probability-Density Function of Concentration in Turbulent Diffusion

The probability dΓ, that at location and time t contaminant fluid with concentration between Γ and Γ + dΓwill be encountered, is investigated. When a finite quantity of contaminant material is released in a large-Reynolds-number flow, and while the contaminant cloud so formed remains of smaller dimension than the energy containing scales of turbulent motion, it is argued that will be of self-similar form over the range of Γ that is indicative of values in the strands of contaminant fluid of which the cloud is comprised. A nondimensional stringiness factor S(t) is defined, using , as a measure of the extent to which contaminant material has been pulled out by the convective turbulent motion into long threads. S(t) is shown to relate the average of the median value of concentration throughout each realization of the cloud to the ensemble-average concentration . It is suggested that many of the results of the paper apply in a more general category of diffusion problems, and some experimental results are reviewed.

Turbulence Measurements in Boundary Layers Along Mildly Curved Surfaces

This paper presents results of turbulence measurements in boundary layers over surfaces of mild longitudinal curvature. The study indicates that convex wall curvature decreases both the length and velocity scales of turbulent motions, whereas concave curvature has the opposite effect. White being qualitatively similar to those brought about by stronger wall curvature, mild curvature effects are found to be much larger than what one expects from a linear interpolation between the effects of zero and strong curvature. It is also observed that curvature has a relatively larger effect on the Reynolds shear stress than on the turbulent kinetic energy. The present study, however, indicates that it is still possible to use some of the phenomenological models of turbulence (e.g., the mixing length model, the Prandtl-Kolmogorov model), provided an appropriate curvature model is available for describing the effect of curvature on the relevant length scale in the boundary layer. The present data are used to test the validity and limitations of such a curvature model (based on an analogy between streamline curvature and buoyancy) currently in use.

Evidence for the Hydrodynamic Character of Microturbulence

Worrall and Wilson1 have questioned the validity of determinations of the chemical composition of stellar atmospheres from observations of absorption lines in stellar spectra. Their main argument is directed against the concept of “microturbulence”, which has been used for several decades to explain the high level of the flat part of the curve of growth. It was first introduced by Struve and Elvey2 to account for the apparent systematic variation of the abundances with the total amount of absorption (equivalent width) of the spectral lines from which they are derived. Microturbulence is thought of as a statistical velocity field in the stellar atmosphere, with moving gas elements whose optical depths for the photons to be absorbed are smaller than unity. This small scale velocity field widens the frequency interval for the absorption of photons; this has no influence on the strength of the weak lines, but the equivalent width of saturated lines is increased. In the curve of growth, which represents the relation between the effective number of absorbing particles in the stellar atmosphere and the equivalent width of the absorption line, the flat part of the saturated lines is lifted. Thermal motion of the absorbing atoms frequently fails to account for the level of the flat part of the curve of growth; according to Worrall and Wilson this is the only independent evidence for the existence of small scale turbulent motion in stellar atmospheres. Their statements on this point are strong: “ … There are no independent observations even suggesting that such small-scale, non-thermal motion exists, much less defining its amplitude. . . . ”. Worrall and Wilson suggest that the level of the flat part of the curve of growth is determined by non-local thermodynamic equilibrium (LTE) effects. I show here that other observations, supporting the concept of microturbulence, do exist.