Assumption Of Isotropic Turbulence Research Articles

DUST COLLECTION EFFICIENCY UNDER IN-PHASE TURBULENCE CONDITIONS IN THE PRESENCE OF PHASE TRANSITIONS

The article presents the results of a study of the dust collection efficiency in a regular packing layer of a rotoclone-type hybrid apparatus on the particle inertia index in the presence of phase transition processes. The effect of phase transitions on the efficiency of gas purification processes under inphase turbulence conditions is considered. Based on the conditions of stability of the in-phase vortex formation regime of the gas phase in a regular packing layer, the dominant influence of turbulent diffusion mechanisms on the intensity of phase transition processes and, as a consequence, on the dust collection efficiency has been established. In this case, the predominant influence is in the area of highly dispersed and finely dispersed dust fractions. The results of the experimental studying the patterns of dust collection efficiency depending on the particle inertia index in the presence of phase transition processes are presented. The studies were carried out for three phase transition modes: condensation of vaporsfrom a vapour-gas mixture, evaporation of a spraying liquid as well as a neutral mode. Using A.N. Kolmogorov’s hypothesis,the basic equations and results of calculating the numerical values of local characteristics of a turbulent gas flow in a regular packing layer are presented under the assumption of isotropic turbulence realized in a layer of a regular packing, whose local characteristics do not depend on coordinates and direction.

Experimental investigation of scalar dispersion in indoor spaces

The scalar dispersion from point sources in indoor spaces is experimentally investigated using simultaneous particle–image velocimetry and planar laser-induced fluorescence techniques in a 20:1 and a 60:1 full-to-model scale room model. The ventilation inlets dominate turbulence production, with magnitudes of the velocities and Reynolds stresses observed to increase with air changes per hour (ACH). Mean concentration maps show a dependence on the ACH and source location which is attributed to the flow field at the near-source region. The peak-to-mean concentration shows a weak dependence on the mean concentration and concentration variance maps, indicating risk for toxic chemicals may be underpredicted if based only on these information. The concentration PDFs are generally well-described by exponential distributions with C99/crms′ values never exceeding 5.0. The magnitudes of the advective and turbulent scalar fluxes are strongly dependent on the ACH and source location, neither of which are able to dominate the other by more than an order of magnitude. The eddy diffusivity tensor was measured and a conditional-averaging based method is proposed to approximate it to an isotropic eddy diffusion coefficient, K. For real applications where K is used to estimate magnitudes of the turbulent scalar flux using the gradient transport model, the assumption of isotropic turbulence can introduce an uncertainty of around 17.8%.

The Spatial Structure of Passively Simulated Atmospheric Boundary Layer Turbulence

Three types of turbulence fields were investigated using a research method combining wind tunnel tests and theoretical analysis to further explore the spatial structure of atmospheric boundary layer turbulence, which was passively simulated by a wind tunnel. The fundamental theory of turbulence is introduced, and some traditional theoretical coherence models based on isotropic turbulence theory are derived. The difference between the theoretical results and the passive simulation of atmospheric boundary layer turbulence was compared and discussed. The analysis results show that the passively simulated atmospheric turbulence basically conformed to the homogeneous isotropic turbulence assumption on the horizontal plane, but the interference of the nonisotropic turbulence components cannot be ignored either. Finally, some improvements were made to the traditional coherence function model based on the experimental results to apply the passively simulated atmospheric boundary layer turbulence.

Assessment of advanced RANS turbulence models for the stability analysis of low specific speed pump-turbines

Reversible pump-turbines, which can switch between pump and turbine operation, provide important support for the stabilization of the electrical grid. In order to fulfill their task, fast transition between the operation modes is required. This includes stable synchronization with the electrical grid during the process of turbine start at small guide vane openings (GVOs). However, the special geometry of pump-turbine impellers tends to produce unstable flow behavior, which can affect the synchronization process in a negative way.The prediction of the stability behavior with the help of CFD during the design process is not yet fully developed. The simulation of small specific speed pump-turbines operating at small GVOs sets high requirements on the underlying numerical model. To capture all relevant flow structures accordingly, 3-dimensional unsteady computation of the entire pump-turbine domain is required. Further, it has been shown that turbulence modeling is a key factor in order to reproduce the 4-quadrant characteristic in the unstable S-shape region. Vortex structures in the vaneless space and runner channels are considered the root-cause for the occurring instabilities. Standard two-equation models are not able to predict the stability behavior under these difficult circumstances (highly separated flows, small specific speed, small GVO angle). Models, which consider the anisotropic behavior of Reynolds-stresses have shown to produce better results.Considering the accurate prediction of mixing processes at off-design conditions, the focus was oriented to the anisotropy present in the turbulent structures. Standard models are often not sufficient to accurately predict vortices, which can have a huge impact on the performance, since based on the assumption of isotropic turbulence. Accordingly, they tend to dissipate and diffuse vortices too quickly. Improved models, which take the anisotropic nature of the Reynolds-stresses into account, can help in this context. The models can introduce the anisotropy via an explicit algebraic expression, or model directly the transport equations for the Reynolds-stresses. For this work the performance of a full Reynolds-stress model with improved coupling was investigated.In order to obtain the predictions using advanced turbulence models a particularly robust framework based on a pressure-based fully coupled approach was used. The goal of this work is the development and testing of an improved full Reynolds-stress model for the application in the stability analysis of pump-turbines. The focus lies thereby on separation behavior and mixing/vortex dissipation.

Turbulence Anisotropy Investigations in an Internal Combustion Engine

Abstract The assumption of isotropic turbulence is commonly incorporated into models of the internal combustion engine (ICE) in-cylinder flows. While preliminary analysis with two-dimensional (2D) velocity data indicates that the turbulence may tend to isotropy as the piston approaches top-dead-center (TDC), the validity of this assumption has not been fully investigated, partially due to the lack of three-component velocity data in ICEs. In this work, the velocity was measured using two-dimensional, three-component (2D-3C) particle image velocimetry in a single-cylinder, motored, research engine to investigate the evolution of turbulence anisotropy throughout the compression stroke. Invariants of the Reynolds stress anisotropy tensor were calculated and visualized, through the Lumley triangle, to investigate turbulence states. Results showed the turbulence to be mostly anisotropic, with preferential tendency toward 2D axisymmetry at the beginning of the compression stroke and approaching-isotropy near top-dead-center. Findings provide new insights into turbulence in dynamic, bounded flows to assist with the development of physics-based, quantitative models.

Light field camera study of near-ground turbulence anisotropy and observation of small outer-scales.

Understanding turbulence effects on laser beam propagation is critical to the emerging design, study, and test of many long-range free space optical (FSO) communication and directed energy systems. Conventional studies make the prevalent assumption of isotropic turbulence, while more recent results suggest anisotropic turbulence for atmospheric channels within a few meters elevation above the ground. As countless FSO systems have been and continue to be deployed in such channels, analysis of anisotropic modelings has become one of the fastest growing areas in FSO research. This in turn motivates new tools that can distinguish anisotropic characteristics to improve both modeling accuracy and physical interpretations. Wavefront sensors such as Shack-Hartmann sensors, interferometers, and plenoptic sensors have been devised and used in experiments; however, they all require rigid alignments that lack resilience against temperature gradient buildup and beam wander. We find that by using a light field camera (LFC) that extracts perturbation of individual light rays, the wave structure function of turbulence can be retrieved with high reliability. Furthermore, we find through experiments that the outer scales of near-ground turbulence tend to be a magnitude smaller than conventional theoretical assumptions, agreeing with new findings by others but being absent in current theoretical modelings. As a result, we believe that the LFC is an ideal candidate in the frontier of turbulence research; it is both commercially available and easy to adapt to turbulence experiments.

New analytical models for power spectral density and coherence function of wind turbulence relative to a moving vehicle under crosswinds

In this study, new general analytical models for correlation and power spectral density (PSD) functions of wind turbulence relative to a moving vehicle considering different wind direction angles under crosswinds without the use of Taylor's frozen turbulence hypothesis or the isotropic turbulence assumption were proposed. The auto-PSD calculation models relative to a moving vehicle with two different coherence functions relative to the ground were deduced, and a direct generating scheme, which can more efficiently generate the time histories of fluctuating wind speeds relative to a moving vehicle was developed. The accuracy of the proposed auto-PSD models was validated based on the models and direct generating scheme mentioned above. Furthermore, the coherence function model of wind turbulence relative to a moving vehicle was also proposed, and the accuracy of both the proposed coherence function model and the previous model were compared. The results show that without the use of Taylor's frozen turbulence hypothesis or the isotropic turbulence assumption, the proposed auto-PSD and coherence function models of wind turbulence relative to a moving vehicle are all highly in accordance with the numerical solutions, which are calculated based on only the time histories of fluctuating wind speeds relative to a moving vehicle. However, there are large differences between the results of the auto-PSD and coherence functions obtained from the previous models and the results obtained from the corresponding numerical solutions. These differences can be attributed to the fact that the previous models adopted either Taylor's frozen turbulence hypothesis or the isotropic turbulence assumption, or both. The proposed auto-PSD model and coherence function model of wind turbulence relative to a moving vehicle could provide a foundation for considering the effects of crosswinds on moving vehicles in terms of unsteady aerodynamic forces, ride comfort and running safety.

Experimental verification of boundary conditions for numerical simulation of airflow in a benchmark ventilation channel

Correct definition of boundary conditions is crucial for the appropriate simulation of a flow. It is a common practice that simulation of sufficiently long upstream entrance section is performed instead of experimental investigation of the actual conditions at the boundary of the examined area, in the case that the measurement is either impossible or extremely demanding. We focused on the case of a benchmark channel with ventilation outlet, which models a regular automotive ventilation system. At first, measurements of air velocity and turbulence intensity were performed at the boundary of the examined area, i.e. in the rectangular channel 272.5 mm upstream the ventilation outlet. Then, the experimentally acquired results were compared with results obtained by numerical simulation of further upstream entrance section defined according to generally approved theoretical suggestions. The comparison showed that despite the simple geometry and general agreement of average axial velocity, certain difference was found in the shape of the velocity profile. The difference was attributed to the simplifications of the numerical model and the isotropic turbulence assumption of the used turbulence model. The appropriate recommendations were stated for the future work.

Atmospheric turbulence MTF for optical waves׳ propagation through anisotropic non-Kolmogorov atmospheric turbulence

Abstract The conventional investigations for atmospheric turbulence have assumed that the refractive-index fluctuations of atmosphere are statistically homogeneous and isotropic. Developments of experimental and theoretical investigations have shown that the isotropic turbulence generally exists near the ground, and in the free atmosphere layer above the ground the anisotropic turbulence appears. Hence, deviations from the previously published results obtained with the isotropic turbulence assumption are possible. In this study, new analytic expressions for the anisotropic atmospheric turbulence modulation transfer function (MTF) are derived for optical plane and spherical waves propagating through anisotropic non-Kolmogorov turbulence. They consider both an anisotropic coefficient and a general spectral power law value in the range 3 to 4. When the anisotropic coefficient equals one (corresponding to the isotropic turbulence), the new results obtained in this work can reduce correctly to the previously published analytic expressions under isotropic non-Kolmogorov turbulence. The derived MTF models physically describe the turbulence anisotropic property of high atmospheric layer. Numerical calculations show that with the increase of anisotropic factor which is proportional to the atmospheric layer altitude, the atmospheric turbulence produces less effect on the imaging system.

On Heavy Particle Dispersion in Turbulent Shear Flows: 3-D Analysis of the Effects of Crossing Trajectories

In the approaches used to predict the dispersion of discrete particles moving in a turbulent flow, the effects of crossing trajectories due to gravity (or any other external force field) are generally accounted for by modifying the integral time scales according to the well-known analysis of Csanady (J Atmos Sci 20:201–208, 1963). Here, an alternative theoretical analysis of the time correlation of the fluid velocity fluctuations along a particle trajectory is presented and applied in a turbulent shear flow. The study is carried out in the frame of three-dimensional Langevin-type stochastic models, where the main unknowns are the drift tensor components rather than the conventional integral time scales of the fluid seen by the particles. Starting from a model for the space-time velocity covariance tensor of the turbulence under the assumption of homogeneous shear flow, the various components of the time correlation tensor of the fluid seen are expressed in the asymptotic case of large mean relative velocity (between the particles and the flow) compared to the particle velocity fluctuations. In order to provide comparison with the generally used expressions arising from isotropic turbulence assumption, we examine also the conventional integral time scales of the fluid seen in the directions parallel and perpendicular to the mean relative velocity. The most prominent deviations from isotropic turbulence are observed when the external force field is in the direction of the mean velocity gradient: in this case the loss of correlation in the mean flow direction is significantly lower than expected in a uniform flow, an observation that is in qualitative agreement with the few available data.

Plasma sheet coefficient of diffusion: Predictions and observations

The theory of a plasma sheet with medium scale developed turbulence predicts a value for the plasma sheet diffusion coefficient in the Z direction. Its value becomes very near to the diffusion coefficient calculated from the assumption of isotropic turbulence on the basis of ISEE-2 velocity fluctuations in the X and Y directions. INTERBALL/Tail CORALL bulk velocity measurements make it possible to determine velocity fluctuations in the Z direction and calculate the diffusion coefficient in this Z direction. It is shown that INTERBALL/Tail observations are in very good agreement with theory predictions.

Experimental Investigation of Swirl and Non-Swirl Gas Injections Into Liquid Baths Using Submerged Vertical Lances

The behaviour of the flow of swirl and non-swirl gas injections into a liquid bath was investigated experimentally, using water as modelling fluid to gain an understanding of the mixing process of the Sirosmelt top submerged gas injection system. The effects of swirl intensity, gas injection rates and lance submergence levels on the gas-liquid interaction were determined by measuring the velocity fields and the generation of turbulence in the bath. The results indicate that the swirl gas injection promoted high liquid velocities and high turbulent kinetic energy and hence better mixing in the tank. When two-thirds of the lance was submerged better mixing and high liquid velocities resulted for both gas injection rates investigated. The applicability of the concept of isotropic turbulence for the liquid bath was examined. It was found that the assumption of isotropic turbulence may hold outside the plume region. However, there are a clear indication that turbulence is non-isotropic in the vicinity of the wall region. These findings have implications in the mathematical modelling of gas injection processes.On a étudié expérimentalement le comportement d'écoulement d'injections de gaz, avec et sans tourbillon, dans un bain liquide. On a utilisé des modèles aqueux afin d'obtenir un aperçu du procédé de mélange du système Sirosmelt submergé d'injection de gaz, par le haut. On a déterminé l'effet de l'intensité du tourbillon, des taux d'injection de gaz et des niveaux d'immersion de la lance sur l'interaction gaz-liquide en mesurant les champs de vitesse et la génération de turbulence dans le bain. Les résultats semblent montrer que l'injection de gaz avec tourbillon stimulait des vitesses élevées dans le liquide et une énergie cinétique turbulente élevée et, ainsi, un meilleur mélange dans le réservoir. Les taux élevés d'injection de gaz, comme on s'y attendait, ont produit des vitesses élevées du liquide dans tout le réservoir. L'immersion aux deux tiers de la lance a résulté en un meilleur mélange et en des vitesses élevées du liquide, aux deux taux d'injection de gaz étudiés. On a examiné l'applicabilité au bain liquide du concept de turbulence isotrope. On a trouvé que l'assomption de turbulence isotrope pouvait être retenue en dehors de la région d'injection. Il y a cependant des indications claires que, dans le voisinage de la paroi, la turbulence est non-isotrope. Ces découvertes ont des implications sur la modélisation mathématique des procédés d'injection de gaz.

Role of Anisotropy in Turbulent Mixing Noise

The objective is to explore the role of anisotropy on aerodynamic mixing noise because of fine-scale turbulence. The usual assumption of isotropic turbulence is replaced with that of axisymmetric turbulence. The analysis is based on source terms of Lilley's equation. In addition, flowlacoustic interaction is accounted for in terms of a high-frequency solution to the axisymmetric Lilley's equation. In the limiting case of isotropy, various source correlation terms derived here simplify to those obtained with an isotropic turbulence model of Batchelor. A Reynolds-averaged Navier-Stokes solution with a k-∈ turbulence model for a Mach 1.0 jet is used to make flow and acoustic predictions. A parametric study of the turbulence scales indicates that anisotropy increases the peak noise level.

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet. The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material. The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kϵ turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.

Dynamics of fluid mixing induced at a T-junction. 3. Experimental characterization and fluid dynamic computation of temperature distribution in space

Gas mixing was experimentally characterized by measuring the temperature distributions in space donwstream of a T-junction under turbulent flow conditions. Fluid dynamic computations were also performed for T-mixing using FLUENT based on the two-equation κ-e turbulence model, the wall function approach, the assumption of isotropic turbulence, and a set of six parameters assuming prescribed values. Qualitative agreement emerged from the comparison between experiment and prediction without adjusting any parameter values. To enhance the quantitative capability of computational fluid dynamics as a generic tool for simulating mixing involving turbulent flows, several areas amenable to improvement are suggested for future research

Intense turbulence in the polar mesosphere : rocket and radar measurements

Simultaneous observations of polar mesospheric summer echoes (PMSE) have been made with two different frequency radars during the launch of a sounding rocket designed to measure the fluctuations in the electron density in the same height range. The cross-section for radar backscatter deduced from the rocket probe data under the assumption of isotropic turbulence is in reasonable agreement with the measured signals at both 53.5 MHz with the mobile SOUSY radar and 224 MHz with the EISCAT VHF radar, which correspond to backscatter wavelengths of about 3 and 0.75 m, respectively. Some controversy exists over the relative roles of turbulent scatter vs specular reflections in PMSE. A number of characteristics of the data obtained in this experiment are consistent with nearly isotropic, intense meter-scale turbulence on this particular day. Since equally compelling arguments for the importance of an anisotropic-type mechanism have been presented by other experimenters studying PMSE, we conclude that both isotropic and anisotropic mechanisms must operate. We have found the inner scale for the electron fluctuation spectrum, which corresponds to the diffusive subrange for that fluid, and have compared it to the inner scale for the neutral gas. The latter was found from the Kolmogorov microscale, which in turn depends on the energy dissipation rate in the gas. We found the dissipation rate from the spectral width of the 53.5 MHz backscatter signal and from the rocket electron density fluctuation data. The diffusive subrange was found to occur at a wavelength a factor of about 10 times smaller than the viscous subrange. This corresponds to a Schmidt number of about 100. High Schmidt numbers have been reported in recent measurements of the diffusion coefficient of the electrons in this height range made with the EISCAT incoherent scatter radar. About 15 min after the rocket flight an extremely high radar reflectivity was found with the SOUSY system. We have been able to reproduce this high level theoretically by scaling the rocket data with an increase in the neutral turbulence energy dissipation rate by a factor of 14 as deduced from the SOUSY spectral width, an increase in the electron density which is consistent with riometer data, and a 33% decrease in the electron density gradient scale length which is hypothesized. We also estimate the radar reflectivity at 933 MHz and conclude that signals in excess of thermal scatter levels would have occurred at the peak of the event studied, provided that the electron fluctuation spectrum decreases as k −7 in the viscous subrange. If the spectrum has an exponential form, however, a turbulent source cannot explain the enhanced 933 MHz echoes reported by EISCAT.

Temperature-field structure within atmospheric buoyant thermals

Using stationary rakes of hot-wire anemometer probes, a series of temperature measurements have been conducted within rising buoyant thermals created by detonation of large-diameter gas-filled balloons. These atmospheric detonation simulation tests were performed at the SANDIA Laboratories Aerial Cable Test Facility, Kirtland AFB, during the late fall of 1973. All measurements were performed after pressure equilibrium (t > 1 s) but prior to completion of the toroid formation process and within the time required (t > 4 s) for the fireball to rise one diameter.Based on an extensive processing of measured data for two detonation events, unique results describing the mean flow field and turbulent structure statistics for the early-time large-scale buoyant thermal have been determined. Final results include: mean-velocity and temperature data; temperature and temperature gradient intensities; space, auto- and ‘eddy-lifetime’ correlation scales; power-spectral densities; probability density distributions and approximate microscale data.The present temperature data illustrate that the early-time rising fireball is characterized by a highly intermittent irregular top or cap, a constant (high-) temperature core and a thermal wake exhibiting a linear decay in mean temperature. Mean convection velocities for the fireball wake were measured to be approximately twice as large as fireball cap velocities (13.1 m/s). Maximum fireball temperatures (1100 °C) were in good agreement with peak brightness-temperature data determined from an independent IR measurements experiment. Core leading-edge mean-temperature gradients compare favourably with predictions (10 °C/cm) whereas trailing-edge gradients (0.4 °C/cm) are smaller than predicted results (3 °C/cm).Normalized temperature intensities at the fireball top and within the thermal wake were substantial (≈ 0.6) in contrast with quiescent fireball core levels (0.1). Moving-frame autocorrelation times (‘eddy lifetimes’, 0.17 + 0.04 s) were approximately four times larger than measured autocorrelation times. This result illustrates that the early-time fireball eddy structure is highly persistent, a finding which tends to substantiate those radar models for large-scale fireballs which postulate relatively slow ‘smearing’ of early-time electron density gradients. Wake integral scales, determined from vertical space correlation data, were approximately 5% of the fireball mean radius. Probability density distributions for the fireball thermal wake were ‘spiky’ in nature, with some evidence of bimodal behaviour, and slightly skewed to the negative side of their normalized values. Normalized spectra data, in general, follow a − &5/3; falloff behaviour for several decades in spectral power. The noted large ‘spread’ in the inertial subrange is consistent with measured turbulence Reynolds numbers (2000) and with the large-scale fully developed turbulent structure for the GEST fireballs (ReD= 3 × 107). Wake microscale data, estimated from temperature and temperature-gradient intensity data and the isotropic turbulence assumption, varied from 2 to 4 ern and were in favourable agreement with predicted microscale magnitudes.

Scale effect on breakup process in liquid-liquid agitated tanks.

The effect of scale on the breakup process in liquid-liquid agitated tanks was investigated. Transient drop size distributions in the breakup process were measured in geometrically similar mixing vessels at equal power input per unit mass, which was taken as a scale-up criterion under the assumption of isotropic turbulence for the flow around drops. The distributions in each vessel, however, did not undergo the same variation with time and the condition of equal power input per unit mass was found to be inappropriate as a scale-up criterion for the breakup process. The experimental result was explained from direct observation of breakups in the mixing vessels by high-speed cine-photography. The observations made it clear that breakups occurred not only in the isotropic turbulent region but also in the nonisotropic turbulent region. A new model for the breakup process was proposed which considers breakups in both regions. This model successfully predicted the transient drop size distributions.

浮選セル中の乱流混合エネルギーおよびエネルギー伝達について

As a hydrodynamic approach to the flotation process, the turbulent energy propagation in flotation cells was considered on the basis of the fluctuation velocity and the velocity correlation to yield the following results:(1) The power number in a Agitair type flotation cell or a Warman type flotation cell was constant in the region of Reynolds number>104.(2) The power consumption without gas phase could be expressed by eq.(4).(3) The power consumption containing gas phase was decreased with the larger air flow number and this tendency was enhanced by the addition of frother because of the recirculation of dispersed bubbles to the impeller zone.(4) The energy spectrum function was expressed by eq.(10) or eq.(11) under assumption of isotropic turbulence.(5) The velocity correlation function in the upper zone of the cell was in accord with the function derived by neglecting the transfer spectrum function, 'whereas it was recognized that such mixing process was a diffusional mixing process.(6) Nearly 90% of the input energy was reckoned to be dissipated in the impeller zone and about 1% of it was consumed for generation of bubbles.

Effect of anisotropic turbulence on aerodynamic noise

A model based on Lighthill's theory for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. It does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic turbulence by the more realistic one of axisymmetric turbulence. In the course of the analysis, a hierarchy of equations is developed wherein each succeeding equation involves more assumptions than the preceding equation but requires less experimental information for its use. The implications of the model for jet noise are discussed. It is shown that for the particular turbulence data considered anisotropy causes the high-frequency self-noise to be beamed downstream.