Turbulent Statistics of Nearly Isotropic Turbulence Generated by Four Rotating Grids and the Mean Falling Velocity of Particle Through Turbulence

2007 ◽  
Author(s):  
Tatsuo Ushijima ◽  
Osami Kitoh
Keyword(s):  
Isotropic Turbulence ◽  
Terminal Velocity ◽  
Mean Velocity ◽  
Velocity Autocorrelation ◽  
Air Turbulence ◽  
Turbulent Statistics ◽  
Experimental Apparatus ◽  
Particle Property ◽  
The Mean ◽  
Lda Measurement

Box air turbulence is experimentally generated in a rectangular box by using four counter-rotating grids installed inside. Turbulence statistics are obtained from one-point measurement of LDA. Nearly isotropic turbulence with zero-mean velocity is realised in the midst of four rotating grids. The dissipation rate is estimated from the Taylor time microscale of velocity autocorrelation obtained from LDA measurement, since Taylor’s frozen turbulence hypothesis is not applicable. From this estimation, the Reynolds number based on the Taylor length microscale becomes about 200 at maximum in the present experimental apparatus. The mean falling velocity of small particle in turbulent flow is measured in the box turbulence. It is found that the mean falling velocity of the inertia particle could be smaller or larger than the terminal velocity, depending on the particle property, if the ratios of particle response time to turbulence time scale are the same.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

scholarly journals Wind Turbulence Statistics of the Atmospheric Inertial Sublayer under Near-Neutral Conditions

Atmosphere ◽  
2020 ◽  
Vol 11 (10) ◽  
pp. 1087
Author(s):  
Eslam Reda Lotfy ◽  
Zambri Harun
Keyword(s):  
Boundary Layer ◽  
Atmospheric Stability ◽  
Turbulent Velocity ◽  
Stability Conditions ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Turbulent Statistics ◽  
The Mean ◽  
The Law ◽  
Velocity Variances

The inertial sublayer comprises a considerable and critical portion of the turbulent atmospheric boundary layer. The mean windward velocity profile is described comprehensively by the Monin–Obukhov similarity theory, which is equivalent to the logarithmic law of the wall in the wind tunnel boundary layer. Similar logarithmic relations have been recently proposed to correlate turbulent velocity variances with height based on Townsend’s attached-eddy theory. The theory is particularly valid for high Reynolds-number flows, for example, atmospheric flow. However, the correlations have not been thoroughly examined, and a well-established model cannot be reached for all turbulent variances similar to the law of the wall of the mean-velocity. Moreover, the effect of atmospheric thermal condition on Townsend’s model has not been determined. In this research, we examined a dataset of free wind flow under a near-neutral range of atmospheric stability conditions. The results of the mean velocity reproduce the law of the wall with a slope of 2.45 and intercept of −13.5. The turbulent velocity variances were fitted by logarithmic profiles consistent with those in the literature. The windward and crosswind velocity variances obtained the average slopes of −1.3 and −1.7, respectively. The slopes and intercepts generally increased away from the neutral state. Meanwhile, the vertical velocity and temperature variances reached the ground-level values of 1.6 and 7.8, respectively, under the neutral condition. The authors expect this article to be a groundwork for a general model on the vertical profiles of turbulent statistics under all atmospheric stability conditions.

Evolution and modelling of subgrid scales during rapid straining of turbulence

1999 ◽  
Vol 387 ◽  
pp. 281-320 ◽  
Author(s):  
SHEWEN LIU ◽  
JOSEPH KATZ ◽  
CHARLES MENEVEAU
Keyword(s):  
Constant Coefficient ◽  
Mixed Model ◽  
Isotropic Turbulence ◽  
A Priori ◽  
Constant Strain Rate ◽  
Water Tank ◽  
Smagorinsky Model ◽  
Mean Velocity ◽  
Similarity Model ◽  
The Mean

The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model. Analysis of the evolution of total SGS energy dissipation reveals, surprisingly, that the Smagorinsky model with a constant coefficient (determined from isotropic turbulence data) underpredicts the dissipation during rapid straining. While the partial dissipation −〈τ(T)ijS˜ij〉 (due only to the turbulent part of the stress) is overpredicted by the Smagorinsky model, addition of the cross-terms reverses the trend. The similarity model with a constant coefficient appropriate for isotropic turbulence, on the other hand, overpredicts SGS dissipation. Owing to these opposite trends a linear combination of both models (mixed model) provides better prediction of SGS dissipation during rapid straining. However, the mixed model with coefficients determined from dissipation balance underpredicts the SGS stress.

Separated and Reattached Flow Over Square, Rectangular and Semi-Circular Blocks

2007 ◽  
Author(s):  
M. Agelinchaab ◽  
M. F. Tachie
Keyword(s):  
Boundary Layer ◽  
Cross Sections ◽  
Recirculation Region ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Block Height ◽  
Turbulent Statistics ◽  
Image Velocimetry ◽  
The Mean ◽  
Separated And Reattached Flow

A particle image velocimetry is used to study the characteristics of separated and reattached turbulent flow over two-dimensional transverse blocks of square, rectangular and semi-circular cross-sections fixed to the bottom wall of an open channel. The ratio of upstream boundary layer thickness to block height is considerably higher than in prior studies. The results show that the mean and turbulent statistics in the recirculation region and downstream of reattachment are significantly different from the upstream boundary layer. The variation of the Reynolds stresses along the separating streamlines is discussed within the context of vortex stretching, longitudinal strain rate and wall damping. It appears wall damping is a more dominant mechanism in the vicinity of reattachment. The levels of turbulence diffusion and production by the normal stresses are significantly higher than in classical turbulent boundary layers. The bulk of turbulence production occurs in mid-layer and transported into the inner and outer layers. The results also reveal that the curvature of separating streamline, separating bubble beneath it as well as the mean velocity and turbulent quantities depend strongly on block geometry.

The mean velocity of slightly buoyant and heavy particles in turbulent flow in a pipe

1958 ◽  
Vol 4 (1) ◽  
pp. 87-96 ◽  
Author(s):  
A. M. Binnie ◽  
O. M. Phillips
Keyword(s):  
Turbulent Flow ◽  
Relative Density ◽  
Terminal Velocity ◽  
Neutral Density ◽  
Mean Velocity ◽  
Heavy Particles ◽  
Horizontal Pipe ◽  
The Mean ◽  
The Times

A large number of small spheres of the same size were injected successively into a horizontal pipe conveying water at constant mean velocity, and their times of transit were measured. The mean velocity of the spheres that were either somewhat heavier or lighter than water was less than that of those of neutral density; for those having a terminal velocity in water within ± 1% of the mean velocity of the water in the pipe, the discrepancy was only about 0.1%. The dispersion of the times of transit of the spheres was almost independent of their density. A theory is developed to show how the mean velocity of the spheres depends upon their relative density and size.

Three-Dimensional Laser Anemometer Measurements in an Annular Seal

1991 ◽  
Vol 113 (3) ◽  
pp. 421-427 ◽  
Author(s):  
G. L. Morrison ◽  
M. C. Johnson ◽  
G. B. Tatterson
Keyword(s):  
Reynolds Stress ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Mean Velocity ◽  
Anisotropic Turbulence ◽  
Laser Anemometer ◽  
Annular Seal ◽  
The Mean ◽  
Tensor Distributions ◽  
Anemometer System

The flow field inside an annular seal with a 1.27 mm clearance is investigated using a 3-D laser Doppler anemometer system. Through the use of this system, the mean velocity vector and the entire Reynolds stress tensor distributions are measured for the entire length of the seal (37.3 mm). The seal is operated at a Reynolds number of 18,600 and a Taylor number of 4500. The annular seal is found to produce anisotropic turbulence since the Reynolds stress measurements show the flow entering the seal with isotropic turbulence but exiting the seal with anisotropic turbulence.

The vertical diffusivity and mean velocity of particles in a horizontal water pipe

1963 ◽  
Vol 15 (1) ◽  
pp. 35-48 ◽  
Author(s):  
B. J. S. Barnard ◽  
A. M. Binnie
Keyword(s):  
Relative Density ◽  
Cross Section ◽  
Terminal Velocity ◽  
Galvanized Steel ◽  
Water Pipe ◽  
Mean Velocity ◽  
Vertical Diffusivity ◽  
The Mean ◽  
The Times

Small spheres of the same size but of relative density varying from 0·92 to 1·25 were injected in turn into a horizontal water pipe, in which the flow was turbulent and the mean velocity was constant. A cross-section near the outlet was illuminated; the positions of the spheres as they crossed it were measured by photography, and the relation was established between the terminal velocity of the of the spheres in water and the vertical diffusivity. The velocity of the spheres along the pipe was found to be somewhat different in the galvanized steel and Perspex lengths of which the pipe was composed. The dispersion of the times of transit of the spheres increased slightly with their densisty. For purposes of comparison the theoretical velocity along the pipe was also calculated from the photographic measurements.

Rapid distortion of turbulence into an open turbine rotor

2017 ◽  
Vol 825 ◽  
pp. 764-794 ◽  
Author(s):  
J. M. R. Graham
Keyword(s):  
Isotropic Turbulence ◽  
Strain Analysis ◽  
Turbine Rotor ◽  
Small Scale ◽  
Mean Flow ◽  
Mean Velocity ◽  
Actuator Disc ◽  
Tidal Turbine ◽  
Tidal Stream ◽  
The Mean

Rapid distortion of turbulence (RDT) theory is applied to homogeneous, isotropic turbulence incident on a horizontal axis turbine rotor such as a wind turbine or tidal-stream turbine. The mean flow field of the rotor which distorts the turbulence is represented by the commonly used axisymmetric actuator disc model due to Betz and Joukowski. The fluctuating streamwise component of the turbulence distorted by this field is calculated at the actuator disc plane. Turbulence velocity intensities and spectra are evaluated for general ratios of turbulence integral length scale to the rotor diameter, including the small-scale limit for which the original homogeneous strain analysis of Batchelor and Proudman may be applied. The distortion of the mean velocity profile of an incident rotor wake which may be considered a zero frequency disturbance relevant to wind and tidal turbine operation in large arrays is also analysed by the same method, treating it as a deterministic disturbance in the incident flow.

On the motion of gas bubbles in homogeneous isotropic turbulence

1997 ◽  
Vol 336 ◽  
pp. 221-244 ◽  
Author(s):  
P. D. M. SPELT ◽  
A. BIESHEUVEL
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Gas Bubbles ◽  
Numerical Data ◽  
Equation Of Motion ◽  
Equivalent Diameter ◽  
Approximate Analysis ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Velocity ◽  
The Mean

This paper is concerned with the motion of small gas bubbles, equivalent diameter about 1.0 mm, in isotropic turbulent flows. Data on the mean velocity of rise and the dispersion of the bubbles have been obtained numerically by simulating the turbulence as a sum of Fourier modes with random phases and amplitudes determined by the Kraichnan and the von Kármán–Pao energy-spectrum functions, and by calculating the bubble trajectories from a reasonably well-established equation of motion. The data cover the range β[les ]1, where β is the ratio between the turbulence intensity and the velocity of rise of the bubbles in still fluid. An approximate analysis based on the assumption that β is small yields results that compare favourably with the numerical data, and clarifies the important role played by the lift forces exerted by the fluid.

Large-Eddy Simulation of Turbulent Flow in a Curved Pipe

1996 ◽  
Vol 118 (2) ◽  
pp. 248-254 ◽  
Author(s):  
B. J. Boersma ◽  
F. T. M. Nieuwstadt
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flow ◽  
Mean Velocity ◽  
Curved Pipe ◽  
Eddy Simulation ◽  
Turbulent Statistics ◽  
Large Eddy ◽  
Secondary Motion ◽  
Fully Developed Turbulent Flow ◽  
The Mean

In this paper, we use Large-Eddy Simulation (LES) to compute a fully-developed turbulent flow in a curved pipe. The results allow us to study how the curvature influences the mean velocity profile and also various turbulent statistics. We find reasonable agreement with the few experiments that are available. Our simulation also allows a detailed study of secondary motion in the cross section of the pipe which are caused by the centrifugal acceleration due to the pipe curvature. It is known that this secondary motion may consist of one, two, or three circulation cells. In our simulation results we find one circulation cell.

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