The Fully Developed Wake of a Circular Cylinder

1949 ◽  
Vol 2 (4) ◽  
pp. 451 ◽  
Author(s):  
AA Townsend
Keyword(s):  
Circular Cylinder ◽  
Diffusion Coefficients ◽  
Large Scale ◽  
Turbulent Transport ◽  
Turbulent Energy ◽  
Small Scale ◽  
Mean Velocity ◽  
Turbulent Fluid ◽  
Air Stream ◽  
Scale Motion

Extending previous work on turbulent diffusion in the wake of a circular-cylinder, a series of measurements have been made of the turbulent transport of mean stream momentum, turbulent energy, and heat in the wake of a cylinder of 0.169 cm. diameter, placed in an air-stream of velocity 1280 cm. sec.-1. It has been possible to extend the measurements to 960 diameters down-stream from the cylinder, and it 1s found that, at distances in excess of 600 diameters, the requirements of dynamical similarity are very nearly satisfied. To account for the observed rates of transport of turbulent energy and heat, it is necessary that only part of this transport be due to bulk convection by the slow large-scale motion of the jets of turbulent fluid emitted by the central, fully turbulent core of the wake, which had been supposed previously to perform most of the transport. The remainder of the transport is carried out by the small-scale diffusive motion of the turbulent eddies within the jets, and may be described by assigning diffusion coefficients to the turbulent fluid. It is found that the diffusion coefficients for momentum and heat are approximately equal, but that for turbulent energy is considerably smaller. On the basis of these hypotheses, it is possible to calculate $he form of the mean velocity distribution in good agreement with experiment, and to give a qualitative explanation of the apparently more rapid diffusion of heat.

Two-Component Phase-Averaged Turbulence Statistics Downstream of a Rotating Spoked-Wheel Wake Generator

1989 ◽  
Vol 111 (4) ◽  
pp. 475-482 ◽  
Author(s):  
J. E. O’Brien ◽  
S. P. Capp
Keyword(s):  
Vortex Shedding ◽  
Large Scale ◽  
Guide Vane ◽  
Turbulent Transport ◽  
Turbulent Energy ◽  
Tangential Component ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Velocity Probability ◽  
Probability Density Distributions

Measurements of the axial and tangential components of the unsteady turbulent flow downstream of a rotating spoked-wheel wake generator have been obtained. The results of this study have implications for the use of this type of wake generator to produce simulated turbine guide vane wakes. Instantaneous velocity information was phase averaged based on a signal synchronized with the bar-passing frequency. Mean velocity profiles and phase-averaged Reynolds stress results were found to be consistent with measurements obtained behind a stationary cylinder. Reynolds stresses were significantly higher than corresponding measurements obtained in large-scale research turbomachines, however. Phase-averaged triple velocity correlations, also calculated from the digital velocity records, reveal the sign and magnitude of skewness in the velocity probability density distributions for the two components. Large crossflow gradients observed in the triple correlations in the wake indicate the importance of the tangential-component fluctuations in the net turbulent transport of turbulent energy across the wake. Streamwise-component wake velocity spectra for low values of reduced bar-passing frequency include a peak associated with vortex shedding from the cylindrical wake-generating bars at a shedding Strouhal number of 0.2. For higher bar-passing frequencies, the energy associated with vortex shedding is shifted to lower frequencies and becomes broadband from the stationary reference frame viewpoint.

A numerical study of the transition of jet diffusion flames

1990 ◽  
Vol 431 (1882) ◽  
pp. 301-314 ◽  
Keyword(s):  
Reynolds Number ◽  
Diffusion Coefficient ◽  
Large Scale ◽  
Numerical Study ◽  
Small Scale ◽  
Surface Model ◽  
Flame Surface ◽  
Transition Mechanism ◽  
Air Stream ◽  
Scale Fluctuation

A numerical study on the transition from laminar to turbulent of two-dimensional fuel jet flames developed in a co-flowing air stream was made by adopting the flame surface model of infinite chemical reaction rate and unit Lewis number. The time dependent compressible Navier–Stokes equation was solved numerically with the equation for coupling function by using a finite difference method. The temperature-dependence of viscosity and diffusion coefficient were taken into account so as to study effects of increases of these coefficients on the transition. The numerical calculation was done for the case when methane is injected into a co-flowing air stream with variable injection Reynolds number up to 2500. When the Reynolds number was smaller than 1000 the flame, as well as the flow, remained laminar in the calculated domain. As the Reynolds number was increased above this value, a transition point appeared along the flame, downstream of which the flame and flow began to fluctuate. Two kinds of fluctuations were observed, a small scale fluctuation near the jet axis and a large scale fluctuation outside the flame surface, both of the same origin, due to the Kelvin–Helmholtz instability. The radial distributions of density and transport coefficients were found to play dominant roles in this instability, and hence in the transition mechanism. The decreased density in the flame accelerated the instability, while the increase in viscosity had a stabilizing effect. However, the most important effect was the increase in diffusion coefficient. The increase shifted the flame surface, where the large density decrease occurs, outside the shear layer of the jet and produced a thick viscous layer surrounding the jet which effectively suppressed the instability.

scholarly journals On the structure of the self-sustaining cycle in separating and reattaching flows

2018 ◽  
Vol 857 ◽  
pp. 907-936 ◽  
Author(s):  
A. Cimarelli ◽  
A. Leonforte ◽  
D. Angeli
Keyword(s):  
Shear Layer ◽  
Rectangular Plate ◽  
Large Scale ◽  
Reverse Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
The Self ◽  
Small Scale ◽  
Spectral Evolution ◽  
Mean Velocity

The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle.

The power distribution between the symmetric and anti-symmetric components of the tropical wavenumber-frequency spectrum

2021 ◽  
Author(s):  
Ofer Shamir ◽  
Chen Schwartz ◽  
Chaim Garfinkel ◽  
Nathan Paldor
Keyword(s):  
Frequency Spectrum ◽  
Power Distribution ◽  
Large Scale ◽  
Spectral Power ◽  
Spatial Scales ◽  
Turbulent Energy ◽  
Heat Fluxes ◽  
Small Scale ◽  
Ample Evidence ◽  
Parity Distribution

<p>A yet unexplained feature of the tropical wavenumber-frequency spectrum is its parity distributions, i.e., the distribution of power between the meridionally symmetric and anti-symmetric components of the spectrum. Due to the linearity of the decomposition to symmetric and anti-symmetric components and the Fourier analysis, the total spectral power equals the sum of the power contained in each of these two components. However, the spectral power need not be evenly distributed between the two components. Satellite observations and reanalysis data provide ample evidence that the parity distribution of the tropical wavenumber-frequency spectrum is biased towards its symmetric component. Using an intermediate-complexity model of an idealized moist atmosphere, we find that the parity distribution of the tropical spectrum is nearly insensitive to large-scale forcing, including topography, ocean heat fluxes, and land-sea contrast. On the other hand, by adding a small-scale (stochastic) forcing, we find that the parity distribution of the tropical spectrum is sensitive to asymmetries on small spatial scales compared to the observed large-scale spectrum. Physically, such forcing can be thought of as small-scale convection, which is believed to trigger some of the Tropics' large-scale features via an upscale (inverse) turbulent energy cascade. These results are qualitatively explained by considering the effects of triad interactions on the parity distribution. According to the proposed mechanism, any small-scale asymmetry (symmetric or anti-symmetric) in the forcing leads to symmetric bias in the spectrum, regardless of the source of variability providing the forcing.</p>

Turbulent spots in a channel: large-scale flow and self-sustainability

2013 ◽  
Vol 731 ◽  
Author(s):  
Grégoire Lemoult ◽  
Jean-Luc Aider ◽  
José Eduardo Wesfreid
Keyword(s):  
Large Scale ◽  
Large Time ◽  
Rectangular Channel ◽  
Small Scale ◽  
Turbulent Spot ◽  
Time Resolved ◽  
Image Velocimetry ◽  
Streamwise Streaks ◽  
Large Scale Flow ◽  
Scale Motion

AbstractUsing a large-time-resolved particle image velocimetry field of view, a developing turbulent spot is followed in space and time in a rectangular channel flow for more than 100 advective time units. We show that the flow can be decomposed into a large-scale motion consisting of an asymmetric quadrupole centred on the spot and a small-scale part consisting of streamwise streaks. From the temporal evolution of the energy of the streamwise and spanwise velocity perturbations, it is suggested that a self-sustaining process can occur in a turbulent spot above a given Reynolds number.

scholarly journals Anisotropic Characteristics of Turbulence Dissipation in Swirling Flow: A Direct Numerical Simulation Study

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xingtuan Yang ◽  
Nan Gui ◽  
Gongnan Xie ◽  
Jie Yan ◽  
Jiyuan Tu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Energy Dissipation ◽  
Direct Numerical Simulation ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Turbulent Energy ◽  
Swirling Flows ◽  
Small Scale

This study investigates the anisotropic characteristics of turbulent energy dissipation rate in a rotating jet flow via direct numerical simulation. The turbulent energy dissipation tensor, including its eigenvalues in the swirling flows with different rotating velocities, is analyzed to investigate the anisotropic characteristics of turbulence and dissipation. In addition, the probability density function of the eigenvalues of turbulence dissipation tensor is presented. The isotropic subrange of PDF always exists in swirling flows relevant to small-scale vortex structure. Thus, with remarkable large-scale vortex breakdown, the isotropic subrange of PDF is reduced in strongly swirling flows, and anisotropic energy dissipation is proven to exist in the core region of the vortex breakdown. More specifically, strong anisotropic turbulence dissipation occurs concentratively in the vortex breakdown region, whereas nearly isotropic turbulence dissipation occurs dispersively in the peripheral region of the strong swirling flows.

Triadic scale interactions in a turbulent boundary layer

2015 ◽  
Vol 767 ◽  
Author(s):  
Subrahmanyam Duvvuri ◽  
Beverley J. McKeon
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Small Scale ◽  
Velocity Signal ◽  
Small Scales ◽  
Amplitude Modulation Coefficient ◽  
Scale Turbulence ◽  
Scale Motion ◽  
Phase Relationships

AbstractA formal relationship between the skewness and the correlation coefficient of large and small scales, termed the amplitude modulation coefficient, is established for a general statistically stationary signal and is analysed in the context of a turbulent velocity signal. Both the quantities are seen to be measures of phase in triadically consistent interactions between scales of turbulence. The naturally existing phase relationships between large and small scales in a turbulent boundary layer are then manipulated by exciting a synthetic large-scale motion in the flow using a spatially impulsive dynamic wall roughness perturbation. The synthetic scale is seen to alter the phase relationships, or the degree of modulation, in a quasi-deterministic manner by exhibiting a phase-organizing influence on the small scales. The results presented provide encouragement for the development of a practical framework for favourable manipulation of energetic small-scale turbulence through large-scale inputs in a wall-bounded turbulent flow.

scholarly journals A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation

2002 ◽  
Vol 450 ◽  
pp. 377-407 ◽  
Author(s):  
S. A. STANLEY ◽  
S. SARKAR ◽  
J. P. MELLADO
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Direct Numerical Simulation ◽  
Large Scale ◽  
Computational Study ◽  
Practical Interest ◽  
Small Scale ◽  
Mixing Process ◽  
Mean Velocity ◽  
Small Scales

Turbulent plane jets are prototypical free shear flows of practical interest in propulsion, combustion and environmental flows. While considerable experimental research has been performed on planar jets, very few computational studies exist. To the authors' knowledge, this is the first computational study of spatially evolving three-dimensional planar turbulent jets utilizing direct numerical simulation. Jet growth rates as well as the mean velocity, mean scalar and Reynolds stress profiles compare well with experimental data. Coherency spectra, vorticity visualization and autospectra are obtained to identify inferred structures. The development of the initial shear layer instability, as well as the evolution into the jet column mode downstream is captured well.The large- and small-scale anisotropies in the jet are discussed in detail. It is shown that, while the large scales in the flow field adjust slowly to variations in the local mean velocity gradients, the small scales adjust rapidly. Near the centreline of the jet, the small scales of turbulence are more isotropic. The mixing process is studied through analysis of the probability density functions of a passive scalar. Immediately after the rollup of vortical structures in the shear layers, the mixing process is dominated by large-scale engulfing of fluid. However, small-scale mixing dominates further downstream in the turbulent core of the self-similar region of the jet and a change from non-marching to marching PDFs is observed. Near the jet edges, the effects of large-scale engulfing of coflow fluid continue to influence the PDFs and non-marching type behaviour is observed.

Study of the Reduction of Turbulent Drag by Photon Correlation Spectroscopy

1991 ◽  
Vol 248 ◽  
Author(s):  
P. Tong ◽  
W. I. Goldburg ◽  
J. S. Huang
Keyword(s):  
Large Scale ◽  
Functional Form ◽  
Photon Correlation Spectroscopy ◽  
Turbulent Energy ◽  
Correlation Spectroscopy ◽  
Small Scale ◽  
Concentric Cylinder ◽  
Photon Correlation ◽  
Suppression Effect ◽  
Turbulent Drag

AbstractTurbulent drag reduction in a dilute polymer solution has been studied using the technique of photon-correlation homodyne spectroscopy to measure velocity differences in a concentric cylinder cell, in which the inner cylinder rotates. A large anisotropic suppression of turbulent velocity differences is found in the bulk region of the turbulent fluid. The suppression effect occurs at various length scales up to ∼ 1 mm, which is far beyond the Kolmogorov dissipation length ℓd (∼ 0.04 mm). The large-scale velocity fluctuations are suppressed, but their statistical properties remain unchanged. The small-scale fluctuations, on the other hand, are damped out much more strongly, resulting in a different functional form for the velocity density function. The latter observation is consistent with the notion that the polymer-turbulence interaction causes a truncation of the turbulent energy cascade at small scales.

A description of the organized motion in the turbulent far wake of a cylinder at low Reynolds number

1987 ◽  
Vol 184 ◽  
pp. 423-444 ◽  
Author(s):  
R. A. Antonia ◽  
L. W. B. Browne ◽  
D. K. Bisset ◽  
L. Fulachier
Keyword(s):  
Reynolds Number ◽  
Saddle Point ◽  
Large Scale ◽  
Heat Fluxes ◽  
Small Scale ◽  
Shear Stresses ◽  
Temperature Variance ◽  
Large Scale Motion ◽  
Scale Motion ◽  
Far Wake

The topology of the organized motion has been obtained in the slightly heated self-preserving far wake of a circular cylinder at a Reynolds number, based on the cylinder diameter, of about 1200. In a frame of reference moving with the organized motion, the toplogy in the plane of main shear reduces to a succession of centres and saddles, located at about the wake half-width. Centres are identifiable by large values of spanwise vorticity associated with the coherent large-scale motion. Saddles occur at the intersection of converging and diverging separatrices, the latter being identifiable with the high strain rate due to the large-scale motion. Large values of the longitudinal turbulence intensity associated with the smaller-scale motion occur at the centres. High values of the normal and shear stresses, the temperature variance and heat fluxes associated with the large-scale motion occur on either side of each saddle point along the direction of the diverging separatrix. Contours for the production of energy and temperature variance associated with the small-scale motion are aligned along the diverging separatrices, and have maxima near the saddle point. Contours for one component of the dissipation of small-scale temperature variance also have a high concentration along the diverging separatrix. Flow visualizations in the far wake suggest the existence of groups of three-dimensional bulges which are made up of clusters of vortex loops.

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