The turbulent mixing layer with an asymmetrical distribution of temperature

1978 ◽  
Vol 89 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Claude Béguier ◽  
Louis Fulachier ◽  
James F. Keffer
Keyword(s):  
Mixing Layer ◽  
Low Frequency ◽  
Passive Scalar ◽  
Frequency Component ◽  
Temperature Fields ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Turbulent Mixing Layer ◽  
The Mean ◽  
Large Eddies

An experimental programme has been carried out to examine the spread of heat as a passive scalar contaminant in a turbulent shear flow. The situation involves a slightly heated two-dimensional jet expanding into a quiescent medium on one side and a uniform stream with velocity equal to that of the warm jet on the other. Thus the developed flow is a typical mixing layer with an asymmetric mean temperature profile superimposed on it. Measurements of the mean and fluctuating velocity and temperature fields show the existence of a region where the production of temperature fluctuations is negative. Spectral analysis in this zone indicates a separation of large and small wavenumber components of the cospectrum into two regimes. The sign of the high-frequency portion is consistent with gradient-transport concepts while the low-frequency component is of opposite sign. From this it is inferred that the large eddies are mainly responsible for the negative production. A mathematical model has been developed to describe the transport within this region.

Anisotropic pressure correlation spectra in turbulent shear flow

2012 ◽  
Vol 694 ◽  
pp. 50-77 ◽  
Author(s):  
Yoshiyuki Tsuji ◽  
Yukio Kaneda
Keyword(s):  
Mixing Layer ◽  
Inertial Subrange ◽  
Turbulent Shear ◽  
Pressure Probe ◽  
Anisotropic Pressure ◽  
Turbulent Shear Flow ◽  
Velocity Correlation ◽  
Mean Velocity ◽  
Correlation Spectrum ◽  
The Mean

AbstractWe measured the correlation spectrum ${\hat {Q} }_{p} (\mathbi{k})$ of pressure fluctuations in a driving mixing layer with a Taylor-scale Reynolds number ${R}_{\lambda } $ up to ${\simeq }700$ by a newly developed pressure probe with spatial and temporal resolutions that are sufficient to analyse inertial-subrange statistics. The influence of the mean velocity gradient tensor ${S}_{ij} $ in the mixing layer, which is almost constant near its centreline, is studied using an idea similar to that underlying the linear response theory developed in statistical mechanics for systems at or near thermal equilibrium. If we write the spectrum ${\hat {Q} }_{p} (\mathbi{k})$ as ${\hat {Q} }_{p} (\mathbi{k})= { \hat {Q} }_{p}^{(0)} (\mathbi{k})+ \mrm{\Delta} {\hat {Q} }_{p} (\mathbi{k})$, where ${ \hat {Q} }_{p}^{(0)} (\mathbi{k})$ is the isotropic Kolmogorov spectrum in the absence of mean shear, then for small ${S}_{ij} $ the deviation $ \mrm{\Delta} {\hat {Q} }_{p} (\mathbi{k})$ due to the shear is approximately linear and is determined by a few non-dimensional universal constants in addition to ${S}_{ij} $, $k$ and the mean energy dissipation rate. We also measured the pressure–velocity and velocity–velocity correlation spectra. Deviations from isotropy due to shear are shown to be approximately proportional to ${S}_{ij} $ at large ${R}_{\lambda } $.

The maintenance of Reynolds stress in turbulent shear flow

1967 ◽  
Vol 27 (1) ◽  
pp. 131-144 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Reynolds Stress ◽  
Mixing Layer ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
The Mean

A mechanism is proposed for the manner in which the turbulent components support Reynolds stress in turbulent shear flow. This involves a generalization of Miles's mechanism in which each of the turbulent components interacts with the mean flow to produce an increment of Reynolds stress at the ‘matched layer’ of that particular component. The summation over all the turbulent components leads to an expression for the gradient of the Reynolds stress τ(z) in the turbulence\[ \frac{d\tau}{dz} = {\cal A}\Theta\overline{w^2}\frac{d^2U}{dz^2}, \]where${\cal A}$is a number, Θ the convected integral time scale of thew-velocity fluctuations andU(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate thatA= 0·24 in this case. In other flows, it would be expected to be of the same order, though its precise value may vary somewhat from one to another.

An experimental examination of the large-eddy equilibrium hypothesis

1966 ◽  
Vol 24 (1) ◽  
pp. 89-98 ◽  
Author(s):  
Ian S. Gartshore
Keyword(s):  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Turbulent Shear Flow ◽  
Mean Velocity ◽  
Large Eddy ◽  
Energy Equilibrium ◽  
The Mean ◽  
Large Eddies ◽  
Made In

The large-eddy energy equilibrium hypothesis states that the largest eddies of a turbulent shear flow are in approximate energy equilibrium throughout a significant part of their lives. This hypothesis leads to a relationship between the mean rate of shear strain and the Reynolds shear stress which involves the scale of the large eddies. By assuming that the large-eddy scale is proportional to the standard deviation of the free turbulent boundary, or laminar superlayer, the validity of this hypothesis may be checked experimentally. Intermittency and mean velocity measurements made in five different two-dimensional shear flows are presented and these results, together with values calculated from Townsend's measurements in a two-dimensional wake, support the form of relationship suggested by the energy equilibrium hypothesis.

On the logarithmic region in wall turbulence

2013 ◽  
Vol 716 ◽  
Author(s):  
Ivan Marusic ◽  
Jason P. Monty ◽  
Marcus Hultmark ◽  
Alexander J. Smits
Keyword(s):  
Wall Turbulence ◽  
Turbulent Shear ◽  
Recent Experimental Data ◽  
Turbulent Shear Flow ◽  
Number Range ◽  
The Past ◽  
Logarithmic Region ◽  
The Mean ◽  
Logarithmic Functions ◽  
Considerable Discussion

AbstractConsiderable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally$2\times 1{0}^{4} \lt {\mathit{Re}}_{\tau } \lt 6\times 1{0}^{5} $for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall.

Second-order modeling of a passive scalar in a turbulent shear flow

AIAA Journal ◽  
1990 ◽  
Vol 28 (4) ◽  
pp. 610-617 ◽  
Author(s):  
T.-H. Shih ◽  
J. L. Lumley ◽  
J.-Y. Chen
Keyword(s):  
Shear Flow ◽  
Passive Scalar ◽  
Second Order ◽  
Turbulent Shear ◽  
Turbulent Shear Flow

scholarly journals The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study

1997 ◽  
Vol 330 ◽  
pp. 307-338 ◽  
Author(s):  
A. SIMONE ◽  
G.N. COLEMAN ◽  
C. CAMBON
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Kinetic Energy ◽  
Shear Flow ◽  
Direct Numerical Simulation ◽  
Pure Shear ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Rapid Distortion Theory ◽  
The Mean

The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure–strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure–dilatation correlation or the dilatational dissipation. The central role of a ‘distortion Mach number’ Md =  S[lscr ]/a, where S is the mean strain or shear rate, [lscr ] a lengthscale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the distortion Mach number increases; for St > 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This ‘crossover’ behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier–Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.

Analysis of Surface Topography Characteristics in Electrochemical Mechanical Finishing

2010 ◽  
Vol 126-128 ◽  
pp. 658-663 ◽  
Author(s):  
Ze Fei Wei ◽  
Wen Ji Xu ◽  
Gui Bing Pang ◽  
Xu Yue Wang
Keyword(s):  
Surface Topography ◽  
Low Frequency ◽  
Surface Profile ◽  
Frequency Component ◽  
Original Surface ◽  
Auto Correlation ◽  
Before And After ◽  
Auto Correlation Function ◽  
The Mean ◽  
Quality Material

In this paper, surface topography characteristics of electrochemical mechanical finishing (ECMF) for steel was investigated. The scanning electron microscopy (SEM) was used to observe the surface topography. And the microcosmic geometry parameters were measured by Talysurf SLI2000. Compared with original surface, the surface topography characteristics of the workpiece machined by ECMF have been analyzed with altitude density function (ADF) and auto correlation function (ACF). The results show that there exist periodicity component in surface profile before and after finishing. The auto correlation curves of ECMF surface have a smaller average period compared with grinding surface. The low-frequency component and the mean ripple peak distance of original surface profile are obviously decreased. Furthermore, the ripples and peak density are increased, and the surface roughness Ra is decreased from 0.231μm to 0.023μm. The results indicate that surface quality, material ratio of the profile and wear resistance machined by ECMF are improved obviously.

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