The structure and dynamics of backflow in turbulent channels

2019 ◽  
Vol 880 ◽  
Author(s):  
J. I. Cardesa ◽  
J. P. Monty ◽  
J. Soria ◽  
M. S. Chong
Keyword(s):  
Streamwise Velocity ◽  
Viscous Sublayer ◽  
Spanwise Direction ◽  
Streamwise Direction ◽  
Mean Velocity ◽  
Number Range ◽  
Structure And Dynamics ◽  
The Mean ◽  
Turbulent Plane ◽  
Increasing Function

A statistical description of flow regions with negative streamwise velocity is provided based on simulations of turbulent plane channels in the Reynolds number range $547\leqslant Re_{\unicode[STIX]{x1D70F}}\leqslant 2003$. It is found that regions of backflow are attached and their density per surface area – in wall units – is an increasing function of $Re_{\unicode[STIX]{x1D70F}}$. Their size distribution along the three coordinates reveals that, even though in the mean they appear to be circular in the wall-parallel plane, they tend to become more elongated in the spanwise direction after reaching a certain height. Time-tracking of backflow regions in a $Re_{\unicode[STIX]{x1D70F}}=934$ simulation showed they convect downstream at the mean velocity corresponding to $y^{+}\approx 12$, they seldom interact with other backflow events, their statistical signature extends in the streamwise direction for at least $300$ wall units, and they result from a complex interaction between regions of high and low spanwise vorticity far beyond the viscous sublayer. This could explain why some statistical aspects of these near-wall events do not scale in viscous units; they are dependent on the $Re_{\unicode[STIX]{x1D70F}}$-dependent dynamics further away from the wall.

The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow

1974 ◽  
Vol 65 (3) ◽  
pp. 439-459 ◽  
Author(s):  
Helmut Eckelmann
Keyword(s):  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Viscous Sublayer ◽  
Wall Region ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Mean Values ◽  
The Mean

Hot-film anemometer measurements have been carried out in a fully developed turbulent channel flow. An oil channel with a thick viscous sublayer was used, which permitted measurements very close to the wall. In the viscous sublayer between y+ ≃ 0·1 and y+ = 5, the streamwise velocity fluctuations decreased at a higher rate than the mean velocity; in the region y+ [lsim ] 0·1, these fluctuations vanished at the same rate as the mean velocity.The streamwise velocity fluctuations u observed in the viscous sublayer and the fluctuations (∂u/∂y)0 of the gradient at the wall were almost identical in form, but the fluctuations of the gradient at the wall were found to lag behind the velocity fluctuations with a lag time proportional to the distance from the wall. Probability density distributions of the streamwise velocity fluctuations were measured. Furthermore, measurements of the skewness and flatness factors made by Kreplin (1973) in the same flow channel are discussed. Measurements of the normal velocity fluctuations v at the wall and of the instantaneous Reynolds stress −ρuv were also made. Periods of quiescence in the − ρuv signal were observed in the viscous sublayer as well as very active periods where ratios of peak to mean values as high as 30:1 occurred.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

Investigation of Boundary Layer Flows Over a Flat Plate With Different-Size Transverse Square Grooves at s/w = 10

2007 ◽  
Author(s):  
Redha Wahidi ◽  
Walid Chakroun ◽  
Sami Al-Fahad
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Viscous Sublayer ◽  
Velocity Profiles ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Uncertainty Range ◽  
The Mean

Turbulent boundary layer flows over a flat plate with multiple transverse square grooves spaced 10 element widths apart were investigated. Mean velocity profiles, turbulence intensity profiles, and the distributions of the skin-friction coefficients (Cf) and the integral parameters are presented for two grooved walls. The two transverse square groove sizes investigated are 5mm and 2.5mm. Laser-Doppler Anemometer (LDA) was used for the mean velocity and turbulence intensity measurements. The skin-friction coefficient was determined from the gradient of the mean velocity profiles in the viscous sublayer. Distribution of Cf in the first grooved-wall case (5mm) shows that Cf overshoots downstream of the groove and then oscillates within the uncertainty range and never shows the expected undershoot in Cf. The same overshoot is seen in the second grooved-wall case (2.5mm), however, Cf continues to oscillate above the uncertainty range and never returns to the smooth-wall value. The mean velocity profiles clearly represent the behavior of Cf where a downward shift is seen in the Cf overshoot region and no upward shift is seen in these profiles. The results show that the smaller grooves exhibit larger effects on Cf, however, the boundary layer responses to these effects in a slower rate than to those of the larger grooves.

Simplified theory of the near-wall turbulent layer of Newtonian and drag-reducing fluids

1982 ◽  
Vol 119 ◽  
pp. 423-441 ◽  
Author(s):  
M. A. Goldshtik ◽  
V. V. Zametalin ◽  
V. N. Shtern
Keyword(s):  
Velocity Profile ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Outer Boundary ◽  
Viscous Sublayer ◽  
Viscous Layer ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
The Mean ◽  
Near Wall

We propose a simplified theory of a viscous layer in near-wall turbulent flow that determines the mean-velocity profile and integral characteristics of velocity fluctuations. The theory is based on the concepts resulting from the experimental data implying a relatively simple almost-ordered structure of fluctuations in close proximity to the wall. On the basis of data on the greatest contribution to transfer processes made by the part of the spectrum associated with the main size of the observed structures, the turbulent fluctuations are simulated by a three-dimensional running wave whose parameters are found from the problem solution. Mathematically the problem reduces to the solution of linearized Navier-Stokes equations. The no-slip condition is satisfied on the wall, whereas on the outer boundary of a viscous layer the conditions of smooth conjunction with the asymptotic shape of velocity and fluctuation-energy profiles resulting from the dimensional analysis are satisfied. The formulation of the problem is completed by the requirement of maximum curvature of the mean-velocity profile on the outer boundary applied from stability considerations.The solution of the problem does not require any quantitative empirical data, although the conditions of conjunction were formulated according to the well-known concepts obtained experimentally. As a result, the near-wall law for the averaged velocity has been calculated theoretically and is in good agreement with experiment, and the characteristic scales for fluctuations have also been determined. The developed theory is applied to turbulent-flow calculations in Maxwell and Oldroyd media. The elastic properties of fluids are shown to lead to near-wall region reconstruction and its associated drag reduction, as is the case in turbulent flows of dilute polymer solutions. This theory accounts for several features typical of the Toms effect, such as the threshold character of the effect and the decrease in the normal fluctuating velocity. The analysis of the near-wall Oldroyd fluid flow permits us to elucidate several new aspects of the drag-reduction effect. It has been established that the Toms effect does not always result in thickening of the viscous sublayer; on the contrary, the most intense drag reduction takes place without thickening in the viscous sublayer.

The distortion of turbulence by a circular cylinder

1979 ◽  
Vol 92 (2) ◽  
pp. 269-301 ◽  
Author(s):  
R. E. Britter ◽  
J. C. R. Hunt ◽  
J. C. Mumford
Keyword(s):  
Circular Cylinder ◽  
Spectral Energy ◽  
Cylinder Surface ◽  
List Type ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Mean Velocity ◽  
Number Range ◽  
Velocity Fluctuations ◽  
The Mean

The flow of grid-generated turbulence past a circular cylinder is investigated using hot-wire anemometry over a Reynolds number range from 4·25 × 103 to 2·74 × 104 and a range of intensities from 0·025 to 0·062. Measurements of the mean velocity distribution, and r.m.s. intensities and spectral energy densities of the turbulent velocity fluctuations are presented for various radial and circumferential positions relative to the cylinder, and for ratios of the cylinder radius a to the scale of the incident turbulence Lx ranging from 0·05 to 1·42. The influence of upstream conditions on the flow in the cylinder wake and its associated induced velocity fluctuations is discussed.For all measurements, detailed comparison is made with the theoretical predictions of Hunt (1973). We conclude the following. The amplification and reduction of the three components of turbulence (which occur in different senses for the different components) can be explained qualitatively in terms of the distortion by the mean flow of the turbulent vorticity and the ‘blocking’ or ‘source’ effect caused by turbulence impinging on the cylinder surface. The relative importance of the first effect over the second increases as a/Lx increases or the distance from the cylinder surface increases.Over certain ranges of the variables involved, the measurements are in quantitative agreement with the predictions of the asymptotic theory when a/Lx [Lt ] 1, a/Lx [Gt ] 1 or |k| a [Gt ] 1 (where k is the wavenumber).The incident turbulence affects the gross properties of the flow in the cylinder wake, but the associated velocity fluctuations are probably statistically independent of those in the incident flow.The dissipation of turbulent energy is greater in the straining flow near the cylinder than in the approach flow. Some estimates for this effect are proposed.

Stokes Mechanism of Drag Reduction

2005 ◽  
Vol 73 (3) ◽  
pp. 483-489 ◽  
Author(s):  
Promode R. Bandyopadhyay
Keyword(s):  
Drag Reduction ◽  
Attenuation Factor ◽  
Viscous Sublayer ◽  
Wall Region ◽  
Mean Velocity ◽  
Turbulence Suppression ◽  
Maximum Drag Reduction ◽  
The Mean ◽  
Stokes Second Problem ◽  
Better Than

The mechanism of drag reduction due to spanwise wall oscillation in a turbulent boundary layer is considered. Published measurements and simulation data are analyzed in light of Stokes’ second problem. A kinematic vorticity reorientation hypothesis of drag reduction is first developed. It is shown that spanwise oscillation seeds the near-wall region with oblique and skewed Stokes vorticity waves. They are attached to the wall and gradually align to the freestream direction away from it. The resulting Stokes layer has an attenuated nature compared to its laminar counterpart. The attenuation factor increases in the buffer and viscous sublayer as the wall is approached. The mean velocity profile at the condition of maximum drag reduction is similar to that due to polymer. The final mean state of maximum drag reduction due to turbulence suppression appears to be universal in nature. Finally, it is shown that the proposed kinematic drag reduction hypothesis describes the measurements significantly better than what current direct numerical simulation does.

Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers

2016 ◽  
Vol 795 ◽  
pp. 210-240 ◽  
Author(s):  
D. T. Squire ◽  
C. Morrill-Winter ◽  
N. Hutchins ◽  
M. P. Schultz ◽  
J. C. Klewicki ◽  
...  
Keyword(s):  
Outer Region ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Rough Wall ◽  
Turbulent Shear ◽  
Smooth Wall ◽  
Mean Velocity ◽  
Wide Range ◽  
Velocity Variance ◽  
The Mean

Turbulent boundary layer measurements above a smooth wall and sandpaper roughness are presented across a wide range of friction Reynolds numbers, ${\it\delta}_{99}^{+}$, and equivalent sand grain roughness Reynolds numbers, $k_{s}^{+}$ (smooth wall: $2020\leqslant {\it\delta}_{99}^{+}\leqslant 21\,430$, rough wall: $2890\leqslant {\it\delta}_{99}^{+}\leqslant 29\,900$; $22\leqslant k_{s}^{+}\leqslant 155$; and $28\leqslant {\it\delta}_{99}^{+}/k_{s}^{+}\leqslant 199$). For the rough-wall measurements, the mean wall shear stress is determined using a floating element drag balance. All smooth- and rough-wall data exhibit, over an inertial sublayer, regions of logarithmic dependence in the mean velocity and streamwise velocity variance. These logarithmic slopes are apparently the same between smooth and rough walls, indicating similar dynamics are present in this region. The streamwise mean velocity defect and skewness profiles each show convincing collapse in the outer region of the flow, suggesting that Townsend’s (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) wall-similarity hypothesis is a good approximation for these statistics even at these finite friction Reynolds numbers. Outer-layer collapse is also observed in the rough-wall streamwise velocity variance, but only for flows with ${\it\delta}_{99}^{+}\gtrsim 14\,000$. At Reynolds numbers lower than this, profile invariance is only apparent when the flow is fully rough. In transitionally rough flows at low ${\it\delta}_{99}^{+}$, the outer region of the inner-normalised streamwise velocity variance indicates a dependence on $k_{s}^{+}$ for the present rough surface.

The Ultimate Asymptote and Mean Flow Structure in Toms’ Phenomenon

1970 ◽  
Vol 37 (2) ◽  
pp. 488-493 ◽  
Author(s):  
P. S. Virk ◽  
H. S. Mickley ◽  
K. A. Smith
Keyword(s):  
Velocity Profile ◽  
Drag Reduction ◽  
Flow Structure ◽  
Viscous Sublayer ◽  
Mixing Length ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Length Constant ◽  
The Mean

The maximum drag reduction in turbulent pipe flow of dilute polymer solutions is ultimately limited by a unique asymptote described by the experimental correlation: f−1/2=19.0log10(NRef1/2)−32.4 The semilogarithmic mean velocity profile corresponding to and inferred from this ultimate asymptote has a mixing-length constant of 0.085 and shares a trisection (at y+ ∼ 12) with the Newtonian viscous sublayer and law of the wall. Experimental mean velocity profiles taken during drag reduction lie in the region bounded by the inferred ultimate profile and the Newtonian law of the wall. At low drag reductions the experimental profiles are well correlated by an “effective slip” model but this fails progressively with increasing drag reduction. Based on the foregoing a three-zone scheme is proposed to model the mean flow structure during drag reduction. In this the mean velocity profile segments are (a) a viscous sublayer, akin to Newtonian, (b) an interactive zone, characteristic of drag reduction, in which the ultimate profile is followed, and (c) a turbulent core in which the Newtonian mixing-length constant applies. The proposed model is consistent with experimental observations and reduces satisfactorily to the Taylor-Prandtl scheme and the ultimate profile, respectively, at the limits of zero and maximum drag reductions.

Analysis of Transitional and Fully Turbulent Plane Couette Flow

1983 ◽  
Vol 105 (3) ◽  
pp. 364-368 ◽  
Author(s):  
J. R. Missimer ◽  
L. C. Thomas
Keyword(s):  
Couette Flow ◽  
Flow Analysis ◽  
Wall Region ◽  
Turbulent Regime ◽  
Plane Couette Flow ◽  
Burst Frequency ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulent Plane ◽  
Turbulent Burst

The two-dimensional, incompressible, fully-developed, turbulent plane Couette flow is a limiting case of circular Couette flow. As such, plane Couette flow analyses have been used in lubrication theory to analyze the lubrication flow in an unloaded journal bearings. A weakness of existing analyses, other than the turbulent burst analysis, is that they are not capable of characterizing the transitional turbulent regime. The objective of the proposed paper is to develop a model of the turbulent burst phenomenon for momentum in transitional turbulent and fully turbulent plane Couette flow. Model closure is obtained by specification of the mean turbulent burst frequency and, for moderate to high Reynolds numbers, by interfacing with classical eddy diffusivity models for the turbulent core. The analysis is shown to produce predictions for the mean velocity profile and friction factor that are in good agreement with published experimental data for transitional turbulent and fully turbulent flow. This approach to modeling the wall region involves a minimum level of empiricism and provides a fundamental basis for generalization. The use of the present analysis extends the applicability of plane Couette flow analysis in lubrication problems to the transitional turbulent regime.

Measurements in a Transitional Boundary Layer With Görtler Vortices

1996 ◽  
Author(s):  
Ralph J. Volino ◽  
Terrence W. Simon
Keyword(s):  
Boundary Layer ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Görtler Vortices ◽  
Concave Wall ◽  
The Mean ◽  
Gortler Vortices

The laminar-turbulent transition process has been documented in a concave-wall boundary layer subject to low (0.6%) free-stream turbulence intensity. Transition began at a Reynolds number, Rex (based on distance from the leading edge of the test wall), of 3.5×105 and was completed by 4.7×105. The transition was strongly influenced by the presence of stationary, streamwise, Görtler vortices. Transition under similar conditions has been documented in previous studies, but because concave-wall transition tends to be rapid, measurements within the transition zone were sparse. In this study, emphasis is on measurements within the zone of intermittent flow. Twenty-five profiles of mean streamwise velocity, fluctuating streamwise velocity, and intermittency have been acquired at five values of Rex, and five spanwise locations relative to a Görtler vortex. The mean velocity profiles acquired near the vortex downwash sites exhibit inflection points and local minima. These minima, located in the outer part of the boundary layer, provide evidence of a “tilting” of the vortices in the spanwise direction. Profiles of fluctuating velocity and intermittency exhibit peaks near the locations of the minima in the mean velocity profiles. These peaks indicate that turbulence is generated in regions of high shear, which are relatively far from the wall. The transition mechanism in this flow is different from that on flat walls, where turbulence is produced in the near-wall region. The peak intermittency values in the profiles increase with Rex, but do not follow the “universal” distribution observed in most flat-wall, transitional boundary layers. The results have applications whenever strong concave curvature may result in the formation of Görtler vortices in otherwise 2-D flows. Because these cases were run with a low value of free-stream turbulence intensity, the flow is not a replication of a gas turbine flow. However, the results do provide a base case for further work on transition on the pressure side of gas turbine airfoils, where concave curvature effects are combined with the effects of high free-stream turbulence and strong streamwise pressure gradients, for they show the effects of embedded streamwise vorticity in a flow that is free of high-turbulence effects.

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