Dilute Polymers and Coherent Structures in Wall Turbulence

1999 ◽  
Author(s):  
Elisabetta De Angelis ◽  
Carlo M. Casciola ◽  
Renzo Piva
Keyword(s):  
Coherent Structures ◽  
Wall Layer ◽  
Wall Turbulence ◽  
Viscoelastic Flows ◽  
Mean Velocity ◽  
Newtonian Flows ◽  
Level Of Activity ◽  
Main Effect ◽  
The Mean ◽  
Low Speed Streaks

Abstract Both numerical and experimental data confirm that the introduction of dilute polymers in a turbulent flow changes some mean characteristics of the flow: the wall drag can decrease up to 40% while the average spacing among streaks can even double. Actually a link exists between streaks spacing and mean velocity gradient at the wall. In such viscoelastic flows the wall turbulence regeneration is still influenced by the mean shear and by the interaction of the coherent structures even if they appear more ordered and larger with respect to Newtonian flows. These phenomena, which have been repeatedly observed since the findings of Toms, would require a better understanding of the mechanisms that locally induce this behaviour. The analysis of data from direct numerical simulation with FENE-P model for the polymers, seems to suggest, as the main effect of the viscoelastic reaction, a stabilizing action on the low speed streaks and a related decrease in the population of the wall layer coherent structures. The decreased level of activity induces relevant changes in the scales of the turbulence and originates the observed drag reduction.

scholarly journals Transfer, Segregation and Deposition of Heavy Particles in Horizontal and Vertical Turbulent Channel Flows

2003 ◽  
Author(s):  
Cristian Marchioli ◽  
Fabio Sbrizzai ◽  
Alfredo Soldati
Keyword(s):  
Coherent Structures ◽  
Particle Distribution ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Transfer Mechanism ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Structure ◽  
Low Speed ◽  
Low Speed Streaks

Particle transfer in the wall region of turbulent boundary layers is dominated by the coherent structures which control the turbulence regeneration cycle. Coherent structures bring particles toward the wall and away from the wall and favour particle segregation in the viscous region giving rise to nonuniform particle distribution profiles which peak close to the wall. In this work, we focus on the transfer mechanism of different size particles and on the influence of gravity on particles deposition. By tracking O(105) particles in Direct Numerical Simulation (DNS) of a turbulent channel flow at Reτ = 150, we find that particles may reach the wall directly or may accumulate in the wall region, under the low-speed streaks. Even though low-speed streaks are ejection-like environments, particles are not re-entrained into the outer region. Particles segregated very near the wall by the trapping mechanisms we investigated in a previous work [1] are slowly driven to the wall. We find that gravity plays a role on particle distribution but, for small particles (τp+ < 3), the controlling transfer mechanism is related to near-wall turbulence structure.

On the size of the energy-containing eddies in the outer turbulent wall layer

2012 ◽  
Vol 702 ◽  
pp. 521-532 ◽  
Author(s):  
Sergio Pirozzoli
Keyword(s):  
Outer Part ◽  
Eddy Diffusivity ◽  
Wall Layer ◽  
Wall Turbulence ◽  
Normal Velocity ◽  
Mixing Length ◽  
Mean Velocity ◽  
Local Mean ◽  
Turbulent Wall ◽  
Good Agreement

AbstractWe investigate the scaling of the energy-containing eddies in the outer part of turbulent wall layers. Their spanwise integral length scales are extracted from a direct numerical simulation (DNS) database, which includes compressible turbulent boundary layers and incompressible turbulent Couette–Poiseuille flows. The results indicate similar behaviour for all classes of flows, with a general increasing trend in the eddy size with the wall distance. A family of scaling relationships are proposed based on simple dimensional arguments, of which the classical mixing length approximation constitutes one example. As in previous studies, we find that the mixing length is in good agreement with the size distribution of the eddies carrying wall-normal velocity, which are active in establishing the mean velocity distribution. However, we find that the eddies associated with wall-parallel motions obey a different scaling, which is controlled by the local mean shear and by an effective eddy diffusivity ${\nu }_{t} = { u}_{\tau }^{\ensuremath{\ast} } \delta $, where ${ u}_{\tau }^{\ensuremath{\ast} } $ is the compressible counterpart of the friction velocity, and $\delta $ is the thickness of the wall layer. The validity of the proposed scalings is checked against DNS data, and the potential implications for the understanding of wall turbulence are discussed.

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.

Spectral analogues of the law of the wall, the defect law and the log law

2014 ◽  
Vol 757 ◽  
pp. 498-513 ◽  
Author(s):  
Carlo Zúñiga Zamalloa ◽  
Henry Chi-Hin Ng ◽  
Pinaki Chakraborty ◽  
Gustavo Gioia
Keyword(s):  
Turbulent Energy ◽  
Wall Turbulence ◽  
Spectral Domain ◽  
Energy Spectra ◽  
Scaling Relations ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean ◽  
Log Law ◽  
The Law

AbstractUnlike the classical scaling relations for the mean-velocity profiles of wall-bounded uniform turbulent flows (the law of the wall, the defect law and the log law), which are predicated solely on dimensional analysis and similarity assumptions, scaling relations for the turbulent-energy spectra have been informed by specific models of wall turbulence, notably the attached-eddy hypothesis. In this paper, we use dimensional analysis and similarity assumptions to derive three scaling relations for the turbulent-energy spectra, namely the spectral analogues of the law of the wall, the defect law and the log law. By design, each spectral analogue applies in the same spatial domain as the attendant scaling relation for the mean-velocity profiles: the spectral analogue of the law of the wall in the inner layer, the spectral analogue of the defect law in the outer layer and the spectral analogue of the log law in the overlap layer. In addition, as we are able to show without invoking any model of wall turbulence, each spectral analogue applies in a specific spectral domain (the spectral analogue of the law of the wall in the high-wavenumber spectral domain, where viscosity is active, the spectral analogue of the defect law in the low-wavenumber spectral domain, where viscosity is negligible, and the spectral analogue of the log law in a transitional intermediate-wavenumber spectral domain, which may become sizable only at ultra-high$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }$), with the implication that there exist model-independent one-to-one links between the spatial domains and the spectral domains. We test the spectral analogues using experimental and computational data on pipe flow and channel flow.

On the mechanism of wall turbulence

1982 ◽  
Vol 119 ◽  
pp. 173-217 ◽  
Author(s):  
A. E. Perry ◽  
M. S. Chong
Keyword(s):  
Velocity Distribution ◽  
Turbulence Intensity ◽  
Scaling Laws ◽  
Heated Surface ◽  
Broad Band ◽  
Wall Turbulence ◽  
Mean Velocity ◽  
Quantitative Measurements ◽  
Temperature Distributions ◽  
The Mean

In this paper an attempt is made to formulate a model for the mechanism of wall turbulence that links recent flow-visualization observations with the various quantitative measurements and scaling laws established from anemometry studies. Various mechanisms are proposed, all of which use the concept of the horse-shoe, hairpin or ‘A’ vortex. It is shown that these models give a connection between the mean-velocity distribution, the broad-band turbulence-intensity distributions and the turbulence spectra. Temperature distributions above a heated surface are also considered. Although this aspect of the work is not yet complete, the analysis for this shows promise.

Coherent Structures in the Similarity Region of Two-Dimensional Turbulent Jets

1984 ◽  
Vol 106 (2) ◽  
pp. 187-192 ◽  
Author(s):  
J. W. Oler ◽  
V. W. Goldschmidt
Keyword(s):  
Velocity Profile ◽  
Coherent Structures ◽  
Turbulent Jets ◽  
Jet Flows ◽  
Two Dimensional ◽  
Ordered Structure ◽  
Mean Velocity ◽  
The Mean ◽  
Plane Jet ◽  
Average Position

The strongest indication of an ordered structure in the similarity region of plane jet flows is the well documented (but controversial) apparent “flapping” behavior. Previously, the negative correlation between probes placed on opposite sides of the jet centerline has been attributed to the periodic displacement of the mean velocity profile centerline about its average position, i.e., a flapping motion. The present investigation is directed at evaluating the premise of an essentially two-dimensional von Karman vortex street as being responsible for the apparent “flapping” behavior.

Turbulent flow between a rotating and a stationary disk

2001 ◽  
Vol 426 ◽  
pp. 297-326 ◽  
Author(s):  
MAGNE LYGREN ◽  
HELGE I. ANDERSSON
Keyword(s):  
Shear Stress ◽  
Boundary Layers ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mean Flow ◽  
Mean Velocity ◽  
Stationary Disk ◽  
Dimensional Boundary ◽  
The Mean

Turbulent flow between a rotating and a stationary disk is studied. Besides its fundamental importance as a three-dimensional prototype flow, such flow fields are frequently encountered in rotor–stator configurations in turbomachinery applications. A direct numerical simulation is therefore performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached and with the aim of providing both long-time statistics and an exposition of coherent structures obtained by conditional sampling. The simulated flow has local Reynolds number r2ω/v = 4 × 105 and local gap ratio s/r = 0.02, where ω is the angular velocity of the rotating disk, r the radial distance from the axis of rotation, v the kinematic viscosity of the fluid, and s the gap width.The three components of the mean velocity vector and the six independent Reynolds stresses are compared with experimental measurements in a rotor–stator flow configuration. In the numerically generated flow field, the structural parameter a1 (i.e. the ratio of the magnitude of the shear stress vector to twice the mean turbulent kinetic energy) is lower near the two disks than in two-dimensional boundary layers. This characteristic feature is typical for three-dimensional boundary layers, and so are the misalignment between the shear stress vector and the mean velocity gradient vector, although the degree of misalignment turns out to be smaller in the present flow than in unsteady three-dimensional boundary layer flow. It is also observed that the wall friction at the rotating disk is substantially higher than at the stationary disk.Coherent structures near the disks are identified by means of the λ2 vortex criterion in order to provide sufficient information to resolve a controversy regarding the roles played by sweeps and ejections in shear stress production. An ensemble average of the detected structures reveals that the coherent structures in the rotor–stator flow are similar to the ones found in two-dimensional flows. It is shown, however, that the three-dimensionality of the mean flow reduces the inter-vortical alignment and the tendency of structures of opposite sense of rotation to overlap. The coherent structures near the disks generate weaker sweeps (i.e. quadrant 4 events) than structures in conventional two-dimensional boundary layers. This reduction in the quadrant 4 contribution from the coherent structures is believed to explain the reduced efficiency of the mean flow in producing Reynolds shear stress.

Nonlinear internal gravity waves in a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 497-512 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Gravity Waves ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Mean Velocity ◽  
Main Effect ◽  
Local Wave ◽  
The Mean ◽  
The Waves ◽  
Circulation Theorem

The interaction between internal gravity waves in a rotating frame and the mean flow is discussed for the case when the properties of the mean flow vary slowly on a scale determined by the local wave structure. The principle of conservation of wave action is established. It is shown that the main effect of the waves on the Lagrangian mean velocity is due to an appropriate ‘radiation stress’ tensor. A circulation theorem and a potential-vorticity equation are derived for the mean velocity.

Characteristics of a turbulent boundary layer with an external turbulent uniform shear flow

1976 ◽  
Vol 77 (2) ◽  
pp. 369-396 ◽  
Author(s):  
Q. A. Ahmad ◽  
R. E. Luxton ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Shear Flow ◽  
Free Stream ◽  
Reynolds Shear Stress ◽  
Wall Layer ◽  
Turbulence Level ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
The Mean

Measurements are presented of both mean and fluctuating velocity components in a turbulent boundary layer subjected to a nearly homogeneous external turbulent shear flow. The Reynolds shear stress in the external shear flow is small compared with the wall shear stress. Its transverse mean velocity gradient λ (≃ 6 s−l) is also small compared with typical gradients based on outer variables (say Uw/δ, where Uwis the value of the linear velocity profile extrapolated to the wall and δ is the boundary-layer thickness), but is of the same order as Ut/δ (Ur is the friction velocity). The influence of both positive and negative transverse velocity gradients on the turbulent wall layer is investigated over a streamwise region where the normal Reynolds stresses in the external flow are approximately equal and constant in the streamwise direction. In this region, the integral length scale of the external flow is of the same order of magnitude as that of the wall layer. Measurements in the boundary layer are also given for an un-sheared external turbulent flow (λ = 0) with a turbulence level Tu of 1.5%, approximately the same as that for h = ± 6 s−1. (Tu, is defined as the ratio of the r.m.s. longitudinal velocity fluctuation to Uw.) The measurements are in good agreement with those available in the literature for a similar free-stream turbulence level and show that the external turbulence level and length scale exert a large influence on the turbulence structure in the boundary layer. The additional effect of the external shear on the mean velocity and turbulent energy budget distributions in the inner region of the boundary layer is found to be small. In the outer region, the ‘wake’ component of the mean velocity defect is lowered by the presence of free-stream turbulence and one extra effect due to the external shear is an increase in the Reynolds shear stress when h is positive and a decrease when h is negative. Another interesting effect due to the shear is the appearance near the edge of the layer of a small but distinct region where the local mean velocity is constant and the Reynolds shear stress is negligible.

Effects of a Large Eddy Breakup Device on the Fluctuating Wall Pressure Field (Data Bank Contribution)

1993 ◽  
Vol 115 (3) ◽  
pp. 389-397 ◽  
Author(s):  
W. L. Keith ◽  
J. J. Barclay
Keyword(s):  
Coherent Structures ◽  
Field Data ◽  
Pressure Field ◽  
Data Bank ◽  
Turbulent Boundary Layers ◽  
Wall Pressure ◽  
Mean Velocity ◽  
Large Eddy ◽  
The Mean ◽  
Log Law

Wall pressure spectra and mean velocity profiles were measured with and without a large eddy breakup device (LEBU) located upstream in high Rθ turbulent boundary layers. Changes of the order of 5 percent occurred in the mean wall shear stress. The wall pressure spectra of the manipulated flow did not show the existence of any highly energized coherent structures, but rather moderate changes occurring over broad frequency ranges. Reductions in the wall pressure autospectra occurred at lower frequencies associated with turbulence activity in the outer layer and the outer portion of the log law layer. Increases occurred at higher frequencies associated with the inner portion of the log law layer. The changes in the wall pressure coherence levels were similar, but generally more complex with greater spatial persistence. The changes in both the autospectra and coherence indicate a conversion of energy from lower to higher convective wavenumbers.

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