scholarly journals Statistical structure of self-sustaining attached eddies in turbulent channel flow

2015 ◽  
Vol 767 ◽  
pp. 254-289 ◽  
Author(s):  
Yongyun Hwang
Keyword(s):  
Large Scale ◽  
Turbulent Channel Flow ◽  
Coherent Motion ◽  
Length Scale ◽  
Wall Region ◽  
Logarithmic Region ◽  
Self Similar ◽  
Attached Eddies ◽  
The Given ◽  
Near Wall

AbstractThe linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend’s attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend’s attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length ${\it\lambda}_{z}$ between ${\it\lambda}_{z}^{+}=100$ and ${\it\lambda}_{z}\simeq 1.5h$, where $h$ is half the height of the channel, the former is found to be self-similar along $y\simeq 0.1{\it\lambda}_{z}$ and ${\it\lambda}_{x}\simeq 10{\it\lambda}_{z}$, while the latter is self-similar along $y\simeq 0.5{\it\lambda}_{z}\sim 0.7{\it\lambda}_{z}$ and ${\it\lambda}_{x}\simeq 2{\it\lambda}_{z}\sim 3{\it\lambda}_{z}$ where $y$ is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of $k_{x}^{-1}$ spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend’s inactive motion and several recent theoretical findings.

scholarly journals Self-sustaining process of minimal attached eddies in turbulent channel flow

2016 ◽  
Vol 795 ◽  
pp. 708-738 ◽  
Author(s):  
Yongyun Hwang ◽  
Yacine Bengana
Keyword(s):  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Turnover Time ◽  
The Self ◽  
Friction Reduction ◽  
Length Scale ◽  
Wall Region ◽  
Streamwise Vortices ◽  
Temporal Oscillation ◽  
Attached Eddies

It has been recently shown that the energy-containing motions (i.e. coherent structures) in turbulent channel flow exist in the form of Townsend’s attached eddies by a numerical experiment which simulates the energy-containing motions only at a prescribed spanwise length scale using their self-sustaining nature (Hwang, J. Fluid Mech., vol. 767, 2015, pp. 254–289). In the present study, a detailed investigation of the self-sustaining process of the energy-containing motions at each spanwise length scale (i.e. the attached eddies) in the logarithmic and outer regions is carried out with an emphasis on its relevance to ‘bursting’, which refers to an energetic temporal oscillation of the motions (Flores & Jiménez, Phys. Fluids, vol. 22, 2010, 071704). It is shown that the attached eddies in the logarithmic and outer regions, composed of streaks and quasi-streamwise vortical structures, bear the self-sustaining process remarkably similar to that in the near-wall region: i.e. the streaks are significantly amplified by the quasi-streamwise vortices via the lift-up effect; the amplified streaks subsequently undergo a ‘rapid streamwise meandering motion’, reminiscent of streak instability or transient growth, which eventually results in breakdown of the streaks and regeneration of new quasi-streamwise vortices. For the attached eddies at a given spanwise length scale ${\it\lambda}_{z}$ between ${\it\lambda}_{z}^{+}\simeq 100$ and ${\it\lambda}_{z}\simeq 1.5h$, the single turnover time period of the self-sustaining process is found to be $Tu_{{\it\tau}}/{\it\lambda}_{z}\simeq 2$ ($u_{{\it\tau}}$ is the friction velocity), which corresponds well to the time scale of the bursting. Two additional numerical experiments, designed to artificially suppress the lift-up effect and the streak meandering motions, respectively, reveal that these processes are essential ingredients of the self-sustaining process of the attached eddies in the logarithmic and outer regions, consistent with several previous theoretical studies. It is also shown that the artificial suppression of the lift-up effect of the attached eddies in the logarithmic and outer regions leads to substantial amounts of turbulent skin-friction reduction.

scholarly journals Velocity and spatial distribution of inertial particles in a turbulent channel flow

2019 ◽  
Vol 872 ◽  
pp. 367-406 ◽  
Author(s):  
Kee Onn Fong ◽  
Omid Amili ◽  
Filippo Coletti
Keyword(s):  
Spatial Distribution ◽  
Particle Velocity ◽  
Turbulent Channel Flow ◽  
Wall Turbulence ◽  
Buffer Layers ◽  
Working Fluid ◽  
Wall Region ◽  
Inertial Particles ◽  
Velocity Fluctuations ◽  
Near Wall

We present experimental observations of the velocity and spatial distribution of inertial particles dispersed in turbulent downward flow through a vertical channel at friction Reynolds numbers $\mathit{Re}_{\unicode[STIX]{x1D70F}}=235$ and 335. The working fluid is air laden with size-selected glass microspheres, having Stokes numbers $St=\mathit{O}(10)$ and $\mathit{O}(100)$ when based on the Kolmogorov and viscous time scales, respectively. Cases at solid volume fractions $\unicode[STIX]{x1D719}_{v}=3\times 10^{-6}$ and $5\times 10^{-5}$ are considered. In the more dilute regime, the particle concentration profile shows near-wall and centreline maxima compatible with a turbophoretic drift down the gradient of turbulence intensity; the particles travel at speed similar to that of the unladen flow except in the near-wall region; and their velocity fluctuations generally follow the unladen flow level over the channel core, exceeding it in the near-wall region. The denser regime presents substantial differences in all measured statistics: the near-wall concentration peak is much more pronounced, while the centreline maximum is absent; the mean particle velocity decreases over the logarithmic and buffer layers; and particle velocity fluctuations and deposition velocities are enhanced. An analysis of the spatial distributions of particle positions and velocities reveals different behaviours in the core and near-wall regions. In the channel core, dense clusters form which are somewhat elongated, tend to be preferentially aligned with the vertical/streamwise direction and travel faster than the less concentrated particles. In the near-wall region, the particles arrange in highly elongated streaks associated with negative streamwise velocity fluctuations, several channel heights in length and spaced by $\mathit{O}(100)$ wall units, supporting the view that these are coupled to fluid low-speed streaks typical of wall turbulence. The particle velocity fields contain a significant component of random uncorrelated motion, more prominent for higher $St$ and in the near-wall region.

scholarly journals Large eddy simulation of turbulent channel flow using differential equation wall model

2018 ◽  
Vol 15 (2) ◽  
pp. 75-89
Author(s):  
Muhammad Saiful Islam Mallik ◽  
Md. Ashraf Uddin
Keyword(s):  
Differential Equation ◽  
Flow Field ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Wall Region ◽  
Computational Domain ◽  
Wall Model ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Near Wall

A large eddy simulation (LES) of a plane turbulent channel flow is performed at a Reynolds number Re? = 590 based on the channel half width, ? and wall shear velocity, u? by approximating the near wall region using differential equation wall model (DEWM). The simulation is performed in a computational domain of 2?? x 2? x ??. The computational domain is discretized by staggered grid system with 32 x 30 x 32 grid points. In this domain the governing equations of LES are discretized spatially by second order finite difference formulation, and for temporal discretization the third order low-storage Runge-Kutta method is used. Essential turbulence statistics of the computed flow field based on this LES approach are calculated and compared with the available Direct Numerical Simulation (DNS) and LES data where no wall model was used. Comparing the results throughout the calculation domain we have found that the LES results based on DEWM show closer agreement with the DNS data, especially at the near wall region. That is, the LES approach based on DEWM can capture the effects of near wall structures more accurately. Flow structures in the computed flow field in the 3D turbulent channel have also been discussed and compared with LES data using no wall model.

scholarly journals Exact coherent states of attached eddies in channel flow

2019 ◽  
Vol 862 ◽  
pp. 1029-1059 ◽  
Author(s):  
Qiang Yang ◽  
Ashley P. Willis ◽  
Yongyun Hwang
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Coherent Structures ◽  
Time Scale ◽  
Coherent States ◽  
Plane Channel ◽  
Reynolds Numbers ◽  
Wall Region ◽  
Self Similar ◽  
Near Wall

A new set of exact coherent states in the form of a travelling wave is reported in plane channel flow. They are continued over a range in $Re$ from approximately $2600$ up to $30\,000$, an order of magnitude higher than those discovered in the transitional regime. This particular type of exact coherent states is found to be gradually more localised in the near-wall region on increasing the Reynolds number. As larger spanwise sizes $L_{z}^{+}$ are considered, these exact coherent states appear via a saddle-node bifurcation with a spanwise size of $L_{z}^{+}\simeq 50$ and their phase speed is found to be $c^{+}\simeq 11$ at all the Reynolds numbers considered. Computation of the eigenspectra shows that the time scale of the exact coherent states is given by $h/U_{cl}$ in channel flow at all Reynolds numbers, and it becomes equivalent to the viscous inner time scale for the exact coherent states in the limit of $Re\rightarrow \infty$. The exact coherent states at several different spanwise sizes are further continued to a higher Reynolds number, $Re=55\,000$, using the eddy-viscosity approach (Hwang & Cossu, Phys. Rev. Lett., vol. 105, 2010, 044505). It is found that the continued exact coherent states at different sizes are self-similar at the given Reynolds number. These observations suggest that, on increasing Reynolds number, new sets of self-sustaining coherent structures are born in the near-wall region. Near this onset, these structures scale in inner units, forming the near-wall self-sustaining structures. With further increase of Reynolds number, the structures that emerged at lower Reynolds numbers subsequently evolve into the self-sustaining structures in the logarithmic region at different length scales, forming a hierarchy of self-similar coherent structures as hypothesised by Townsend (i.e. attached eddy hypothesis). Finally, the energetics of turbulent flow is discussed for a consistent extension of these dynamical systems notions to high Reynolds numbers.

Assessing the Effects of Near Wall Corrections of the Force Acting on Particles in Gas-Solid Channel Flows

2005 ◽  
Author(s):  
Boris Arcen ◽  
Anne Tanie`re ◽  
Benoiˆt Oesterle´
Keyword(s):  
Channel Flow ◽  
Lift Force ◽  
Particle Concentration ◽  
Turbulent Channel Flow ◽  
Shear Velocity ◽  
Solid Particles ◽  
Wall Region ◽  
Wall Effects ◽  
Strong Shear ◽  
Near Wall

The importance of using the lift force and wall-corrections of the drag coefficient for modeling the motion of solid particles in a fully-developed channel flow is investigated by means of direct numerical simulation (DNS). The turbulent channel flow is computed at a Reynolds number based on the wall-shear velocity and channel half-width of 185. Contrary to most of the numerical simulations, we consider in the present study a lift force formulation that accounts for the weak and strong shear as well as for the wall effects (hereinafter referred to as optimum lift force), and the wall-corrections of the drag force. The DNS results show that the optimum lift force and the wall-corrections of the drag together have little influence on most of the statistics (particle concentration, mean velocities, and mean relative and drift velocities), even in the near wall region.

The structure of the near-wall region of two-dimensional turbulent separated flow

1991 ◽  
Vol 336 (1640) ◽  
pp. 5-17 ◽  
Keyword(s):  
Kinetic Energy ◽  
Shear Layer ◽  
Large Scale ◽  
Outer Region ◽  
Turbulence Kinetic Energy ◽  
Shear Stresses ◽  
Wall Region ◽  
Freestream Velocity ◽  
Outer Flow ◽  
Near Wall

The time-dependent structure of the wall region of separating, separated, and reattaching flows is considerably different than that of attached turbulent boundary layers. Large-scale structures, whose frequency of passage scales on the freestream velocity and shear layer thickness, produce large Reynolds shearing stresses and most of the turbulence kinetic energy in the outer region of the shear layer and transport it into the low velocity reversed flow next to the wall. This outer flow impresses a near wall streamwise streaky structure of spanwise spacing λ z simultaneously across the wall over a distance of the order of several λ z . The near wall structures produce negligible Reynolds shear stresses and turbulence kinetic energy.

Skin-friction generation by attached eddies in turbulent channel flow

2016 ◽  
Vol 808 ◽  
pp. 511-538 ◽  
Author(s):  
Matteo de Giovanetti ◽  
Yongyun Hwang ◽  
Haecheon Choi
Keyword(s):  
Reynolds Number ◽  
Skin Friction ◽  
Large Scale ◽  
Reynolds Numbers ◽  
The Self ◽  
Friction Reduction ◽  
Computational Domain ◽  
Cutoff Wavelength ◽  
Self Similar ◽  
Attached Eddies

Despite a growing body of recent evidence on the hierarchical organization of the self-similar energy-containing motions in the form of Townsend’s attached eddies in wall-bounded turbulent flows, their role in turbulent skin-friction generation is currently not well understood. In this paper, the contribution of each of these self-similar energy-containing motions to turbulent skin friction is explored up to $Re_{\unicode[STIX]{x1D70F}}\simeq 4000$. Three different approaches are employed to quantify the skin-friction generation by the motions, the spanwise length scale of which is smaller than a given cutoff wavelength: (i) FIK (Fukagata, Iwamoto, Kasagi) identity in combination with the spanwise wavenumber spectra of the Reynolds shear stress; (ii) confinement of the spanwise computational domain; (iii) artificial damping of the motions to be examined. The near-wall motions are found to continuously reduce their role in skin-friction generation on increasing the Reynolds number, consistent with the previous finding at low Reynolds numbers. The largest structures given in the form of very-large-scale and large-scale motions are also found to be of limited importance: due to a non-trivial scale interaction process, their complete removal yields only a 5–8 % skin-friction reduction at all of the Reynolds numbers considered, although they are found to be responsible for 20–30 % of total skin friction at $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$. Application of all the three approaches consistently reveals that the largest amount of skin friction is generated by the self-similar motions populating the logarithmic region. It is further shown that the contribution of these motions to turbulent skin friction gradually increases with the Reynolds number, and that these coherent structures are eventually responsible for most of turbulent skin-friction generation at sufficiently high Reynolds numbers.

Wall accumulation and spatial localization in particle-laden wall flows

2012 ◽  
Vol 699 ◽  
pp. 50-78 ◽  
Author(s):  
G. Sardina ◽  
P. Schlatter ◽  
L. Brandt ◽  
F. Picano ◽  
C. M. Casciola
Keyword(s):  
Turbulent Flows ◽  
Pair Correlation ◽  
Turbulent Channel Flow ◽  
Wall Turbulence ◽  
Small Scale ◽  
Wall Region ◽  
Inertial Particles ◽  
Wall Flows ◽  
Domain Truncation ◽  
Near Wall

AbstractWe study the two main phenomenologies associated with the transport of inertial particles in turbulent flows, turbophoresis and small-scale clustering. Turbophoresis describes the turbulence-induced wall accumulation of particles dispersed in wall turbulence, while small-scale clustering is a form of local segregation that affects the particle distribution in the presence of fine-scale turbulence. Despite the fact that the two aspects are usually addressed separately, this paper shows that they occur simultaneously in wall-bounded flows, where they represent different aspects of the same process. We study these phenomena by post-processing data from a direct numerical simulation of turbulent channel flow with different populations of inertial particles. It is shown that artificial domain truncation can easily alter the mean particle concentration profile, unless the domain is large enough to exclude possible correlation of the turbulence and the near-wall particle aggregates. The data show a strong link between accumulation level and clustering intensity in the near-wall region. At statistical steady state, most accumulating particles aggregate in strongly directional and almost filamentary structures, as found by considering suitable two-point observables able to extract clustering intensity and anisotropy. The analysis provides quantitative indications of the wall-segregation process as a function of the particle inertia. It is shown that, although the most wall-accumulating particles are too heavy to segregate in homogeneous turbulence, they exhibit the most intense local small-scale clustering near the wall as measured by the singularity exponent of the particle pair correlation function.

Radial Profiles of Particle Velocity in a Large Scale CFB Downer

2004 ◽  
Vol 2 (1) ◽  
Author(s):  
Zhen Qian ◽  
Minghui Zhang ◽  
Hao Yu ◽  
Fei Wei
Keyword(s):  
Particle Velocity ◽  
Large Scale ◽  
Circulating Fluidized Bed ◽  
Scale Up ◽  
Radial Profile ◽  
Small Scale ◽  
Wall Region ◽  
Radial Profiles ◽  
Peak Value ◽  
Near Wall

Radial profiles of particle velocity in a large scale (418 mm I.D.) downward Circulating Fluidized Bed (CFB downer) were obtained via a Laser Doppler Velocimetry (LDV) system. Results show that particle velocity is gradually increasing along the radial direction and there exists a peak value in the near wall region. Such unique radial profile shape can be explained by the solids accumulating trend in the near wall region of the downer. Experiment results in this large scale downer are also compared with those obtained by other researchers in small scale units so as to investigate the scale-up effect on the radial particle velocity distribution in the downer.

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