scholarly journals Sources and fluxes of scale energy in the overlap layer of wall turbulence

2015 ◽  
Vol 771 ◽  
pp. 407-423 ◽  
Author(s):  
A. Cimarelli ◽  
E. De Angelis ◽  
P. Schlatter ◽  
G. Brethouwer ◽  
A. Talamelli ◽  
...  
Keyword(s):  
Energy Source ◽  
Reynolds Number ◽  
Source Region ◽  
Outer Region ◽  
Wall Turbulence ◽  
Kolmogorov Equation ◽  
Wall Region ◽  
Outer Scale ◽  
Turbulence Production ◽  
Near Wall

Direct numerical simulations of turbulent channel flows at friction Reynolds numbers (Re) of 550, 1000 and 1500 are used to analyse the turbulent production, transfer and dissipation mechanisms in the compound space of scales and wall distances by means of the Kolmogorov equation generalized to inhomogeneous anisotropic flows. Two distinct peaks of scale-energy source are identified. The first, stronger one, belongs to the near-wall cycle. Its location in the space of scales and physical space is found to scale in viscous units, while its intensity grows slowly with $\mathit{Re}$, indicating a near-wall modulation. The second source peak is found further away from the wall in the putative overlap layer, and it is separated from the near-wall source by a layer of significant scale-energy sink. The dynamics of the second outer source appears to be strongly dependent on the Reynolds number. The detailed scale-by-scale analysis of this source highlights well-defined features that are used to make the properties of the outer turbulent source independent of Reynolds number and wall distance by rescaling the problem. Overall, the present results suggest a strong connection of the observed outer scale-energy source with the presence of an outer region of turbulence production whose mechanisms are well separated from the near-wall region and whose statistical features agree with the hypothesis of an overlap layer dominated by attached eddies. Inner–outer interactions between the near-wall and outer source region in terms of scale-energy fluxes are also analysed. It is conjectured that the near-wall modulation of the statistics at increasing Reynolds number can be related to a confinement of the near-wall turbulence production due to the presence of increasingly large production scales in the outer scale-energy source region.

Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow

2007 ◽  
Vol 584 ◽  
pp. 281-299 ◽  
Author(s):  
KYOUNGYOUN KIM ◽  
CHANG-F. LI ◽  
R. SURESHKUMAR ◽  
S. BALACHANDAR ◽  
RONALD J. ADRIAN
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Buffer Layer ◽  
Outer Region ◽  
Wall Turbulence ◽  
Channel Height ◽  
Large Contribution ◽  
Streamwise Vortices ◽  
Vortical Structures ◽  
Near Wall

The effects of polymer stresses on near-wall turbulent structures are examined by using direct numerical simulation of fully developed turbulent channel flows with and without polymer stress. The Reynolds number based on friction velocity and half-channel height is 395, and the stresses created by adding polymer are modelled by a finite extensible nonlinear elastic, dumbbell model. Both low- (18%) and high-drag reduction (61%) cases are investigated. Linear stochastic estimation is employed to compute the conditional averages of the near-wall eddies. The conditionally averaged flow fields for Reynolds-stress-maximizing Q2 events show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses in a manner similar to that found by Stone et al. (2004) for low-Reynolds-number quasi-streamwise vortices (‘exact coherent states: ECS’). The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag-reduced turbulence are very similar to those for the Q2 events, i.e. counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. More fundamentally, the torques due to polymer stress are shown to oppose the rotation of the vortices, thereby accounting for their weakening. The observations also extend concepts of the vortex retardation by viscoelastic counter-torques to the heads of hairpins above the buffer layer, and offer an explanation of the mechanism of drag reduction in the outer region of wall turbulence, as well as in the buffer layer.

Shear stress-driven flow: the state space of near-wall turbulence as

2019 ◽  
Vol 874 ◽  
pp. 606-638 ◽  
Author(s):  
Patrick Doohan ◽  
Ashley P. Willis ◽  
Yongyun Hwang
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Wall Turbulence ◽  
Phase Portraits ◽  
Wall Region ◽  
Velocity Statistics ◽  
Near Wall Turbulence ◽  
Near Wall

An inner-scaled, shear stress-driven flow is considered as a model of independent near-wall turbulence as the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\rightarrow \infty$. In this limit, the model is applicable to the near-wall region and the lower part of the logarithmic layer of various parallel shear flows, including turbulent Couette flow, Poiseuille flow and Hagen–Poiseuille flow. The model is validated against damped Couette flow and there is excellent agreement between the velocity statistics and spectra for the wall-normal height $y^{+}<40$. A near-wall flow domain of similar size to the minimal unit is analysed from a dynamical systems perspective. The edge and fifteen invariant solutions are computed, the first discovered for this flow configuration. Through continuation in the spanwise width $L_{z}^{+}$, the bifurcation behaviour of the solutions over the domain size is investigated. The physical properties of the solutions are explored through phase portraits, including the energy input and dissipation plane, and streak, roll and wave energy space. Finally, a Reynolds number is defined in outer units and the high-$Re$ asymptotic behaviour of the equilibria is studied. Three lower branch solutions are found to scale consistently with vortex–wave interaction (VWI) theory, with wave forcing localising around the critical layer.

On the dynamics of near-wall turbulence

1991 ◽  
Vol 336 (1641) ◽  
pp. 131-175 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Surface Layer ◽  
Turbulent Boundary Layer ◽  
Wall Turbulence ◽  
Wall Region ◽  
Hairpin Vortices ◽  
Basic Fluid ◽  
High Reynolds ◽  
Near Wall

A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described. The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer. It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall. The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface. The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of ‘kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer. Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given. An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow.

scholarly journals Cascades and wall-normal fluxes in turbulent channel flows

2016 ◽  
Vol 796 ◽  
pp. 417-436 ◽  
Author(s):  
A. Cimarelli ◽  
E. De Angelis ◽  
J. Jiménez ◽  
C. M. Casciola
Keyword(s):  
Energy Source ◽  
Turbulent Flows ◽  
Wall Turbulence ◽  
Wall Region ◽  
Cascade Process ◽  
Driving Mechanisms ◽  
Energy Excess ◽  
Multidimensional Behaviour ◽  
Generation Mechanisms ◽  
Near Wall

The present work describes the multidimensional behaviour of scale-energy production, transfer and dissipation in wall-bounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scale-by-scale among different regions of the flow. Two driving mechanisms are identified. A strong scale-energy source in the buffer layer related to the near-wall cycle and an outer scale-energy source associated with an outer turbulent cycle in the overlap layer. These two sourcing mechanisms lead to a complex redistribution of scale energy where spatially evolving reverse and forward cascades coexist. From a hierarchy of spanwise scales in the near-wall region generated through a reverse cascade and local turbulent generation processes, scale energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, still ascending towards the channel centre. The attached scales of wall-bounded turbulence are then recognized to sustain a spatial reverse cascade process towards the bulk flow. On the other hand, the detached scales are involved in a direct forward cascade process that links the scale-energy excess at large attached scales with dissipation at the smaller scales of motion located further away from the wall. The unexpected behaviour of the fluxes and of the turbulent generation mechanisms may have strong repercussions on both theoretical and modelling approaches to wall turbulence. Indeed, actual turbulent flows are shown here to have a much richer physics with respect to the classical notion of turbulent cascade, where anisotropic production and inhomogeneous fluxes lead to a complex redistribution of energy where a spatial reverse cascade plays a central role.

scholarly journals Reynolds stress scaling in the near-wall region of wall-bounded flows

2021 ◽  
Vol 926 ◽  
Author(s):  
Alexander J. Smits ◽  
Marcus Hultmark ◽  
Myoungkyu Lee ◽  
Sergio Pirozzoli ◽  
Xiaohua Wu
Keyword(s):  
Reynolds Number ◽  
Reynolds Stress ◽  
Wall Turbulence ◽  
Wall Region ◽  
Boundary Layer Flows ◽  
Wall Bounded Flows ◽  
Large Eddies ◽  
Near Wall Turbulence ◽  
Reynolds Number Dependence ◽  
Near Wall

A new scaling is derived that yields a Reynolds-number-independent profile for all components of the Reynolds stress in the near-wall region of wall-bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behaviour.

Turbulent Mass Transfer Simulations of Binary Electrolyte in Parallel-Plate Electrode Channel

2012 ◽  
Vol 550-553 ◽  
pp. 2014-2018
Author(s):  
Xiao Lan Zhou ◽  
Cai Xi Liu ◽  
Yu Hong Dong
Keyword(s):  
Mass Transfer ◽  
Turbulent Flows ◽  
Primary Objective ◽  
Wall Turbulence ◽  
Limiting Current ◽  
Solid Boundary ◽  
Wall Region ◽  
Schmidt Numbers ◽  
Near Wall ◽  
Turbulent Mass Transfer

Electrochemical mass transfer in turbulent flows and binary electrolytes is investigated. The primary objective is to provide information about mass transfer in the near-wall region between a solid boundary and a turbulent fluid flow at different Schmidt numbers. Based on the computational fluid dynamics and electrochemistry theories, a model for turbulent electrodes channel flow is established. The turbulent mass transfer in electrolytic processes has been predicted by the direct numerical simulation method under limiting current and galvanostatic conditions, we investigate mean concentration and the structure of the concentration fluctuating filed for different Schmidt numbers from 0.1 to 100 .The effect of different concentration boundary conditions at the electrodes on the near-wall turbulence statistics is also discussed.

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+ &lt; 3), the controlling transfer mechanism is related to near-wall turbulence structure.

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 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.

Direct numerical simulation of turbulence in injection-driven three-dimensional cylindrical flows

2011 ◽  
Vol 670 ◽  
pp. 176-203 ◽  
Author(s):  
JU ZHANG ◽  
THOMAS L. JACKSON
Keyword(s):  
Reynolds Number ◽  
Root Mean Square ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Wall Friction ◽  
Mean Square ◽  
The Mean ◽  
Wall Shear ◽  
Strong Injection ◽  
Near Wall

Incompressible turbulent flow in a periodic circular pipe with strong injection is studied as a simplified model for the core flow in a solid-propellant rocket motor and other injection-driven internal flows. The model is based on a multi-scale asymptotic approach. The intended application of the current study is erosive burning of solid propellants. Relevant analysis for easily accessible parameters for this application, such as the magnitudes, main frequencies and wavelengths associated with the near-wall shear, and the assessment of near-wall turbulence viscosity is focused on. It is found that, unlike flows with weak or no injection, the near-wall shear is dominated by the root mean square of the streamwise velocity which is a function of the Reynolds number, while the mean streamwise velocity is only weakly dependent on the Reynolds number. As a result, a new wall-friction velocity $\(u_\tau{\,=\,}\sqrt{\tau_w/\rho}\)$, based on the shear stress derived from the sum of the mean and the root mean square, i.e. $\(\tau_{w,inj} {\,=\,} \mu |{\partial (\bar{u}+u_{rms})}/{\partial r}|_w\)$, is proposed for the scaling of turbulent viscosity for turbulent flows with strong injection. We also show that the mean streamwise velocity profile has an inflection point near the injecting surface.

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