scholarly journals Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number

2018 ◽  
Vol 860 ◽  
pp. 886-938 ◽  
Author(s):  
Myoungkyu Lee ◽  
Robert D. Moser
Keyword(s):  
Reynolds Number ◽  
Outer Layer ◽  
Large Scale ◽  
Turbulent Energy ◽  
Channel Flows ◽  
Small Scale ◽  
Wall Region ◽  
Transfer Energy ◽  
Energy Flows ◽  
Near Wall

The transport equations for the variances of the velocity components are investigated using data from direct numerical simulations of incompressible channel flows at friction Reynolds number ($Re_{\unicode[STIX]{x1D70F}}$) up to$Re_{\unicode[STIX]{x1D70F}}=5200$. Each term in the transport equation has been spectrally decomposed to expose the contribution of turbulence at different length scales to the processes governing the flow of energy in the wall-normal direction, in scale and among components. The outer-layer turbulence is dominated by very large-scale streamwise elongated modes, which are consistent with the very large-scale motions (VLSM) that have been observed by many others. The presence of these VLSMs drives many of the characteristics of the turbulent energy flows. Away from the wall, production occurs primarily in these large-scale streamwise-elongated modes in the streamwise velocity, but dissipation occurs nearly isotropically in both velocity components and scale. For this to happen, the energy is transferred from the streamwise-elongated modes to modes with a range of orientations through nonlinear interactions, and then transferred to other velocity components. This allows energy to be transferred more-or-less isotropically from these large scales to the small scales at which dissipation occurs. The VLSMs also transfer energy to the wall region, resulting in a modulation of the autonomous near-wall dynamics and the observed Reynolds number dependence of the near-wall velocity variances. The near-wall energy flows are more complex, but are consistent with the well-known autonomous near-wall dynamics that gives rise to streaks and streamwise vortices. Through the overlap region between outer- and inner-layer turbulence, there is a self-similar structure to the energy flows. The VLSM production occurs at spanwise scales that grow with$y$. There is transport of energy away from the wall over a range of scales that grows with$y$. Moreover, there is transfer of energy to small dissipative scales which grows like$y^{1/4}$, as expected from Kolmogorov scaling. Finally, the small-scale near-wall processes characterised by wavelengths less than 1000 wall units are largely Reynolds number independent, while the larger-scale outer-layer processes are strongly Reynolds number dependent. The interaction between them appears to be relatively simple.

Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number

2012 ◽  
Vol 693 ◽  
pp. 319-344 ◽  
Author(s):  
Xueming Shao ◽  
Tenghu Wu ◽  
Zhaosheng Yu
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Large Scale ◽  
Horizontal Channel ◽  
Small Scale ◽  
Channel Height ◽  
Wall Region ◽  
Sediment Layer ◽  
Particle Settling ◽  
Volume Fractions

AbstractA fictitious domain method is used to perform fully resolved numerical simulations of particle-laden turbulent flow in a horizontal channel. The effects of large particles of diameter 0.05 and 0.1 times the channel height on the turbulence statistics and structures are investigated for different settling coefficients and volume fractions (0.79 %–7.08 %) for the channel Reynolds number being 5000. The results indicate the following. (a) When the particle sedimentation effect is negligible (i.e. neutrally buoyant), the presence of particles decreases the maximum r.m.s. of streamwise velocity fluctuation near the wall by weakening the intensity of the large-scale streamwise vortices, while increasing the r.m.s. of the streamwise fluctuating velocity in the region very close to the wall and in the centre region. On the other hand, the particles increase the r.m.s. of transverse and spanwise fluctuating velocities in the near-wall region by inducing the small-scale vortices. (b) When the particle settling effect is so substantial that most particles settle onto the bottom wall and form a particle sediment layer (SL), the SL plays the role of a rough wall and parts of the vortex structures shedding from the SL ascend into the core region and substantially increase the turbulence intensity there. (c) When the particle settling effect is moderate, the effects of particles on the turbulence are a combination of the former two situations, and the Shields number is a good parameter for measuring the particle settling effects (i.e. the particle concentration distribution in the transverse direction). The average velocities of the particle are smaller in the lower half-channel and larger in the upper half-channel compared to the local fluid velocities in the presence of gravity effects. The effects of the smaller particles on the turbulence are found to be stronger at the same particle volume fractions.

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.

scholarly journals Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160077 ◽  
Author(s):  
W. J. Baars ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Wall Turbulence ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Scale Interaction ◽  
High Reynolds ◽  
Near Wall

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

The Effects of Spatial Resolution in Turbulent Boundary Layers with Pressure Gradients

2012 ◽  
Vol 225 ◽  
pp. 109-117 ◽  
Author(s):  
Zambri Harun ◽  
Mohamad Dali Isa ◽  
Mohammad Rasidi Rasani ◽  
Shahrir Abdullah
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Spatial Resolution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Wall Region ◽  
Pressure Gradients ◽  
Layer Flow ◽  
Near Wall

Single normal hot-wire measurements of the streamwise component of velocity were taken in boundary layer flows subjected to pressure gradients at matched friction Reynolds numbers Reτ ≈ 3000. To evaluate spatial resolution effects, the sensor lengths are varied in both adverse pressure gradient (APG) and favorable pressure gradient (FPG). A control boundary layer flow in zero pressure gradient ZPG is also presented. It is shown here that, when the sensor length is maintained a constant value, in a contant Reynolds number, the near-wall peak increases with (adverse) pressure gradient. Both increased contributions of the small- and especially large-scale features are attributed to the increased broadband turbulence intensities. The two-mode increase, one centreing in the near-wall region and the other one in the outer region, makes spatial resolution studies in boundary layer flow more complicated. The increased large-scale features in the near-wall region of an APG flow is similar to large-scales increase due to Reynolds number in ZPG flow. Additionally, there is also an increase of the small-scales in the near-wall region when the boundary layer is exposed to adverse pressure gradient (while the Reynolds number is constant). In order to collapse the near-wall peaks for APG, ZPG and FPG flows, the APG flow has to use the longest sensor and conversely, the FPG has to use the shortest sensor. This study recommends that the empirical prediction by Huthins et. al. (2009) to be reevaluated if pressure gradient flows were to be considered such that the magnitude of the near-wall peak is also a function of the adverse pressure gradient parameter.

scholarly journals Large-scale influences in near-wall turbulence

2007 ◽  
Vol 365 (1852) ◽  
pp. 647-664 ◽  
Author(s):  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Scale Separation ◽  
Large Scale Motion ◽  
High Reynolds ◽  
Scale Motion ◽  
Near Wall Turbulence ◽  
Near Wall

Hot-wire data acquired in a high Reynolds number facility are used to illustrate the need for adequate scale separation when considering the coherent structure in wall-bounded turbulence. It is found that a large-scale motion in the log region becomes increasingly comparable in energy to the near-wall cycle as the Reynolds number increases. Through decomposition of fluctuating velocity signals, it is shown that this large-scale motion has a distinct modulating influence on the small-scale energy (akin to amplitude modulation). Reassessment of DNS data, in light of these results, shows similar trends, with the rate and intensity of production due to the near-wall cycle subject to a modulating influence from the largest-scale motions.

scholarly journals Transfer functions for flow predictions in wall-bounded turbulence

2019 ◽  
Vol 864 ◽  
pp. 708-745 ◽  
Author(s):  
Kenzo Sasaki ◽  
Ricardo Vinuesa ◽  
André V. G. Cavalieri ◽  
Philipp Schlatter ◽  
Dan S. Henningson
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Large Scale ◽  
Transfer Functions ◽  
Streamwise Velocity ◽  
Wall Region ◽  
Multiple Input ◽  
Wall Shear ◽  
Near Wall

Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-thickness-based Reynolds number up to $Re_{\unicode[STIX]{x1D703}}\simeq 8200$, using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45 % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case $Re_{\unicode[STIX]{x1D703}}=4430$. These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single- and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20 % were also observed in the determination of the near-wall spectral peak, depending on the employed method.

Prediction of Brownout Inception Beneath a Full-Scale Helicopter Downwash

2012 ◽  
Vol 57 (4) ◽  
pp. 1-13 ◽  
Author(s):  
Gregory Jasion ◽  
John Shrimpton
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Aerodynamic Force ◽  
Dust Cloud ◽  
Full Scale ◽  
Small Scale ◽  
Wall Region ◽  
Analytical Prediction ◽  
Characteristic Particle ◽  
Near Wall

Dust entrained by low flying helicopters leads to the degraded visual environment, brownout. Particle inception is a critical stage in the development of the dust cloud. Here, near-wall Lagrangian particle forces are considered through analyzing an approximate time-averaged full-scale rotor flow. This simplified flow does not attempt to predict brownout, instead it provides scales and velocity data in the near-wall region, compares the role of particle-fluid forces, and provides a foundation for Lagrangian entrainment models. The analysis shows that three characteristic particle sizes are exposed to different physics in different boundary layer zones, a function of the distance from the helicopter. Drag is the dominant aerodynamic force, cohesion is large for small particles, but wall-bounded lift is sufficient to entrain medium-sized particles. A complementary analytical prediction of tip vortices found that both large-scale inviscid features and small-scale viscous features of the boundary layer are significant.

Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow

2011 ◽  
Vol 667 ◽  
pp. 1-37 ◽  
Author(s):  
JIARONG HONG ◽  
JOSEPH KATZ ◽  
MICHAEL P. SCHULTZ
Keyword(s):  
Channel Flow ◽  
Outer Layer ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Dissipation Rates ◽  
Near Wall Turbulence ◽  
Near Wall

Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow for Reτ in the 3520–5360 range. The scales of pyramidal roughness elements satisfy the ‘well-characterized’ flow conditions, with h/k ≈ 50 and k+ = 60 ~ 100, where h is half height of the channel and k is the roughness height. The near-wall turbulence measurements are sensitive to spatial resolution, and vary with Reynolds number. Spatial variations in the mean flow, Reynolds stresses, as well as the turbulent kinetic energy (TKE) production and dissipation rates are confined to y < 2k. All the Reynolds stress components have local maxima at slightly higher elevations, but the streamwise-normal component increases rapidly at y < k, peaking at the top of the pyramids. The TKE production and dissipation rates along with turbulence transport also peak near the wall. The spatial energy and shear spectra show an increasing contribution of large-scale motions and a diminishing role of small motions with increasing distance from the wall. As the spectra steepen at low wavenumbers, they flatten and develop bumps in wavenumbers corresponding to k − 3k, which fall in the dissipation range. Instantaneous realizations show that roughness-scale eddies are generated near the wall, and lifted up rapidly by large-scale structures that populate the outer layer. A linear stochastic estimation-based analysis shows that the latter share common features with hairpin packets. This process floods the outer layer with roughness-scale eddies, in addition to those generated by the energy-cascading process. Consequently, although the imprints of roughness diminish in the outer-layer Reynolds stresses, consistent with the wall similarity hypothesis, the small-scale turbulence contains a clear roughness signature across the entire channel.

Reynolds number effects in the near-wall region of turbulent channel flows

2001 ◽  
Vol 13 (6) ◽  
pp. 1755-1767 ◽  
Author(s):  
M. Fischer ◽  
J. Jovanović ◽  
F. Durst
Keyword(s):  
Reynolds Number ◽  
Channel Flows ◽  
Wall Region ◽  
Turbulent Channel Flows ◽  
Reynolds Number Effects ◽  
Near Wall

scholarly journals Turbulent plane Couette flow at moderately high Reynolds number

2014 ◽  
Vol 751 ◽  
Author(s):  
V. Avsarkisov ◽  
S. Hoyas ◽  
M. Oberlack ◽  
J. P. García-Galache
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Wall Layer ◽  
Wall Region ◽  
Plane Couette Flow ◽  
Turbulent Plane ◽  
High Reynolds ◽  
Near Wall

AbstractA new set of numerical simulations of turbulent plane Couette flow in a large box of dimension ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}20\pi h,\, 2h,\, 6\pi h$) at Reynolds number $(\mathit{Re}_{\tau }) =125$, 180, 250 and 550 is described and compared with simulations at lower Reynolds numbers, Poiseuille flows and experiments. The simulations present a logarithmic near-wall layer and are used to verify and revise previously known results. It is confirmed that the fluctuation intensities in the streamwise and spanwise directions do not scale well in wall units. The scaling failure occurs both near to and away from the wall. On the contrary, the wall-normal intensity scales in inner units in the near-wall region and in outer units in the core region. The spectral ridge found by Hoyas & Jiménez (Phys. Fluids, vol. 18, 2003, 011702) for the turbulent Poiseuille flow can also be seen in the present flow. Away from the wall, very large-scale motions are found spanning through all the length of the channel. The statistics of these simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.

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