Self-similarity of wall-attached turbulence in boundary layers

2017 ◽  
Vol 823 ◽  
Author(s):  
Woutijn J. Baars ◽  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Streamwise Velocity ◽  
Wall Region ◽  
Self Similarity ◽  
Number Range ◽  
Reference Position ◽  
Normal Distance ◽  
Logarithmic Region ◽  
Layer Flow ◽  
O 10 ◽  
Near Wall

An assessment of the turbulent boundary layer flow structure, which is coherent with the near-wall region, is carried out through a spectral coherence analysis. This spectral method is applied to datasets comprising synchronized two-point streamwise velocity signals at a near-wall reference position and a range of wall-normal positions spanning a Reynolds-number range $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{3}){-}O(10^{6})$. Within each dataset, a self-similar structure is identified from the coherence between the turbulence in the logarithmic region and at the near-wall reference position. This self-similarity is described by a streamwise/wall-normal aspect ratio of $\unicode[STIX]{x1D706}_{x}/z\approx 14$, where $\unicode[STIX]{x1D706}_{x}$ and $z$ are the streamwise wavelength and wall-normal distance respectively.

Direct numerical simulations of Rayleigh–Bénard convection in water with non-Oberbeck–Boussinesq effects

2019 ◽  
Vol 881 ◽  
pp. 1073-1096 ◽  
Author(s):  
Andreas D. Demou ◽  
Dimokratis G. E. Grigoriadis
Keyword(s):  
Numerical Simulations ◽  
Two Dimensions ◽  
Direct Numerical Simulations ◽  
Wall Region ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Near Wall

Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

scholarly journals Active control of multiscale features in wall-bounded turbulence

2019 ◽  
Vol 36 (1) ◽  
pp. 12-21 ◽  
Author(s):  
Xiaotong Cui ◽  
Nan Jiang ◽  
Xiaobo Zheng ◽  
Zhanqi Tang
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Turbulent Energy ◽  
Streamwise Velocity ◽  
Discrete Wavelet ◽  
Wall Region ◽  
Mean Velocity ◽  
Pzt Actuator ◽  
The Impact ◽  
Near Wall

Abstract This study experimentally investigates the impact of a single piezoelectric (PZT) actuator on a turbulent boundary layer from a statistical viewpoint. The working conditions of the actuator include a range of frequencies and amplitudes. The streamwise velocity signals in the turbulent boundary layer flow are measured downstream of the actuator using a hot-wire anemometer. The mean velocity profiles and other basic parameters are reported. Spectra results obtained by discrete wavelet decomposition indicate that the PZT vibration primarily influences the near-wall region. The turbulent intensities at different scales suggest that the actuator redistributes the near-wall turbulent energy. The skewness and flatness distributions show that the actuator effectively alters the sweep events and reduces intermittency at smaller scales. Moreover, under the impact of the PZT actuator, the symmetry of vibration scales’ velocity signals is promoted and the structural composition appears in an orderly manner. Probability distribution function results indicate that perturbation causes the fluctuations in vibration scales and smaller scales with high intensity and low intermittency. Based on the flatness factor, the bursting process is also detected. The vibrations reduce the relative intensities of the burst events, indicating that the streamwise vortices in the buffer layer experience direct interference due to the PZT control.

Characteristics of large- and small-scale structures in the turbulent boundary layer over a drag-reducing riblet surface

2019 ◽  
Vol 234 (3) ◽  
pp. 796-807
Author(s):  
Zi-Liang Zhang ◽  
Ming-Ming Zhang ◽  
Chang Cai ◽  
Yu Cheng
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Small Scale ◽  
Wall Region ◽  
Hot Wire ◽  
Logarithmic Region ◽  
Scale Structures ◽  
Riblet Surface ◽  
Small Scale Structures ◽  
Near Wall

Riblet is one of the most promising passive drag reduction techniques in turbulent flows. In this paper, hot-wire measurements on a turbulent boundary layer perturbed by a drag-reducing riblet surface are carried out to further understand the riblet effects on the turbulent flows and the drag reduction mechanism. Compared with the smooth case, different energy variations in the near-wall region and the logarithmic region are observed over riblets. Then, by using a spectral filter of a given wavelength, the time series of the hot-wire data are decomposed into large- and small-scale components. It is indicated that large-scale structures in the logarithmic region impose a footprint (amplitude modulating effect) on the near-wall small-scale structures. By quantifying this footprint, it is found that the interactions between large- and small-scale structures over riblets are weakened in the near-wall region. Furthermore, the bursting process of large and small scales is studied. For both large- and small-scale structures, a shorter bursting duration and a higher bursting frequency are observed over the riblet surface, which indicates that riblets impede the formation of large- and small-scale bursting events. The flow physics behind these phenomena are also discussed in detail.

scholarly journals A comparison of turbulent pipe, channel and boundary layer flows

2009 ◽  
Vol 632 ◽  
pp. 431-442 ◽  
Author(s):  
J. P. MONTY ◽  
N. HUTCHINS ◽  
H. C. H. NG ◽  
I. MARUSIC ◽  
M. S. CHONG
Keyword(s):  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Energy Spectra ◽  
Wall Region ◽  
Velocity Measurements ◽  
Boundary Layer Flows ◽  
Velocity Fluctuations ◽  
Measurement Resolution ◽  
Structural Differences ◽  
Near Wall

The extent or existence of similarities between fully developed turbulent pipes and channels, and in zero-pressure-gradient turbulent boundary layers has come into question in recent years. This is in contrast to the traditionally accepted view that, upon appropriate normalization, all three flows can be regarded as the same in the near-wall region. In this paper, the authors aim to provide clarification of this issue through streamwise velocity measurements in these three flows with carefully matched Reynolds number and measurement resolution. Results show that mean statistics in the near-wall region collapse well. However, the premultiplied energy spectra of streamwise velocity fluctuations show marked structural differences that cannot be explained by scaling arguments. It is concluded that, while similarities exist at these Reynolds numbers, one should exercise caution when drawing comparisons between the three shear flows, even near the wall.

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.

PHYSICS OF COHERENT STRUCTURES OF TURBULENT FLOW IN NEAR-WALL REGION OF A VIBRATING PLATE

2010 ◽  
Vol 24 (13) ◽  
pp. 1433-1436
Author(s):  
L. X. ZHANG
Keyword(s):  
Boundary Layer ◽  
Coherent Structures ◽  
Boundary Layer Flow ◽  
Wall Layer ◽  
Basis Functions ◽  
Galerkin Projection ◽  
Wall Region ◽  
Layer Flow ◽  
Near Wall ◽  
Vibrating Plate

The focus of this paper is on physics of coherent structures in boundary layer flow in near-wall region of a vibrating plate. A dynamical model is developed based on Galerkin projection of the governing equation of the wall layer flow onto a subspace spanned by the orthogonal divergence-free Fourier basis functions. The interactive physics of the coherent structures with the wall vibration is studied with the established model truncated at any order. The compared results show that the prevailing coherent structures in the layer flow near a vibrating wall region are captured.

Measurements in the near-wall region of a boundary layer over a wall with large transverse curvature

2010 ◽  
Vol 664 ◽  
pp. 33-50 ◽  
Author(s):  
M. H. KRANE ◽  
L. M. GREGA ◽  
T. WEI
Keyword(s):  
Boundary Layer ◽  
Direct Determination ◽  
Streamwise Velocity ◽  
Wall Region ◽  
Wall Velocity ◽  
Transverse Curvature ◽  
Spatially Resolved ◽  
Streamwise Location ◽  
Image Velocimetry ◽  
Near Wall

Measurements of the near-wall velocity field of the flow over cylinders aligned with a uniform flow are presented. The broader objective of this investigation was to quantify and understand the role of transverse curvature in the limit as cylinder diameter approaches zero. The specific goal was to begin with a turbulent boundary layer over a larger radius cylinder and see what happens as the radius is reduced. Spatially and temporally resolved digital particle image velocimetry (DPIV) measurements were made on three different radius cylinders, 0.14 cm ≤ a ≤ 3.05 cm, extending along the length of a large free-surface water tunnel. Mean and fluctuating profiles are presented at a fixed streamwise location and free-stream speed. For the first time, spatially resolved measurements were made very close to the wall, permitting direct determination of wall shear stress, i.e. uτ, from near-wall velocity profiles. The measurements revealed a region close to the wall for small radii where the mean streamwise velocity profile is inflectional. This has significant implications on assumptions regarding what happens in the limit of a vanishing cylinder radius.

Influence of Wall Heating on Turbulent Structure

2007 ◽  
Author(s):  
Shivani T. Gajusingh ◽  
Kamran Siddiqui
Keyword(s):  
Flow Behavior ◽  
Streamwise Velocity ◽  
Wall Region ◽  
Turbulent Regime ◽  
Square Channel ◽  
Wall Heating ◽  
Turbulent Characteristics ◽  
The Mean ◽  
The Impact ◽  
Near Wall

An experimental study was conducted to investigate the impact of wall heating on the flow structure in the near-wall region inside a square channel. PIV was used to measure the two-dimensional velocity fields. The measurements were conducted for a range of mass flow rates that cover laminar and turbulent regimes. The results have shown that when a flow is unstably stratified via heating through a bottom wall, both the mean and turbulent characteristics are affected. The results have shown that the impact of wall heating on the flow behavior is significantly different for laminar and turbulent flow regimes. It was found that when a flow that is originally laminar is heated, the mean streamwise velocity in the near-wall region is significantly increased and turbulence is generated in the flow predominantly due to buoyancy. When the flow is in the turbulent regime, addition of heat reduces the magnitudes of mean streamwise velocity and turbulent properties. The reduction in the magnitudes of turbulent properties in this flow regime is due to the working of turbulence against the buoyancy forces.

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 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.

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