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.

Low-Reynolds-number effects on near-wall turbulence

1994 ◽  
Vol 276 ◽  
pp. 61-80 ◽  
Author(s):  
R. A. Antonia ◽  
J. Kim
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Kinematic Viscosity ◽  
Average Energy ◽  
Wall Region ◽  
Streamwise Vorticity ◽  
Wall Pressure Fluctuations ◽  
Wall Shear ◽  
Near Wall

Direct numerical simulations of a fully developed turbulent channel flow for two relatively small values of the Reynolds number are used to examine its influence on various turbulence quantities in the near-wall region. The limiting wall behaviour of these quantities indicates important increases in the r.m.s. value of the wall pressure fluctuations and its derivatives, the r.m.s. streamwise vorticity and in the average energy dissipation rate and the Reynolds shear stress. If the normalization is based on the wall shear stress and the kinematic viscosity, these changes are shown to be consistent with an increase in strength – but not the average diameter or average location – of the quasi-streamwise vortices in the buffer region. Evidence of this strengthening is provided by the increased sum of the stretching terms for the meansquare streamwise vorticity. It is also shown that a normalization based on Kolmogorov velocity and lengthscales, defined at the wall, is more appropriate in the near-wall region than scaling on the wall shear stress and kinematic viscosity.

A Dynamic Procedure for Wall-Modeled Large-Eddy Simulation of High Reynolds Number Flows

2011 ◽  
Author(s):  
Soshi Kawai
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Large Eddy Simulation ◽  
High Reynolds Number ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Wall Shear ◽  
High Reynolds ◽  
Near Wall

This paper addresses the error in large-eddy simulation with wall-modeling (i.e., when the wall shear stress is modeled and the viscous near-wall layer is not resolved): the error in estimating the wall shear stress from a given outer-layer velocity field using auxiliary near-wall RANS equations where convection is not neglected. By considering the behavior of turbulence length scales near a wall, the cause of the errors is diagnosed and solutions that remove the errors are proposed based solidly on physical reasoning. The resulting method is shown to accurately predict equilibrium boundary layers at very high Reynolds number, with both realistic instantaneous fields (without overly elongated unphysical near-wall structures) and accurate statistics (both skin friction and turbulence quantities).

The Law of the Wall for Swirling Flow in Annular Ducts

1989 ◽  
Vol 111 (2) ◽  
pp. 160-164 ◽  
Author(s):  
R. J. Kind ◽  
F. M. Yowakim ◽  
S. A. Sjolander
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Swirling Flow ◽  
Tangential Velocity ◽  
Wall Region ◽  
Law Of The Wall ◽  
Resultant Velocity ◽  
The Law ◽  
Wall Shear ◽  
Near Wall

Expressions for the logarithmic portion of the law of the wall are derived for the axial and tangential velocity components of swirling flow in annular ducts. These expressions involve new shear-velocity scales and curvature terms. They are shown to agree well with experiment over a substantial portion of the flow near both walls of an annulus. The resultant velocity data also agree with the law of the wall. The success of the proposed logarithmic expressions implies that the mixing-length model used in deriving them correctly describes flow-velocity behavior. This model indicates that the velocity gradient at any height y in the near-wall region is determined by the wall shear stress, not by the local shear stress. This suggests that the influence of wall shear stress is dominant and that it determines the near-wall wall flow even in flows with curvature and pressure gradient. A physical explanation is suggested for this.

scholarly journals Effect of reverse flow on the pattern of wall shear stress near arterial branches

2011 ◽  
Vol 8 (64) ◽  
pp. 1594-1603 ◽  
Author(s):  
A. Kazakidi ◽  
A. M. Plata ◽  
S. J. Sherwin ◽  
P. D. Weinberg
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Steady Flow ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Side Branch ◽  
Navier Stokes ◽  
Wall Region ◽  
Wall Shear ◽  
Near Wall

Atherosclerotic lesions have a patchy distribution within arteries that suggests a controlling influence of haemodynamic stresses on their development. The distribution near aortic branches varies with age and species, perhaps reflecting differences in these stresses. Our previous work, which assumed steady flow, revealed a dependence of wall shear stress (WSS) patterns on Reynolds number and side-branch flow rate. Here, we examine effects of pulsatile flow. Flow and WSS patterns were computed by applying high-order unstructured spectral/hp element methods to the Newtonian incompressible Navier–Stokes equations in a geometrically simplified model of an aorto-intercostal junction. The effect of pulsatile but non-reversing side-branch flow was small; the aortic WSS pattern resembled that obtained under steady flow conditions, with high WSS upstream and downstream of the branch. When flow in the side branch or in the aortic near-wall region reversed during part of the cycle, significantly different instantaneous patterns were generated, with low WSS appearing upstream and downstream. Time-averaged WSS was similar to the steady flow case, reflecting the short duration of these events, but patterns of the oscillatory shear index for reversing aortic near-wall flow were profoundly altered. Effects of reverse flow may help explain the different distributions of lesions.

Wall shear stress and velocity in a turbulent axisymmetric boundary layer

1994 ◽  
Vol 259 ◽  
pp. 191-218 ◽  
Author(s):  
Anthony Wietrzak ◽  
Richard M. Lueptow
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Large Scale ◽  
Low Frequency ◽  
Streamwise Velocity ◽  
Outer Flow ◽  
Planar Wall ◽  
Wall Bounded Flows ◽  
Wall Shear

Instantaneous streamwise fluctuations of the wall shear stress have been measured using a hot-element probe in a thick axisymmetric turbulent boundary layer on a cylinder aligned parallel to the flow. The measurements were made at a momentum-thickness Reynolds number Rθ = 3050 and a ratio of boundary-layer thickness to cylinder radius of δ/a = 5.7. The ratio of the r.m.s. of the fluctuation to the mean value of the wall shear stress, $\tau_{rms}/\bar{\tau}$, is about 0.32, a value slightly lower than that for recent measurements for flow over a flat plate. The probability density function of the wall shear stress is similar to that for planar wall-bounded flows within experimental error. The power spectral density of the wall shear stress shows that a cylindrical boundary layer contains less energy at lower frequencies and more energy at higher frequencies than other wall-bounded flows. Analysis of simultaneous measurement of the streamwise wall shear stress and the streamwise velocity using VITA and peak detection suggests that transverse curvature has little effect on the near-wall burst–sweep cycle compared to planar wall-bounded flows. The angle of inclination of the structures is similar to that measured for large-scale structures in planar wall-bounded flows. However, measurements of the cross-correlation between the shear stress and the velocity suggest the existence of smaller structures yawed to the axis of the cylinder. The coherence between shear stress and velocity shows a low frequency associated with the inclined structures and a higher frequency associated with the yawed structures. The yawed structures could have an arrowhead or half-arrowhead shape and may be associated with fluid from the outer flow washing over the cylinder.

Very Large-Scale Structures and Their Effects on the Wall Shear-Stress Fluctuations in a Turbulent Channel Flow up to Reτ=640

2004 ◽  
Vol 126 (5) ◽  
pp. 835-843 ◽  
Author(s):  
Hiroyuki Abe ◽  
Hiroshi Kawamura ◽  
Haecheon Choi
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
High Reynolds Number ◽  
Large Scale ◽  
Turbulent Channel Flow ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Wall Shear ◽  
High Reynolds

Direct numerical simulation of a fully developed turbulent channel flow has been carried out at three Reynolds numbers, 180, 395, and 640, based on the friction velocity and the channel half width, in order to investigate very large-scale structures and their effects on the wall shear-stress fluctuations. It is shown that very large-scale structures exist in the outer layer and that they certainly contribute to inner layer structures at high Reynolds number. Moreover, it is revealed that very large-scale structures exist even in the wall shear-stress fluctuations at high Reynolds number, which are essentially associated with the very large-scale structures in the outer layer.

Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to 13650

2014 ◽  
Vol 743 ◽  
pp. 202-248 ◽  
Author(s):  
Sébastien Deck ◽  
Nicolas Renard ◽  
Romain Laraufie ◽  
Pierre-Élie Weiss
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flat Plate ◽  
Skin Friction ◽  
High Reynolds Number ◽  
Large Scale ◽  
Wall Shear ◽  
High Reynolds

AbstractA numerical investigation of the mean wall shear stress properties on a spatially developing turbulent boundary layer over a smooth flat plate was carried out by means of a zonal detached eddy simulation (ZDES) technique for the Reynolds number range $3060\leq Re_{\theta }\leq 13\, 650$. Some asymptotic trends of global parameters are suggested. Consistently with previous findings, the calculation confirms the occurrence of very large-scale motions approximately $5\delta $ to $6 \delta $ long which are meandering with a lateral amplitude of $0.3 \delta $ and which maintain a footprint in the near-wall region. It is shown that these large scales carry a significant amount of Reynolds shear stress and their influence on the skin friction, denoted $C_{f,2}$, is revisited through the FIK identity by Fukagata, Iwamoto & Kasagi (Phys. Fluids, vol. 14, 2002, p. L73). It is argued that $C_{f,2}$ is the relevant parameter to characterize the high-Reynolds-number turbulent skin friction since the term describing the spatial heterogeneity of the boundary layer also characterizes the total shear stress variations across the boundary layer. The behaviour of the latter term seems to follow some remarkable self-similarity trends towards high Reynolds numbers. A spectral analysis of the weighted Reynolds stress with respect to the distance to the wall and to the wavelength is provided for the first time to our knowledge and allows us to analyse the influence of the largest scales on the skin friction. It is shown that structures with a streamwise wavelength $\lambda _x >\delta $ contribute to more than $60\, \%$ of $C_{f,2}$, and that those larger than $\lambda _x >2\delta $ still represent approximately $45\, \%$ of $C_{f,2}$.

scholarly journals Simultaneous Stereo PIV and MPS3 Wall-Shear Stress Measurements in Turbulent Channel Flow

Optics ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 40-51
Author(s):  
Esther Mäteling ◽  
Michael Klaas ◽  
Wolfgang Schröder
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Channel Flow ◽  
Inclination Angle ◽  
Large Scale ◽  
Turbulent Channel Flow ◽  
Two Dimensional ◽  
Velocity Fluctuations ◽  
Wall Shear ◽  
Near Wall

An extended experimental method is presented in which the micro-pillar shear-stress sensor (MPS 3 ) and high-speed stereo particle-image velocimetry measurements are simultaneously performed in turbulent channel flow to conduct concurrent time-resolved measurements of the two-dimensional wall-shear stress (WSS) distribution and the velocity field in the outer flow. The extended experimental setup, which involves a modified MPS 3 measurement setup and data evaluation compared to the standard method, is presented and used to investigate the footprint of the outer, large-scale motions (LSM) onto the near-wall small-scale motions. The measurements were performed in a fully developed, turbulent channel flow at a friction Reynolds number R e τ = 969 . A separation between large and small scales of the velocity fluctuations and the WSS fluctuations was performed by two-dimensional empirical mode decomposition. A subsequent cross-correlation analysis between the large-scale velocity fluctuations and the large-scale WSS fluctuations shows that the streamwise inclination angle between the LSM in the outer layer and the large-scale footprint imposed onto the near-wall dynamics has a mean value of Θ ¯ x = 16.53 ∘ , which is consistent with the literature relying on direct numerical simulations and hot-wire anemometry data. When also considering the spatial shift in the spanwise direction, the mean inclination angle reduces to Θ ¯ x z = 13.92 ∘ .

scholarly journals Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

2007 ◽  
Vol 579 ◽  
pp. 1-28 ◽  
Author(s):  
N. HUTCHINS ◽  
IVAN MARUSIC
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
High Speed ◽  
Large Scale ◽  
Sonic Anemometer ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Wall Region ◽  
Velocity Fluctuations ◽  
Near Wall

A regime of very long meandering positive and negative streamwise velocity fluctuations, that we term ‘superstructures’, are found to exist in the log and lower wake regions of turbulent boundary layers. Measurements are made with a spanwise rake of 10 hot-wires in two separate facilities (spanning more than a decade of Reτ) and are compared with existing PIV and DNS results. In all cases, we note evidence of a large-scale stripiness in the streamwise velocity fluctuations. The length of these regions can commonly exceed 20δ. Similar length scales have been previously reported for pipes and DNS channel flows. It is suggested that the true length of these features is masked from single-point statistics (such as autocorrelations and spectra) by a spanwise meandering tendency. Support for this conjecture is offered through the study of a synthetic flow composed only of sinusoidally meandering elongated low- and high-speed regions. From detailed maps of one-dimensional spectra, it is found that the contribution to the streamwise turbulence intensities associated with the superstructures appears to be increasingly significant with Reynolds number, and scales with outer length variables (δ). Importantly, the superstructure maintains a presence or footprint in the near-wall region, seeming to modulate or influence the near-wall cycle. This input of low-wavenumber outer-scaled energy into the near-wall region is consistent with the rise in near-wall streamwise intensities, when scaled with inner variables, that has been noted to occur with increasing Reynolds number. In an attempt to investigate these structures at very high Reynolds numbers, we also report on recent large-scale sonic anemometer rake measurements, made in the neutrally stable atmospheric surface layer. Preliminary results indicate that the superstructure is present in the log region of this atmospheric flow at Reτ = 6.6×105, and has a size consistent with outer scaling.

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