On the use of the Reynolds decomposition in the intermittent region of turbulent boundary layers

2016 ◽  
Vol 794 ◽  
pp. 5-16 ◽  
Author(s):  
Y. S. Kwon ◽  
N. Hutchins ◽  
J. P. Monty
Keyword(s):  
Structural Analysis ◽  
Boundary Layers ◽  
Outer Region ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Velocity Fields ◽  
Wall Distance ◽  
Reynolds Decomposition

In the analysis of velocity fields in turbulent boundary layers, the traditional Reynolds decomposition is universally employed to calculate the fluctuating component of streamwise velocity. Here, we demonstrate the perils of such a determination of the fluctuating velocity in the context of structural analysis of turbulence when applied in the outer region where the flow is intermittently turbulent at a given wall distance. A new decomposition is postulated that ensures non-turbulent regions in the flow do not contaminate the fluctuating velocity components in the turbulent regions. Through this new decomposition, some of the typical statistics concerning the scale and structure of turbulent boundary layers are revisited.

Large coherence of spanwise velocity in turbulent boundary layers

2018 ◽  
Vol 847 ◽  
pp. 161-185 ◽  
Author(s):  
Charitha M. de Silva ◽  
Kevin Kevin ◽  
Rio Baidya ◽  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Velocity Fields ◽  
Spatial Extent ◽  
Large Field ◽  
Logarithmic Region ◽  
Spanwise Velocity

The spatial signature of spanwise velocity coherence in turbulent boundary layers has been studied using a series of unique large-field-of-view multicamera particle image velocimetry experiments, which were configured to capture streamwise/spanwise slices of the boundary layer in both the logarithmic and the wake regions. The friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 2600$ was chosen to nominally match the simulation of Sillero et al. (Phys. Fluids, vol. 26 (10), 2014, 105109), who had previously reported oblique features of the spanwise coherence at the top edge of the boundary layer based on the sign of the spanwise velocity, and here we find consistent observations from experiments. In this work, we show that these oblique features in the spanwise coherence relate to the intermittent turbulent bulges at the edge of the layer, and thus the geometry of the turbulent/non-turbulent interface, with the clear appearance of two counter-oriented oblique features. Further, these features are shown to be also present in the logarithmic region once the velocity fields are deconstructed based on the sign of both the spanwise and the streamwise velocity, suggesting that the often-reported meandering of the streamwise-velocity coherence in the logarithmic region is associated with a more obvious diagonal pattern in the spanwise velocity coherence. Moreover, even though a purely visual inspection of the obliqueness in the spanwise coherence may suggest that it extends over a very large spatial extent (beyond many boundary layer thicknesses), through a conditional analysis, we show that this coherence is limited to distances nominally less than two boundary layer thicknesses. Interpretation of these findings is aided by employing synthetic velocity fields of a boundary layer constructed using the attached eddy model, where the range of eddy sizes can be prescribed. Comparisons between the model, which employs an array of self-similar packet-like eddies that are randomly distributed over the plane of the wall, and the experimental velocity fields reveal a good degree of agreement, with both exhibiting oblique features in the spanwise coherence over comparable spatial extents. These findings suggest that the oblique features in the spanwise coherence are likely to be associated with similar structures to those used in the model, providing one possible underpinning structural composition that leads to this behaviour. Further, these features appear to be limited in spatial extent to only the order of the large-scale motions in the flow.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Some Characteristics of the Vortical Motions in the Outer Region of Turbulent Boundary Layers (Data Bank Contribution)

1992 ◽  
Vol 114 (4) ◽  
pp. 530-536 ◽  
Author(s):  
J. C. Klewicki ◽  
R. E. Falco ◽  
J. F. Foss
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Outer Region ◽  
Signal Amplitude ◽  
Threshold Level ◽  
Data Bank ◽  
Turbulent Boundary Layers ◽  
Spanwise Vorticity

Time-resolved measurements of the spanwise vorticity component, ωz, are used to investigate the motions in the outer region of turbulent boundary layers. The measurements were taken in very thick zero pressure gradient boundary layers (Rθ = 1010, 2870, 4850) using a four wire probe. As a result of the large boundary layer thickness, at the outer region locations where the measurements were taken the wall-normal and spanwise dimensions of the probe ranged between 0.7 < Δy/η < 1.2 and 2.1 < Δz/η < 3.9, respectively, where η is the local Kolmogorov length. An analysis of vorticity based intermittency is presented near y/δ = 0.6 and 0.85 at each of the Reynolds numbers. The average intermittency is presented as a function of detector threshold level and position in the boundary layer. The spanwise vorticity signals were found to yield average intermittency values at least as large as previous intermittency studies using “surrogate” signals. The average intermittency results do not indicate a region of threshold independence. An analysis of ωz event durations conditioned on the signal amplitude was also performed. The results of this analysis indicate that for decreasing Rθ, regions of single-signed ωz increase in size relative to the boundary layer thickness, but decrease in size when normalized by inner variables.

Governing Parameters of Adverse Pressure Gradient Turbulent Boundary Layers

2018 ◽  
Author(s):  
Yvan Maciel ◽  
Tie Wei ◽  
Ayse G. Gungor ◽  
Mark P. Simens
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Inertial Parameter ◽  
Velocity Scale ◽  
Gradient Parameter

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer velocity scale that is considered, with the help of seven boundary layer databases. We find the impressive result that if the Zagarola-Smits velocity is used as the outer velocity scale, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with these non-dimensional parameters in all these flows — not just the order of magnitude of these ratios. This cannot be achieved with three other outer velocity scales commonly used for pressure gradient turbulent boundary layers. Consequently, the three new nondimensional parameters, when expressed with the Zagarola-Smits velocity, can be used to follow — in a global sense — the streamwise evolution of the stream-wise mean momentum balance in the outer region. This study provides a clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers.

High Freestream Turbulence Effects on Turbulent Boundary Layers

1996 ◽  
Vol 118 (2) ◽  
pp. 276-284 ◽  
Author(s):  
K. A. Thole ◽  
D. G. Bogard
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Outer Region ◽  
Power Spectra ◽  
Turbulent Boundary Layers ◽  
Freestream Turbulence ◽  
Length Scales ◽  
Turbulent Eddies ◽  
Viscous Shear

High freestream turbulence levels significantly alter the characteristics of turbulent boundary layers. Numerous studies have been conducted with freestreams having turbulence levels of 7 percent or less, but studies using turbulence levels greater than 10 percent have been essentially limited to the effects on wall shear stress and heat transfer. This paper presents measurements of the boundary layer statistics for the interaction between a turbulent boundary layer and a freestream with turbulence levels ranging from 10 to 20 percent. The boundary layer statistics reported in this paper include mean and rms velocities, velocity correlation coefficients, length scales, and power spectra. Although the freestream turbulent eddies penetrate into the boundary layer at high freestream turbulence levels, as shown through spectra and length scale measurements, the mean velocity profile still exhibits a log-linear region. Direct measurements of total shear stress (turbulent shear stress and viscous shear stress) confirm the validity of the log-law at high freestream turbulence levels. Velocity defects in the outer region of the boundary layer were significantly decreased resulting in negative wake parameters. Fluctuating rms velocities were only affected when the freestream turbulence levels exceeded the levels of the boundary layer generated rms velocities. Length scales and power spectra measurements showed large scale turbulent eddies penetrate to within y+ = 15 of the wall.

Mean momentum balance in moderately favourable pressure gradient turbulent boundary layers

2008 ◽  
Vol 617 ◽  
pp. 107-140 ◽  
Author(s):  
M. METZGER ◽  
A. LYONS ◽  
P. FIFE
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Present Theory ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Physical Layers ◽  
Multi Scale ◽  
The Mean

Moderately favourable pressure gradient turbulent boundary layers are investigated within a theoretical framework based on the unintegrated two-dimensional mean momentum equation. The present theory stems from an observed exchange of balance between terms in the mean momentum equation across different regions of the boundary layer. This exchange of balance leads to the identification of distinct physical layers, unambiguously defined by the predominant mean dynamics active in each layer. Scaling domains congruent with the physical layers are obtained from a multi-scale analysis of the mean momentum equation. Scaling behaviours predicted by the present theory are evaluated using direct measurements of all of the terms in the mean momentum balance for the case of a sink-flow pressure gradient generated in a wind tunnel with a long development length. Measurements also captured the evolution of the turbulent boundary layers from a non-equilibrium state near the wind tunnel entrance towards an equilibrium state further downstream. Salient features of the present multi-scale theory were reproduced in all the experimental data. Under equilibrium conditions, a universal function was found to describe the decay of the Reynolds stress profile in the outer region of the boundary layer. Non-equilibrium effects appeared to be manifest primarily in the outer region, whereas differences in the inner region were attributed solely to Reynolds number effects.

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