The Skewed Boundary Layer

1959 ◽  
Vol 81 (3) ◽  
pp. 297-300 ◽  
Author(s):  
Edward S. Taylor
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Outer Region ◽  
Experimental Results ◽  
Improved Design

The geometry of the skewed boundary layer is described, and two methods of producing it are discussed. Experimental results show that the form of the usual skewed boundary layer is a thin collateral sublayer under a quasi-collateral outer region. The geometry of separation of a skewed boundary layer is discussed. It is concluded that separation of a skewed boundary layer may differ radically from that of a collateral boundary layer and that separation criteria used for collateral boundary layers may give misleading results when applied to skewed boundary layers. It is concluded that the understanding of the skewed boundary layer can contribute to improved design of turbomachinery.

scholarly journals Boundary Layers on Rough Compressor Blades

1972 ◽  
Author(s):  
K. Bammert ◽  
R. Milsch
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Boundary Layers ◽  
Axial Flow ◽  
Experimental Results ◽  
Experimental Investigations ◽  
Compressor Blades ◽  
Turbulent Transition ◽  
Good Reproduction ◽  
Compressor Efficiency

Blades of axial flow compressors are often roughened by corrosion or erosion. There is only scant information about the influence of this roughening on the boundary layers of the blades and thereby on the compressor efficiency. To obtain detailed information for calculating the efficiency drop due to the roughness, experimental investigations with an enlarged cascade have been executed. The results enabled to develop new formulas for a modified friction coefficient in the laminar region and for the laminar-turbulent transition and the separation points of the boundary layer. Thus, together with the Truckenbrodt theory, it was possible, to get a good reproduction of the experimental results.

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.

scholarly journals On the decay of dispersive motions in the outer region of rough-wall boundary layers

2019 ◽  
Vol 862 ◽  
Author(s):  
Johan Meyers ◽  
Bharathram Ganapathisubramani ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Outer Layer ◽  
Stokes Equations ◽  
Outer Region ◽  
Rough Wall ◽  
Rough Boundary ◽  
Mean Flow ◽  
Wall Boundary

In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the wall, but typically disappear in the outer layer. A theoretical framework is presented to study the decay of dispersive motions in the outer layer. To this end, the problem is formulated in Fourier space, and a set of governing ordinary differential equations per mode in wavenumber space is derived by linearizing the Reynolds-averaged Navier–Stokes equations around a constant background velocity. With further simplifications, analytically tractable solutions are found consisting of linear combinations of $\exp (-kz)$ and $\exp (-Kz)$, with $z$ the wall distance, $k$ the magnitude of the horizontal wavevector $\boldsymbol{k}$, and where $K(\boldsymbol{k},Re)$ is a function of $\boldsymbol{k}$ and the Reynolds number $Re$. Moreover, for $k\rightarrow \infty$ or $k_{1}\rightarrow 0$ (with $k_{1}$ the stream-wise wavenumber), $K\rightarrow k$ is found, in which case solutions consist of a linear combination of $\exp (-kz)$ and $z\exp (-kz)$, and are independent of the Reynolds number. These analytical relations are compared in the limit of $k_{1}=0$ to the rough boundary layer experiments by Vanderwel & Ganapathisubramani (J. Fluid Mech., vol. 774, 2015, R2) and are in reasonable agreement for $\ell _{k}/\unicode[STIX]{x1D6FF}\leqslant 0.5$, with $\unicode[STIX]{x1D6FF}$ the boundary-layer thickness and $\ell _{k}=2\unicode[STIX]{x03C0}/k$.

A three-dimensional turbulent boundary layer

1965 ◽  
Vol 22 (2) ◽  
pp. 285-304 ◽  
Author(s):  
A. E. Perry ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Outer Part ◽  
Outer Region ◽  
Experimental Results ◽  
Mean Velocity ◽  
Polar Plot ◽  
Law Of The Wall ◽  
The Mean

The purpose of this paper is to provide some possible explantions for certain observed phenomena associated with the mean-velocity profile of a turbulent boundary layer which undergoes a rapid yawing. For the cases considered the yawing is caused by an obstruction attached to the wall upon which the boundary layer is developing. Only incompressible flow is considered.§1 of the paper is concerned with the outer region of the boundary layer and deals with a phenomenon observed by Johnston (1960) who described it with his triangular model for the polar plot of the velocity distribution. This was also observed by Hornung & Joubert (1963). It is shown here by a first-approximation analysis that such a behaviour is mainly a consequence of the geometry of the apparatus used. The analysis also indicates that, for these geometries, the outer part of the boundary-layer profile can be described by a single vector-similarity defect law rather than the vector ‘wall-wake’ model proposed by Coles (1956). The former model agrees well with the experimental results of Hornung & Joubert.In §2, the flow close to the wall is considered. Treating this region as an equilibrium layer and using similarity arguments, a three-dimensional version of the ‘law of the wall’ is derived. This relates the mean-velocity-vector distribution with the pressure-gradient vector and wall-shear-stress vector and explains how the profile skews near the wall. The theory is compared with Hornung & Joubert's experimental results. However at this stage the results are inconclusive because of the lack of a sufficient number of measured quantities.

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.

scholarly journals On the identification of well-behaved turbulent boundary layers

2017 ◽  
Vol 822 ◽  
pp. 109-138 ◽  
Author(s):  
C. Sanmiguel Vila ◽  
R. Vinuesa ◽  
S. Discetti ◽  
A. Ianiro ◽  
P. Schlatter ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Shape Factor ◽  
Outer Region ◽  
The Other ◽  
Diagnostic Plot ◽  
Other Hand

This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.

scholarly journals Phase-Averaged Method Applied to Periodic Flow Between Shrouded Corotating Disks

2003 ◽  
Vol 9 (4) ◽  
pp. 293-301 ◽  
Author(s):  
Shen-Chun Wu ◽  
Yau-Ming Chen
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Dynamic Behavior ◽  
Outer Region ◽  
Experimental Results ◽  
Periodic Flow ◽  
Vortical Structures ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Inner Region

This study investigates the coherent flow fields between corotating disks in a cylindrical enclosure. By using two laser velocimeters and a phase-averaged technique, the vortical structures of the flow could be reconstructed and their dynamic behavior was observed. The experimental results reveal clearly that the flow field between the disks is composed of three distinct regions: an inner region near the hub, an outer region, and a shroud boundary layer region. The outer region is distinguished by the presence of large vortical structures. The number of vortical structures corresponds to the normalized frequency of the flow.

Turbulent heat and momentum transport on a rotating disk

2000 ◽  
Vol 402 ◽  
pp. 225-253 ◽  
Author(s):  
CHRISTOPHER J. ELKINS ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Boundary Layers ◽  
Outer Region ◽  
Temperature Fluctuations ◽  
Rotating Disk ◽  
Transport Processes ◽  
Turbulent Heat ◽  
Two Dimensional ◽  
The Mean

Measurements in the turbulent momentum and thermal boundary layers on a rotating disk with a uniform heat flux surface are described for Reynolds numbers up to 106. Measurements include mean velocities and temperatures, all six Reynolds stresses, turbulent temperature fluctuations, and three turbulent heat fluxes. The mean velocity profiles have no wake region, but the mean temperature profiles do. The turbulent temperature fluctuations have a large peak in the outer layer, and there is a third turbulent heat flux in the cross-flow direction. Correlation coefficients and structure parameters are not constant across the boundary layer as they are in two-dimensional boundary layers (2DBLs), and their values are lower. The turbulent Prandtl number agrees with 2DBL values in the lower part of the outer region but is reduced from the 2DBL values higher in the boundary layer. In the outer region of the boundary layer, the transport processes differ significantly from what is observed in two-dimensional turbulent boundary layers: ejections dominate the transport of momentum while both ejections and sweeps contribute to the transport of the passive scalar.

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