Convex Turbulent Boundary Layers With Zero and Favorable Pressure Gradients

1996 ◽  
Vol 118 (4) ◽  
pp. 787-794 ◽  
Author(s):  
A. C. Schwarz ◽  
M. W. Plesniak
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Boundary Layers ◽  
Reynolds Stress ◽  
Strain Rates ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
The Mean ◽  
Stress Profiles

A turbulent boundary layer subjected to multiple, additional strain rates, namely convex curvature coupled with streamwise pressure gradients (zero and favorable, ZPG and FPG) was investigated experimentally using laser Doppler velocimetry. The inapplicability of the universal flat-plate log-law to curved flows is discussed. However, a logarithmic region is found in the curved and accelerated turbulent boundary layer examined here. Similarity of the mean velocity and Reynolds stress profiles was achieved by 45 deg of curvature even in the presence of the strongest FPG investigated (k = 1.01 × 10−6). The Reynolds stresses were suppressed (with respect to flat plate values) due primarily to the effects of strong convex curvature (δo/R ≈ 0.10). In curved boundary layers subjected to different favorable pressure gradients, the mean velocity and normal Reynolds stress profiles collapsed in the inner region, but deviated in the outer region (y+ ≥ 100). Thus, inner scaling accounted for the impact of the extra strain rates on these profiles in the near-wall region. Combined with curvature, the FPG reduced the strength of the wake component, resulted in a greater suppression of the fluctuating velocity components and a reduction of the primary Reynolds shear stress throughout almost the entire boundary layer relative to the ZPG curved case.

LDA Measurements on Rough Turbulent Boundary Layers Subject to Strong Favorable Pressure Gradients

2006 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Brian Brzek ◽  
Gunnar Johansson ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Rough Surface ◽  
Reynolds Stress ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Velocity Deficit ◽  
The Mean ◽  
Stress Profiles

Laser-Doppler anemometry (LDA) measurements of the mean velocity and Reynolds stresses are carried out on a rough surface favorable pressure gradient (FPG) turbulent boundary layer. These data is compared with smooth FPG turbulent boundary layer data possessing with the same strength of pressure gradient and also with rough zero pressure gradient (ZPG) data. The scales for the mean velocity deficit and Reynolds stresses are obtained through means of equilibrium similarity analysis of the RANS equations [1]. The mean velocity deficit profiles collapse, but to different curves when normalized using the free-stream velocity. The effects of the pressure gradient and roughness are clearly distinguished and separated. However, these effects are removed from the outer flow when the profiles are normalized using the Zagarola and Smits [2] scaling. It is also found that there is a clear effect of the roughness and pressure gradient on the Reynolds stresses. The Reynolds stress profiles augment due to the rough surface. Furthermore, the strength of the pressure gradient imposed of the flow changes the shape of the Reynolds stress profiles especially on the < v2 > and < uv > components. The rough surface influence is mostly noticed on the < u2 > component of the Reynolds stress, where the shape of the profiles change entirely. The boundary layer parameter δ*/δ shows the effects of the roughness and a dependence on the Reynolds number for the smooth FPG case. The pressure parameter, A, describes a development of the turbulent boundary layer and no influence of the roughness is linked with the parameter, k+. The boundary layers grow differently and depict the influence of the studied effects in their development. These measurements are the first of their nature due to the extensive number in downstream locations (12) and the combination of the studied external conditions (i.e., the strength of the pressure gradient and the surface roughness).

Intermittency measurements in the turbulent boundary layer

1966 ◽  
Vol 25 (4) ◽  
pp. 719-735 ◽  
Author(s):  
H. Fiedler ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Focal Point ◽  
Pressure Gradients ◽  
Narrow Beam ◽  
Hot Wire ◽  
Characteristic Parameters ◽  
Mean Velocity ◽  
Form Parameter ◽  
The Mean

An improved version of Corrsin & Kistler's method has been used to measure intermittency in favourable and adverse pressure gradients, and the characteristic parameters of the intermittency have been related to the form parameterHof the mean velocity profiles.It is found that with adverse pressure gradients the centre of intermittency moves outward from the surface while the width of the intermittent zone decreases. The converse is true of favourable pressure gradients, and it seems likely that at sufficiently low values ofHthe flow over the full depth of the layer is only intermittently turbulent.A new method of intermittency measurement is presented which makes use of a photo-electric probe. Smoke is introduced into the boundary layer and illuminated by a narrow beam of parallel light normal to the surface. The photoelectric probe is focused on the illuminated region and a signal is generated when smoke passes through the focal point of the probe lens. Comparison of this signal with the output from a hot-wire at very nearly the same point shows the identity of smoke and turbulence distributions.

On turbulent boundary layers in oscillatory flow

1977 ◽  
Vol 353 (1672) ◽  
pp. 121-144 ◽  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Travelling Wave ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Freestream Velocity ◽  
The Mean

An experimental investigation has been made of turbulent boundary layer response to harmonic oscillations associated with a travelling wave imposed on an otherwise constant freestream velocity and convected in the freestream direction. The tests covered oscillation frequencies of 4-12 Hz for freestream amplitudes of up to 11% of the mean velocity. Additional steady flow measurements were used to infer the quasi-steady response to freestream oscillations. The results show a welcome insensitivity of the mean flow and turbulent intensity distributions to the freestream oscillations tested. An approximate analysis based on these results has been developed. It is probably of limited validity but it does provide a useful guide to the physical processes involved. The effects on boundary layer response of varying the travelling wave convection velocity and frequency of oscillation are illustrated by the analysis and show a behaviour broadly similar to that of laminar boundary layers. The travelling wave convection velocity exhibits a dominant influence on the turbulent boundary layer response to freestream oscillations.

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

1974 ◽  
Vol 64 (4) ◽  
pp. 763-774 ◽  
Author(s):  
R. G. Deissler
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Shear Stress ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Mass Injection ◽  
The Mean ◽  
Theoretical Results

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

The Effects of Splitter Plates on Turbulent Boundary Layer on a Long Flat Plate Near the Trailing Edge

2007 ◽  
Author(s):  
Yoshifumi Jodai ◽  
Yoshikazu Takahashi ◽  
Masashi Ichimiya ◽  
Hideo Osaka
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Pressure Coefficient ◽  
Pressure Rise ◽  
Splitter Plate ◽  
Base Pressure ◽  
Trailing Edge ◽  
Mean Velocity ◽  
The Mean

An experimental investigation has been made on a turbulent boundary layer near the trailing edge on a long flat plate. The flow was controlled by an additional splitter plate fitted to the trailing edge along the wake center line. The length of the splitter plate, l, was varied from a half, to five times the trailing edge thickness, h. Measurements of base pressure behind the trailing edge and of mean velocity and pressure distribution in the turbulent boundary layer on the flat plate were made under the freestream zero-pressure gradient. The absolute value of the base pressure coefficient of the long flat plate was considerably smaller than that of the short flat plate without the splitter plate. A significant increase in the base pressure coefficient was achieved with the splitter plate (l / h ≧ 1), fitted to the long flat plate. Within an inner layer in the turbulent boundary layer near the trailing edge, the mean velocity increased more than that in the upstream position in the case without the splitter plate. With the splitter plate, however, the base pressure rise made the mean velocity distribution more closely approach that of a fully-developed turbulent boundary layer.

scholarly journals The rough favourable pressure gradient turbulent boundary layer

2009 ◽  
Vol 641 ◽  
pp. 129-155 ◽  
Author(s):  
RAÚL BAYOÁN CAL ◽  
BRIAN BRZEK ◽  
T. GUNNAR JOHANSSON ◽  
LUCIANO CASTILLO
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Rough Surface ◽  
Reynolds Stress ◽  
Friction Velocity ◽  
Free Stream ◽  
Stream Velocity ◽  
The Mean ◽  
Stress Profiles

Laser Doppler anemometry measurements of the mean velocity and Reynolds stresses are carried out for a rough-surface favourable pressure gradient turbulent boundary layer. The experimental data is compared with smooth favourable pressure gradient and rough zero-pressure gradient data. The velocity and Reynolds stress profiles are normalized using various scalings such as the friction velocity and free stream velocity. In the velocity profiles, the effects of roughness are removed when using the friction velocity. The effects of pressure gradient are not absorbed. When using the free stream velocity, the scaling is more effective absorbing the pressure gradient effects. However, the effects of roughness are almost removed, while the effects of pressure gradient are still observed on the outer flow, when the mean deficit velocity profiles are normalized by the U∞ δ∗/δ scaling. Furthermore, when scaled with U2∞, the 〈u2〉 component of the Reynolds stress augments due to the rough surface despite the imposed favourable pressure gradient; when using the friction velocity scaling u∗2, it is dampened. It becomes ‘flatter’ in the inner region mainly due to the rough surface, which destroys the coherent structures of the flow and promotes isotropy. Similarly, the pressure gradient imposed on the flow decreases the magnitude of the Reynolds stress profiles especially on the 〈v2〉 and -〈uv〉 components for the u∗2 or U∞2 scaling. These effects are reflected in the boundary layer parameter δ∗/δ, which increase due to roughness, but decrease due to the favourable pressure gradient. Additionally, the pressure parameter Λ found not to be in equilibrium, describes the development of the turbulent boundary layer, with no influence of the roughness linked to this parameter. These measurements are the first with an extensive number of downstream locations (11). This makes it possible to compute the required x-dependence for the production term and the wall shear stress from the full integrated boundary layer equation. The finding indicates that the skin friction coefficient depends on the favourable pressure gradient condition and surface roughness.

Reynolds-number scaling of the flat-plate turbulent boundary layer

2000 ◽  
Vol 422 ◽  
pp. 319-346 ◽  
Author(s):  
DAVID B. DE GRAAFF ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Extensive Study ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.

Effects of free-stream turbulence on rough surface turbulent boundary layers

2009 ◽  
Vol 635 ◽  
pp. 207-243 ◽  
Author(s):  
BRIAN BRZEK ◽  
SHEILLA TORRES-NIEVES ◽  
JOSÉ LEBRÓN ◽  
RAÚL CAL ◽  
CHARLES MENEVEAU ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Rough Surface ◽  
Boundary Layers ◽  
Reynolds Stress ◽  
Isotropic Turbulence ◽  
Free Stream ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Stress Profiles ◽  
Inner Region

Several effects of nearly isotropic free-stream turbulence in transitionally rough turbulent boundary layers are studied using data obtained from laser Doppler anemometry measurements. The free-stream turbulence is generated with the use of an active grid, resulting in free-stream turbulence levels of up to 6.2%. The rough surface is characterized by a roughness parameterk+≈ 53, and measurements are performed at Reynolds numbers of up toReθ= 11300. It is confirmed that the free-stream turbulence significantly alters the mean velocity deficit profiles in the outer region of the boundary layer. Consequently, the previously observed ability of the Zagarola & Smits (J. Fluid Mech., vol. 373, 1998, p. 33) velocity scaleU∞δ*/δ to collapse results from both smooth and rough surface boundary layers, no longer applies in this boundary layer subjected to high free-stream turbulence. In inner variables, the wake region is significantly reduced with increasing free-stream turbulence, leading to decreased mean velocity gradient and production of Reynolds stress components. The effects of free-stream turbulence are clearly identifiable and significant augmentation of the streamwise Reynolds stress profiles throughout the entire boundary layer are observed, all the way down to the inner region. In contrast, the Reynolds wall-normal and shear stress profiles increase due to free-stream turbulence only in the outer part of the boundary layer due to the blocking effect of the wall. As a consequence, there is a significant portion of the boundary layer in which the addition of nearly isotropic turbulence in the free-stream, results in significant increases in anisotropy of the turbulence. To quantify which turbulence length scales contribute to this trend, second-order structure functions are examined at various distances from the wall. Results show that the anisotropy created by adding nearly isotropic turbulence in the free-stream resides mostly in the larger scales of the flow. Furthermore, by analysing the streamwise Reynolds stress equation, it can be predicted that it is the wall-normal gradient of 〈u2v〉 term that is responsible for the increase in 〈u2〉 profiles throughout the boundary layer (i.e. an efficient turbulent transport of turbulence away from the wall). Furthermore, a noticeable difference between the triple correlations for smooth and rough surfaces exists in the inner region, but no significant differences are seen due to free-stream turbulence. In addition, the boundary layer parameters δ*/δ95,Handcfare also evaluated from the experimental data. The flow parameters δ*/δ95andHare found to increase due to roughness, but decrease due to free-stream turbulence, which has significance for flow control, particularly in delaying separation. Increases incfdue to high free-stream turbulence are also observed, associated with increased momentum flux towards the wall.

Turbulent Flow Near a Rough Wall

1992 ◽  
Vol 114 (4) ◽  
pp. 537-542 ◽  
Author(s):  
Yang-Moon Koh
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Simple Formula ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
Friction Factors ◽  
Special Cases ◽  
The Mean

By introducing the equivalent roughness which is defined as the distance from the wall to where the velocity gets a certain value (u/uτ ≈ 8.5) and which can be represented by a simple function of the roughness, a simple formula to represent the mean-velocity distribution across the inner layer of a turbulent boundary layer is suggested. The suggested equation is general enough to be applicable to turbulent boundary layers over surfaces of any roughnesses covering from very smooth to completely rough surfaces. The suggested velocity profile is then used to get expressions for pipe-friction factors and skin friction coefficients. These equations are consistent with existing experimental observations and embrace well-known equations (e.g., Prandtl’s friction law for smooth pipes and Colebrook’s formula etc.) as special cases.

A shear-free turbulent boundary layer

1967 ◽  
Vol 28 (4) ◽  
pp. 803-821 ◽  
Author(s):  
T. Uzkan ◽  
W. C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Isotropic Turbulence ◽  
Wall Turbulence ◽  
Statistical Features ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Velocity ◽  
Velocity Gradients ◽  
The Mean

A simple wall-turbulence interaction has been studied experimentally. In the idealized model an infinite flat plate is suddenly inserted into a pre-existing field of homogeneous isotropic turbulence, and subsequent changes in the turbulence field examined. The experiment involved passing grid-produced turbulence over a wall moving at the mean speed. Mean velocity gradients vanish in both the model and experiment, and hence production of new turbulence is absent. This allowed the inhibiting effects of the wall to be studied separately. The growth of the ‘inhomogeneity layer’ into the impressed turbulence field and other statistical features of the turbulence were measured.

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