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.

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).

On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

2008 ◽  
Vol 616 ◽  
pp. 195-203 ◽  
Author(s):  
M. B. JONES ◽  
T. B. NICKELS ◽  
IVAN MARUSIC
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Similarity Solution ◽  
Friction Velocity ◽  
Free Stream ◽  
Outer Region ◽  
Free Stream Velocity ◽  
Stream Velocity

We investigate similarity solutions for the outer part of a zero-pressure-gradient turbulent boundary layer in the limit of infinite Reynolds number. Previous work by George (Phil. Trans. R. Soc. vol. 365, 2007 p. 789) has suggested that the only appropriate velocity scale for the outer region is U1, the free-stream velocity. This is based on the fact that scaling with U1 leads to a mathematically valid similarity solution of the momentum equation for the outer region in the asymptotic limit of infinite Reynolds number. Here we show that the classical scaling using the friction velocity also leads to a valid similarity solution for the outer flow in this limit. Therefore on this basis it is not possible to dismiss the friction velocity as a possible scaling as has been suggested by George (2007) and others. We show that both the free-stream velocity and the friction velocity are potentially valid scalings according to this theoretical criterion.

The Effects of Surface Roughness on the Mean Velocity Profile in a Turbulent Boundary Layer

2002 ◽  
Vol 124 (3) ◽  
pp. 664-670 ◽  
Author(s):  
Donald J. Bergstrom ◽  
Nathan A. Kotey ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Friction Velocity ◽  
Outer Region ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Outer Flow ◽  
The Mean

Experimental measurements of the mean velocity profile in a canonical turbulent boundary layer are obtained for four different surface roughness conditions, as well as a smooth wall, at moderate Reynolds numbers in a wind tunnel. The mean streamwise velocity component is fitted to a correlation which allows both the strength of the wake, Π, and friction velocity, Uτ, to vary. The results show that the type of surface roughness affects the mean defect profile in the outer region of the turbulent boundary layer, as well as determining the value of the skin friction. The defect profiles normalized by the friction velocity were approximately independent of Reynolds number, while those normalized using the free stream velocity were not. The fact that the outer flow is significantly affected by the specific roughness characteristics at the wall implies that rough wall boundary layers are more complex than the wall similarity hypothesis would allow.

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.

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.

The Wake Dynamics Behind a Near-Wall Square Cylinder

2021 ◽  
Author(s):  
Samuel Addai ◽  
Xingjun Fang ◽  
Afua A Mante ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Wake Flow ◽  
Stream Velocity ◽  
Reynolds Stresses ◽  
Square Cylinder ◽  
Gap Ratio ◽  
The Mean

Abstract Particle image velocimetry is used to experimentally study the wake dynamics behind a near-wall square cylinder subjected to a thick oncoming turbulent boundary layer. The turbulent boundary layer thickness was 3.6 times the cylinder height (h) while the Reynolds number based on the free-stream velocity and the cylinder height was 12750. The gap distance (G) between the bottom face of the cylinder and the wall was varied, resulting in gap ratios (G/h) of 0, 0.3, 0.5, 1.0, 2.0, 4.0 and 8.0. The effects of varying the gap ratio on the mean flow, Reynolds stresses, triple velocity correlation, two-point autocorrelation and the unsteady wake characteristics were examined. The results indicate that as gap ratio decreases, asymmetry in the wake flow becomes more pronounced and the size of the mean separation bubbles increases. The magnitudes of the Reynolds stresses and triple velocity correlations generally decrease with decreasing gap ratio. Moreover, the size of the large-scale structures increases with decreasing gap ratio and the critical gap ratio, below which Kármán vortex shedding suppression occurs, is found to be 0.3. The dominant Strouhal number in the wake flow expressed in terms of the streamwise mean velocity at the cylinder vertical midpoint increases as gap ratio decreases while that based on the free-stream velocity is less sensitive to gap ratio for the offset cases (G/h &gt; 0).

Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat Transfer and Mean Profile Development, Part I—Experimental Data

1983 ◽  
Vol 105 (1) ◽  
pp. 33-40 ◽  
Author(s):  
M. F. Blair
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Full Range ◽  
Stream Velocity ◽  
Free Stream Turbulence ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

An experimental research program was conducted to determine the influence of free-stream turbulence on zero pressure gradient, fully turbulent boundary layer flow. Connective heat transfer coefficients and boundary layer mean velocity and temperature profile data were obtained for a constant free-stream velocity of 30 m/s and free-stream turbulence intensities ranging from approximately 1/4 to 7 percent. Free-stream multicomponent turbulence intensity, longitudinal integral scale, and spectral distributions were obtained for the full range of turbulence levels. The test results with 1/4 percent free-stream turbulence indicate that these data were in excellent agreement with classic two-dimensional, low free-stream turbulence, turbulent boundary layer correlations. For fully turbulent boundary layer flow, both the skin friction and heat transfer were found to be substantially increased (up to ∼ 20 percent) for the higher levels of free-stream turbulence. Detailed results of the experimental study are presented in the present paper (Part I). A comprehensive analysis is provided in a companion paper (Part II).

Experimental Investigation of a Turbulent Boundary Layer Subjected to an Adverse Pressure Gradient

2011 ◽  
Author(s):  
Takanori Nakamura ◽  
Takatsugu Kameda ◽  
Shinsuke Mochizuki
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Friction Velocity ◽  
Adverse Pressure Gradient ◽  
Turbulent Intensity ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Velocity Scale ◽  
The Mean ◽  
The Law

Experiments were performed to investigate the effect of an adverse pressure gradient on the mean velocity and turbulent intensity profiles for an equilibrium boundary layer. The equilibrium boundary layer, which makes self-similar profiles, was constructed using a power law distribution of free stream velocity. The exponent of the law was adjusted to −0.188. The wall shear stress was measured with a drag balance by a floating element. The investigation of the law of the wall and the similarity of the streamwise turbulent intensity profile was made using both a friction velocity and new proposed velocity scale. The velocity scale is derived from the boundary layer equation. The mean velocity gradient profile normalized with the height and the new velocity scale exists the region where the value is almost constant. The turbulent intensity profiles normalized with the friction velocity strongly depend on the nondimensional pressure gradient near the wall. However, by mean of the local velocity scale, the profiles might be achieved to be similar with that of a zero pressure gradient.

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