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.

Measurements in a Turbulent Boundary Layer Over a d-Type Surface Roughness

1975 ◽  
Vol 42 (3) ◽  
pp. 591-597 ◽  
Author(s):  
D. H. Wood ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Turbulent Energy ◽  
Shear Stresses ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Outer Flow ◽  
Intensity Measurements ◽  
Normal And Shear Stresses

Mean velocity and turbulence intensity measurements have been made in a fully developed turbulent boundary layer over a d-type surface roughness. This roughness is characterised by regular two-dimensional elements of square cross section placed one element width apart, with the cavity flow between elements being essentially isolated from the outer flow. The measurements show that this boundary layer closely satisfies the requirement of exact self-preservation. Distribution across the layer of Reynolds normal and shear stresses are closely similar to those found over a smooth surface except for the region immediately above the grooves. This similarity extends to distributions of third and fourth-order moments of longitudinal and normal velocity fluctuations and also to the distribution of turbulent energy dissipation. The present results are compared with those obtained for a k-type or sand grained roughness.

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.

scholarly journals The law of the wake in the turbulent boundary layer

1956 ◽  
Vol 1 (2) ◽  
pp. 191-226 ◽  
Author(s):  
Donald Coles
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Three Dimensional ◽  
Shearing Stress ◽  
Universal Functions ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean ◽  
The Law

After an extensive survey of mean-velocity profile measurements in various two-dimensional incompressible turbulent boundary-layer flows, it is proposed to represent the profile by a linear combination of two universal functions. One is the well-known law of the wall. The other, called the law of the wake, is characterized by the profile at a point of separation or reattachment. These functions are considered to be established empirically, by a study of the mean-velocity profile, without reference to any hypothetical mechanism of turbulence. Using the resulting complete analytic representation for the mean-velocity field, the shearing-stress field for several flows is computed from the boundary-layer equations and compared with experimental data.The development of a turbulent boundary layer is ultimately interpreted in terms of an equivalent wake profile, which supposedly represents the large-eddy structure and is a consequence of the constraint provided by inertia. This equivalent wake profile is modified by the presence of a wall, at which a further constraint is provided by viscosity. The wall constraint, although it penetrates the entire boundary layer, is manifested chiefly in the sublayer flow and in the logarithmic profile near the wall.Finally, it is suggested that yawed or three-dimensional flows may be usefully represented by the same two universal functions, considered as vector rather than scalar quantities. If the wall component is defined to be in the direction of the surface shearing stress, then the wake component, at least in the few cases studied, is found to be very nearly parallel to the gradient of the pressure.

Can a turbulent boundary layer become independent of the Reynolds number?

2018 ◽  
Vol 851 ◽  
pp. 1-22 ◽  
Author(s):  
L. Djenidi ◽  
K. M. Talluru ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Rough Wall ◽  
Asymptotic State ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Independent State ◽  
Velocity Defect ◽  
The Mean

This paper examines the Reynolds number ($Re$) dependence of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) which develops over a two-dimensional rough wall with a view to ascertaining whether this type of boundary layer can become independent of $Re$. Measurements are made using hot-wire anemometry over a rough wall that consists of a periodic arrangement of cylindrical rods with a streamwise spacing of eight times the rod diameter. The present results, together with those obtained over a sand-grain roughness at high Reynolds number, indicate that a $Re$-independent state can be achieved at a moderate $Re$. However, it is also found that the mean velocity distributions over different roughness geometries do not collapse when normalised by appropriate velocity and length scales. This lack of collapse is attributed to the difference in the drag coefficient between these geometries. We also show that the collapse of the $U_{\unicode[STIX]{x1D70F}}$-normalised mean velocity defect profiles may not necessarily reflect $Re$-independence. A better indicator of the asymptotic state of $Re$ is the mean velocity defect profile normalised by the free-stream velocity and plotted as a function of $y/\unicode[STIX]{x1D6FF}$, where $y$ is the vertical distance from the wall and $\unicode[STIX]{x1D6FF}$ is the boundary layer thickness. This is well supported by the measurements.

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.

Debate Concerning the Mean-Velocity Profile of a Turbulent Boundary Layer

AIAA Journal ◽  
2003 ◽  
Vol 41 (4) ◽  
pp. 565-572 ◽  
Author(s):  
Matthias H. Buschmann ◽  
Mohamed Gad-El-Hak
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Mean Velocity ◽  
The Mean

On the evolution of a turbulent boundary layer induced by a three-dimensional roughness element

1992 ◽  
Vol 237 ◽  
pp. 101-187 ◽  
Author(s):  
P. S. Klebanoff ◽  
W. G. Cleveland ◽  
K. D. Tidstrom
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Laminar Boundary Layer ◽  
Roughness Element ◽  
Three Dimensional ◽  
Outer Region ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Roughness Elements

An experimental investigation is described which has as its objectives the extension of the technical data base pertaining to roughness-induced transition and the advancement of the understanding of the physical processes by which three-dimensional roughness elements induce transition from laminar to turbulent flow in boundary layers. The investigation was carried out primarily with single hemispherical roughness elements surface mounted in a well-characterized zero-pressure-gradient laminar boundary layer on a flat plate. The critical roughness Reynolds number at which turbulence is regarded as originating at the roughness was determined for the roughness elements herein considered and evaluated in the context of data existing in the literature. The effect of a steady and oscillatory free-stream velocity on eddy shedding was also investigated. The Strouhal behaviour of the ‘hairpin’ eddies shed by the roughness and role they play in the evolution of a fully developed turbulent boundary layer, as well as whether their generation is governed by an inflexional instability, are examined. Distributions of mean velocity and intensity of the u-fluctuation demonstrating the evolution toward such distributions for a fully developed turbulent boundary layer were measured on the centreline at Reynolds numbers below and above the critical Reynolds number of transition. A two-region model is postulated for the evolutionary change toward a fully developed turbulent boundary layer: an inner region where the turbulence is generated by the complex interaction of the hairpin eddies with the pre-existing stationary vortices that lie near the surface and are inherent to a flow about a three-dimensional obstacle in a laminar boundary layer; and an outer region where the hairpin eddies deform and generate turbulent vortex rings. The structure of the resulting fully developed turbulent boundary layer is discussed in the light of the proposed model for the evolutionary process.

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 turbulent boundary layer disturbed by a cylinder

1978 ◽  
Vol 87 (1) ◽  
pp. 121-141 ◽  
Author(s):  
Eisuke Marumo ◽  
Kenjiro Suzuki ◽  
Takashi Sato
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Turbulent Boundary Layer ◽  
Flow Direction ◽  
Outer Region ◽  
Wall Region ◽  
Mean Velocity ◽  
Turbulent Length Scale ◽  
Axis Parallel ◽  
The Mean

This paper deals with a two-dimensional turbulent boundary layer disturbed by a circular cylinder. The cylinder was placed inside or outside the boundary layer with its axis parallel to the wall and normal to the flow direction. The mean velocity, wall shear stress, longitudinal turbulent intensity, autocorrelations and turbulent length scale were measured and here the relaxation features of the disturbed boundary layer are discussed. The measurements were made for a ratio of the cylinder diameter d to the undisturbed boundary-layer thickness δ0 equal to 0·30 and for three values of the ratio of the height h of the cylinder axis to δ0 equal to 0·222, 0·556 and 1·24.The results show that the near-wall region of the disturbed boundary layer recovers much more quickly than the outer region and that in the case h/δ0 = 0·222 the recovery is faster than in other cases, as reported by Clauser (1956). Moreover, it is found that the fluctuating velocity field recovers more slowly than the mean velocity field, and that the characteristics of the turbulence in the outer region are still close to those in the wake of an isolated cylinder at the last measurement station, although the mean velocity profile has almost completely returned to its natural shape.

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