The Three-Dimensional Turbulent Boundary Layer

1960 ◽  
Vol 64 (599) ◽  
pp. 692-694 ◽  
Author(s):  
D. R. Blackman ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Vector ◽  
Three Dimensional ◽  
Universal Function ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Law Of The Wall ◽  
The Law ◽  
Universal Law

An experimental verification of coles’ postulate of the Law of the Wake in three dimensions has been attempted. This hypothesis, which is strongly supported by experimental evidence in two dimensions, purports to represent the velocity vector in a yawed boundary layer by the sum of two vectors, whose magnitudes are found from the universal law of the wall, and a second universal function, the law of the wake. It has been found that the velocity vector can be represented in this way and the wake function required for this is very similar to Coles’ form. Limitations of the experimental arrangement however prohibited the comparison of vector directions with that proposed by Coles.

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.

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.

Wall Shear Stress Inference From Two and Three-Dimensional Turbulent Boundary Layer Velocity Profiles

1973 ◽  
Vol 95 (1) ◽  
pp. 61-67 ◽  
Author(s):  
F. J. Pierce ◽  
B. B. Zimmerman
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Three Dimensional ◽  
Law Of The Wall ◽  
Layer Velocity ◽  
Wall Shear ◽  
Near Wall

A method is developed to infer a local wall shear stress from a two-dimensional turbulent boundary layer velocity profile using all near-wall data with the Spalding single formula law of the wall. The method is used to broaden the Clauser chart scheme by providing for the inclusion of data in the laminar sublayer and transition region, as well as the data in the fully turbulent near-wall flow region. For a skewed velocity profile typical of pressure driven three-dimensional turbulent boundary layer flows, the method is extended to infer a wall shear stress for a three-dimensional turbulent boundary layer. Either wall shear stress or shear velocity values are calculated for two different sets of three-dimensional experimental data, with good agreement found between calculated and experimental results.

The Law of the Wake and Plane of Symmetry Flows in Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Vol 88 (1) ◽  
pp. 101-108 ◽  
Author(s):  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Three Dimensional Model ◽  
Law Of The Wall ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
The Law

Coles’ model incorporating the law of the wall and the law of the wake, proposed for two and three-dimensional turbulent boundary-layer flows, is examined for the special case of plane of symmetry flows in collateral and skewed three-dimensional boundary layers. Contrary to other published results, it is shown that the model is appropriate for adverse pressure gradient plane of symmetry flows in collateral environments away from separation. Additional, it appears that the departure from Coles’ law of the wake for recently reported three-dimensional flows is of the same basic form as that observed for plane of symmetry flows in transient development or two-dimensional flow with imminent separation. Since the Coles’ model, as most velocity profile models, is proposed only in an asymptotic sense for a well-developed flow, the fact that most of the three-dimensional flows heretofore reported are in transient or undeveloped states, suggests that the three-dimensional model be examined in well-developed three-dimensional boundary-layer flows before the question of the model’s validity can be properly answered.

The mean velocity profile in three-dimensional turbulent oundary layers

1963 ◽  
Vol 15 (3) ◽  
pp. 368-384 ◽  
Author(s):  
H. G. Hornung ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Three Dimensional ◽  
Leading Edge ◽  
Viscous Sublayer ◽  
Scale Model ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

The mean velocity distribution in a low-speed three-dimensional turbulent boundary-layer flow was investigated experimentally. The experiments were performed on a large-scale model which consisted of a flat plate on which secondary flow was generated by the pressure field introduced by a circular cylinder standing on the plate. The Reynolds number based on distance from the leading edge of the plate was about 6 x 106.It was found that the wall-wake model of Coles does not apply for flow of this kind and the model breaks down in the case of conically divergent flow with rising pressure, for example, in the results of Kehl (1943). The triangular model for the yawed turbulent boundary layer proposed by Johnston (1960) was confirmed with good correlation. However, the value ofyuτ/vwhich occurs at the vertex of the triangle was found to range up to 150 whereas Johnston gives the highest value as about 16 and hence assumes that the peak lies within the viscous sublayer. Much of his analysis is based on this assumption.The dimensionless velocity-defect profile was found to lie in a fairly narrow band when plotted againsty/δ for a wide variation of other parameters including the pressure gradient. The law of the wall was found to apply in the same form as for two-dimensional flow but for a more limited range ofy.

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