scholarly journals An experimental study of a three-dimensional pressure-driven turbulent boundary layer

1995 ◽  
Vol 290 ◽  
pp. 225-262 ◽  
Author(s):  
Semİh M. Ölçmen ◽  
Roger L. Simpson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Coordinate System ◽  
Normal Stress ◽  
Three Dimensional ◽  
Mean Velocity ◽  
Vector Direction ◽  
The Mean ◽  
Pressure Driven

A three-dimensional, pressure-driven turbulent boundary layer created by an idealized wing–body junction flow was studied experimentally. The data presented include time-mean static pressure and directly measured skin-friction magnitude on the wall. The mean velocity and all Reynolds stresses from a three-velocity-component fibre-optic laser-Doppler anemometer are presented at several stations along a line determined by the mean velocity vector component parallel to the wall in the layer where the $\overline{u^2}$ kinematic normal stress is maximum (normal-stress coordinate system). This line was selected by intuitively reasoning that overlap of the near-wall flow and outer-region flow occurs at the location where $\overline{u^2}$ is maximum. Along this line the flow is subjected to a strong crossflow pressure gradient, which changes sign for the downstream stations. The shear-stress vector direction in the flow lags behind the flow gradient vector direction. The flow studied here differs from many other experimentally examined three-dimensional flows in that the mean flow variables depend on three spatial axes rather than two axes, such as flows in which the three-dimensionality of the flow has been generated either by a rotating cylinder or by a pressure gradient in one direction only throughout the flow.The data show that the eddy viscosity of the flow is not isotropic. These and other selected data sets show that the ratio of spanwise to streamwise eddy viscosities in the wall-shear-stress coordinate system is less scattered and more constant (about 0.6) than in the local free-stream coordinate system or the normal stress coordinate system. For y+ > 50 and y/δ < 0.8, the ratio of the magnitude of the kinematic shear stress |τ/ρ| to the kinematic normal stress $\overline{v^2}$ is approximately a constant for three-dimensional flow stations of both shear-driven and pressure-driven three-dimensional flows. In the same region, the ratio of the kinematic shear stresses $-\overline{vw}/-\overline{uw}$ appears to be a function of y+ in wall-stress coordinates for three-dimensional pressure-driven flows.

Measurements in a three-dimensional turbulent boundary layer induced by a swept, forward-facing step

1970 ◽  
Vol 42 (4) ◽  
pp. 823-844 ◽  
Author(s):  
James P. Johnston
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Shear Stresses ◽  
Stress Vector ◽  
Mean Velocity ◽  
Vector Direction ◽  
The Mean

An experiment is reported, in which turbulent shear-stresses as well as mean velocities have been measured in a three-dimensional turbulent boundary layer approaching separation. It is shown that even very close to the wall the stress vector does not align itself with the mean velocity gradient vector, as would be required by a scalar ‘eddy viscosity’ or ‘mixing length’ type assumption. The calculation method of Bradshaw (1969) is tested against the data, and found to give good results, except for the prediction of shear-stress vector direction.

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.

Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer

1982 ◽  
Vol 119 ◽  
pp. 121-153 ◽  
Author(s):  
Udo R. Müller
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Flow Field ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Acceleration ◽  
The Mean

An experimental study of a steady, incompressible, three-dimensional turbulent boundary layer approaching separation is reported. The flow field external to the boundary layer was deflected laterally by turning vanes so that streamwise flow deceleration occurred simultaneous with cross-flow acceleration. At 21 stations profiles of the mean-velocity components and of the six Reynolds stresses were measured with single- and X-hot-wire probes, which were rotatable around their longitudinal axes. The calibration of the hot wires with respect to magnitude and direction of the velocity vector as well as the method of evaluating the Reynolds stresses from the measured data are described in a separate paper (Müller 1982, hereinafter referred to as II). At each measuring station the wall shear stress was inferred from a Preston-tube measurement as well as from a Clauser chart. With the measured profiles of the mean velocities and of the Reynolds stresses several assumptions used for turbulence modelling were checked for their validity in this flow. For example, eddy viscosities for both tangential directions and the corresponding mixing lengths as well as the ratio of resultant turbulent shear stress to turbulent kinetic energy were derived from the data.

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 Response of a Developed Turbulent Boundary Layer to Local Transverse Surface Motion

1976 ◽  
Vol 98 (3) ◽  
pp. 354-363 ◽  
Author(s):  
R. P. Lohmann
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Turbulent Energy ◽  
Transverse Motion ◽  
Mean Velocity ◽  
Surface Motion ◽  
The Mean ◽  
Structure Lead

Measurements were obtained of the mean velocity, Reynolds stress tensor components and spectral distribution of turbulent energy in a boundary layer that was adjusting spatially from a collateral to a three-dimensional state because of transverse motion of the bounding wall. The results indicate that changes to the turbulent structure lead to a strong coupling between the axial and transverse components of mean velocity. The influence of the imposed motion was found to be confined to a discrete region near the wall over the first ten initial boundary layer thicknesses, after which it became more global in nature.

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.

Near-wall measurements in a three-dimensional turbulent boundary layer

1997 ◽  
Vol 350 ◽  
pp. 189-208 ◽  
Author(s):  
DEBORA A. COMPTON ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Three Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Near Wall

An experiment was performed to measure near-wall velocity and Reynolds stress profiles in a pressure-driven three-dimensional turbulent boundary layer. An initially two-dimensional boundary layer (Reθ≈4000) was exposed to a strong spanwise pressure gradient. At the furthest downstream measurement locations there was also a fairly strong favourable streamwise pressure gradient.Measurements were made using a specially designed near-wall laser-Doppler anemometer (LDA), in addition to conventional methods. The LDA used short focal length optics, a mirror probe suspended in the flow, and side-scatter collection to achieve a measuring volume 35 μm in diameter and approximately 65 μm long.The data presented include mean velocity measurements and Reynolds stresses, all extending well below y+=10, at several profile locations. Terms of the turbulent kinetic energy transport equation are presented at two profile locations. The mean flow is nearly collateral (i.e. W is proportional to U) at the wall. Turbulent kinetic energy is mildly suppressed in the near-wall region and the shear stress components are strongly affected by three-dimensionality. As a result, the ratio of shear stress to turbulent kinetic energy is suppressed throughout most of the boundary layer. The angles of stress and strain are misaligned, except very near the wall (around y+=10) where the angles nearly coincide with the mean flow angle. Three-dimensionality appears to mildly reduce the production of turbulent kinetic energy.

On turbulent boundary-layer separation

1968 ◽  
Vol 32 (2) ◽  
pp. 293-304 ◽  
Author(s):  
V. A. Sandborn ◽  
C. Y. Liu
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Analytical Study ◽  
Boundary Layer Separation ◽  
Mean Velocity ◽  
Laminar Separation ◽  
Layer Separation ◽  
Turbulent Separation ◽  
Separation Model

An experimental and analytical study of the separation of a turbulent boundary layer is reported. The turbulent boundary-layer separation model proposed by Sandborn & Kline (1961) is demonstrated to predict the experimental results. Two distinct turbulent separation regions, an intermittent and a steady separation, with correspondingly different velocity distributions are confirmed. The true zero wall shear stress turbulent separation point is determined by electronic means. The associated mean velocity profile is shown to belong to the same family of profiles as found for laminar separation. The velocity distribution at the point of reattachment of a turbulent boundary layer behind a step is also shown to belong to the laminar separation family.Prediction of the location of steady turbulent boundary-layer separation is made using the technique employed by Stratford (1959) for intermittent separation.

Sign in / Sign up

Export Citation Format

Share Document