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.

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 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.

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.

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.

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.

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 theory of turbulence in stratified fluids

1970 ◽  
Vol 42 (2) ◽  
pp. 349-365 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Density Profile ◽  
Richardson Number ◽  
Mixed Volume ◽  
Volume Of Fluid ◽  
Velocity Shear ◽  
Mean Velocity ◽  
Large Wave ◽  
The Mean

An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with heightzabove a turbulent boundary layer and the mean density decreases asz3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.Thecurvatureof the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.

scholarly journals Active control of multiscale features in wall-bounded turbulence

2019 ◽  
Vol 36 (1) ◽  
pp. 12-21 ◽  
Author(s):  
Xiaotong Cui ◽  
Nan Jiang ◽  
Xiaobo Zheng ◽  
Zhanqi Tang
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Turbulent Energy ◽  
Streamwise Velocity ◽  
Discrete Wavelet ◽  
Wall Region ◽  
Mean Velocity ◽  
Pzt Actuator ◽  
The Impact ◽  
Near Wall

Abstract This study experimentally investigates the impact of a single piezoelectric (PZT) actuator on a turbulent boundary layer from a statistical viewpoint. The working conditions of the actuator include a range of frequencies and amplitudes. The streamwise velocity signals in the turbulent boundary layer flow are measured downstream of the actuator using a hot-wire anemometer. The mean velocity profiles and other basic parameters are reported. Spectra results obtained by discrete wavelet decomposition indicate that the PZT vibration primarily influences the near-wall region. The turbulent intensities at different scales suggest that the actuator redistributes the near-wall turbulent energy. The skewness and flatness distributions show that the actuator effectively alters the sweep events and reduces intermittency at smaller scales. Moreover, under the impact of the PZT actuator, the symmetry of vibration scales’ velocity signals is promoted and the structural composition appears in an orderly manner. Probability distribution function results indicate that perturbation causes the fluctuations in vibration scales and smaller scales with high intensity and low intermittency. Based on the flatness factor, the bursting process is also detected. The vibrations reduce the relative intensities of the burst events, indicating that the streamwise vortices in the buffer layer experience direct interference due to the PZT control.

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.

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.

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