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.

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.

Reynolds-number scaling of the flat-plate turbulent boundary layer

2000 ◽  
Vol 422 ◽  
pp. 319-346 ◽  
Author(s):  
DAVID B. DE GRAAFF ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Extensive Study ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.

Experimental Investigation of the Effect of Upstream Conditions on Smooth and Rough Zero Pressure Gradient Turbulent Boundary Layer Flows at Very High Reynolds Numbers

2002 ◽  
Author(s):  
Luciano Castillo ◽  
Junghwa Seo ◽  
T. Gunnar Johansson ◽  
Horia Hangan
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Wind Tunnel ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
The Mean ◽  
High Reynolds ◽  
Very High

A 2D turbulent boundary layer experiment in a zero pressure gradient (ZPG) has been carried out using two cross hot-wire probes. The mean velocity and all non-zero Reynolds stresses were measured in a number of positions, 14–28 m from the inlet of the wind tunnel over a rough and a smooth surface. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to test the effect of the upstream conditions on the downstream flow. The long test section allowed us to investigate the mean velocity and Reynolds stresses dependence on the local Reynolds number and the initial conditions at very high Reynolds number (i.e. Rθ ∼ 120,000). Furthermore, it will be shown that the mean velocity deficit profiles and some of the Reynolds stresses collapse when the upstream conditions are kept fixed for smooth and rough surface.

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.

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.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

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.

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.

The turbulent boundary layer over a wall with progressive surface waves

1970 ◽  
Vol 41 (2) ◽  
pp. 259-281 ◽  
Author(s):  
James M. Kendall
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
Rubber Sheet ◽  
Pressure Drag ◽  
Generation Theory ◽  
The Mean ◽  
The Waves ◽  
Vertical Height

An experimental study of the interaction of a turbulent boundary layer with a wavy wall was conducted in a wind tunnel. A smooth neoprene rubber sheet comprising a portion of the floor of the tunnel was mechanically deformed into 12 sinusoidal waves which progressed upwind or down at controlled speed. The turbulent layer thickness was a little less than the wavelength. The mean velocity profile was linear on a semi-log plot over a substantial range of vertical height.The wall pressure was observed to be asymmetrical about the wave profile, resulting in a pressure drag. Flow separation was not the cause of the drag. The drag was found to be larger than that predicted by the inviscid wave generation theory. The measurements indicate that the waves strongly modulate the turbulent structure. The phase of the turbulent stresses with respect to the waves varies with wave speed, indicating that the dynamical reaction time of the turbulence is not negligible in comparison with the wave period.

Numerical simulation of a spatially developing accelerating boundary layer over roughness

2015 ◽  
Vol 780 ◽  
pp. 192-214 ◽  
Author(s):  
J. Yuan ◽  
U. Piomelli
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Isotropic Turbulence ◽  
Free Stream ◽  
Rough Wall ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Wake Field ◽  
Near Wall

The direct numerical simulation of an accelerating boundary layer over a rough wall has been carried out to investigate the coupling between the effects of roughness and strong free-stream acceleration. While the favourable pressure gradient is sufficient to achieve quasi-laminarization on a smooth wall, the flow reversion is prevented on a rough wall, and a higher friction coefficient, a faster increase of turbulence intensity compared to the free-stream velocity and more isotropic turbulence near the wall are observed. The logarithmic region of the mean-velocity profile presents an initial decrease in slope as in the smooth case, but soon recovers, as the fully rough regime is reached and a new overlap region is established. A strong coupling between the roughness and acceleration effects develops as roughness leads to more responsive turbulence and prevents the strong acceleration from stabilizing the turbulence, and the acceleration intensifies the velocity scale of the wake field (i.e. the near-wall spatial heterogeneity of the time-averaged velocity distribution). The combined effect is a ‘rougher’ surface as the flow accelerates. In addition, the link between the local values of the free stream and the near-wall velocity depends on the flow history; this explains the different flow responses observed in previous studies, in terms of friction coefficient, turbulent kinetic energy and Reynolds-stress anisotropy. This study elucidates the near-wall flow dynamics, which may be used to explain other non-canonical flows over rough walls.

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