Effect of Surface Wave on Development of Turbulent Boundary Layer Over a Train of Rib Roughness

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Santosh Kumar Singh ◽  
Pankaj Kumar Raushan ◽  
Koustuv Debnath ◽  
B. S. Mazumder
Keyword(s):  
Boundary Layer ◽  
Surface Wave ◽  
Turbulent Boundary Layer ◽  
Mean Flow ◽  
Mean Velocity ◽  
Measured Velocity ◽  
Law Of The Wall ◽  
Wave Channel ◽  
Surface Data ◽  
Large Roughness

In this paper, detailed experimental results are reported to study the effect of the surface wave of different frequencies on unidirectional current over the bed-mounted train of rib roughness. The model roughness used in this study is transverse square ribs that lengthened across the entire width of the recirculating wave channel. The center-to-center rib pitch (P) was constant during the experiments, thus generating a broad range of near-bed flow patterns for each of the three different surface wave frequencies studied here. The relative submergence associated with the roughness height (k) was 8, which fall in the category of large roughness. Velocity measurements were conducted using acoustic Doppler velocimeter (ADV), and a surface wave of different frequencies was generated using the plunger-type wavemaker. The measured velocity data were analyzed to determine the relative importance of mean flow over the train of rib roughness. Mean velocity profiles illustrate the well-known downward shift from the flat surface data of the semi-logarithmic portion of the law of the wall. The width of the turbulent boundary layer increases with the superposition of surface wave compared to that of the current-only flow. The results also show that the mean reattachment length decreases due to the superposition of surface wave on unidirectional current.

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.

Turbulent boundary-layer interaction with a shock wave at a compression corner

1984 ◽  
Vol 143 ◽  
pp. 23-46 ◽  
Author(s):  
S. Agrawal ◽  
A. F. Messiter
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Momentum Equation ◽  
Wall Layer ◽  
Oblique Shock Wave ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Compression Corner ◽  
Boundary Layer Interaction

The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.

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.

A model for inhomogeneous turbulent flow

1970 ◽  
Vol 317 (1530) ◽  
pp. 417-433 ◽  
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
The Self ◽  
Diffusion Equations ◽  
Mean Flow ◽  
Mean Velocity ◽  
Closed Set ◽  
Law Of The Wall ◽  
The Mean ◽  
Model Equations

A set of model equations is given to describe the gross features of a statistically steady or 'slowly varying’ inhomogeneous field of turbulence and the mean velocity distribution. The equations are based on the idea that turbulence can be characterized by ‘densities’ which obey nonlinear diffusion equations. The diffusion equations contain terms to describe the convection by the mean flow, the amplification due to interaction with a mean velocity gradient, the dissipation due to the interaction of the turbulence with itself, and the dif­fusion also due to the self interaction. The equations are similar to a set proposed by Kolmo­gorov (1942). It is assumed that both an ‘energy density’ and a ‘vorticity density’ satisfy diffusion equations, and that the self diffusion is described by an eddy viscosity which is a function of the energy and vorticity densities; the eddy viscosity is also assumed to describe the diffu­sion of mean momentum by the turbulent fluctuations. It is shown that with simple and plausible assumptions about the nature of the interaction terms, the equations form a closed set. The appropriate boundary conditions at a solid wall and a turbulent interface, with and without entrainment, are discussed. It is shown that the dimensionless constants which appear in the equations can all be estimated by general arguments. The equations are then found to predict the von Kármán constant in the law of the wall with reasonable accuracy. An analytical solution is given for Couette flow, and the result of a numerical study of plane Poiseuille flow is described. The equations are also applied to free turbulent flows. It is shown that the model equations completely determine the structure of the similarity solutions, with the rate of spread, for instance, determined by the solution of a nonlinear eigenvalue problem. Numerical solutions have been obtained for the two-dimensional wake and jet. The agreement with experiment is good. The solutions have a sharp interface between turbulent and non-turbulent regions and the mean velocity in the turbulent part varies linearly with distance from the interface. The equations are applied qualitatively to the accelerating boundary layer in flow towards a line sink, and the decelerating boundary layer with zero skin friction. In the latter case, the equations predict that the mean velocity should vary near the wall like the 5/3 power of the distance. It is shown that viscosity can be incorporated formally into the model equations and that a structure can be given to the interface between turbulent and non-turbulent parts of the flow.

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.

On turbulent boundary layers in oscillatory flow

1977 ◽  
Vol 353 (1672) ◽  
pp. 121-144 ◽  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Travelling Wave ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Freestream Velocity ◽  
The Mean

An experimental investigation has been made of turbulent boundary layer response to harmonic oscillations associated with a travelling wave imposed on an otherwise constant freestream velocity and convected in the freestream direction. The tests covered oscillation frequencies of 4-12 Hz for freestream amplitudes of up to 11% of the mean velocity. Additional steady flow measurements were used to infer the quasi-steady response to freestream oscillations. The results show a welcome insensitivity of the mean flow and turbulent intensity distributions to the freestream oscillations tested. An approximate analysis based on these results has been developed. It is probably of limited validity but it does provide a useful guide to the physical processes involved. The effects on boundary layer response of varying the travelling wave convection velocity and frequency of oscillation are illustrated by the analysis and show a behaviour broadly similar to that of laminar boundary layers. The travelling wave convection velocity exhibits a dominant influence on the turbulent boundary layer response to freestream oscillations.

Simulation of Thick Turbulent Boundary Layer Via Jet Array

2013 ◽  
Vol 8 (1) ◽  
pp. 78-91
Author(s):  
Vladimir Kornilov ◽  
Andrey Boiko
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Experimental Studies ◽  
Outer Region ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Air Jets ◽  
Flow Parameters ◽  
Mass Flow Rates

Experimental studies directed to qualify the potential of simulation of an equilibrium (by Klauser) thick incompressible turbulent boundary layer on a flat plate of limited length with the help of an array of jets were carried out. It is shown that in the range of flow parameters and the mass flow rates of blowing under consideration the air jets through some rows of the holes with different diameter increase substantially the thickness of turbulent boundary layer within a comparatively small distance of the blowing region. In most cases studied, the mean and fluctuating characteristics of the boundary layer reach values specific for naturally developed turbulent boundary layer at downstream distances of about 22 thickness of regular boundary layer. Mean velocity profiles in the logarithmic part of the artificially thickened boundary layer are described by the law-of-the-wall variables with a good accuracy and generalized by a single dependence with the help of empiric velocity scale for the outer region. Disturbance characteristics of the flow are also close to those in the canonic boundary layer. However, as the blowing intensity grows, a systematic deviation of the disturbance streamwise velocity from the canonic values is observed, which indicates the limitation of the present approach and points out the need of further refinement of the method of simulation under consideration

Turbulent boundary layer relaxation from convex curvature

1990 ◽  
Vol 211 ◽  
pp. 529-556 ◽  
Author(s):  
Amy E. Alving ◽  
Alexander J. Smits ◽  
Jonathan H. Watmuff
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Stable State ◽  
Relaxation Behaviour ◽  
Mean Flow ◽  
Mean Velocity ◽  
Measuring Station ◽  
The Mean ◽  
Convex Curvature

A study was undertaken to examine the flat plate relaxation behaviour of a turbulent boundary layer recovering from 90° of strong convex curvature (δ0/R = 0.08), for a length of ≈ 90δ0 after the end of curvature, where δ0 is the boundary layer thickness at the start of the curvature. The results show that the relaxation behaviour of the mean flow and the turbulence are quite different. The mean velocity profile and skin friction coefficient asymptotically approach the unperturbed state and at the last measuring station appear to be fully recovered. The turbulence relaxation, however, occurs in several stages over a much longer distance. In the first stage, a stress ‘bore’ (a region of elevated stress) is generated near the wall, and the bore thickens with distance downstream. Eventually it fills the whole boundary layer, but the stress levels continue to rise beyond their self-preserving values. Finally the stresses begin a gradual decline, but at the last measuring station they are still well above the unperturbed levels, and the ratios of the Reynolds stresses are distorted. These results imply a reorganization of the large-scale structure into a new quasi-stable state. The long-lasting effects of curvature highlight the sensitivity of a boundary layer to its condition of formation.

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.

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.

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