Effects of sandpaper roughness and stream turbulence on the turbulent boundary layer

1999 ◽  
Vol 213 (5) ◽  
pp. 507-515 ◽  
Author(s):  
J. C. Gibbings ◽  
S. M. Al-Shukri
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Pipe Flow ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Experimental Measurements ◽  
Two Dimensional

This paper reports experimental measurements of two-dimensional turbulent boundary layers over sandpaper surfaces under turbulent streams to complement the Nikuradse experiments on pipe flow. The study included the recovery region downstream of the end of transition. Correlations are given for the thickness, the shape factor, the skin friction and the parameters of the velocity profile of the layer. Six further basic differences from the pipe flow are described to add to the five previously reported.

Prediction of Turbulent Boundary Layer Development in Conical Diffusers

1966 ◽  
Vol 8 (4) ◽  
pp. 426-436 ◽  
Author(s):  
A. D. Carmichael ◽  
G. N. Pustintsev
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Energy Deficit ◽  
Momentum Thickness ◽  
Boundary Layer Development ◽  
Layer Development

Methods of predicting the growth of turbulent boundary layers in conical diffusers using the kinetic-energy deficit equation were developed. Three different forms of auxiliary equations were used. Comparison between the measured and predicted results showed that there was fair agreement although there was a tendency to underestimate the predicted momentum thickness and over-estimate the predicted shape factor.

Velocity Profiles of Turbulent Boundary Layers

1969 ◽  
Vol 73 (698) ◽  
pp. 143-147 ◽  
Author(s):  
M. K. Bull
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Experimental Work ◽  
Constant Pressure ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Equations

Although a numerical solution of the turbulent boundary-layer equations has been achieved by Mellor and Gibson for equilibrium layers, there are many occasions on which it is desirable to have closed-form expressions representing the velocity profile. Probably the best known and most widely used representation of both equilibrium and non-equilibrium layers is that of Coles. However, when velocity profiles are examined in detail it becomes apparent that considerable care is necessary in applying Coles's formulation, and it seems to be worthwhile to draw attention to some of the errors and inconsistencies which may arise if care is not exercised. This will be done mainly by the consideration of experimental data. In the work on constant pressure layers, emphasis tends to fall heavily on the author's own data previously reported in ref. 1, because the details of the measurements are readily available; other experimental work is introduced where the required values can be obtained easily from the published papers.

scholarly journals On the identification of well-behaved turbulent boundary layers

2017 ◽  
Vol 822 ◽  
pp. 109-138 ◽  
Author(s):  
C. Sanmiguel Vila ◽  
R. Vinuesa ◽  
S. Discetti ◽  
A. Ianiro ◽  
P. Schlatter ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Shape Factor ◽  
Outer Region ◽  
The Other ◽  
Diagnostic Plot ◽  
Other Hand

This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.

A Simple Integral Method for the Calculation of Thick Axisymmetric Turbulent Boundary Layers

1974 ◽  
Vol 25 (1) ◽  
pp. 47-58 ◽  
Author(s):  
V C Patel
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Integral Method ◽  
Turbulent Boundary Layers ◽  
Acceptable Accuracy ◽  
Approximate Form ◽  
Momentum Integral

SummaryA simple integral method is described for the calculation of a thick axisymmetric turbulent boundary layer. It is shown that the development of the boundary layer can be predicted with acceptable accuracy by using an approximate form of the momentum-integral equation, an appropriate skin-friction law, and an entrainment equation obtained for axisymmetric boundary layers. The method also involves the explicit use of a velocity profile family in order to interrelate some of the integral parameters. Available experimental results have been used to demonstrate the general accuracy of the method.

Supersonic Turbulent Boundary Layers: Some Comparisons Between Experiment and a Simple Theory

1976 ◽  
Vol 27 (2) ◽  
pp. 87-98 ◽  
Author(s):  
J L Stollery
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Simple Theory ◽  
Axisymmetric Bodies ◽  
Explicit Expressions

SummaryComparisons are made between some measurements of skin friction and heat transfer over five axisymmetric bodies and the predictions of a simple theory. The development of the theory is outlined and explicit expressions obtained for all the gross turbulent boundary-layer characteristics (δ*,θ,H,Cf and St).

A New Empirical Relationship Between The Form-Parameters H32 and H12 in Boundary Layer Theory

1962 ◽  
Vol 66 (621) ◽  
pp. 588-589 ◽  
Author(s):  
Hans Fernholz
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Empirical Relationship ◽  
Boundary Layer Theory ◽  
Two Dimensional ◽  
Energy Integral ◽  
The Third ◽  
The Relationship

Provided the relationship between the form-parameters H32 and H12is known, the two-dimensional turbulent boundary layer may be calculated by means of the approximate theories of Walz and Truckenbrodt without the necessity for an explicit law for the velocity profile. This relationship H32=f(H12) introduces the influence of the velocity profiles into the calculation. It is the third empirical relationship—beside those for skin friction and dissipation— which is needed to solve the momentum and energy integral equations. The formulae or curves for H32=f(H12) which are given in published papers show considerable deviations from each other so that it was felt necessary to investigate this relationship again. Fig. 1 shows the different curves.

Turbulent Flow Near a Rough Wall

1992 ◽  
Vol 114 (4) ◽  
pp. 537-542 ◽  
Author(s):  
Yang-Moon Koh
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Simple Formula ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
Friction Factors ◽  
Special Cases ◽  
The Mean

By introducing the equivalent roughness which is defined as the distance from the wall to where the velocity gets a certain value (u/uτ ≈ 8.5) and which can be represented by a simple function of the roughness, a simple formula to represent the mean-velocity distribution across the inner layer of a turbulent boundary layer is suggested. The suggested equation is general enough to be applicable to turbulent boundary layers over surfaces of any roughnesses covering from very smooth to completely rough surfaces. The suggested velocity profile is then used to get expressions for pipe-friction factors and skin friction coefficients. These equations are consistent with existing experimental observations and embrace well-known equations (e.g., Prandtl’s friction law for smooth pipes and Colebrook’s formula etc.) as special cases.

The Computation of Optimum Pressure Recovery in Two-Dimensional Diffusers

1978 ◽  
Vol 100 (4) ◽  
pp. 419-426 ◽  
Author(s):  
S. Ghose ◽  
S. J. Kline
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Incompressible Flow ◽  
Inviscid Flow ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Optimum Pressure ◽  
Fixed Length ◽  
Optimum Recovery

A method is presented for computation of optimum recovery at fixed length (Cp*) in two-dimensional diffusers with incompressible flow and turbulent inlet boundary layers. Since Cp* lies in the zone of transitory stall, the method involves computation of not only attached but also detaching and detached turbulent boundary layers. The results agree with available data to the level of the uncertainty in the data. The model is zonal in character. Results suggest that the most important feature in computing detaching flows is the treatment of the interaction between the outer (inviscid) flow and the boundary layer; the use of velocity-profile forms that represent average back-flows adequately is also important.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

scholarly journals A robust post-processing method to determine skin friction in turbulent boundary layers from the velocity profile

2015 ◽  
Vol 56 (4) ◽  
Author(s):  
Eduardo Rodríguez-López ◽  
Paul J. K. Bruce ◽  
Oliver R. H. Buxton
Keyword(s):  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Processing Method ◽  
Post Processing
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