Experiment on convex curvature effects in turbulent boundary layers

1973 ◽  
Vol 60 (1) ◽  
pp. 43-62 ◽  
Author(s):  
Ronald M. C. So ◽  
George L. Mellor
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Reynolds Stress ◽  
Convex Surface ◽  
Turbulent Boundary Layers ◽  
Turbulence Measurements ◽  
Curvature Effects ◽  
Convex Wall ◽  
Complete Set

Turbulent boundary layers along a convex surface of varying curvature were investigated in a specially designed boundary-layer tunnel. A fairly complete set of turbulence measurements was obtained.The effect of curvature is striking. For example, along a convex wall the Reynolds stress is decreased near the wall and vanishes about midway between the wall and the edge of a boundary layer where there exists a velocity profile gradient created upstream of the curved wall.

Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer

1966 ◽  
Vol 33 (2) ◽  
pp. 429-437 ◽  
Author(s):  
J. C. Rotta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Calculation Methods ◽  
Recent Developments ◽  
Incompressible Boundary

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.

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.

Boundary Layer Calculation Including the Prediction of Transition and Curvature Effects

1989 ◽  
Author(s):  
B. Guyon ◽  
T. Arts
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Convex Surface ◽  
Turbine Blades ◽  
Operating Conditions ◽  
Detailed Knowledge ◽  
Flat Plates ◽  
Transfer Rates ◽  
Curvature Effects

The calculation of surface temperature on gas turbine blades in severe operating conditions requires a detailed knowledge of boundary layers behaviour. The prediction of laminar to turbulent transition as to existence and location, as well as the evaluation of heat transfer rates are major concerns. The program developed by SNECMA for this purpose is presented, in which models are introduced to take into account the main effects occuring on blades without film-cooling. The algorithm and discretisation scheme for boundary layer equations is Patankar and Spalding’s, with profiles initialization by Pohlhausen’s method. The turbulence and transition model, after Mc Donald and Fish, was improved in search for more stability and to have a better detection of the beginning of the transition. Adams and Johnston’s model for curvature, including propagation effects, was adapted to a transitional boundary layer. The validation tests of this program are described, which are based on numerous experimental data taken from a bibliography of tests over flat plates and blades. Other tests use heat transfer rate measurements conducted by SNECMA, together with VKI, on vanes and blades in non-rotating grids. The calculation results are further compared to the STAN5 program results; they show a superiority in predicting the transfer rates on a convex surface and for transitional boundary layers.

Turbulence Measurements in Boundary Layers Along Mildly Curved Surfaces

1978 ◽  
Vol 100 (1) ◽  
pp. 37-45 ◽  
Author(s):  
B. G. Shivaprasad ◽  
B. R. Ramaprian
Keyword(s):  
Boundary Layers ◽  
Opposite Effect ◽  
Reynolds Shear Stress ◽  
Linear Interpolation ◽  
Curved Surfaces ◽  
Turbulence Measurements ◽  
Streamline Curvature ◽  
Curvature Effects ◽  
Convex Wall ◽  
Strong Curvature

This paper presents results of turbulence measurements in boundary layers over surfaces of mild longitudinal curvature. The study indicates that convex wall curvature decreases both the length and velocity scales of turbulent motions, whereas concave curvature has the opposite effect. White being qualitatively similar to those brought about by stronger wall curvature, mild curvature effects are found to be much larger than what one expects from a linear interpolation between the effects of zero and strong curvature. It is also observed that curvature has a relatively larger effect on the Reynolds shear stress than on the turbulent kinetic energy. The present study, however, indicates that it is still possible to use some of the phenomenological models of turbulence (e.g., the mixing length model, the Prandtl-Kolmogorov model), provided an appropriate curvature model is available for describing the effect of curvature on the relevant length scale in the boundary layer. The present data are used to test the validity and limitations of such a curvature model (based on an analogy between streamline curvature and buoyancy) currently in use.

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.

Calculation of Turbulent Boundary Layers Using Equilibrium Thermal Wakes

2005 ◽  
Vol 127 (2) ◽  
pp. 159-164 ◽  
Author(s):  
James Sucec
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Thermal Energy ◽  
Energy Equation ◽  
Turbulent Boundary Layers ◽  
Stanton Number ◽  
Law Of The Wall ◽  
Number Distribution

The combined thermal law of the wall and wake is used as the approximating sequence for the boundary layer temperature profile to solve an integral thermal energy equation for the local Stanton number distribution. The velocity profile in the turbulent boundary layer was taken to be the combined law of the wall and wake of Coles. This allows the solution of an integral form of the x-momentum equation to give the skin friction coefficient distribution. This, along with the velocity profile, is used to solve the thermal energy equation using inner coordinates. The strength of the thermal wake was found by analysis of earlier research results, in the literature, for equilibrium, constant property, turbulent boundary layers. Solutions for the Stanton number distribution with position are found for some adverse pressure gradient boundary layers as well as for those having zero pressure gradient. The zero pressure gradient results cover both fully heated plates and those with unheated starting lengths, including both isothermal surfaces and constant flux surfaces. Comparison of predictions of the present work is made with experimental data in the literature.

Similarity-Law Entrainment Method for Thick Axisymmetric Turbulent Boundary Layers in Pressure Gradients

1978 ◽  
Vol 22 (03) ◽  
pp. 131-139
Author(s):  
Paul S. Granville
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Shape Parameter ◽  
Turbulent Boundary Layers ◽  
Local Skin ◽  
Local Skin Friction ◽  
Dimensional Shape ◽  
Analytical Relations ◽  
Similarity Laws

Analytical relations have been derived for calculation of developing thick, axisymmetric, turbulent boundary layers in a pressure gradient from two simultaneous differential equations: momentum and shape parameter. An entrainment method is used to obtain the shape parameter equation. Both equations incorporate the velocity similarity laws that provide a two-parameter velocity profile general enough to include any range of Reynolds numbers. Newly defined "quadratic" shape parameters which arise from the geometry of the thick axisymmetric boundary layer are analytically related to the two-dimensional shape parameter by means of these velocity similarity laws. The variation of momentum loss, boundary-layer thickness, local skin friction, and local velocity profile may be calculated for the axisymmetric turbulent boundary layers on underwater bodies, including the thick boundary layers on the tails. The various formulations are shown to correlate well with available experimental data.

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.

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.

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