A New Integral Method for Analyzing the Turbulent Boundary Layer With Arbitrary Pressure Gradient

1969 ◽  
Vol 91 (3) ◽  
pp. 371-376 ◽  
Author(s):  
F. M. White
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Shape Factor ◽  
Single Equation ◽  
Skin Friction Coefficient ◽  
New Method ◽  
Momentum Thickness ◽  
New Approach

For routine calculations of the properties of the incompressible turbulent boundary layer with arbitrary pressure gradient, the presently accepted method is the Karman integral technique, which consists of three simultaneous equations, the three unknowns being the momentum thickness, the skin friction, and the shape factor. Considerable empiricism is contained in the Karman method, so that the reliability is only fair. The present paper derives an entirely new method, based upon a suggestion of R. Brand and L. Persen. The new approach results in a single equation for the skin friction coefficient, with the only parameter being the nominal Reynolds number and the only empiricism being a single assumption about the effect of pressure gradient. No other variables, such as shape factor or momentum thickness, are needed, although they can of course be calculated as byproducts of the analysis. The new method also contains a built-in separation criterion, which was the most glaring omission of the Karman technique. Agreement with experiment is as good or better than the most reliable Karman methods in use today.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

Measurement and Calculation of Fluid Dynamic Characteristics of Rough-Wall Turbulent Boundary-Layer Flows

1993 ◽  
Vol 115 (3) ◽  
pp. 383-388 ◽  
Author(s):  
M. H. Hosni ◽  
H. W. Coleman ◽  
R. P. Taylor
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Rough Surface ◽  
Skin Friction Coefficient ◽  
Rough Wall ◽  
Momentum Thickness ◽  
Boundary Layer Flows ◽  
Mean Velocity

Experimental measurements of profiles of mean velocity and distributions of boundary-layer thickness and skin friction coefficient from aerodynamically smooth, transitionally rough, and fully rough turbulent boundary-layer flows are presented for four surfaces—three rough and one smooth. The rough surfaces are composed of 1.27 mm diameter hemispheres spaced in staggered arrays 2, 4, and 10 base diameters apart, respectively, on otherwise smooth walls. The current incompressible turbulent boundary-layer rough-wall air flow data are compared with previously published results on another, similar rough surface. It is shown that fully rough mean velocity profiles collapse together when scaled as a function of momentum thickness, as was reported previously. However, this similarity cannot be used to distinguish roughness flow regimes, since a similar degree of collapse is observed in the transitionally rough data. Observation of the new data shows that scaling on the momentum thickness alone is not sufficient to produce similar velocity profiles for flows over surfaces of different roughness character. The skin friction coefficient data versus the ratio of the momentum thickness to roughness height collapse within the data uncertainty, irrespective of roughness flow regime, with the data for each rough surface collapsing to a different curve. Calculations made using the previously published discrete element prediction method are compared with data from the rough surfaces with well-defined roughness elements, and it is shown that the calculations are in good agreement with the data.

scholarly journals Analysis of the Contribution of Large Scale Motions to the Skin Friction of a Zero-Pressure-Gradient Turbulent Boundary Layer Using the Renard-Deck Decomposition

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Bihai Sun ◽  
Muhammad Shehzad ◽  
Daniel Jovic ◽  
Christophe Cuvier ◽  
Christian Willert ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Large Scale ◽  
Skin Friction Coefficient ◽  
Turbulent Shear ◽  
The Mean ◽  
Component Particle

Coherent flow structures in turbulent boundary layers have been an active field of research for many decades, as they might be the key to reveal the mechanics of turbulence production and transport in turbulent shear flows. Renard and Deck (2016) proposed a theoretical decomposition for the mean skin-friction coefficient based on the mean kinetic energy budget in the streamwise direction. This decomposition, referred to as the Renard-Deck (RD) decomposition, decomposes the mean skin friction generation into three physical mechanisms in an absolute reference frame, namely, direct viscous dissipation, turbulent kinetic energy production, and spatial growth. In this study, the large scale motions (LSMs) are extracted using a proper orthogonal decomposition (POD) of the velocity field based on high-spatial-resolution two-dimensional – two-component particle image velocimetry (HSR 2C-2D PIV) of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL), and their effect on the skin friction via RD decomposition.

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.

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