Discussion: “A New Integral Method for Analyzing the Turbulent Boundary Layer With Arbitrary Pressure Gradient” (White, F. M., 1969, ASME J. Basic Eng., 91, pp. 371–376)

1969 ◽  
Vol 91 (3) ◽  
pp. 377-378
Author(s):  
S. J. Kline
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Integral Method

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.

A Superposition Analysis of the Turbulent Boundary Layer in an Adverse Pressure Gradient

1951 ◽  
Vol 18 (1) ◽  
pp. 95-100
Author(s):  
Donald Ross ◽  
J. M. Robertson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Pressure Recovery ◽  
Stress Coefficient ◽  
Wall Shear

Abstract As an interim solution to the problem of the turbulent boundary layer in an adverse pressure gradient, a super-position method of analysis has been developed. In this method, the velocity profile is considered to be the result of two effects: the wall shear stress and the pressure recovery. These are superimposed, yielding an expression for the velocity profiles which approximate measured distributions. The theory also leads to a more reasonable expression for the wall shear-stress coefficient.

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