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An Approximate Method for the Calculation of Turbulent Boundary Layers in Diffusers

Published online by Cambridge University Press:  07 June 2016

J. F. Norbury
J. F. Norbury*
Affiliation:
Department of Fluid Mechanics, University of Liverpool
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Summary

An approximate method is described for the calculation of turbulent boundary layers in which the turbulence is developed before the commencement of the adverse pressure gradient, as in most diffuser layers. It is based on a method due to Spence which has been modified and also extended to the calculation of three-dimensional diverging layers such as occur in ducts whose breadth is increasing. The velocity profiles occurring in a diverging layer are examined and it is shown that the inner part obeys the universal logarithmic law, as in two-dimensional layers. This result is used to obtain an equation for the form parameter in diverging layers, by substitution in the equation of motion and incorporation of the equations of momentum and continuity for diverging flow. The form parameter equation contains a term involving the gradient of shear stress at y = θ and values of this term are obtained by the analysis of experimental data and the substitution of known values for all the other terms in the form parameter equation. Values of the term involving shear stress gradient are then correlated in terms of known boundary layer quantities, and the resulting correlation allows the formulation of a step-by-step method for the solution of the form parameter equation. This may be used in conjunction with the momentum equation to predict the boundary layer growth. It was not found possible to effect a satisfactory correlation for boundary layers on lifting aerofoils, in which the turbulence develops within the adverse pressure gradient, and the method cannot be used for the prediction of such layers. The results of a number of calculations are given.

Type
Research Article
Information
Aeronautical Quarterly , Volume 8 , Issue 1 , February 1957 , pp. 58 - 77
Copyright
Copyright © Royal Aeronautical Society. 1957

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References

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