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Self-preserving turbulent wall jets over convex surfaces

Published online by Cambridge University Press:  12 April 2006

D. E. Guitton  and
B. G. Newman
D. E. Guitton
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Quebec
B. G. Newman
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Quebec
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Abstract

The flow of an ostensibly two-dimensional wall jet over a logarithmic spiral has been studied both experimentally and theoretically. It is established that, if the skin friction is effectively constant, the flow may be self-preserving, and this is confirmed experimentally for the two spirals studied ($x/R = \frac{2}{3}$ and x/R = 1). The rate of growth has been predicted using the integral momentum equation and the integral equation for the combined mean and turbulent energy. Important assumptions in this theory are that the turbulence structure parameter $\overline{u^{\prime}v^{\prime}}/\overline{q^{\prime 2}}$ and the normalized mean position of the superlayer are invariant with curvature, and the experiments show that this is nearly true. The growth is constant for each spiral and increases with curvature. Using the measured rate of growth, the integral energy equation gives a satisfactory prediction of the turbulent shear stress, but the two-dimensional integral momentum does not. The turbulence is very intense in these flows and the Reynolds stresses were corrected using correlations of up to fourth order. However, the corrections may still have been too small, which would account for some of the difference between the calculated and measured shear stress. The outer flow of a wall jet strongly influences the inner boundary layer and this effect is found to increase with curvature. The conventional logarithmic law of the wall ceases to apply for $x/R >\frac{2}{3}$.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 1 , 9 June 1977 , pp. 155 - 185
Copyright
© 1977 Cambridge University Press

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