Incomplete similarity of a plane turbulent wall jet on smooth and transitionally rough surfaces

Abstract

This study assesses the hypothesis of incomplete similarity for a plane turbulent wall jet on smooth and transitionally rough surfaces. Typically, a wall jet is considered to consist of two regions: an inner layer and an outer layer. The degree to which these two regions reach equilibrium with each other and interact to produce the property of self-similarity remains an open question. In this study, the analysis of the outer and inner regions indicates that each region is characterised by a half-width which exhibits its own distinct dependence on the streamwise distance x from the slot, and a single self-similar structure for both regions does not exist. More specifically, the inner and outer layers of the wall jet exhibit different scaling laws, which results in two self-similar mean velocity profiles, both of which retain a dependence on the slot height H. As such, incomplete similarity of the wall jet on smooth and transitionally rough surfaces is confirmed by this study. In addition, comparison of the experimental results for the transitionally rough surface with the smooth wall case indicates that the surface roughness modifies the development of the mean velocity profile in both the inner and outer regions, although the effect on the outer region is relatively small and close to the experimental uncertainty.

Keywords:

• incomplete similarity
• scaling laws
• plane turbulent wall jet
• roughness
• laser Doppler anemometry (LDA)

Acknowledgements

The authors acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). The technical assistance of D.M. Deutscher is gratefully appreciated. Mr Matthew Dunn is also acknowledged for leading the development of the experimental facilities.

Disclosure statement

No potential conflict of interest was reported by the authors.