Experimental Support for Townsend's Reynolds Number Similarity Hypothesis on Rough Walls
Abstract
The Reynolds number similarity hypothesis of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1976)] states that the turbulence beyond a few roughness heights from the wall is independent of the surface condition. The underlying assumption is that the boundary layer thickness delta is large compared to the roughness height k. This hypothesis was tested experimentally on two types of three-dimensional rough surfaces. Boundary layer measurements were made on flat plates covered with sand grain and woven mesh roughness in a closed return water tunnel at a momentum thickness Reynolds number Re(theta) of ,14 000. The boundary layers on the rough walls were in the fully rough flow regime (k(+/s) greater or equal 100) with the ratio of the boundary layer thickness to the equivalent sand roughness height delta /k(s) greater than 40. The results show that the mean velocity profiles for rough and smooth walls collapse well in velocity defect form in the overlap and outer regions of the boundary layer. The Reynolds stresses for the two rough surfaces agree well throughout most of the boundary layer and collapse with smooth wall results outside of 3k(s). Higher moment turbulence statistics and quadrant analysis also indicate the differences in the rough wall boundary layers are confined to y<5k(s). The present results provide support for Townsend s Reynolds number similarity hypothesis for uniform three-dimensional roughness in flows where delta /k(s)greater or equal 40.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 28, 2005
- Accession Number
- ADA575012
Entities
People
- Karen A. Flack
- Michael P. Schultz
- Thomas A. Shapiro