Similarity Scaling for the Inner Region of the Turbulent Boundary Layer
Abstract
For the first time it is shown that the Prandtl length scale has a natural interpretation in terms of the physical structure of the boundary layer for a 2-0 wall bounded flow. Both the Prandtl length scale and a newly developed parameter are first moments associated with the mean location value of the second derivative of the velocity profile. These two parameters therefore track the mean location of the viscous forces present in the boundary layer. A simple mathematical proof is offered to show that the new parameter must be a similarity scaling parameter for all 2-0 boundary layer flows. From the parameter definitions, one can show that the new scaling parameter is identical to the Prandtl parameter scaling for the case where the ratio of the free stream velocity at the boundary layer edge to the Prandtl scaling velocity, the so called friction velocity, is a constant. This similarity condition is found in certain turbulent boundary layer flow data sets. We show that to experimental accuracy, a subset of these datasets exhibit whole profile similarity using the new scaling parameters if one assumes that the reported skin friction coefficients are in error by +-10%. The results lead to a new conceptual picture for similarity of the turbulent boundary layer.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 20, 2009
- Accession Number
- ADA519312
Entities
People
- David W. Weyburne
Organizations
- Air Force Research Laboratory