The Mathematics of Flow Similarity of the Velocity Boundary Layer
Abstract
New results for similarity scaling of the velocity profile of the 2-D wall-bounded flows are presented. The theoretical results are based on a simple concept; the area under similar scaled velocity profile curves must be equal. By taking certain integrals of the scaled velocity profiles and its first derivative, we obtain a number of similarity scaling requirements. For example, it is shown that if whole profile similarity exists, then: 1) the similar length scaling variable must be proportional to the displacement thickness, and 2) the velocity similarity scaling variable must be proportional to the free-stream velocity. Conventional thinking is that whole profile similarity is limited to laminar flow boundary layers. If true, this would drastically restrict the utility of the new scaling results. However, we show that to experimental accuracy, certain turbulent boundary layer flow datasets can display whole profile similarity and that as predicted the new scaling works well. In addition, we develop new definitions for partial similarity for the inner, the outer, and the log law regions of a turbulent boundary layer. These definitions are most suitable for quantifying similarity of experimental profiles.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 11, 2008
- Accession Number
- ADA519319
Entities
People
- David W. Weyburne
Organizations
- Air Force Research Laboratory