The Prandtl Plus Scaling Parameters and Velocity Profile Similarity
Abstract
Numerous experimental results have demonstrated similar behavior of the velocity profile in the near-wall region of the turbulent boundary layer using Prandtl's "Plus" scaling variables. However, the implications for similarity behavior of the near-wall turbulent boundary velocity profiles using Prandtl's Plus scaling variables have not been carefully explored. In the following report, we apply the momentum balance type approach to study velocity profile similarity using Prandtl's Plus scaling variables. It is shown that the Plus scaling variables do in fact satisfy the requirements for similarity based on this approach so long as the friction velocity is proportional to 1/(x-x0) where x is the distance along the wall in the flow direction and x0 is a constant. Experimental results are examined and found to confirm that certain datasets we tested do in fact have the friction velocity values behaving as 1/(x-x0). We show the Plus scaling variables satisfy all of the conditions for similarity using the momentum balance type approach for these datasets. However, the same velocity profile dataset plots also confirm that Prandtl's Plus scaling variables do not show whole profile similarity. Hence, we conclude that the scaling variables discovered by the momentum balance type approach as presently constituted are a necessary but not sufficient condition for velocity profile similarity..
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 2012
- Accession Number
- ADA566297
Entities
People
- David Weyburne
Organizations
- Air Force Research Laboratory