Prandtl Plus Scaling Parameters and Velocity Profile Similarity: Part 2.

摘要

In a previous report (Weyburne, AFRL-RY-WP-TR-2012-0227) it was pointed out that the momentum balance type approach to velocity profile similarity cannot always properly identify scaling variables that result in similar velocity profiles. Example datasets were found for which the Prandtl's 'Plus' scaling variables satisfied all of the momentum balance requirements for similarity yet the velocity profile plots indicate the profiles were NOT similar. It was concluded 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. In that report, it was speculated that there is some other factor that is not being captured with the momentum balance type approach that would explain the failure. In this report we use the results from another report (Weyburne, AFRL-RY-HS-TR-2010-0014) to show the nature of the failure. In this earlier report, Weyburne described some new results for similarity of the velocity profile of the 2-D wall-bound boundary layer flow. By looking at the area under a set of scaled velocity profile curves, it was shown that if similarity exists, then: (1) the similarity velocity and length scaling parameters cannot be independent, (2) the displacement thickness must be a similar length scaling parameter, and (3) the velocity scaling parameter must be proportional to the free stream value of the stream-wise velocity above the boundary layer edge. By using these new results, it becomes possible to predict which datasets will show similar behavior and which will not.