LINE SOURCE DISTRIBUTIONS IN AXISYMMETRIC INCOMPRESSIBLE FLOW. III. SOLUTION OF THE DIRECT PROBLEM
Abstract
The axisymmetric flow field about a given body of revolution in uniform motion through a perfect fluid is determined. Analysis is restricted to slender bodies whose ends are blunt with finite radius of curvature. The power-series expansions of the body cross-sectional area distribution about the stagnation points are assumed to converge over the entire body length. For such bodies, the use of source distributions along the body axis yields at least an asymptotic expansion of the exact solution in even powers of the body thickness (maximum diameter/length) ratio. A successive-approximation procedure is set up for finding the source strength to arbitrarily high order in the thickness ratio. The second approximation differs from Van Dyke's formal secondorder slender-body theory only in the extent of the singularity distribution. This suggests a technique for rendering slender-body theory uniformly valid. It is also shown that there exist body shapes within the family studied for which the successive approximations do not converge. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1962
- Accession Number
- AD0276402
Entities
People
- John P. Moran