A STUDY OF AXISYMMETRIC TRANSONIC FLOW USING THE METHOD OF PARAMETRIC DIFFERENTIATION.
Abstract
The method of parametric differentiation was applied to the problem of inviscid transonic flow about a slender body of revolution at zero angle of attack. The method consists of differentiating the equation governing the axial velocity with respect to the characteristic body thickness ratio and solving for the rate of change of the velocity with this ratio, using the method of multiple scales. An integral equation for the velocity at a given radius from the body is thus developed and it is shown how this velocity may be matched to that given by the inner and outer expansion method to compute pressures on the body. It is demonstrated that the results of this new approach reduce to the well-known Spreiter-Alksne theory for slender bodies in the limits of small radial distance and local linearization with respect to the source velocity and thickness ratio. The major problem is to take into account the dependence of the velocity on the radial coordinate. One method of doing this is presented, but difficulties arise in the mathematics due to changes in orders in the assumed asymptotic series. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1965
- Accession Number
- AD0624683
Entities
People
- Norman English Dupee Iii.
Organizations
- Massachusetts Institute of Technology