Homogeneous Flow Fields of Degree Greater than Zero

Author: Lampert, Seymour

Year: 1954

Degree: Dissertation (Ph.D.)

Advisor: Stewart, Homer Joseph

Committee Member: Unknown, Unknown

Option: Aeronautics; Mathematics

DOI: 10.7907/W215-QX89

Abstract

Solutions to the Prandtl-Glauert differential equation expressed in terms of polynomial type Lame functions can be applied to the problem of the thin delta wings with subsonic leading edges in a supersonic flow field. It is demonstrated how these functions of different species and degrees of homogeneity may be employed to obtain previously known results for certain lifting cases. For the non-lifting or thickness case which is treated in detail in this paper it is shown that a large class of thickness distributions with blunt leading edges my be obtained by systematically studying the Lame functions of the first species. In particular these functions have been investigated up to, and including, n = 5. It is further shown by the methods of this paper that the prescription of the pressure distribution in problems of this sort is not always sufficient to determine the thickness distribution uniquely.

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