Expansion Procedures and Similarity Laws for Transonic Flow

Author: Messiter, Arthur Frederic

Year: 1957

Degree: Dissertation (Ph.D.)

Advisor: Cole, Julian D.

Committee Member: Unknown, Unknown

Option: Aeronautics; Mathematics

DOI: 10.7907/4HK0-K279

Abstract

The transonic flow past slender bodies and thin wings is investigated with the use of a general theory of expansion procedures. It is assumed that the solutions for the velocity components possess asymptotic expansions of a very general form, and the differential equations and boundary conditions for the first and higher approximations are obtained by applying appropriate limiting procedures to the full equations. The following cases are treated: 1) bodies of revolution at zero incidence; 2) bodies of nearly circular cross-section, at zero incidence; 3) bodies of revolution at an angle of attack; and 4) thin wings at zero incidence. Certain first-order similarity laws are derived for these problems, and the order of magnitude of the error is stated in each case.

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