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National Advisory Committee for Aeronautics, Technical Notes - Supersonic Nozzle Design

The theory of supersonic flow in nozzles is discussed, emphasis
being placed on the physical rather than the mathematical point of
view. Methods, both graphic and analytic, for designing nozzles are
described together with a discussion of design factors. In addition,
the analysis of given nozzle shapes to determine velocity distribution
and possible existence of shock waves is considered. A description of
a supersonic protractor is included in conjunction with a discussion
of its application to nozzle analysis and design.

One of the major problems in the design of a supersonic wind
tunnel is the determination of the contours of the supersonic nozzle
so that parallel and uniform flow in the test section may be assured.
Consequently, it is not surprising that the literature contains
numerous papers on the subject of supersonic‘nozzle design. These
vary widely in their degree of complexity and general availability.
It is the purpose of this report to discuss these various methods
and present a guide for nozzle design. Only tweadimensional nozzles
will be considered.

The most prominent method for determining nozzle contours is,
perhaps, that of Prandtl and Busemann (reference 1). The usual
presentation of their method of characteristics is rather mathematical
in nature. (See,e.g., Preiswerk, reference 2.) In order to provide
the designer with a clearer physical picture of the flow in a nozzle,
a different interpretation of the Prandterusemann method is presented.
The diverse systems for constructing nozzle shapes by this method are
also presented, together with certain ramifications and supplementary
useful information.

The Foelsch method (reference 3) is included because its analytic
nature offers certain advantages, , These will be discussed later.
Shapiro (reference 1+) has still another approach to the problem. His
method, due to its approximate nature and because it-has no special
advantages, will not be considered.