Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Similarity laws for supersonic flows


Authors: D. C. Pack and S. I. Pai
Journal: Quart. Appl. Math. 11 (1954), 377-384
MSC: Primary 76.1X
DOI: https://doi.org/10.1090/qam/57694
MathSciNet review: 57694
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Abstract: The non-linear differential equation for the velocity potential of three-dimensional steady irrotational supersonic flow past wings of finite span has been investigated. It is found that the whole Mach number range from 1 to $ \infty $ may be divided into two regions (not strictly divided), in each of which similarity laws are obtained, with two parameters $ {K_1} = {\left( {{M^2} - 1} \right)^{1/2}}/{\tau ^n}$ and $ {K_2} = A{\left( {{M^2} - 1} \right)^{1/2}}$; $ \tau $ is the non-dimensional thickness ratio, $ A$ the aspect ratio of the wing, $ M$ the Mach number of the uniform stream in which the wing is placed. The factor $ n$ is given explicitly as a function of $ M$ and $ \tau $; in the lower region of Mach numbers it tends to $ 1/3$ as $ M \to 1$, for all $ \tau $, giving the ordinary transonic rule, and in the upper region it tends to $ - 1$ as $ M \to \infty $, for all $ \tau $, as in the ordinary hypersonic rule.


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DOI: https://doi.org/10.1090/qam/57694
Article copyright: © Copyright 1954 American Mathematical Society

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