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.
H. Glauert, The effect of compressibility on the lift of an aerofoil, Proc. Roy. Soc. London (A) 118, 113 (1928).
L. Prandtl, Über Strömungen, deren Geschwindigkeit mit der Schallgeschwindigkeit vergleichbar sind, J. Aer. Res. Inst., Univ. of Tokyo, No. 6 (1930).
J. Ackeret, Über Luftkräfte bei sehr grossen Geschwindigkeiten, insbesondere bei ebenen Strömungen, Helv. Phys. Acta 1, 301 (1928).
- W. R. Sears, On compressible flow about bodies of revolution, Quart. Appl. Math. 4 (1946), 191–193. MR 17089, DOI https://doi.org/10.1090/S0033-569X-1946-17089-7
- W. R. Sears, A second note on compressible flow about bodies of revolution, Quart. Appl. Math. 5 (1947), 89–91. MR 20393, DOI https://doi.org/10.1090/S0033-569X-1947-20393-4
- Theodore von Karman, The similarity law of transonic flow, J. Math. Phys. Mass. Inst. Tech. 26 (1947), 182–190. MR 22504, DOI https://doi.org/10.1002/sapm1947261182
- John R. Spreiter, Similarity laws for transonic flow about wings of finite span, Tech. Notes Nat. Adv. Comm. Aeronaut. 1951 (1951), no. 2273, 24. MR 0040912
- Hsue-shen Tsien, Similarity laws of hypersonic flows, J. Math. Phys. Mass. Inst. Tech. 25 (1946), 247–251. MR 18074, DOI https://doi.org/10.1002/sapm1946251247
- Wallace D. Hayes, On hypersonic similitude, Quart. Appl. Math. 5 (1947), 105–106. MR 20904, DOI https://doi.org/10.1090/S0033-569X-1947-20904-4
M. D. Van Dyke, The combined supersonic-hypersonic similarity rule, J. Aer. Sci. 18, 499 (1951).
H. Glauert, The effect of compressibility on the lift of an aerofoil, Proc. Roy. Soc. London (A) 118, 113 (1928).
L. Prandtl, Über Strömungen, deren Geschwindigkeit mit der Schallgeschwindigkeit vergleichbar sind, J. Aer. Res. Inst., Univ. of Tokyo, No. 6 (1930).
J. Ackeret, Über Luftkräfte bei sehr grossen Geschwindigkeiten, insbesondere bei ebenen Strömungen, Helv. Phys. Acta 1, 301 (1928).
W. R. Sears, On compressible flow about bodies of revolution, Q. Appl. Math. 4, 191 (1946).
W. R. Sears, A second note on compressible flow about bodies of revolution, Q. Appl. Math.5,89(1947).
Th. von Kármán, The similarity law of transonic flow, J. Math. Phys. 26, 182 (1947).
J. R. Spreiter, Similarity laws for transonic flow about wings of finite span, N.A.C.A., T.N. No. 2273 (1951).
H. S. Tsien, Similarity laws of hypersonic flows, J. Math. Phys. 25, 247 (1946).
W. D. Hayes, On hypersonic similitude, Q. Appl. Math. 5, 105 (1947).
M. D. Van Dyke, The combined supersonic-hypersonic similarity rule, J. Aer. Sci. 18, 499 (1951).
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Article copyright:
© Copyright 1954
American Mathematical Society