Higher approximations for transonic flows
Author:
Nisiki Hayasi
Journal:
Quart. Appl. Math. 29 (1971), 291-302
MSC:
Primary 76.41
DOI:
https://doi.org/10.1090/qam/281407
MathSciNet review:
281407
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Abstract: Using the results of the WKBI method, two hypothetical gases are introduced, whose graphs in the pressure-density plane and that of the polytropic gas have contact of order 4 and 5 at the sonic point. This is in contrast to the fact that such graphs for the Tricomi gas and the generalized Tricomi gas have contact of order 2 and 3, respectively, to that of the polytropic gas there. Various relations for these gases are derived and compared to those of the air, the Tricomi gas and the generalized Tricomi gas. Applicable range of the approximations to the airflow are $0.65 < M < 1.4$ for the first approximation, and $0.5 < M < 1.5$ for the second approximation, $M$ being the local Mach number. This is compared to such ranges as $0.9 < M < 1.2$ for the Tricomi gas, and $0.75 < M < 1.3$ for the generalized Tricomi gas. Flow solutions for the hypothetical gases are expressed by the Airy functions.
- Milton Abramowitz and Irene A. Stegun (eds.), Handbook of mathematical functions, with formulas, graphs and mathematical tables, National Bureau of Standards Applied Mathematics Series, Vol. 55, National Bureau of Standards, Washington, D.C., (for sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402), 1966. Fifth printing, with corrections. MR 0208798
- Stefan Bergman, On two-dimensional flows of compressible fluids, Tech. Notes Nat. Adv. Comm. Aeronaut. 1945 (1945), no. 972, 81 pp. (3 plates). MR 0014874
- S. Chaplygin, Gas jets, Tech. Notes Nat. Adv. Comm. Aeronaut. 1944 (1944), no. 1063, 112 pp. (3 plates). MR 15979
- J. B. Diaz and G. S. S. Ludford, A transonic approximation, Proceedings of the Second U. S. national congress of Applied Mechanics, Ann Arbor, 1954, American Society of Mechanical Engineers, New York, 1955, pp. 651–658. MR 0078134
C. Ferrari and F. G. Tricomi, Transonic aerodynamics, Academic Press, New York and London, 1968
- Isao Imai, On a refinement of the W.K.B. method, Phys. Rev. (2) 74 (1948), 113. MR 25653
- Isao Imai, Application of the W.K.B. method to the flow of a compressible fluid. I, J. Math. Physics 28 (1949), 173–182. MR 0031892
- John A. Tierney, An approximation to transonic flow of a polytropic gas, Amer. J. Math. 75 (1953), 43–56. MR 52941, DOI https://doi.org/10.2307/2372613
M. Abramowitz and I. A. Stegun (Editors), Handbook of mathematical functions with formulas, graphs and mathematical tables, 5th printing, with corrections, Nat. Bur. Standards, Appl. Math. Series, 55, U. S. Government Printing Office, Washington, D. C., 1966, pp. 446–450
S. Bergman, On two-dimensional flows of compressible fluids, NACA Tech. Note No. 972, 1945
S. Chaplygin, Gas jets, Scientific Memoirs, Moscow Univ., Math. Phys. Sec. 21, 1–121 (1902); also NACA Tech. Memo. No. 1063, 1944
J. B. Diaz and G. S. S. Ludford, A transonic approximation, Proc. Second U. S. Nat. Congr. Appl. Mech. (Ann Arbor, 1954), Amer. Soc. Mech. Engineers, New York, 1955, pp. 651–658
C. Ferrari and F. G. Tricomi, Transonic aerodynamics, Academic Press, New York and London, 1968
I. Imai, On a refinement of the W. K. B. method, Phys. Rev. 74, 113 (1948)
I. Imai, Application of the W. K. B. method to the flow of a compressible fluid. I, J. Math. Phys. 28, 173–182 (1949)
J. A. Tierney, An approximation to transonic flow of a polytropic gas, Amer. J. Math. 75, 43–56 (1953)
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Article copyright:
© Copyright 1971
American Mathematical Society
