Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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.

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  • [1] 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 MR 0208798
  • [2] S. Bergman, On two-dimensional flows of compressible fluids, NACA Tech. Note No. 972, 1945 MR 0014874
  • [3] S. Chaplygin, Gas jets, Scientific Memoirs, Moscow Univ., Math. Phys. Sec. 21, 1-121 (1902); also NACA Tech. Memo. No. 1063, 1944 MR 0015979
  • [4] 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 MR 0078134
  • [5] C. Ferrari and F. G. Tricomi, Transonic aerodynamics, Academic Press, New York and London, 1968
  • [6] I. Imai, On a refinement of the W. K. B. method, Phys. Rev. 74, 113 (1948) MR 0025653
  • [7] I. Imai, Application of the W. K. B. method to the flow of a compressible fluid. I, J. Math. Phys. 28, 173-182 (1949) MR 0031892
  • [8] J. A. Tierney, An approximation to transonic flow of a polytropic gas, Amer. J. Math. 75, 43-56 (1953) MR 0052941

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DOI: https://doi.org/10.1090/qam/281407
Article copyright: © Copyright 1971 American Mathematical Society

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