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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 for the first approximation, and for the second approximation, being the local Mach number. This is compared to such ranges as for the Tricomi gas, and for the generalized Tricomi gas. Flow solutions for the hypothetical gases are expressed by the Airy functions.

**[1]***Handbook of mathematical functions, with formulas, graphs and mathematical tables*, Edited by Milton Abramowitz and Irene A. Stegun. Fifth printing, with corrections. 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. MR**0208798****[2]**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****[3]**S. Chaplygin,*Gas jets*, Tech. Memos. Nat. Adv. Comm. Aeronaut.,**1944**(1944), no. 1063, 112 pp. (3 plates). MR**0015979****[4]**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****[5]**C. Ferrari and F. G. Tricomi,*Transonic aerodynamics*, Academic Press, New York and London, 1968**[6]**Isao Imai,*On a refinement of the W.K.B. method*, Physical Rev. (2)**74**(1948), 113. MR**0025653****[7]**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****[8]**John A. Tierney,*An approximation to transonic flow of a polytropic gas*, Amer. J. Math.**75**(1953), 43–56. MR**0052941**, https://doi.org/10.2307/2372613

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
76.41

Retrieve articles in all journals with MSC: 76.41

Additional Information

DOI:
https://doi.org/10.1090/qam/281407

Article copyright:
© Copyright 1971
American Mathematical Society