Abstract
In [1] the problem of optimal profiling of the supersonic portion of a plane or axisymmetric nozzle for nonequilibrium flow is reduced to a boundary-value problem for a hyperbolic system of equations which includes the flow equations and the equations for the Lagrange multipliers. In view of the complexity of the solution of that system, the present paper presents an analogous study based on the one-dimensional formulation. The solution is illustrated by examples. It is noted that a similar solution undertaken in [2] is in error.
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A. N. Kraiko, “Variational problems in gasdynamics of nonequilibrium and equilibrium flows,” PMM, vol. 28, no. 2, pp. 285–295, 1964.
A. Widawsky and G. A. McCue, “Optimum nozzles for nonequilibrium expansions.” ARS J., vol. 32, no. 1, p. 86–88, 1962.
A. N. Kraiko, I. N. Naumova, and Yu. D. Shmyglevskii, “On the design of bodies of optimal form in a supersonic flow,” PMM, vol. 28, no. 1, pp. 178–182, 1964.
M. J. Lighthill, “Dynamics of a dissociating gas, Part 1,” Fluid Mech., vol. 2, part 1, p. 1–32, 1957.
N. C. Freeman, “Nonequilibrium flow of an ideal dissociating gas,” J. Fluid Mech., vol. 4, part 4, pp. 407–425, 1958.
J. P. Rink, H. T. Knight, and R. E. Duff, “Shock tube determination of dissociation rates of oxygen,” J. Chem. Phys., vol. 34, no. 6, pp. 1942–1947.
O. N. Katskova and A. N. Kraiko, “Calculation of plane and axisymmetric supersonic flows with irreversible processes,” PMTF, no. 4, pp. 116–118, 1963.
N. S. Galyun and A. N. Kraiko, “Calculation of nonequilibrium flows,” Izv. AN SSSR, Mekhanika i mashinostroenie, no. 6, pp. 41–47, 1964.
G. Guderley and E. Hantsch, “Beste Formen für achsensymmetrische Überschallschubdüsen,” Z. Flugwissenschaften, vol. 3, no. 9, 305–315, 1955.
Yu. D. Shmyglevskii, “Some variational problems of gasdynamics,” Tr. VTs AN SSSR, 1963.
A. N. Kraiko, “Variational problems of supersonic gas flows with arbitrary thermodynamic properties,” Tr. VTs AN SSSR, 1963.
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Galyun, N.S., Kraiko, A.N. A variational problem of one-dimensional nonequilibrium gasdynamics. Fluid Dyn 1, 16–22 (1966). https://doi.org/10.1007/BF01013807
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DOI: https://doi.org/10.1007/BF01013807