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Smooth transonic flow in an array of counter-rotating vortices

Published online by Cambridge University Press:  09 February 2005

G. K. O'REILLY
Affiliation:
Graduate Aeronautical Laboratories, 105-50, California Institute of Technology, Pasadena, CA 91125, USA
D. I. PULLIN
Affiliation:
Graduate Aeronautical Laboratories, 105-50, California Institute of Technology, Pasadena, CA 91125, USA

Abstract

Numerical solutions to the steady two-dimensional compressible Euler equations corresponding to a compressible analogue of the Mallier & Maslowe (Phys. Fluids, vol. A 5, 1993, p. 1074) vortex are presented. The steady compressible Euler equations are derived for homentropic flow and solved using a spectral method. A solution branch is parameterized by the inverse of the sound speed at infinity, $c_{\infty}^{-1}$, and the mass flow rate between adjacent vortex cores of the corresponding incompressible solution, $\epsilon$. For certain values of the mass flux, the solution branches followed numerically were found to terminate at a finite value of $c_{\infty}^{-1}$. Along these branches numerical evidence for the existence of extensive regions of smooth steady transonic flow, with local Mach numbers as large as 1.276, is presented.

Type
Papers
Copyright
© 2005 Cambridge University Press

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