Author:
Van Dyke M. D.,Guttmann A. J.
Abstract
AbstractThe Mach-number series expansion of the potential function for the two-dimensional flow of an inviscid, compressible, perfect, diatomic gas past a circular cylinder is obtained to 29 terms. Analysis of this expansion allows the critical Mach number, at which flow first becomes locally sonic, to be estimated as M* = 0.39823780 ± 0.00000001. Analysis also permits the following estimate of the radius of convergence of the series for the maximum velocity to be made: Mc = 0.402667605 ± 0.00000005, though we have been unable to determine the nature of the singularity of M = Mc. Since Mc exceeds M* by some 1.1%, it follows that this particular “airfoil” can possess a continuous range of shock-free potential flows above the critical Mach number. This result hopefully resolves a 70-year old controversy.
Publisher
Cambridge University Press (CUP)
Reference29 articles.
1. The critical behaviour of two-dimensional isotropic spin systems
2. The exterior Neumann problem for nonlinear elliptic differential equations with application to the theory of a wing in a compressible gas;Frankl;Izv. Akad. Nauk SSSR,1934
3. On a new method of series analysis in lattice statistics
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