Analytical solution of subsonic gas flow past a circle

[摘要] The Mach-Number series expansion of the potential function for the two dimensional flow of an inviscid, compressible, frozen gas past a circular cylinder are obtained to 29 terms. Analysis of these expansion allows the estimates for the critical Mach-Number M∗, (at which flow first becomes locally Sonic), and the radius of convergence of the series Mcfor the maximum velocity. In this case of two-dimensional circular cylinder we obtain consistent results with 29 terms obtained by Van Dyke and Guttmann [19] for the case of diatomic gas with gamma equal to 7/5. For this case of two dimensions, we have been unable to determine the nature of singularities. We hope this work help to shed a light for resolving the 80-years old conterversary which says that whether the airfoil can posses a continuous range of shock free potential flow above the critical Mach-Number (Mc> M∗).

[发布机构] Department of Aerospace Engineering, AmirKabir University of Technology, Tehran; 1587-4413, Iran^1;Flow Research and Engineering, 788 Maplewood Avenue, Palo Alto; CA; 94303, Iran^2

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Diatomic gas;Maximum velocity;Potential function;Radius of convergence;Series expansion;Two-dimension;Two-dimensional flow