Browsing 3. Tεχνικές Αναφορές by Subject "Airfoil equation"
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- ItemOpen AccessA modification of the generalized airfoil equation and the corresponding numerical methods
Γενικό Τμήμα (Τεχνικές Αναφορές)Ioakimidis, Nikolaos; Ιωακειμίδης, ΝικόλαοςThe two-dimensional problem of steady, inviscid, irrotational, subsonic flow around a straight or curvilinear thin airfoil or an array of such airfoils inside a wind tunnel is generally reduced to a one-dimensional Cauchy type real or complex singular integral equation called generalized airfoil equation. Here a new form of this equation is suggested (with no change in the unknown function) with index equal to 1 instead of 0. The new equation is supplemented by an integral condition assuring the uniqueness of its solution. This modification of the generalized airfoil equation permits the application of the theoretical results and the algorithms for the numerical solution of Cauchy type singular integral equations with index equal to 1 (mainly appearing in crack problems in the theory of plane elasticity) to the generalized airfoil equation and it establishes the relationship between crack and airfoil problems. Moreover, it permits the utilization of the classical Chebyshev polynomials instead of the airfoil polynomials. Three applications are also made and numerical results are presented.