Optimal airfoil in an inverse problem of jet aerodynamics
Abstract
The paper deals with a special inverse boundary problem, when the boundary of the domain is completely unknown and a singular integral equation for the velocity angle is obtained. For the model of free plane symmetric incompressible jet forked by an airfoil, the boundary equations and airfoil shape are "a posteriori" determined, while the velocity along them is "a priori" prescribed. With the aim to obtain minimum drag, in the present paper there is solved the optimization problem for airfoils, using the penalty method and the golden section method. In the case of optimum, numerical computations are performed and the airfoil design together with the drag coefficient are obtained.
Keywords
inviscid jets, inverse problems, singular integral equation, optimum airfoil, optimization,References
[1] U. Cisotti. Idromeccanica Piana. Libreria Editice Politecnica Milano, t1. 1921, t2. 1922.[2] A.A. Hamidov. Plane and Axial Symmetrical Jet Problems (in Russian). Tashkent University Press, Tashkent, 1978.
[3] C. Iacob. Introduction Mathématique à la Mécanique des Fluides. Gauthier-Villars, Bucarest- Paris, 1959.
[4] V. Karmanov. Programmation Mathématique. Mir Publishers, Moscow, 1977.
[5] M. Lupu. Obtaining and studying Beltrami type equations for axial-symmetric jets in M.G.D. In: V. Barbu, ed., Differential equations and control theory" 171-181. Ed. Longman Sci. & Tech., NY, 1991.
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