FLEXURAL OSCILLATIONS OF FLEXIBLE AIRFOILS IN SUBSONIC COMPRESSIBLE FLOWS

Abstract

This paper presents simple and efficient analytical solutions for unsteady subsonic compressible flows past flexible airfoils executing low frequency oscillations. These analytical solutions are obtained with a method using velocity singularities related to the airfoil leading edge and ridges. The method has been validated for the pitching and plunging oscillations of the rigid airfoils by comparison with results based on Jordan’s data for compressible flows and by comparison with the solutions obtained by Theodorsen, Postel & Leppert and Mateescu & Abdo for incompressible flows. The method has been applied to obtain efficient analytical solutions for the flexural oscillations of airfoils in compressible flows, which can be efficiently used in solving aeroelastic problems. Professor Carafoli’s contributions to the aerodynamics of airfoils and wings Starting from 1924, in Paris, Elie Carafoli made significant contributions to the aerodynamic studies of wings and airfoils, included in Aerodynamics of airplane wings [5], Theory of lifting airfoils [6], in which he presented the aerodynamics of airfoils with rounded trailing edge, named later Carafoli airfoils, Influence of ailerons on the aerodynamic characteristics of lifting surfaces [7], and in Experimental studies on monoplane wings [8]. After 1928, he continued his research and academic activity in Romania, bringing new contributions to the aerodynamics of wings and airfoils in incompressible flows, which were mostly included in Aerodynamics [9], book also translated from Romanian into German and Russian. After 1950, Elie Carafoli developed a special interest for compressible flows and published High Speed Aerodynamics [10], initially in Romanian and then translated in English. He made, together with his collaborators, important contributions on the aerodynamics of wings and airfoils in supersonic flows, most of them included in the monograph Wing Theory in Supersonic Flow [11] published by Pergamon Press, to which the present author also collaborated. INCAS BULLETIN No. 2/ 2009 51 DOI: 10.13111/2066-8201.2009.1.2.11 For his outstanding achievements in aerodynamics, Elie Carafoli received very numerous international distinctions and awards, such as Diploma “Paul Tisandier” of the International Aeronautical Federation, Gauss Medal attributed yearly to the best scientist in the world by the Scientific Society Braunschweig, Germany, Apollo 11 Medal, Tsiolkovski Medal and many others distinctions which can not be listed here due to the space limitation. Elie Carafoli was one of the few Honorary Fellows of the Royal Aeronautical Society, Great Britain, and one of the first members of the International Academy of Astronautics (proposed by Theodor von Karman), and he was elected first Vice-President and then President of the International Astronautic Federation. In Romania, Carafoli was elected member of the Romanian Academy in 1948, and later named President of the Technical Sciences Section of the Academy, and he received the greatest Romanian medals, prizes and awards. One of the important realizations of Academician Carafoli was the foundation in 1949 of a research institute of the Romanian Academy, known as the Institute of Fluid Mechanics, which is presently named the National Institute for Aerospace Research “Elie Carafoli”. This institute contributed to the scientific formation of numerous former students and collaborators of Professor Carafoli, who distinguished themselves by contributions in aerodynamics and other related aerospace domains. Many of the former students and collaborators of Professor Carafoli became professors at their turn in Romania, as well as in other countries, such as Canada, France, Germany and United States of America, to name only a few. The present author had the privilege to study Aerodynamics with Professor Carafoli, who was also the Ph. D. supervisor, and to be his close collaborator for more than two decades. He is indebted to Professor Carafoli for many research advices, which materialized not only in many publications resulted from their direct scientific collaboration, but also in his further research and academic activity, first in Romania, and since 1982 in Canada. This author, together with his Masters’ and Ph. D. students, aims to continue the best scientific tradition of Professor Carafoli, with new contributions to the aerodynamics of wings and airfoils in steady and unsteady flows in incompressible, compressible subsonic and supersonic regimes and at low Reynolds numbers, in addition to other contributions in related aerospace domains (a few selected examples from the last ten years are included in references [20–37, 43].