Métodos inversos para o projeto aerodinâmico de grades de turbomáquinas axiais

Abstract

In this work, two inverse methods for isolated airfoil and turbomachinery cascades design are presented. The first method is based on an iterative correction algorithm with an efficient panel technique for potential flow calculations. Linear vortex distributions on the panels and a consistent procedure for imposing the Kutta condition are applied in order to eliminate the spurious aerodynamic loading that usually appears in the vicinity of a cusped trailing edge. A semi-analytical scheme is applied for calculating the influence matrix elements of cascade airfoils. The scheme is purely analytical for isolated bodies. The algorithm searches the airfoil ordinates attending to a given surface velocity distribution with fixed abscissas. The second proposed method is a hybrid numerical technique based on a suitable combination of conformal mapping and the linear vortex panel method cited above. The coordinates of a circle or quasi-circle in the transformed plane are searched in order to satisfy a required velocity distribution on the target airfoil contour at the physical plane. The velocity distribution is now prescribed as a function of the natural coordinate. The use of a conformal mapping increases the precision of the inverse procedure, by damping possible geometrical oscillations at the leading edge region caused by the panel slope variations during the iterative process. In this way, smooth aerodynamic shapes are guaranteed to be produced on the whole contour. The geometrical marching is conducted by varying the panel slopes as a function of the normal velocity excess induced by the difference between the required and calculated velocities. A scheme is applied in order to close the body shape. Various benchmark tests are presented for isolated airfoils (Joukowski and Gostelow as isolated airfoil) as well cascades (Weinig, Gostelow and Joukowski mounted in cascade).