The stability criteria of a heavy bluff airfoil equilibrium

I.K.Marchevskiy

N.E.Bauman Moscow State Technical University, Moscow, Russia

 

In the present paper movement in an air stream of an airfoil with three various perfectly elastic or viscous-elastic constraints (with three degrees of freedom) is investigated. Position of the airfoil in space is defined by fastening point coordinates and airfoil angle of incidence.

Wind influence on the airfoil is considered by introduction of drag force, lift force and aerodynamic moment. They could be calculated using dimensionless stationary aerodynamic coefficients. It's supposed that these coefficients depend only on the incidence.

In this case it is possible to write down system of the differential equations describing movement of the airfoil in a stream. It's shown that there is at least one equilibrium of the airfoil for any wind velocity.

This equilibrium point stability is investigated using equations of the first approximation. It's supposed that the airfoil has two close typical dimensions and its material density is much bigger than air density. Such airfoils are called heavy and bluff. In order to define signs of real parts of characteristic equation roots Gurvits's criterion is used.

Analytical expressions for necessary and sufficient stability conditions of equilibrium of heavy bluff airfoils are obtained for systems with one, two or three degrees of freedom. These conditions generalize known conditions.

Some of obtained instability sufficient conditions depend only on aerodynamic coefficients of the airfoil and they are invariant to a choice of the airfoil fastening point, mass and the moment of inertia of the airfoil, rigidity of constraints. Therefore change of these mechanical parameters of construction does not influence on character of stability of its equilibrium point.

In case of viscous-elastic constraints all the received stability conditions depend only on airfoil aerodynamic coefficients and constraints damping coefficients.

The received results could be used for investigation of equilibrium stability for heavy bluff airfoils in the stream.