Oncoming alternating vortices

The present investigation examines a simple fluid-structure interaction pro blem, which is represented by the unsteady response of an airfoil/blade to a Karman vortex street in an inviscid uniform how. Two different cases were examined; one with a rigid airfoil/blade, where the structural stiffness i s infinite, another with an elastic blade. In both cases, the how remains a ttached to the airfoil/blade surface. A time-marching technique solving the Euler equations and a two-degree-of-freedom structural dynamic model is us ed to examine the interactions between the fluid and the structure. The int eractions between the convected vortices and the structure modify the shed wake whose energy, in turn, feeds into the forces and moments acting on the structure. For a rigid airfoil/blade, it is found that the amplitude of th e aerodynamic response is not proportional to the density of the oncoming v ortex street, but depends on c/d, the ratio of the chord length (c) to the axial spacing (d) of the convected vortices. When the number of vortices pe r unit length is increased, the amplitudes of the aerodynamic response incr ease and then decrease even though the density of the vorticity keeps incre asing and so is the energy of the excitation wake. Maxima are observed at c /d = 0.5, 1.5 and 2.5. This behaviour is analogous to the structural resona nce phenomenon and is labeled "aerodynamic resonance". The existence of suc h an "aerodynamic resonance" is important to turbomachinery applications wh ere the blade is elastic, the how is unsteady and the shed vortices from th e previous row are convected downstream by the mean flow. Thus, "aerodynami c resonance" alone or in conjunction with structural resonance could impact negatively on the fatigue life of turbine blades and their combined effect s should be accounted for in blade design. A preliminary attempt to assess this impact has been carried out. It is found that the relative fatigue lif e of a blade could be reduced by four orders of magnitude as a result. (C) 1999 Academic Press.