Acoustic Resonances in Aircraft High Lift Configurations

Abstract

High lift devices have been pinpointed as important source of airframe noise during aircraft landing and approach. In addition to broadband noise strong tones were observed. The occurrence of low- and high-frequency tones under different operating conditions suggests the presence of different source mechanisms which are usually traced to unstable shear layers. These sources can be enhanced by weakly damped resonances. The objective of the present investigation is the computation of such resonances in a generic two-element high lift configuration. Neglecting mean flow effects an eigenvalue problem for the Laplace operator has to be solved numerically subject to homogeneous Neumann boundary conditions on the airfoils in conjunction with a radiation condition at infinity. Using the finite element method the latter is approximated by perfectly matched layer (PML) absorbing boundary conditions at the necessarily finite grid boundaries. The calculation of resonances reduces then to solving a large eigenvalue problem via Arnoldi algorithm.

The physics behind the low- and high-frequency resonances is first demonstrated for the simple model of a circular cylinder with a rectangular cut-out. Without the cut out cavity the resonances of the circular cylinder are simply highly damped resonances of surface waves which can be computed analytically and thus provide a good check of our numerical method. On the other hand if the rectangular cavity is considered by itself damped cavity resonances are obtained for longitudinal and transversal cavity modes. For the cylinder with cut out cavity these two different resonances interact but are dominated by the longitudinal cavity resonances. It is shown that similar resonances are behind the low- and high-frequency resonances of a high-lift configuration albeit the more complicated geometry and the not completely closed slat cove cavity obliterates this. The surface wave resonances correspond to the low-frequency peaks observed in model tests whereas the resonances of the slat cove cavity enhance the high-frequency peaks found for different operating conditions.