A Navier Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping

Abstract

An unsteady, compressible, two dimensional, thin shear layer Navier Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi 3-D formulation is used to account for the streamwise variation of streamtube height. The code uses Ni’s Lax-Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin-Lomax turbulence model. Computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unstructured computational grid was adapted to the flow to better resolve shocks and wakes. Motion of each airfoil was simulated at each time step by stretching and compressing the mesh within the O-grid. This imposed motion consists of harmonic solid body translation in two directions and rotation, combined with the correct inter-blade phase angles. Validity of the code is illustrated by comparing its predictions to a number of test cases, including an axially oscillating flat plate in laminar flow, the Aeroelasticity of Turbomachines Symposium Fourth Standard Configuration (a transonic turbine cascade), the Seventh Standard Configuration (a transonic compressor cascade). The overall comparison between the predictions and the test data is reasonably good. A numerical study on a generic transonic compressor rotor was performed in which the impact of varying the amplitude of the airfoil oscillation on the normalized predicted magnitude and phase of the unsteady pressure around the airfoil was studied. It was observed that for this transonic compressor, the non-dimensional aerodynamic damping was influenced by the amplitude of the oscillation.