On Multidimensional Global Eigenvalue Problems for Hydrodynamic and Aeroacoustic instabilities

Abstract

The present effort discusses multi-dimensional eigenvalue problems as applied to the solution of hydro- dynamic and aeroacoustic instability problems on complex geometries. As a demonstrator, global linear instability analyses of steady lamina flows on an elliptic cone in compressible ¿¿ows are monitored; one such flow, obtained using a standard aerodynamics solver, is presented figure 1. Flows on this geometry are intrinsically three-dimensional; as a matter of fact the three-dimensionality of the geometry of the elliptic cone accounts for the departure of the laminar-turbulent transition process from the fairly well-understood scenarios on circular cones and other axisymmetric bodies of revolution. Shedding light on the essentially three-dimensional transition process on the elliptic cone provides motivation for several recent experimental and numerical efforts, as well as for the theoretical/numerical methodology described herein.