Aeroacoustic Research in Europe: The CEAS-ASC Report on 2000 Highlights. CAA Simulation of Sound Generation By Linear Interaction of Vorticity with a Wedge

Abstract

THE STUDY OF AIRFRAME NOISE IS INTIMATELY CONNECTED WITH THE INTERACTION OF FLOW WITH EDGES. IN THIS CONTEXT THE QUESTION ARISES, WHETHER LINEARIZED CONSERVATION EQUATIONS DESCRIBE SUCH SOURCES. LILLEY'S AEROACOUSTIC WAVE EQUATION STATES THAT IN A SUBSONIC PARALLEL STEADY MEAN SHEAR FLOW SOUND IS GENERATED BY NONLINEAR PROCESSES ONLY, BECAUSE THE RESPECTIVE AEROACOUSTIC SOURCE TERM VANISHES UPON LINEARIZATION ABOUT THE BASIC STATE. THE LINEAR DYNAMICS OF WHATSOEVER SMALL PERTURBATIONS, E.G. DUE TO SMALL FLUCTUATIONS OF THE VORTICITY, WILL THEREFORE NOT CONTRIBUTE TO THE GENERATION OF NOISE. IN ORDER TO VERIFY THE ABOVE STATEMENT A NUMERICAL SIMULATION OF THE LINEAR DYNAMICS OF A PURELY VORTICAL PERTURBATION EVOLVING IN A FREE PARALLEL SHEARLAYER WAS CARRIED OUT USING THE PIANO CODE. AS A RESULT A DOWNSTREAM CONVECTING UNSTABLE WAVE PACKET EVOLVES REPRESENTING THE CLASSICAL KELVIN-HELMHOLTZ INSTABILITY, WHICH CONSISTS OF PURELY HYDRODYNAMIC (I.E. NON-PROPAGATING) COMPONENTS INDICATING COMPLETE SILENCE AND THUS CONFIRMING THE STATEMENT OF LILLEY'S EQUATION. IF A SHARP VERTICAL WEDGE IS ORIGINALLY PLACED BELOW THE SHEARLAYER THE SOUND IS GENERATED BY SCATTERING OF THE WAVE PACKET'S LINEAR HYDRODYNAMIC PRESSURE FIELD AT THE WEDGE ALTHOUGH THE MEAN FLOW DOES NOT EVEN TOUCH THE WEDGE. THE EXAMPLE SHOWS THAT IN THE PRESENCE OF EDGES THE SOUND GENERATION BY VORTICITY BECOMES A LINEAR PROBLEM EVEN IN THE PRESENCE OF A PARALLEL SHEAR FLOW.