Mixing layer resonance under high-speed stream forcing

Abstract

In the majority of fluid–structure interaction problems, the biggest challenge lies in the fundamental understanding of the flow physics. Forced mixing layers is an important phenomenon found in many cases of flow-induced vibrations and acoustics. The response of a mixing layer to high-speed stream acoustic forcing is investigated with a theoretical and experimental approach. Two different experiments demonstrating the fluid mechanic phenomenon are presented. The first experiment consists of a circular jet impinging on a vibrating plate. The second experiment demonstrates the mixing layer resonance in the context of a fluidelastic instability causing high-amplitude vibrations in gas turbine high-pressure compressor rotor blades. Both the plate and the adjacent blade vibration induce an acoustic feedback that propagates within the jet and blade tip clearance flow, respectively. The resonance was found to occur when the feedback wavelength matched either the jet-to-plate or the inter-blade distance. In both experimental cases, the resonance condition has been simply modeled by the coincidence of a 1D feedback wave, which propagates upstream at reduced velocity by the high-speed flow. The coupling between the jet induced mixing layer and the feedback wave is assumed to naturally occur when one of the wave crests reaches the separation edge. The objective of this study is to improve the understanding of the coupling mechanism between an emanating shear layer and the acoustic forcing originating within a fast flow stream. The study is based on a simplified analytical model in order to enlarge the current understanding of the mixing layer receptivity to the more specific case of its response to high-speed stream forcing. To identify the mixing layer resonant modes, an analytical resonance condition is proposed. It is found that the mixing layer response becomes spatially resonant for specific source locations downstream in the high-speed flow. The study also provides an analytical mean to capture the critical source location periodicity that has been experimentally observed. The resulting theoretical prediction of the resonant source locations is in good agreement with the experimental data. Therefore, it supports the stream forced mixing layer analytical model and the proposed spatial resonance condition. The simple 1D reduced speed feedback wave model, which has been used to identify the experimental resonance conditions, is also in good agreement, and thus validated, with the results of this study.