At low flow Mach numbers, fluid-elastic lock-in may occur when a shear layer instability interacts with an adjoining or nearby structure and the resulting vibration of the structure reinforces the shear layer instability. Despite the significant amount of study of lock-in with acoustic resonators, fluidelastic lock-in of a shear layer fluctuation over a cavity and a structural resonator is not well understood and has not been thoroughly studied. Design of an experimental system is described and preliminary diagnostics are addressed as a basis for a platform for developing a fundamental understanding of the feedback mechanism, analytical models for predicting and describing fluid-elastic lock-in conditions, and the roles of the fluid and structural dynamics in the process. Features of the system investigated here include design for characterization of modal excitation of a beam-like structure from the shear layer fluctuation, isolation of the predominant instability source to the shear layer fluctuation over the cavity, variation of the cavity size to identify critical parameters that govern fluidelastic lock-in, and alteration of the inflow boundary layer momentum thickness. So far, lock-in between the cavity and the distributed elastic resonator has not been achieved. Further investigations to determine the role of the source and resonator attributes are underway. INTRODUCTIONComplex behavior can result from fluid flow interacting with a structure. A wide variety of research in the fields of aeroelasticity and h ydrodynamics has generated numerous results useful in predicting and describing fluid-structure interaction. In flow-induced vibrations, hydrodynamic forces interact with the elastic properties of a structure, resulting in fluid-elastic interaction. Flow interacting with a structure produces vortices which shed at a prescribed frequency. If the shedding frequency coincides with the resonance frequency of an adjoining elastic structure or acoustic fluid volume, the resulting oscillation can reinforce the vorticity, creating a
Lock-in occurs between many different types of flow instabilities and structural-acoustic resonators. Factors that describe the coupling between the fluid and structure have been defined for low flow Mach numbers. This paper discusses how different flow instabilities influence lock-in experimentally and analytically. A key concept to the lock-in process is the relative source generation versus dissipation. The type of fluid instability source dominates the generation component of the process, so a comparison between a cavity shear layer instability with a relatively stronger source, for example wake vortex shedding from a bluff body, will be described as a coupling factor. In the fluid-elastic cavity lock-in case, the shear layer instability produced by flow over a cavity couples to the elastic structure containing the cavity. In this study, this type of lock-in was not achieved experimentally. A stronger source, vortex shedding from a bluff body however, is shown experimentally to locks into the same resonator. This study shows that fluid-elastic cavity lock-in is unlikely to occur given the critical level of damping that exists for a submerged structure and the relatively weak source strength that a cavity produces. Also in this paper, a unified theory is presented based on describing functions, a nonlinear control theory used to predict limit cycles of oscillation, where a self-sustaining oscillation or lock-in is possible. The describing function models capture the primary characteristics of the instability mechanisms, are consistent with Strouhal frequency concepts, capture damping, and are consistent with mass-damping concepts from wake oscillator theory. This study shows a strong consistency between the analytical models and experimental results.
Flow over shallow cavities is a noise concern due to the possibility of flow tone lock-in with acoustic resonators. The principal aim of this work is to understand the factors that contribute to the onset of lock-in using Computational Fluid Dynamics (CFD) models. CFD models of shallow cavity lock-in to longitudinal acoustic resonators are developed and validated against existing test data from Lehigh University. All simulations are performed using AcuSolve™. A key technical contribution is the development of admittance inflow and impedance outflow boundary conditions to model the effects of the pipe resonator. The general trends predicted by the CFD models agree with the test data. In particular, the resonator response at the strong interaction point is well represented.
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