Linear models for control of cavity flow oscillations

Abstract

Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers.

A reduced-order model of diffusive effects on the dynamics of bubbles

“…A well-known method for systematically deriving reduced-order models for PDEs is to first compute a set of orthogonal spatial modes using the proper orthogonal decomposition ͑POD͒, and then perform a Galerkin projection of the PDE onto a reduced set of the POD modes ͑e.g., Rowley 15 and references therein͒. The POD modes ͑or empirical eigenfunctions͒ are obtained from data ͑found, for example, by solving the full PDE as presented in Sec.…”

Drag reduction of a car model by linear genetic programming control

“…The control may be based on a local linearization of the Navier-Stokes equation. Various configurations have been studied, such as boundary layer flow (Liepmann & Nosenchuck 1982;Bagheri et al 2009), circular cylinder wake (Roussopoulos 1993) and open cavity flow (Rowley et al 2006;Samimy et al 2007). However, turbulent flow is characterized by broadband frequency dynamics with complex frequency cross-talk.…”

Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

“…The noise radiated by flow passing over cavities has been studied extensively in the past [23,26,27], is connected to a broad range of aerospace and automotive applications, and a variety of theoretical questions on noise production. The spectrum of cavity noise contains both broadband components introduced by the turbulence in the shear layer, and tonal components.…”

“…The spectrum of cavity noise contains both broadband components introduced by the turbulence in the shear layer, and tonal components. The mechanisms for the intense tonal components in cavities have been identified and can be either [26] 1. a shear-layer mode mechanism in which the shear-layer generated at the upstream edge of the cavity impinges on the rear edge of the cavity, scattering acoustic waves that propagate upstream and further excite the shear layer, or 2. a wake-mode mechanism, induced by periodical vortex shedding at the cavity leading edge. Monitoring point Figure 4.…”