The acoustics of short circular holes and their damping of thermoacoustic oscillations

Abstract

Thermoacoustic instabilities arise from the coupling of acoustic waves and unsteady heat release rate from combustion. This coupling can generate large pressure oscillations which may significantly reduce the life of aero-engine and ground-based gas turbines, or even lead to failure of the whole combustion system. Acoustic dampers, such as Helmholtz resonators, perforated liners and perforated plates, are widely used to absorb acoustic energy and thus damp these thermoacoustic oscillations.

Such acoustic dampers typically comprise a circular hole with mean flow passing through, to convert acoustic energy into vortical energy, and finally into heat by viscous dissipation. A widely used analytical model [M.S. Howe. On the theory of unsteady high Reynolds number flow through a circular aperture, Proc. of the Royal Soc. A. 366, 1725 (1979), 205-223], which assumes an infinitesimally short hole, was recently shown to be insufficient for predicting the acoustics of holes with a finite length. In this thesis, an analytical model based on the Green's function method is developed to take the hole length into consideration. The importance of capturing the modified vortex noise accurately is shown. The vortices shed at the hole inlet edge are convected to the hole outlet and further downstream to form a vortex sheet. This couples with the acoustics, and the coupling may generate as well as absorb acoustic energy at low frequencies. Predictions from this model reveal the importance of capturing the path of the shed vortex. When this is captured accurately, predictions agree well with previous experimental and CFD results, for example predicting the potential for generation of acoustic energy at some frequencies.

The expansion ratios either side of a short hole affect the vortex-sound interaction of it, effects captured by the model developed in this thesis. These hole models are then incorporated into a Helmholtz resonator (HR) model, allowing a systematic investigation into the effect of neck-to-cavity expansion ratio and neck length. The HR models are then incorporated into a low-order network model which applies to both longitudinal and annular combustors. It is firstly shown that previous methods for accounting for a temperature difference between the HR cavity and the combustor are inadequate; improved models are developed, implemented and investigated. Finally, location optimisation for multiple HRs is performed, for both longitudinal and annular geometries, with the latter including both location and geometry optimisations.