The effect of temperature difference on the acoustic performance of Helmholtz resonator

Abstract

Passive control devices such as liners and Helmholtz resonators (HRs) are commonly employed in practical applications to mitigate thermoacoustic instabilities. To safeguard the HR from being corroded by the invasion of hot flow from the combustor, a cooling flow with significantly lower temperature than that in the combustor is injected from the rear of the HR cavity. However, this results in a dynamic mixing of cold bias and hot grazing flows in the combustor, which may generate an entropy wave downstream of the HR, thereby affecting its sound absorption performance. Unfortunately, these effects are often neglected when modelling such systems. In this context, an acoustic model is derived for a one-dimensional combustor duct with distinct temperature compared to that of the attached HR. The model offers physical insights into the underlying mechanisms of the impact of HR on the acoustic fields. It considers not only the mean temperature difference between the cooling bias flow and the main flow in the combustor, but also the mean temperature difference between the up- and downstream sides of the combustor across the HR. The effect of both temperature differences on the HR’s performance will be discussed.