Stabilization of acoustic modes using Helmholtz and Quarter-Wave resonators tuned at exceptional points

Abstract

Acoustic dampers are efficient and cost-effective means for suppressing thermoacoustic instabilities in combustion chambers. However, their design and the choice of their purging air mass flow is a challenging task, when one aims at ensuring thermoacoustic stability after their implementation. In the present experimental and theoretical study, Helmholtz (HH) and Quarter-Wave (QW) dampers are considered. A model for their acoustic impedance is derived and experimentally validated. In a second part, a thermoacoustic instability is mimicked by an electro-acoustic feedback loop in a rectangular cavity, to which the dampers are added. The length of the dampers can be adjusted, so that the system can be studied for tuned and detuned conditions. The stability of the coupled system is investigated experimentally and then analytically, which shows that for tuned dampers, the best stabilization is achieved at the exceptional point. The stabilization capabilities of HH and QW dampers are compared for given damper volume and purge mass flow.

Whistling of deep cavities subject to turbulent grazing flow: intermittently unstable aeroacoustic feedback

“…The specific admittance of a non-dissipative closed duct, below its cut-on frequency (pure one-dimensional acoustic propagation), is . It was shown in § 2.1.2 of the paper from Bourquard & Noiray (2019), that asymptotically behaves, around , as , with . This approximation provides an explicit formulation of quarter wave type resonances as a second-order harmonic oscillator with equivalent mass , i.e.…”

Thermoacoustic modes of intrinsic and acoustic origin and their interplay with exceptional points

“…EPs have been identified as the fundamental concept at the base of many scientific phenomena in several fields, including non-Hermitian quantum mechanics, optics and acoustics [16][17][18]. In thermoacoustics, they have only been recently discussed [19].…”

Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points

“…This has analogies with the EPs arising due to the acoustic coupling between a cavity and an acoustic damper. In this respect, Bourquard & Noiray (2019) experimentally demonstrated the existence of such EPs, and showed that both Helmholtz resonators and quarter-wave tube dampers achieve optimal damping performance when tuned to operate at the EPs of the closed-loop coupled acoustic system. In this study, we relate EPs in the spectrum of thermoacoustic systems with (i) the high sensitivity experienced by some thermoacoustic eigenvalues and (ii) the limits of validity of high-order perturbation methods.…”