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

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.Comment: 34 pages, 19 figures, acepted in the Journal of Sound and Vibratio

Combustion regimes in sequential combustors: Flame propagation and autoignition at elevated temperature and pressure

This numerical study investigates the combustion modes in the second stage of a sequential combustor at atmospheric and high pressure. The sequential burner (SB) features a mixing section with fuel injection into a hot vitiated crossflow. Depending on the dominant combustion mode, a recirculation zone assists flame anchoring in the combustion chamber. The flame is located sufficiently downstream of the injector resulting in partially premixed conditions. First, combustion regime maps are obtained from 0-D and 1-D simulations showing the co-existence of three combustion modes: autoignition, flame propagation and flame propagation assisted by autoignition. These regime maps can be used to understand the combustion modes at play in turbulent sequential combustors, as shown with 3-D large eddy simulations (LES) with semi-detailed chemistry. In addition to the simulation of steady-state combustion at three different operating conditions, transient simulations are performed: (i) ignition of the combustor with autoignition as the dominant mode, (ii) ignition that is initiated by autoignition and that is followed by a transition to a propagation stabilized flame, and (iii) a transient change of the inlet temperature (decrease by 150 K) resulting into a change of the combustion regime. These results show the importance of the recirculation zone for the ignition and the anchoring of a propagating type flame. On the contrary, the autoignition flame stabilizes due to continuous self-ignition of the mixture and the recirculation zone does not play an important role for the flame anchoring

Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation

Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that unwanted attractor, while the system runs problem-less otherwise. In this study, we present experimental results regarding a thermoacoustic system subject to two consecutive and mirrored supercritical Hopf bifurcations: the system exhibits high amplitude thermoacoustic limit cycles for intermediate values of the bifurcation parameter. Changing quickly enough the bifurcation parameter, it was possible to dodge the unwanted limit cycles. A low-order model of the complex thermoacoustic system was developed, in order to describe this interesting transient dynamics. It was afterward used to assess the risk of exceeding an oscillation amplitude threshold as a function of the rate of change of the bifurcation parameter

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared to the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinise the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points and it pinpoints the crucial need of considering this effect when investigating critical transitions

Superradiant Scattering from Nonlinear Wave-Mode Coupling

Waves scattered at a self-oscillating mode can exhibit superradiance, or net amplification of an external harmonic excitation. This exotic behavior, arising from the nonlinear coupling between the mode and the incident wave, is theoretically predicted and experimentally confirmed for the first time in this work. We propose a generic theory of nonlinear wave-mode coupling, which is derived in analogy to the temporal coupled-mode theory of [Fan et al., J. Opt. Soc. Am. A 20, 569 (2003)]. A well-reproducible aeroacoustic realization of a superradiant scatterer was used to test the theory's predictions. It is shown that the nonlinear wave-mode coupling can be exploited to quasi-passively tune the reflection and transmission coefficients of a side cavity in a waveguide. The theoretical framework used to describe this type of superradiance is applicable to non-acoustic systems and may be used to design lossless scattering devices.Comment: 5 pages, 4 figure

Certain features of planar systems

This work is concerned with features of planar dynamical systems governed by a smooth velocity field and additive white noise. By Helmholtz's theorem, the system's velocity field can be decomposed into an irrotational and a solenoidal part, defined by a scalar and a vector potential, respectively. The meaning of this decomposition, however, is generally unclear, because it yields different potentials in different coordinates, and the choice of basis may not be obvious for a given system. In contrast, the dynamics themselves are independent of the basis in which they are represented. To address this discrepancy, we first present a coordinate-independent formulation of the Helmholtz decomposition for general, noise-driven planar systems. In the second part of our investigation, we focus on noise-free, steady planar flows. For this type of system, we analytically derive conditions for ruling out closed orbits in certain regions of phase space. We demonstrate our methods on well-known examples of dynamical systems in the plane.Comment: 11 pages, 3 figure

Coupling-Induced Instability in a Ring of Thermoacoustic Oscillators

Thermoacoustic instabilities in can-annular combustors of stationary gas turbines lead to unstable Bloch modes which appear as rotating acoustic pressure waves along the turbine annulus. The multi-scale, multiphysical nature of the full problem makes a detailed analysis challenging. In this work, we derive a low-order, coupled oscillator model of an idealized can-annular combustor. The unimodal projection of the Helmholtz equation for the can acoustics is combined with the Rayleigh conductivity, which describes the aeroacoustic coupling between neighboring cans. Using a Bloch-wave ansatz, the resulting system is reduced to a single equation for the frequency spectrum. A linear stability analysis is then performed to study the perturbation of the spectrum by the can-to-can interaction. It is observed that the acoustic coupling can suppress or amplify thermoacoustic instabilities, raising the potential for instabilities in nominally stable systems.Comment: 45 pages, 10 figure

Numerical study of ignition and combustion of hydrogen-enriched methane in a sequential combustor

Ignition and combustion behavior in the second stage of a sequential combustor are investigated numerically at atmospheric pressure for pure CH4 fueling and for a CH4/H2 fuel blend in 24:1 mass ratio using Large Eddy Simulation (LES). Pure CH4 fueling results in a turbulent propagating flame anchored by the hot gas recirculation zone developed near the inlet of the sequential combustion chamber. Conversely, CH4/H2 fueling results in a drastic change of the combustion process, with multiple auto-ignition kernels produced upstream of the main flame brush. Chemical Explosive Mode Analysis indicates that, when H2 is added, flame stabilization in the combustion chamber is strongly supported by auto-ignition chemistry. The analysis of fuel decomposition pathways highlights that radicals advected from the first stage flame, in particular OH, induce a rapid fuel decomposition and cause the reactivity enhancement that leads to auto-ignition upstream of the sequential flame. This behavior is promoted by the relatively large mass fraction of OH radicals found in the flow reaching the second stage, which is approximately one order of magnitude greater than it would be at chemical equilibrium. The importance of the out-of-equilibrium vitiated air on the ignition behavior is proven via an additional LES that features weak auto-ignition kernel formation when equilibrium is artificially imposed. It is concluded, therefore, that parameters affecting the relaxation towards chemical equilibrium of the vitiated flow can have an important influence on the operability of sequential combustors fueled with varying fractions of H2 blending