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In this paper, we apply the novel EPTD (Exceptional Point-based Thermoacoustic Design)-method derived in part I of this study (M. Casel & A. Ghani, Combust. Flame, 2024) to two lab-scale combostor test rigs that exhbit thermoacoustic instabilities and demonstrate the method's capability and practicality for stabilizing the originally unstable systems. Furthermore, we study, and refine, certain characteristics of the proposed EPTD method when applied to realistic combustor configurations. While the first configuration is laminar and unconfined, the second features a confined turbulent swirl flame. Both combustor test rigs are modeled by thermoacoustic networks incorporating measured flame responses. The models allow to trace back full system modes to their respective mode origins, which are either of intrinsic thermoacoustic (ITA) or acoustic nature, and are validated by means of experimental data. In both configurations, we identify exceptional points (EPs) that are formed by these respective mode branches. The unconfined, laminar configuration features only one EP, that we first investigate with respect to the system parameter sensitivity, and subsequently analyze its relation to the configuration's spectrum, confirming the characteristics that were previously identified in part I of this study by means of generic (thermoacoustic) systems: not only the EP's position in the complex plane, but also the exceptional parameters have a significant impact on the resulting thermoacoustic spectrum as they incorporate a relation between the respective mode origins and the full system modes. In contrast to the first configuration of this paper, the confined turbulent combustor allows for some further analysis of the EPTD application to realistic combustors as it features a significantly larger system parameter space as well as two EPs. Besides, it exhibits two EPs, for which we show how their respective sensitivities with respect to system parameter variations may already be utilized to identify which system parameters impact on which mode origins in the spectrum. In addition to this, we describe which of the two EPs may be chosen when applying the EPTD method. Finally, in both cases, we adopt the EPTD method derived in part I of this study for stabilizing thermoacoustic systems: Shift the EP towards smaller growth rates while constraining the exceptional parameters, i.e., shift the entire spectrum towards smaller growth rates while enforcing specific relations between the respective mode origins. Subsequently we showcase that this method in fact successfully dampens the entire spectrum of both combustion experiments and that the entire thermoacoustic spectrum shifts in growth rate with the same magnitude of the prescribed shift in EP growth rate. While the relatively small system parameter dimension of the unconfined laminar configuration does not allow for multiple system parameter combinations that realize the same EP, we identify multiple system parameter combinations that feature the same EP in the confined turbulent case. For this, we subsequently show that, as already shown for the generic configurations in part I of this study, different system parameter combinations, realizing the same EP, in fact result in the same thermoacoustic spectrum. This finally demonstrates that our proposed method is especially suited for the design of thermoacoustic systems that feature a large number of system parameters. Novelty and Significance statement: Thermoacoustic instabilities are actively researched for more than half a century. Despite this effort, scientifically sound strategies to design thermoacoustically stable combustors do not exist today. We present a novel method on a conceptual level that takes into account the latest discoveries in our field (e.g. ITA modes between 2014/2015 and Exceptional Points in 2018), connects them into one fast and robust numerical framework and opens the path to design the thermoacoustic stability map. This framework does not require tuning parameters or the like, which translates to an interpretable, parsimonious and computationally cheap design strategy. We demonstrate the Exceptional Point-based Thermoacoustic Design method (called EPTD-method) on two well-known experimental setups with increasing complexity and carefully perform parametric tests to unveil the key aspects of this novel design strategy. Finally, we turn the initially unstable setups into stable ones and explain why and how this was achieved.
Casel et al. (Fri,) studied this question.