Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session M06: Thermoacoustics 
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Chair: Luca Magri, University of Cambridge Room: Georgia World Congress Center B208 
Tuesday, November 20, 2018 8:00AM  8:13AM 
M06.00001: Exceptional points in the thermoacoustic spectrum of longitudinal configurations Luca Magri, Georg A. Mensah, Camilo F. Silva, Philip E. Buschmann, Jonas Pablo Moeck Exceptional points (EPs) are found in the spectrum of a longitudinal thermoacoustic system as the parameters of the flame transfer function are varied. EPs occur when two eigenvalue trajectories with different physical nature collide: One trajectory originates from an acoustic mode, whereas the other trajectory originates from an intrinsic thermoacoustic mode. The system's sensitivity to changes in the parameters is infinite because the EP is a squareroot branch point of the determinant. Traditional iterative methods to find eigenvalues are not robust in the vicinity of EPs. A contourintegrationbased approach is deployed to enable the robust computation of the thermoacoustic spectrum. The appropriate expansion at the EP, which can be used to calculate sensitivities to the system’s parameters for passive control, is in fractional powers (Puiseux series) of the parameters. The large sensitivity at an EP may help design new control schemes to mitigate thermoacoustic instabilities with small changes in the design variables. The existence of EPs in thermoacoustic systems has implications for physical understanding, computing, modelling and control. 
Tuesday, November 20, 2018 8:13AM  8:26AM 
M06.00002: Higherorder degenerate points in annular thermoacoustic systems Jonas Moeck, Alessandro Orchini, Philip E. Buschmann, Georg Atta Mensah, Luca Magri Annular combustors, such as those typically found in gas turbines for power generation and aeroengines, nominally feature discrete rotational symmetry. Most of the eigenvalues associated with azimuthal thermoacoustic modes in these systems are therefore twofold degenerate, with a corresponding twodimensional eigenspace. Moreover, as we have recently shown, exceptional points, which are manifestations of defective eigenvalues, are generic features of thermoacoustic systems and emerge from the collision of an acoustic and an intrinsic mode. In a longitudinal, singleflame system, the exceptional eigenvalue has algebraic and geometric multiplicity two and one, respectively. However, in an annular system with discrete rotational and reflection symmetry, lowerorder azimuthal eigenvalues  acoustic as well as intrinsic  are already twofold degenerate. Consequently, at an exceptional point in an annular system, the defective eigenvalue corresponds to a higherorder degeneracy with algebraic multiplicity four and geometric multiplicity two. We illustrate the formation of exceptional points in annular thermoacoustic systems and discuss implications for modeling and stability analysis. 
Tuesday, November 20, 2018 8:26AM  8:39AM 
M06.00003: Intrinsic thermoacoustic modes in an annular combustor Philip E. Buschmann, Georg A. Mensah, Jonas P. Moeck Thermoacoustic instabilities originate from the interaction between the unsteady heat release rate associated with flames and the acoustic field of a combustor. It was recently shown that thermoacoustic feedback can be established even without acoustic resonances, giving rise to socalled intrinsic thermoacoustic modes. While these modes have been investigated in singleflame configurations, their occurrence in annular combustion chambers, with multiple flames arranged around the circumference, has not been characterized yet. We compute the spectrum of an annular combustor with a 3D thermoacoustic Helmholtz solver. The configuration is similar to those commonly found in gas turbine engines, and we use a generic flame response model. In addition to the observations in previous studies, we find numerous intrinsic modes in the frequency range covering the first few acoustic modes. Most of the intrinsic modes are organized in clusters, at multiples of the inverse flame response time delay. The structure of the intrinsic spectrum is shown to be linked to cutoff effects of the nonpropagating azimuthal modes. The study indicates that intrinsic modes are generically present in annular combustors, even in large numbers, but have eluded previous studies for numerical reasons. 
Tuesday, November 20, 2018 8:39AM  8:52AM 
M06.00004: Degenerate high order perturbation theory of thermoacoustic eigenmodes Alessandro Orchini, Georg Mensah, Jonas Moeck Thermoacoustic instabilities are due to the coupling between the acoustic response of a cavity and the heat release rate of a heat source. In gas turbines, they are detrimental because they cause large amplitude oscillations of the structure, limiting operating conditions and the life span of the gas turbine components. The instabilities can be predicted by identifying the thermoacoustic eigenvalues for a given complex geometry. These eigenvalues are strong nonlinear functions of the system parameters, and obtaining them for many different configurations is numerically demanding. However, by using once large order perturbation theory on the operator governing the dynamics, one can build power series expansions to a desired order that approximate well both eigenvalues and eigenvectors of the system for any value of a parameter of interest within a certain threshold. In particular, we discuss the complications in the perturbation method arising when dealing with degenerate modes, which are often observed in gas turbines due to their discrete rotational symmetry. The theory is tested on an annular atmospheric combustor for various choices of perturbation parameters. 
Tuesday, November 20, 2018 8:52AM  9:05AM 
M06.00005: Data assimilation and parameter estimation of thermoacoustic instabilities in a ducted premixed flame Hans Yu, Thomas Jaravel, Matthias Ihme, Francesco Garita, Matthew P. Juniper, Luca Magri Thermoacoustic instabilities are a persistent challenge in the design of jet and rocket engines. The timeaccurate calculation of thermoacoustic instabilities is challenging due to the presence of both aleatoric and epistemic uncertainties, as well as the extreme sensitivity to small changes in certain parameters. Our thermoacoustic system is a vertical Rijke tube containing a premixed Bunsen flame. We conduct experiments and highfidelity numerical simulations. We then perform data assimilation and parameter estimation using the ensemble Kalman filter to estimate the state and parameters of a simple Gequation model of the flame. Data assimilation provides an optimal estimate of the true state of a system, and improves the predicted shape and location of the flame. Parameter estimation uses the data to find a maximumlikelihood set of parameters for the model while simultaneously quantifying their uncertainty. At the same time, we identify deficiencies in the model with this approach. This process renders the Gequation model quantitatively accurate over the tested range of conditions. As a physicsbased model, we expect the Gequation model to extrapolate smoothly. This is going to be tested in future work. 
Tuesday, November 20, 2018 9:05AM  9:18AM 
M06.00006: A Bayesian Approach for Predicting Thermoacoustic Oscillations in an ElectricallyHeated Rijke Tube Francesco Garita, Hans Yu, Luca Magri, Matthew Juniper Predicting and eliminating thermoacoustic oscillations is a significant challenge in gas turbine design. Here we combine a thermoacoustic experiment with a thermoacoustic model and use data assimilation to infer the parameters of the model, rendering it predictive. The experiment is a vertical Rijke tube containing an electric heater (up to 300 Watts). The heater drives a base flow via natural convection, and thermoacoustic oscillations via velocitydriven heat release fluctuations. The growth/decay rates and frequencies of these oscillations are measured every few seconds. There are two models: one for the base flow and one for the acoustics. Both are unsteady. The parameters of the base flow model (Nusselt numbers and pressure loss coefficients) are estimated from many thousand measurements using an ensemble Kalman filter that accounts for both experimental and state and parameter errors. The parameters of the acoustic model are inferred by regression. This study shows that, with thorough Bayesian inference, a simple model with a few parameters can become a predictive model. The process reveals deficiencies in the model and, when combined with physical insight, shows how to improve it. This study proves the concept for small systems and prepares the ground for complex systems. 
Tuesday, November 20, 2018 9:18AM  9:31AM 
M06.00007: Experimentation with Porous Inert Material to Control Thermoacoustic Instabilities in Lean Direct Injection Combustion Ruth May, Mitchell Johnson, Ajay Agrawal Stringent environmental regulations require more efficient and cleaner jet engines for civil aviation applications. An interesting development has been the introduction of lean direct injection (LDI) combustion techniques. Previous research has proven that the LDI combustion yields lower nitrogen oxides and carbon monoxide emissions in gasturbine jet engines. However, thermoacoustic instabilities remain an issue with LDI combustion. Previous research conducted at the University of Alabama has indicated that the insertion of a Porous Inert Material (PIM) can reduce such instabilities. Positioned on the dump plane, the PIM interferes with the flow field in the corner and central recirculation regions. In this study, a single LDI injector was tested without the PIM to ascertain the equivalence ratio at which a strong instability occurs and establish a baseline case. Then, experiments at several test conditions of interest are performed to determine the effect of the PIM. Measurements include acoustic probes to record the sound spectra and OH* chemiluminescence imaging to characterize the reaction zone. PIM is shown to improve the acoustic performance although geometric optimization would be necessary to achieve the best results. 
Tuesday, November 20, 2018 9:31AM  9:44AM 
M06.00008: Suppression of chaotic thermoacoustic oscillations by external acoustic forcing Yu Guan, Vikrant Gupta, Karthik Kashinath, Larry K.B. Li Previous studies have shown that periodic and quasiperiodic oscillations in selfexcited thermoacoustic systems can be suppressed by applying acoustic forcing at a frequency sufficiently far from the natural frequency to cause a torusdeath bifurcation to lockin. However, whether this control strategy works on more complex thermoacoustic oscillations is not clear. In this experimental study, we investigate the forced synchronization of a ducted premixed flame oscillating chaotically. We find that the oscillation amplitude can be drastically reduced whenever lockin is achieved, regardless of how close the forcing frequency is to the dominant frequency of the strange attractor. This implies that an openloop controller designed for periodic or quasiperiodic oscillations should still be effective on chaotic oscillations, provided that lockin is achieved. However, the reverse is not necessarily true: an openloop controller designed for chaotic oscillations would amplify periodic and quasiperiodic oscillations if the forcing frequency was not sufficiently far from the natural frequency. It is important to recognize this difference when designing openloop control strategies for complex thermoacoustic oscillations.

Tuesday, November 20, 2018 9:44AM  9:57AM 
M06.00009: A LevelSet based Simulation Tool for Rapid Characterization of CombustionInstability Zheng Qiao, Yu Lv This work presents the efforts of the development of a numerical framework for the study of combustion instability. A levelset solver serves as the core of this framework, which solves the Gequation in order to describe the flame dynamics and behaviors under the impact of acoustic perturbations. Theoretical models are employed to delineate the acoustics propagation, reflection, and transmission along the outflow nozzle and combustion injection systems. The levelset solver is coupled with the theoretical models through carefully prescribed boundary conditions. The developed framework is validated in several canonical test problems, and then applied to a study of rockettype combustion configuration. A parametric study is performed in particular to understand the effects of flameshape, injectionsystem impedance, and nozzle operation conditions on the thermoacoustic behaviors. This numerical tool established from this work is expected to be effectively used to enable fast and basic characterization of combustion instability in realistic systems. 
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