Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session X05: Thermoacoustics 
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Chair: Sarma Rani, University of Alabama in Huntsville Room: 102A 
Tuesday, November 21, 2023 8:00AM  8:13AM 
X05.00001: Analytical study of coherence between flame heat release and acoustic pressure fluctuations Sungyoung Ha, Timothy C Lieuwen A number of modeling and experimental studies have considered the role of direct combustion noise relative to other noise sources from aircraft engines. Indeed, in low Mach number flows, these analyses predict that direct combustion noise is dominant. This implies that the coherence between heat release fluctuations and farfield acoustic pressure should have near unity values. Relatively little coherence data exist, however, and the limited data sets show much lower broadband heat releasepressure coherence values typically on the order of 0.1 0.3. This implies that either direct combustion noise is the not the dominant noise production mechanism, that there is a problem with the measurement, or that additional confinement or near field effects reduce coherence. This study analytically considers the role of nearfield effects on these reduced coherence values. The coherence between the globally integrated heat release rate and acoustic pressure fluctuations is analytically and numerically investigated. Asymptotic methods are applied to a canonical problem to investigate scaling laws. Finally, a Green's function approach is investigated as a method to study the effects of a confined boundary. These studies suggest that nearfield effects do reduce coherence values but do not fully account for the values seen in experimental measurements. These results demonstrate that significant open questions exist today about the role of direct combustion noise. 
Tuesday, November 21, 2023 8:13AM  8:26AM 
X05.00002: Triggered Instabilities in a Rocket Motor. Part I. On the Role of Acoustic and Combustion Nonlinearities Swarnalatha K. V. We investigate the role of acoustic and combustion nonlinearities in the occurrence of triggered longitudinal instabilities in a cylindrical combustion chamber with axially varying mean properties. By applying the Galerkin method of weighted averaging, the conservation equations are reduced to nonlinear ordinary differential equations governing the timedependent amplitudes of the natural modes of the chamber. The amplitude equations include linear and nonlinear self and crosscoupling among the modes, as well as the quadratic and cubic acoustic nonlinearities. The combustion mass and energy source terms are modeled using a pressure exponenttimelag ($ extsf{n}$$ar{ au}$) model, which gives rise to the combustion nonlinearities. The effects of acoustic nonlinearities on triggering are first studied by dropping the combustion terms. It is seen that a onemode system has two linearly stable fixed points, while a twomode system has three stable fixed points. We demonstrate quantitatively that the acoustic nonlinearities can result in a triggered bifurcation between any two stable fixed points and in either direction. The direction of bifurcation is conclusively established by considering the dynamical equations governing the perturbations imposed on the reference fixed point, and then varying the magnitude of perturbations to illustrate triggering to all other stable fixed points. We compute the basin of attraction for a visual representation of the initial conditions (or perturbations) leading to a triggered bifurcation, or to unstable oscillations growing without limit. The inclusion of combustion nonlinearities has a marginal effect on the number and coordinates of the stable fixed points, at least for small values of the control parameter determining the magnitude of combustion nonlinearities. However, even for small values of this parameter, it is seen that the combustion terms render the fixed points extremely sensitive to the magnitude of perturbations, which is visually captured in the basin of attraction. Based on these results, a novel nonlinear dynamics perspective is proposed for instability, which is more nuanced than the widely accepted mechanism of the constructive interference of acoustic and heatrelease fluctuations. 
Tuesday, November 21, 2023 8:26AM  8:39AM 
X05.00003: Triggered Instabilities in a Rocket Motor. Part II. One the Role of the Order of Acoustic and Combustion Nonlinearities Sarma L Rani, Swarnalatha K. V. In the companion presentation, we demonstrated that triggered longitudinal instabilities can be realized when the governing equations containing only the acoustic nonlinearities were used to evolve finiteamplitude perturbations imposed on the base state of the combustor. We also identified the specific roles of acoustic and combustion nonlinearities in the occurrence of triggering. In the current study, we shift our focus toward understanding how the orders of the two types of nonlinearities influence stability. Three separate combustion response models are considered, which give rise to different functional forms and orders of combustion nonlinearitiesfifth order being the highest. We perform a systematic analysis of the effects of including the quadratic and/or cubic acoustic terms in conjunction with the combustion nonlinearities arising from each of the three models. Triggering was observed when the acoustic quadratic terms were retained and the cubic terms dropped, but was not obtained for the reverse scenario. Triggering also arises when all acoustic and combustion nonlinearities are included. It is seen that that the stability behavior when considering all acoustic terms with the fifth order combustion model is only marginally different than with the third order model. 
Tuesday, November 21, 2023 8:39AM  8:52AM 
X05.00004: Clusterbased control of selfexcited thermoacoustic oscillations in a Rijke tube Hiromi Kimishima, Bo Yin, Vikrant Gupta, Larry K.B. Li We apply a clusterbased control strategy to a Rijke tube model to weaken its selfexcited thermoacoustic oscillations. Specifically, we partition the pressure and heatreleaserate fluctuations of the system into discrete clusters within a lowdimensional feature space. We then identify the optimal feedback control laws via a NelderMead simplex search applied to a cost function that balances the reduction in thermoacoustic amplitude with the actuation cost. We demonstrate that this datadriven control strategy can suppress a variety of selfexcited thermoacoustic oscillations with minimal actuation cost, even in the presence of strong measurement noise and time delays in the control loop. Overall, this approach shows promise for improving the stability and performance of thermoacoustic systems, opening up potential applications in fields such as energy conversion and combustion. 
Tuesday, November 21, 2023 8:52AM  9:05AM 
X05.00005: Effects of turbulence on the generation of indirect noise in an advanced gasturbine combustor Benyamin Krisna, Davy Brouzet, Matthias Ihme

Tuesday, November 21, 2023 9:05AM  9:18AM 
X05.00006: Correlating hydrodynamic and acoustic fields in a turbulent combustor through communitybased dimensionality reduction of vortical networks Ankit Sahay, Muralikrishnan G Meena, R. I. Sujith

Tuesday, November 21, 2023 9:18AM  9:31AM 
X05.00007: Acoustic Emission of Thermodiffusive Unstable Premixed Lean HydrogenAir Slit Flames Borja P Pedro Beltran, Matthias Meinke, Wolfgang Schröder Combustion noise is coupled to fluctuations of the flow field variables. The heat release fluctuations are a direct noise source term caused by perturbations of the flame surface generated by velocity fluctuations, which are generated by the flow field. Flame front perturbations are damped or amplified by intrinsic stability phenomena, like hydrodynamic and preferential diffusion effects. 
Tuesday, November 21, 2023 9:31AM  9:44AM 
X05.00008: Effect of syngas composition on heat release rate response and thermoacoustic oscillations in swirlstabilized combustors Meenatchidevi Murugesan, Arvind Raj Sakthivel, Manjunath Mailarappa Meti, Abhijit Kumar Kushwaha In this study, we investigate the effect of hydrogen and carbon monoxide addition on the heat release rate response during selfexcited thermoacoustic oscillations in a turbulent swirlstabilized combustor. The combustor exhibits selfsustained limit cycle oscillations at a frequency closer to the fundamental acoustic mode for methaneair combustion above a critical Reynolds number. As the percentage of hydrogen and carbon monoxide addition is increased, we observe the emergence of quasiperiodic and period2 oscillations along with significant increase in acoustic pressure amplitude. However, the thermoacoustic amplitude reduces with further increase in the hydrogen percentage. Dynamic mode decomposition of highspeed chemiluminescence is used to analyze the mode and the flame structure that cause the amplification of thermoacoustic oscillations for different syngas compositions. Further, the phaseaveraged images corresponding to different nonlinear states are investigated. This study shows that moderate percentage of hydrogen modify the spatial distribution of heat release rate and cause the amplification of thermoacoustic oscillations. 
Tuesday, November 21, 2023 9:44AM  9:57AM 
X05.00009: Experimental analyses of the transition to secondary thermoacoustic instabilities of H2CH4air premixed flames in slender tubes. Pedro GatónPérez, Daniel MartínezRuiz, Victor Muntean Thermoacoustic coupling between a premixed flame and the tube that encloses it causes the reactive front to switch from a steadily propagating state into an oscillatory one. For certain parametric sets (tube length, mixture equivalence ratio, gaswall temperature) the primary, lowamplitude, oscillations transform into secondary oscillations, which come with corrugated flames and higher amplitude acoustic waves. 
Tuesday, November 21, 2023 9:57AM  10:10AM 
X05.00010: Modeling the Effects of Spray Number Density on the Global Heat Release Dynamics of Spray Flames Vishal Acharya A large body of work exists for reduced order modeling of the response of premixed and gaseous diffusion flames, however, the focus on spray flames is limited. Recently, the author has presented reduced order models for the response of spray flames to velocity disturbances with a focus on both the flame shape and heat release. The model uses the classical BurkeSchumann diffusion flame configuration as a basis with the fuel introduced in the form of a spray of liquid droplets. The spacetime dynamics in the model uses the fastchemistry limit applied to the mixture fraction equation for both the gaseous and liquid phases. These equations are coupled through evaporation of the liquid droplets in effect resulting in an extension to the SchvabZeldovich formulation. While several coupling mechanisms have been identified for thermoacoustic instabilities, a mechanism unique to spray flames is the dynamics of spray injection, oscillatory evaporation and atomization. This results in new control parameters related to a Damkohler number for vaporization, oscillatory droplet physics, spray injection, to name a few. The results from this formulation present changes to the local and global flame dynamics due to oscillatory spray dynamics. More specifically, the model considers the dynamics of spray number density and its effects on both the local and global response of spray flames. 
Tuesday, November 21, 2023 10:10AM  10:23AM 
X05.00011: Chaos suppression via genetic programming control in a selfexcited thermoacoustic system Bo Yin, Zhijian Yang, Yu Guan, Stephane Redonnet, Larry K.B. Li We demonstrate how genetic programming (GP) control can be used to suppress lowdimensional chaotic oscillations in a selfexcited thermoacoustic system comprising a ducted laminar premixed flame. We start by initializing a generation of candidate modelfree control laws, which are evaluated based on a predefined cost function that balances the reduction in thermoacoustic amplitude with the actuator power consumed. To evolve the control laws from one generation to the next, we use a tournament algorithm involving genetic operations such as replication, elitism, crossover, and mutation. We compare the performance of both closedloop and openloop forms of GP control with that of classic openloop control based on timeperiodic excitation. Our results show that GP closedloop control outperforms both GP and classic openloop control, achieving the highest reduction in thermoacoustic amplitude with the lowest actuator power. We also analyze the optimal GPcontrolled state using various tools from complex systems theory, which enables us to identify the key chaos suppression mechanisms and gain new insights into how the flameacoustic coupling in a chaotic thermoacoustic system can be disrupted. 
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