Session X05: Thermoacoustics

Analytical study of coherence between flame heat release and acoustic pressure fluctuations

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 far-field acoustic pressure should have near unity values. Relatively little coherence data exist, however, and the limited data sets show much lower broadband heat release-pressure 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 near-field 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 near-field 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.   

Triggered Instabilities in a Rocket Motor. Part I. On the Role of Acoustic and Combustion Nonlinearities

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 time-dependent amplitudes of the natural modes of the chamber. The amplitude equations include linear and nonlinear self- and cross-coupling among the modes, as well as the quadratic and cubic acoustic nonlinearities. The combustion mass and energy source terms are modeled using a pressure exponent--timelag ($ 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 one-mode system has two linearly stable fixed points, while a two-mode 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 heat-release fluctuations.   

Triggered Instabilities in a Rocket Motor. Part II. One the Role of the Order of Acoustic and Combustion Nonlinearities

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 finite-amplitude 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 nonlinearities---fifth 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.   

Cluster-based control of self-excited thermoacoustic oscillations in a Rijke tube

We apply a cluster-based control strategy to a Rijke tube model to weaken its self-excited thermoacoustic oscillations. Specifically, we partition the pressure and heat-release-rate fluctuations of the system into discrete clusters within a low-dimensional feature space. We then identify the optimal feedback control laws via a Nelder--Mead simplex search applied to a cost function that balances the reduction in thermoacoustic amplitude with the actuation cost. We demonstrate that this data-driven control strategy can suppress a variety of self-excited 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.   

Effects of turbulence on the generation of indirect noise in an advanced gas-turbine combustor

Turbulent combustion occurring in gas turbine combustors leads to strong temperature and entropy inhomogeneities, which generate indirect combustion noise as they are accelerated through the nozzle stage of the engine. The objective of this work is to examine effects of turbulent and inhomogeneous flow field perturbation on indirect combustion noise. Due to the turbulent nature of the flow at the exit, a multimodal and non-planar thermal wave enters the nozzle downstream of the combustor. A two-dimensional linearized Euler equation (LEE) solver is employed to predict the flow field inside the nozzle, which allows for the evaluation of the generated acoustic waves. By considering canonical subsonic and supersonic nozzle geometries, the influence of the nozzle inlet and outlet Mach numbers, as well as the transverse effects inside the nozzle on the indirect noise generated by a turbulent flow field is discussed. Additionally, a transfer function based approach is assessed, as this method provides an efficient alternative for the evaluation of the indirect noise.   

Correlating hydrodynamic and acoustic fields in a turbulent combustor through community-based dimensionality reduction of vortical networks

We investigate the correlations between acoustic pressure oscillations and vortical interactions in the reactive field of a turbulent combustor susceptible to thermoacoustic instability. The spatial regions characterized by strong vortical interactions are recognized as vortical communities within the network space of weighted directed vortical networks. We subsequently reduce the dimensionality of these vortical networks using inter-community strengths and weighted centroids of the vortical communities. Our study reveals significant delayed correlations between inter-community interactions and acoustic pressure oscillations during the state of thermoacoustic instability. During the state of combustion noise, such correlations are lost due to incoherent spatiotemporal behavior in the reaction field of the combustor. Furthermore, these correlations provide insights into the critical regions detected within the reaction field during the states of intermittency and thermoacoustic instability in previous studies. Our work sheds light on the intricate relationship between vortical interactions and acoustic pressure behavior in turbulent combustors, offering insights into thermoacoustic instabilities and unsteady flows in fluid dynamics.   

Acoustic Emission of Thermodiffusive Unstable Premixed Lean Hydrogen-Air Slit Flames

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.

In this work, two-dimensional lean premixed hydrogen-air slit flames are investigated. The fuel-air-equivalence ratio is varied and the effects on general flame dynamics are investigated. For the various cases, intrinsic instabilities of the non-excited flame lead to strong cellular structures along the flame front, which cause constant pocket shedding and strong pressure fluctuations at the flame tip. Due to Markstein-length related effects, intrinsic differences have been found when compared to more widely investigated methane-air premixed flames. A more detailed investigation of the thermoacoustics by solving the acoustic perturbation equations which contain the input data from the flow field for the source terms enhances the specific understanding of the different acoustic source contributions and the overall acoustic field of hydrogen-air flames compared to methane-air flames.    

Effect of syngas composition on heat release rate response and thermoacoustic oscillations in swirl-stabilized combustors

In this study, we investigate the effect of hydrogen and carbon monoxide addition on the heat release rate response during self-excited thermoacoustic oscillations in a turbulent swirl-stabilized combustor. The combustor exhibits self-sustained limit cycle oscillations at a frequency closer to the fundamental acoustic mode for methane-air combustion above a critical Reynolds number. As the percentage of hydrogen and carbon monoxide addition is increased, we observe the emergence of quasiperiodic and period-2 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 high-speed chemiluminescence is used to analyze the mode and the flame structure that cause the amplification of thermoacoustic oscillations for different syngas compositions. Further, the phase-averaged 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.        

Experimental analyses of the transition to secondary thermoacoustic instabilities of H2-CH4-air premixed flames in slender tubes.

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, gas-wall temperature) the primary, low-amplitude, oscillations transform into secondary oscillations, which come with corrugated flames and higher amplitude acoustic waves.

An experimental set-up has been constructed, consisting in an open-closed round tube of D = 15.25 mm of extendable length L = 0 – 1.8m . The tube is filled with a selected mixture of air, methane and hydrogen which is ignited at the open end. Simultaneous measurements of pressure at various locations, along with high-speed videos of the flame, provide information on the interaction between the detected flame surface and pressure waves.

The transitional mechanism is observed to depend on the radial coordinate. To this end, theoretical analyses of a tube ideal acoustics with realistic non-homogeneous temperature distributions are performed. They predict axisymmetric acoustic velocity modes of much higher amplitude around the axis and, also, vorticity modes in the vicinity of the flame, which are compared against the effect of non-ideal pulsating flow profiles with preliminary PIV measurements to dilucidate the origin of the instability.   

Modeling the Effects of Spray Number Density on the Global Heat Release Dynamics of Spray Flames

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 Burke-Schumann diffusion flame configuration as a basis with the fuel introduced in the form of a spray of liquid droplets. The space-time dynamics in the model uses the fast-chemistry 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 Schvab-Zeldovich 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.   

Chaos suppression via genetic programming control in a self-excited thermoacoustic system

We demonstrate how genetic programming (GP) control can be used to suppress low-dimensional chaotic oscillations in a self-excited thermoacoustic system comprising a ducted laminar premixed flame. We start by initializing a generation of candidate model-free 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 closed-loop and open-loop forms of GP control with that of classic open-loop control based on time-periodic excitation. Our results show that GP closed-loop control outperforms both GP and classic open-loop control, achieving the highest reduction in thermoacoustic amplitude with the lowest actuator power. We also analyze the optimal GP-controlled 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 flame--acoustic coupling in a chaotic thermoacoustic system can be disrupted.