Challenge of Thermoacoustic Instabilities for Low-Emission, Carbon-Neutral Combustion Technology
One of the most important challenges facing humanity in the coming decades is implementing strategies to minimize global warming.
A key approach is reducing the emission of greenhouse gases (CO2, nitrous oxide, methane, ...) into the atmosphere. To achieve this, power generation from renewable sources, such as solar and wind energy, play an increasingly important role in meeting the energy demands of modern society. However, due to the highly fluctuating nature of renewable energy supply, it remains crucial to generate on demand additional power from other sources to ensure a stable energy provision.Gas turbines operating on carbon-free fuels are expected to meet the primary requirement for such power generation systems: providing operational flexibility across different power regimes with high ramp rates, while ensuring zero CO2 emissions. Nevertheless, several challenges must be addressed in developing this technology, such as the complete elimination of harmful gases such as NOx or N2O, which are associated with the combustion of carbon-free fuels such as hydrogen or ammonia. Yet another challenge for low-emission combustion technology is the increased propensity for thermoacoustic combustion instabilities. Controlling and avoidance of these instabilities is a critical challenge, as they generate strong vibrations that may severely damage an engine or render it inoperable. (See for instance the BBC Documentary Space Race discussing in Episode Four briefly the severe difficulties with combustion instability of the Saturn V rocket's F-1 engine. Start watching at about 5:00 minutes into the movie!)
Research of the TFD group focuses on thermoacoustic combustion instabilities, which result from feedback interactions of fluctuating heat release and acoustic waves.
To analyze and control this particular form of self-excited instability fluid mechanics, acoustics, and combustion science are combined in an interdisciplinary approach with methods of system identification and control theory. Intensive exchange with colleagues from research institutes in and outside Europe furthers our efforts.
Combustion thermoacoustic instability is a multi-physics, multi-scale problem that requires diverse modeling approaches and numerical tools capable of capturing the physics of flame, flow, and acoustics, as well as their interactions. In some cases, monolithic approaches -- such as high-fidelity numerical simulations -- are preferred, as resolving the problem by separating the physics and scales is not trivial (see Investigation and Prediction of High Frequency Dynamics in Distributed Combustion Systems with LES).
In other cases, such disentanglement is possible. As a result, the divide et impera approach is a established strategy for investigating combustion instability.
In this method, the overall thermoacoustic problem is separated into flame dynamics and flow–acoustic dynamics. Once these aspects are studied and modeled individually, they are integrated in a final step to evaluate the global thermoacoustic behavior of the system under investigation.
Flame Dynamics
Modeling flame dynamics involves accurately capturing the functional relationship between flow perturbations and the corresponding flame response. Fluctuations of the incoming flow -- such as variations in velocity or fuel concentration -- are regarded as input signals, while fluctuations in flame heat release rate are regarded as output. The latter is known to be the primary source of combustion noise and is therefore directly related to the generation of acoustic or entropy waves (see NoiSI - Combustion Noise and Dynamics of Partially Premixed Flames). Generally, the mapping between inputs and outputs can only be obtained through experiments or high-fidelity numerical simulations, such as Large Eddy Simulation (LES). For such LES, an adequate but computationally affordable description of combustion chemistry is needed. For this purpose, global mechanisms with optimized rate coefficients can be employed.
If LES is preferred over experiments, carefully designed signals are imposed mimicking external acoustic forcing. The subsequent modeling step involves capturing time series data corresponding to the desired inputs and outputs, and applying system identification (SI) techniques to them. If the linear flame response is sought, system identification (SI) can be understood as the application of correlation analysis to inputs and outputs to determine the linear filter best describing the system's impulse response. This impulse response in time domain corresponds to the Flame Transfer Function (FTF) in frequency domain.
To model the evolution of combustion instability from zero amplitude to limit-cycle acoustic oscillations, a nonlinear model of the flame response is required. Accordingly, a broadband forcing signal covering a wide range of amplitudes is necessary. Standard system identification methods, such as correlation analysis, are not suitable for capturing a nonlinear mapping between inputs and outputs. For this purpose, neural networks are often preferred (see PAML- Physics Augmented Machine Learning for Thermoacoustic Modeling). If a deeper understanding of the physics underlying the flame’s nonlinear response is sought, modeling through ordinary as well as universal differential equations (UDEs) is being developed as a promising approach (see FlameODE - Flame Response Modeling via Physically Interpretable Differential Equations).
In the design of a new burner, industry often relies on experience gained from previous designs. In many cases, a novel burner can be viewed as a geometric scaling of a well-established, reliable design. Consequently, deriving appropriate scaling laws for the flow becomes essential to ensure the performance of the `good old' burner is preserved. Moreover, robust operation -- once the flame is stabilized inside the combustion chamber -- can only be ensured if the flame response of the reference design is maintained under the new geometry and flow conditions, scaled according to known principles. The goal is hereby to find a universal or generally valid functionality for the flame response (see FRESCO - Flame Response Scaling in Combustion Dynamics).
Flow dynamics and acoustics
The volumetric expansion induced by fluctuations in the heat release rate generates acoustic waves that propagate, scatter, and reflect within the flame enclosure. These mechanisms are typically modeled using acoustic equations of varying complexity. Approaches range from quasi-1D acoustics based on low Mach number formulations — commonly employed in acoustic network models — to the 2D/3D Helmholtz equation, and further to the 2D/3D Linearized Navier–Stokes Equations (LNSE). The LNSE not only capture the behavior of acoustic waves within the enclosure, accounting for mean flow effects, but also their interaction with vortical and entropy waves. Note that, if mean flow effects are not of interest, the LNSE can be simplified to the Helmholtz equation.
The LNSE or the Helmholtz equation can be coupled with a flame dynamics model (as described above) to investigate the thermoacoustic stability of the system through the formulation of an eigenvalue problem. If the system is predicted to be unstable, geometric modifications or the addition of acoustic damping devices can be proposed to mitigate its susceptibility to thermoacoustic instability.
The linearized reactive flow equations: a monolithic approach to stability
In contrast to models that describe flow dynamics and acoustics -- where a separate flame model is required to close the system of equations -- a (Greek for ''cut from one stone'') approach captures the full physics of the fluctuating quantities without relying on external information or flame dynamics models. This is the case for the Linearized Reactive Flow Equations (LRFE), which can be seen as an extension of the LNSE. In the LRFE, the species transport equations -- including consumption and production by chemical reactions -- as well as the corresponding terms in the energy equation, are linearized around a base flow. If desired, flame dynamics -- characterized by the flame response to flow perturbations -- can be extracted by forcing the system of equations. However, unlike classical CFD, the system to be solved is linear and significantly smaller than that of high-fidelity numerical simulations such as LES, resulting in a substantial reduction in computational cost (see Linearized Reactive Flows).
The reconstruction problem
Typical experiments in engineering involve sparse measurements of a few observables. For example, in thermoacoustics, combustion chambers are often equipped with only a handful of microphones, among other sensors, to monitor pressure fluctuations in the system. Unfortunately, such sparse data may fail to capture important phenomena, such as high-pressure fluctuations occurring in locations where no microphone is present. This problem motivates the challenge of acoustic pressure reconstruction. Beyond reconstructing observables from limited measurements (e.g., pressure signals at discrete locations), there is significant interest in inferring hidden quantities -- such as velocity and heat release rate fluctuations -- which are often inaccessible through direct observation. The reconstruction of both observables and hidden quantities can be addressed using Physics-Informed Neural Networks (PINNs) or Bayesian inference (see Numerical Reconstruction of Thermo-Fluid Dynamic Fields from Sparse Pressure Data).
The inverse problem
In many engineering scenarios, the output of a given model is tied to design guidelines that must be fulfilled. In thermoacoustics, for instance, a specific flame response — characterized by its gain and phase over certain frequencies of interest — may be desired to ensure system stability once the flame is coupled with its acoustic environment. Which parameters (e.g., fuel and air mass flow rates, global equivalence ratio, degree of premixedness, wall temperature at the burner mouth, etc.) should be selected to achieve this target flame response? This constitutes a classical inverse problem and, as such, requires a well-defined optimization framework for its solution. With the advent of numerical solvers featuring automatic differentiation capabilities, solving such optimization problems is becoming increasingly accessible -- though many challenges still remain.
Output-Only System Identification
Inference of parameters in a dynamical system -- such as the coefficients of the impulse response characterizing flame dynamics -- is typically performed using input–output system identification. In this approach, an external input signal is applied to the system, and the resulting output is measured. Both signals are then used to estimate the parameters of interest. In contrast, output-only system identification does not involve any external forcing. Instead, the system is excited by its inherent (intrinsic) forcing mechanisms, such as turbulence or combustion noise (see Output-Only System Identification via Generalized Polynomial Chaos).
Intrinsic Thermoacoustic (ITA) instability
In thermoacoustics, the classical paradigm describes thermoacoustic instability as an unstable feedback loop between the sound source and its acoustic enclosure. Consequently, the characteristic frequency of the oscillation is expected to lie close to the natural frequency of the enclosure. If the flame is not confined, instability is traditionally considered impossible. However, this view has recently been challenged by a series of studies and experimental observations demonstrating that thermoacoustic instability can still occur in anechoic environments. This calls for a paradigm shift in the fundamental understanding of thermoacoustics -- one that also allows for scenarios in which instabilities arise at frequencies significantly different from the natural modes of the enclosure (see The Role of Acoustic Damping Devices in the Stability of Intrinsic Thermoacoustic Modes).