58341 - Gradient-Free Optimization in Thermoacoustics: Application to a Low-Order Model 

In modern combustion systems, additional air is added to the fuel-air mixture to reduce emission of harmful combustion by-products such as nitrogen oxides. The so-called lean premix flames are closely coupled to the flow field, making them highly susceptible to fluctuations in pressure, flow velocity and gas composition. These cause a fluctuating heat release in the flame, which in turn acts as an acoustic source. The feedback cycle between the combustion chamber and the flame can cause thermoacoustic instabilities that can severely affect the performance of the machines. In order to increase the stability of the flames, an increased equivalence ratio and thus increased nitrogen production must be accepted, at least locally. Therefore, the combustion chamber design is always related to the balancing between the levels of emissions and pressure pulsations. In practice, this development process involves computationally and financially costly simulations and experiments, and is based to a large extent on the experience and intuition of the engineers. Machine learning and the adaptation of models through artificial intelligence have experienced a surge in development in the past years, mainly caused by the increasing availability of computing capacity. Data-driven optimization can avoid cumbersome theoretical studies and might be able to find unconventional solutions for complex problems. The goal of this study is to show the potential of these optimization methods on thermoacoustic problems and compare different optimization methods.

In this study we show how optimization algorithms can be applied to thermoacoustic systems in order to reduce pulsations. We use a generic low-order thermoacoustic can-combustor model with fuel injectors at different locations. The acoustics are assumed to be one-dimensional and an interaction with the equivalence ratio is taken into account at the fuel injectors. The transport of equivalence ratio perturbations is modelled by a diffusion-convection equation, which is solved in the frequency domain. A state-space model is fit to the solution to enable time-domain simulations. A semi-empirical model is used to estimate the flame's reaction to the equivalence ratio fluctuations. By including non-linear effects in the model, unstable configurations can be analysed in the time domain and oscillation amplitudes can be predicted. By varying the location of the injectors and the axial distribution of fuel the stability of the thermoacoustic system is affected. Even for a small number of fuel injectors the analysis of the pulsations in the generic thermoacoustic system becomes non-trivial. We use a recently published optimization algorithm (Explorative Gradient Method) to find optimal fuel distributions and locations of fuel injectors while maintaining the amount of consumed fuel constant. The objective is to have minimal pulsation amplitudes. We compare this algorithm to other commonly used ones (e.g., genetic algorithms, simplex or adjoint) and highlight general and thermoacoustic-specific features. We discuss in detail a simplex-based optimizations algorithm which was adopted to find global maxima. The findings of this study show the potential of data-driven optimization methods on combustor design in order to tackle thermoacoustic problems and motivate further research in this direction.