Physics-informed neural networks (PINNs) can be used to solve partial differential equations (PDEs) and identify hidden variables by incorporating the governing equations into neural network training. In this study, we apply PINNs to the assimilation of turbulent mean flow data and investigate the method's ability to identify inaccessible variables and closure terms from sparse data. Using high-fidelity large-eddy simulation (LES) data and particle image velocimetry (PIV) measured mean fields, we show that PINNs are suitable for simultaneously identifying multiple missing quantities in turbulent flows and providing continuous and differentiable mean fields consistent with the provided PDEs. In this way, consistent and complete mean states can be provided, which are essential for linearized mean field methods. The presented method does not require a grid or discretization scheme, is easy to implement, and can be used for a wide range of applications, making it a very promising tool for mean field-based methods in fluid mechanics.
Machine learning and automatized routines for parameter optimization have experienced a surge in development in the past years, mostly caused by the increasing availability of computing capacity. Gradient-free optimization can avoid cumbersome theoretical studies as input parameters are purely adapted based on output data. As no knowledge about the objective function is provided to the algorithms, this approach might reveal unconventional solutions to complex problems that were out of scope of classical solution strategies. In this study, the potential of these optimization methods on thermoacoustic problems is examined. The optimization algorithms are applied to a generic low-order thermoacoustic can-combustor model with several fuel injectors at different locations. We use three optimization algorithms -- the well established Downhill Simplex Method, the recently proposed Explorative Gradient Method, and an evolutionary algorithm -- to find optimal fuel distributions across the fuel lines while maintaining the amount of consumed fuel constant. The objective is to have minimal pulsation amplitudes. We compare the results and efficiency of the gradient-free algorithms. Additionally, we employ model-based linear stability analysis to calculate the growth rates of the dominant thermoacoustic modes. This allows us to highlight general and thermoacoustic-specific features of the optimization methods and results. The findings of this study show the potential of gradient-free optimization methods on combustor design for tackling thermoacoustic problems, and motivate further research in this direction.
Operation under stable conditions is an important prerequisite for gas turbine safety. While recent studies have focused primarily on acoustic design to avoid thermoacoustic instabilities, in the present study we shift the focus to improving stability margins by flame transfer function (FTF) modification. The flame transfer function of premixed flames is affected by various mechanisms such as variations in equivalence ratio, swirl fluctuations and shear layer instabilities. These mechanisms can be influenced by modifying parameters such as fuel distribution, injection location, swirl number or gas composition. Based on the Nyquist stability method we formulate criteria for how and at what frequencies the flame transfer function needs to be modified, in order to increase the stability margins of a thermoacoustic system. Gain and phase margin as well as the sensitivity function serve as measures of stability. The criteria are limited to single frequencies, which allows experimental FTF optimization with manageable effort. In the second part of this study it is shown that the Nyquist method can also be used as an efficient and compact way to determine whether the uncertainties of subsystems can affect the overall stability, without requiring eigenvalue calculations.
Lean premix combustion is the state of the art technology to achieve ultra low NOx emissions in stationary gas turbines. However, lean premix flames are susceptible to thermoacoustic instabilities, lean blowout and flashback. The design of such a combustion system is thus always related to the balancing between the levels of emissions and flame stability. Data-driven optimization methods and the adaptation of models through artificial intelligence have experienced a surge in development in the past years. The goal of this study is to show the potential of these methods for gas turbine burner development. A special pilot burner that features 61 different positions of fuel injection, manufactured by means of selective laser melting is used to modify the gas mixture close to the flame anchoring position. Each of the injector lines is equipped with an individual valve, such that the distribution of fuel-air mixture can be modified variously. Installed into an industrial MGT6000 swirl combustor, a data-driven optimization method is used to find an optimal subset of injection locations by automated experiments. The method uses a surrogate model that is based on Gaussian Processes Regression. It is adopted for experimental optimization, keeping measurement efforts to a minimum. The optimizer controls the fuel valves and uses live measurements to find a distribution that generates minimal NOx emissions, while ensuring flame stability. The solutions found by the optimization scheme are analyzed and advantages and limitations of the approach are discussed.
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