Physics-informed recurrent neural networks for linear and nonlinear flame dynamics |
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| Affiliation: | 1. Technical University of Darmstadt, Department of Mechanical Engineering, Simulation of reactive Thermo-Fluid Systems, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany;2. Engler-Bunte-Institute, Karlsruhe Institute of Technology, Engler-Bunte-Ring 7, 76131 Karlsruhe, Germany;3. Steinbuch Centre for Computing, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany;1. Lehrstuhl für Thermodynamik, Technische Universität München, Garching, Germany;2. Institute for Advanced Study, Technische Universität München, Garching, Germany;3. Institute of Energy Systems and Fluid-Engineering, Zürich Univerity of Applied Sciences, Winterthur, Switzerland;1. CORIA UMR 6614 CNRS, Site Universitaire du Madrillet, Saint Etienne du Rouvray 76801, France;2. EM2C lab, CNRS and CentraleSupélec, University Paris-Saclay, Gif-sur-Yvette 91192, France;1. State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China;2. School of Astronautics, Beihang University, Beijing 100191, China;1. University of Cambridge, Department of Engineering, Cambridge, UK;2. Université Libre de Bruxelles, École Polytechnique de Bruxelles, Aero-Thermo-Mechanics Laboratory, Brussels, Belgium |
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| Abstract: | This paper demonstrates the ability of recurrent neural networks (RNNs) to predict the linear and the nonlinear response of a premixed laminar flame to incoming velocity perturbations. We develop data-driven models, which require the velocity and heat release rate fluctuations as input data. Both time series are obtained from Direct Numerical Simulations (DNS) of a laminar flame. The length of the signals, and, hence, the cost of the simulation, is comparable to those used in the linear framework of System Identification. A more robust type of RNNs, namely long short term memory (LSTM), is employed to reduce the dependency on large datasets. The LSTM framework is modeled as a time series regression problem and four models are trained with decreasing data set lengths. All purely data-driven models accurately predict the unsteady time series of the heat release rate and, hence, the Flame Transfer Functions (FTFs). We further improve the model accuracy by incorporating a physical constraint, namely the low-frequency limit for perfectly-premixed flames, into the LSTM model. This step reduces the required data length compared to the purely data-driven approach. The proposed model, called PI-LSTM, is able to reproduce the linear and the nonlinear FTFs for amplitudes up to 50% of the laminar flame based on one numerical simulation, where the length of the time series is 100 ms. |
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