Michael Mueller
Department of Mechanical and Aerospace Engineering,
Princeton University

"Generalized and Computationally Efficient Modeling of Turbulent Reacting Flows: A Union of Theory and Machine Learning"

Wednesday, Nov 8, 2023


Computational modeling of turbulent reacting flows is immensely challenging due to not only the broad range of length scales and time scales of the turbulence and combustion phenomena but also due to the large number of chemical species required to describe hydrocarbon chemistry, resulting in an extremely high-dimensional thermochemical state-space. “Brute-force” turbulent combustion models tackle this extremely high-dimensionality head-on by solving transport equations for every chemical species at great computational cost but without any approximation to the combustion processes. Conversely, traditional manifold-based turbulent combustion models reduce the dimensionality of the thermochemical state-space by a priori projecting the thermochemical state onto a very low-dimensional manifold by presuming that combustion occurs in a single asymptotic “mode” decreasing the computational cost but restricting generality to real “multi-modal” combustion processes. In this seminar, a new modeling framework will be presented that breaks this fundamental trade-off, leading to a very general turbulent combustion model that is also computationally efficient. On the theoretical front, two-dimensional manifold equations are derived starting from thermodynamic considerations to describe general “multi-modal” combustion. Alone, these theoretical advancements would not be practically useful for engineering-fidelity simulations due to key unclosed terms with no obvious physics-based pathways for closure and being too cumbersome for traditional computational algorithms for manifold-based models. These issues are overcome by leveraging elements of machine learning to (1) close key unclosed terms using data-based models and (2) using ‘on-the-fly’ learning to avoid preprocessing the manifold-based combustion model. The work demonstrates that physics-based approaches and data-based approaches are not an either/or paradigm but rather a both/and paradigm, with data-based approaches from the machine learning community used to enhance and enable more general physics-based models in this work.

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