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Physics-Informed Data-Driven Prediction of Turbulent Reacting Flows with Lyapunov Analysis and Sequential Data Assimilation

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Data Analysis for Direct Numerical Simulations of Turbulent Combustion

Abstract

High-fidelity simulations of turbulent reacting flows enable scientific understanding of the physics and engineering design of practical systems. Whereas Direct Numerical Simulation (DNS) is the most suitable numerical tool to understand the physics, under-resolved and large-eddy simulations offer a good compromise between accuracy and computational effort in the prediction of engineering flows. This compromise speeds up the computations but reduces the space-and-time accuracy of the prediction. The objective of this chapter is to (i) evaluate the predictability horizon of turbulent simulations with chaos theory, and (ii) enable the space-and-time-accurate prediction of rare and transient events using a Bayesian statistical learning approach based on data assimilation. The methods are applied to DNS of Moderate or Intense Low-oxygen Dilution (MILD) combustion. The predictability provides an estimate of the time horizon within which the occurrence of ignition kernels and deflagrative modes, which are considered here as rare and transient events, can be accurately predicted. The accurate detection of ignition kernels and their evolution towards deflagrative structures are well captured on a coarse (under-resolved) grid when data is assimilated from a costly refined DNS. Physically, such an accurate prediction is important to understand the stabilization mechanism of MILD combustion. These techniques enable the space-and-time-accurate prediction of rare and transient events in turbulent flows by combining under-resolved simulations and experimental data, for example, from engine sensors. This opens up new possibilities for on-the-fly calibration of reduced-order models for turbulent reacting flows.

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Acknowledgements

The authors acknowledge the support of the Technical University of Munich - Institute for Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under grant agreement no. 291763. L. Magri also acknowledges the Royal Academy of Engineering Research Fellowships Scheme. This work was performed using resources provided by the Cambridge Service for Data Driven Discovery (CSD3) operated by the University of Cambridge Research Computing Service (www.csd3.cam.ac.uk), provided by Dell EMC and Intel using Tier-2 funding from the Engineering and Physical Sciences Research Council (capital grant EP/P020259/1), and DiRAC funding from the Science and Technology Facilities Council (www.dirac.ac.uk). The authors acknowledge Prof. Cant for providing the code SENGA2. Francisco Huhn and Hans Yu are gratefully acknowledged for their invaluable inputs on Lyapunov analysis (Sect. 9.2) and data assimilation (Sect. 9.3), respectively.

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Authors and Affiliations

  1. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    Luca Magri

  2. (visiting) Institute for Advanced Study, Technische Universität München, Lichtenbergstraße 2a, 85747, Garching, Germany

    Luca Magri

  3. Fakultät für Maschinenwesen, Technische Universität München, Boltzmannstraße 15, 85747, Garching, Germany

    Nguyen Anh Khoa Doan

  4. Institute for Advanced Study, Technische Universität München, Lichtenbergstraße 2a, 85747, Garching, Germany

    Nguyen Anh Khoa Doan

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  1. Luca Magri
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Correspondence to Luca Magri .

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Editors and Affiliations

  1. Institute for Combustion Technology, RWTH Aachen University, Aachen, Germany

    Heinz Pitsch

  2. Institute for Combustion Technology, RWTH Aachen University, Aachen, Germany

    Antonio Attili

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Magri, L., Doan, N.A.K. (2020). Physics-Informed Data-Driven Prediction of Turbulent Reacting Flows with Lyapunov Analysis and Sequential Data Assimilation. In: Pitsch, H., Attili, A. (eds) Data Analysis for Direct Numerical Simulations of Turbulent Combustion. Springer, Cham. https://doi.org/10.1007/978-3-030-44718-2_9

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