A co-kurtosis tensor based featurization of chemistry for scalable combustion simulations

Abstract

For turbulent reacting flow systems, identification of low-dimensional representations of the thermo-chemical state space is vitally important, primarily to significantly reduce the computational cost of device-scale simulations. Moreover, these simulations are often performed to gain fundamental insights into the inception of extreme/anomalous events such as flashbacks, flame extinction, blow-offs, thermoacoustic instabilities, etc., which can have detrimental effects on combustion efficiency and engine performance. With the scale of scientific investigations ever increasing, robust anomaly detection methods are becoming increasingly critical for judicious steering of these simulations and aiding the smooth operations of practical engines. Recent studies have shown that the fourth-order joint statistical moment tensor, i.e., co-kurtosis, effectively captures anomalies/outliers in scientific data. Accordingly, the primary objective of this work centers around leveraging the unique properties of the co-kurtosis tensor to drive low-cost and scalable combustion simulations and build robust algorithms for extreme event detection. In particular, the first part of this work addresses the issue of large computational costs involved in resolving chemistry in these simulations, while the second part focuses on employing a co-kurtosis based detection algorithm for capturing extreme events such as flame instabilities occurring in the reheat combustors of hydrogen-fired gas turbine engines.

To obtain low-dimensional manifolds (LDMs) that describe the original thermo-chemical state, principal component analysis (PCA) and its variants are widely employed. Recently, an alternative dimensionality reduction technique that focuses on higher-order statistics, co-kurtosis PCA (CoK-PCA), has been shown to provide an optimal LDM for effectively capturing the stiff chemical dynamics associated with spatiotemporally localized reaction zones. While its effectiveness has only been demonstrated based on a priori analyses with linear reconstruction, in this work, we employ nonlinear techniques to reconstruct the full thermo-chemical state and evaluate the efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA-/PCA-based dimensionality reduction (encoding) with an artificial neural network (ANN) based reconstruction (decoding) and examine, a priori, the reconstruction errors of the thermo-chemical state. In addition, we evaluate the errors in species production rates and heat release rates, which are nonlinear functions of the reconstructed state, as a measure of the overall accuracy of the dimensionality reduction technique. We employ three combustion test cases to assess CoK-PCA/PCA coupled with ANN-based reconstruction: a zero-dimensional (homogeneous) reactor for autoignition of a premixed ethylene/air mixture that has conventional single-stage ignition kinetics, a one-dimensional freely propagating premixed ethylene/air laminar flame, and a two-dimensional dataset representing turbulent autoignition of ethanol in a homogeneous charge compression ignition (HCCI) engine. Results from the analyses demonstrate the robustness of the CoK-PCA based LDM with ANN reconstruction in accurately capturing the data, specifically from the reaction zones.

For the anomaly detection problem, we focus on hydrogen combustion for its role in decarbonization. The highly reactive and diffusive nature of hydrogen presents significant challenges, such as flashbacks, flame instabilities, and thermoacoustic instabilities. For example, in the case of reheat burners of hydrogen-fired sequential gas turbine engines, intermittent temperature and pressure fluctuations result in flame instabilities, such as intermittent autoignition events at off-design locations that can adversely impact the engine's performance. To address this issue, we employ an unsupervised learning methodology based on the principal components obtained from the singular value decomposition (SVD) of the co-kurtosis tensor of input data to detect the early onset of spontaneous ignition kernels that occur due to temperature fluctuations in lean premixed hydrogen combustion at vitiated conditions. The datasets considered in our study include species mass fractions, temperature, pressure, and velocities obtained through direct numerical simulations at different operating conditions. We observe that the inception of an ignition kernel can be characterized by analyzing the changes in the magnitude of principal values and orientation of principal vectors. This forms the basis of the co-kurtosis tensor based detection algorithm, which is employed in this study for a one-dimensional hydrogen autoignition test case.