We propose an anomaly detection method for multi-variate scientific data based on analysis of high-order joint moments. Using kurtosis as a reliable measure of outliers, we suggest that principal kurtosis vectors, by analogy to principal component analysis (PCA) vectors, signify the principal directions along which outliers appear. The inception of an anomaly, then, manifests as a change in the principal values and vectors of kurtosis. Obtaining the principal kurtosis vectors requires decomposing a fourth order joint cumulant tensor for which we use a simple, computationally less expensive approach that involves performing a singular value decomposition (SVD) over the matricized tensor. We demonstrate the efficacy of this approach on synthetic data, and develop an algorithm to identify the occurrence of a spatial and/or temporal anomalous event in scientific phenomena. The algorithm decomposes the data into several spatial sub-domains and time steps to identify regions with such events. Feature moment metrics, based on the alignments of the principal kurtosis vectors, are computed at each sub-domain and time step for all features to quantify their relative importance towards the overall kurtosis in the data. Accordingly, spatial and temporal anomaly metrics for each sub-domain are proposed using the Hellinger distance of the feature moment metric distribution from a suitable nominal distribution. We apply the algorithm to two turbulent auto-ignition combustion cases and demonstrate that the anomaly metrics reliably capture the occurrence of auto-ignition in relevant spatial sub-domains at the right time steps.
A three-dimensional direct numerical simulation (DNS) is performed for a turbulent hydrogen-air flame, represented with detailed chemistry, stabilized in a model gas-turbine combustor. The combustor geometry consists of a mixing duct followed by a sudden expansion and a combustion chamber, which represents a geometrically simplified version of Ansaldo Energia's GT26/GT36 sequential combustor design. In this configuration, a very lean blend of hydrogen and vitiated air is prepared in the mixing duct and convected into the combustion chamber, where the residence time from the inlet of the mixing duct to the combustion chamber is designed to coincide with the ignition delay time of the mixture. The results show that when the flame is stabilized at its design position, combustion occurs due to both autoignition and flame propagation (deflagration) modes at different locations within the combustion chamber. A chemical explosive mode analysis (CEMA) reveals that most of the fuel is consumed due to autoignition in the bulk-flow along the centerline of the combustor, and lower amounts of fuel are consumed by flame propagation near the corners of the sudden expansion, where the unburnt temperature is reduced by the thermal wall boundary layers. An unstable operating condition is also identified, wherein periodic auto-ignition events occur within the mixing duct. These events appear upstream of the intended stabilization position, due to positive temperature fluctuations induced by pressure waves originating from within the combustion chamber. The present DNS investigation represents the initial step of a comprehensive research effort aimed at gaining detailed physical insight into the rate-limiting processes that govern the sequential combustor behavior and avoid the insurgence of the off-design auto-ignition events.
Direct numerical simulations are performed to investigate the transient upstream flame propagation (flashback) through homogeneous and fuel-stratified hydrogen-air mixtures transported in fully developed turbulent channel flows. Results indicate that, for both cases, the flame maintains steady propagation against the bulk flow direction, and the global flame shape and the local flame characteristics are both affected by the occurrence of fuel stratification. Globally, the mean flame shape undergoes an abrupt change when the approaching reactants transition from an homogeneous to a stratified mixing configuration. A V-shaped flame surface, whose leading-edge is located in the near-wall region, characterizes the nonstratified, homogeneous mixture case, while a U-shaped flame surface, whose leading edge propagates upstream at the channel centerline, distinguishes the case with fuel stratification (fuel-lean in the near-wall region and fuel-rich away from the wall). The characteristic thickness, wrinkling, and displacement speed of the turbulent flame brush are subject to considerable changes across the channel due to the dependence of the turbulence and mixture properties on the distance from the channel walls. More specifically, the flame transitions from a moderately wrinkled, thin-flamelet combustion regime in the homogeneous mixture case to a strongly wrinkled flame brush more representative of a thickened-flame combustion regime in the near-wall region of the fuel-stratified case. The combustion regime may be related to the Karlovitz number, and it is shown that a nominal channel-flow Karlovitz number, Kainch, based on the wall-normal variation of canonical turbulence (tη=(ν/ϵ)1/2) and chemistry (tl=δl/Sl) timescales in fully developed channel flow, compares well with an effective Karlovitz number, Kaflch, extracted from the present DNS datasets using conditionally sampled values of tη and tl in the immediate vicinity of the flame (0.1
We describe our work to embed a Python interpreter in S3D, a highly scalable parallel direct numerical simulation reacting flow solver written in Fortran. Although S3D had no in-situ capability when we began, embedding the interpreter was surprisingly easy, and the result is an extremely flexible platform for conducting machine-learning experiments in-situ.