Combustion instability in gas turbines and rocket engines, as one of the most challenging problems in combustion research, arises from the complex interactions among flames, which are also influenced by chemical reactions, heat and mass transfer, and acoustics. Identifying and understanding combustion instability is essential to ensure the safe and reliable operation of many combustion systems, where exploring and classifying the dynamical behaviors of complex flame systems is a core take. To facilitate fundamental studies, the present work concerns dynamical mode recognition of coupled flame oscillators made of flickering buoyant diffusion flames, which have gained increasing attention in recent years but are not sufficiently understood. The time series data of flame oscillators are generated by fully validated reacting flow simulations. Due to limitations of expertise-based models, a data-driven approach is adopted. In this study, a nonlinear dimensional reduction model of variational autoencoder (VAE) is used to project the simulation data onto a 2-dimensional latent space. Based on the phase trajectories in latent space, both supervised and unsupervised classifiers are proposed for datasets with well known labeling and without, respectively. For labeled datasets, we establish the Wasserstein-distance-based classifier (WDC) for mode recognition; for unlabeled datasets, we develop a novel unsupervised classifier (GMM-DTWC) combining dynamic time warping (DTW) and Gaussian mixture model (GMM). Through comparing with conventional approaches for dimensionality reduction and classification, the proposed supervised and unsupervised VAE-based approaches exhibit a prominent performance for distinguishing dynamical modes, implying their potential extension to dynamical mode recognition of complex combustion problems.

Oscillatory combustion in aero engines and modern gas turbines often has significant adverse effects on their operation, and accurately recognizing various oscillation modes is the prerequisite for understanding and controlling combustion instability. However, the high-dimensional spatial-temporal data of a complex combustion system typically poses considerable challenges to the dynamical mode recognition. Based on a two-layer bidirectional long short-term memory variational autoencoder (Bi-LSTM-VAE) dimensionality reduction model and a two-dimensional Wasserstein distance-based classifier (WDC), this study proposes a promising method (Bi-LSTM-VAE-WDC) for recognizing dynamical modes in oscillatory combustion systems. Specifically, the Bi-LSTM-VAE dimension reduction model was introduced to reduce the high-dimensional spatial-temporal data of the combustion system to a low-dimensional phase space; Gaussian kernel density estimates (GKDE) were computed based on the distribution of phase points in a grid; two-dimensional WD values were calculated from the GKDE maps to recognize the oscillation modes. The time-series data used in this study were obtained from numerical simulations of circular arrays of laminar flame oscillators. The results show that the novel Bi-LSTM-VAE method can produce a non-overlapping distribution of phase points, indicating an effective unsupervised mode recognition and classification. Furthermore, the present method exhibits a more prominent performance than VAE and PCA (principal component analysis) for distinguishing dynamical modes in complex flame systems, implying its potential in studying turbulent combustion.