Common proper orthogonal decomposition-based emulation and system identification for model-based analysis of combustion dynamics
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For high-performance power generation and propulsion systems, such as those of airbreathing and rocket engines, physical experiments are expensive due to the harsh requirements of operating conditions. In addition, it is difficult to gain insight into the underlying mechanisms of the physiochemical processes involved because of the typical reliance upon optical diagnostics for experimental measurements. High-fidelity simulations can be employed to capture more salient features of the flow and combustion dynamics in engines, but these computations are often too expensive and time-consuming for design and development purposes. To enable usage of modeling/simulation in the design workflow, the present study proposes a data-driven framework for modeling and analysis to facilitate decision making for combustor designs. Its core is a surrogate model employing a machine-learning technique called kriging, which is combined with data-driven basis functions to extract and model the underlying coherent structures from high-fidelity simulation results. This emulation framework encompasses key design parameter sensitivity analysis, physics-guided classification of design parameter sets, and flow evolution modeling for efficient design survey. A sensitivity analysis using Sobol’ indices and a decision tree are incorporated into the framework to better inform the model. This information improves the surrogate model training process, which employs basis functions as regression functions over the design space for the kriging model. The novelty of the proposed approach is the construction of the surrogate model through Common Proper Orthogonal Decomposition, allowing for data-reduction and extraction of common coherent structures. The accuracy of prediction of mean flow features for new swirl injector designs is assessed and the dynamic flowfield is captured in the form of power spectrum densities. This data-driven framework also demonstrates the uncertainty quantification of predictions, providing a metric for model fit. The significantly reduced computation time required for evaluating new design points enables efficient survey of the design space. To further utilize model results, a data analytic methodology to quantify the combustion dynamics is used to link the component-level simulations to the system-level stability performance. Comprehensive combustion stability analysis and a good understanding of the coupling process would reduce the amount of testing and level of capital required for engine development. The proposed methodology leverages high-fidelity large eddy simulation (LES) in combination with machine-learning techniques to quantify the spatial combustion response, which is intended to serve as an acoustic source term in the generalized wave equation. The acoustic eigenmode analysis can be used to assess the stability of propulsion systems. Treating the extracted coherent structures as time series signals, the combustion response can be deduced through autoregressive model selection, accounting for data sparsity, multicollinearity, and noise. The results show that acoustic-vortical dynamics is the dominant mechanism determining flame stabilization, affecting the acoustic modes of the combustion chamber. The methodology not only accounts for the distributed combustion response through incorporation of proper orthogonal decomposition (POD) analysis, but also uses the data to identify relevant time scales, replacing the need for forcing and focusing on intrinsic dynamics. A design survey of the system stability based on the injector dynamics can then be conducted using the surrogate model for the combustion response.