Common proper orthogonal decomposition-based spatiotemporal emulator for design exploration

The present study develops a data-driven framework trained with high-fidelity simulation results to facilitate decision making for combustor designs. Its core is a surrogate model employing a machine-learning technique called kriging, which is uniquely combined with data-driven basis functions to extract and model the coherent structures underlying the flow dynamics. This emulation framework encompasses a sensitivity analysis of key design attributes, physics-guided classification of design parameter sets, and flow evolution modeling for a efficient design survey. A sensitivity analysis using Sobol indices and a decision tree is incorporated into the framework to better inform the model. The novelty of the proposed approach is the construction of the model through common proper orthogonal decomposition, allowing for data reduction and extraction of common coherent structures. As a specific example, the spatiotemporal evolution of the flowfields in swirl injectors is considered. The prediction accuracy of the mean flow features for new swirl injector designs is assessed, and the flow dynamics is captured in the form of power spectrum densities. The 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 an efficient survey of the design space.