Two-Step Cross-Variable Gappy Pod for Multi-Scalar Field From Sparse Temperature Measurements in Turbulent Combustion

This study proposes the Two-step Cross-Variable Gappy POD to reconstruct multiple scalar fields from sparse temperature measurements.The method extracts the spatial correlations between temperature and target scalar via POD, predicts the target scalars at sensor locations from temperature inputs and reconstructs the full 3-D scalar field by Gappy POD.The approach is validated for a piloted methane-air turbulent jet flame using OpenFOAM-based parametric snapshot database for reconstruction of temperature, O 2 , NO, OH, CO, and H 2 O.The O 2 has a strong and spatially consistent correlation with temperature, leading to the reconstruction performance comparable to single-step Gappy POD.In contrast, the OH and CO exhibit near-field deviation due to the local reaction-zone structure and sensitivity to the mixing conditions.The H 2 O involves a high Pearson correlation coefficient, which does not necessarily guarantee accurate reconstruction of radial gradients and widths of the flame.The NO requires additional scaling correction due to discrepancy in the scales between simulation and measurement.Overall, the Pearson correlation serves as a useful indicator for the Two-step Cross-Variable Gappy POD, while accurate reconstruction requires additional consideration for scalar-specific spatial structures, sensor locations and scale discrepancy between simulation and measurement.