Reduced-order prediction of unsteady spatial-temporal aerodynamics in a turbine cascade

A low-cost prediction method that effectively captures the detailed dynamics of unsteady motions is necessary for turbomachinery design. This paper applies two data-driven methods for unsteady cascade flow of a T106 low-pressure turbine with periodic incoming wakes under unknown conditions and unknown instants, respectively. For the prediction under unknown conditions, the dominant coherent structures of the unsteady flows are obtained using sparsity-promoting dynamic mode decomposition. An arbitrary case's sparse promoting modes serve as a basis for prediction and polynomial interpolation is employed to predict the characteristic parameters, including the amplitude and frequency. Based on the predicted characteristic parameters and sparse promoting modes, the flow fields within a range of Reynolds numbers can be reconstructed. The results show that the large-scale flow structure at different Reynolds numbers can be predicted with reasonable error. The detailed flow structure of cascade flow fields also agrees well with simulation results, demonstrating the method's excellent applicability. For the prediction under unknown instants, the dominant coherent structures of the unsteady flows are obtained using proper order decomposition. The extreme gradient boosting method is utilized to construct a surrogate model and predict the time coefficients at unknown times. Based on the dominating modes and predicted time coefficients, the flow fields within a range of unknown instants can be reconstructed. The cascade flow fields can be recovered with a relative error of less than 3 %. The vortex structures and blade surface pressure agree well with simulation results. The present work provides a promising approach for turbomachinery design and investigating underlying mechanisms with low data requirements.