A physics-based correction model for swirl number prediction in axial swirlers with surrogate-assisted calibration

The prediction model for swirl number of swirler is essential for swirler design during gas turbine design process, and the underestimation of the predicted swirl number from the classic prediction model for axial swirler is a long standing question. The assumptions underlying the classic model were first checked, and the assumption that the direction of flow velocity aligns with the swirler blade was found to introduce the majority of the prediction error. A new prediction model for swirl number was then proposed with a correction coefficient k = 1.159 , which was evaluated through parameter fitting under various blade angles and diameter ratios. The massive data used for parameter fitting were generated from a data augmentation approach assisted by machine learning model, which requires only half of numerical simulations compared with the direct fitting method. The average and maximum relative errors decreased from 18.83 % and 24.72 % in the original formula to 7.27 % and 12.74 % in the new formula, respectively. When assessed under cold-flow conditions in a single-sector aero-engine combustor with a three-stage swirler, the model yields mean errors of 1.23 %, 1.60 %, and 6.37 % for the three stages. The larger third-stage error arises from momentum redistribution in its contraction–expansion passage, indicating that the model is best suited to approximately straight outlet passages. The proposed coefficient k is further interpreted as an effective aerodynamic correction for the mismatch between the ideal blade-angle-based outlet assumption and the actual momentum-flux distribution at the swirler exit. The proposed data augmentation and parameter fitting method also shows the potential to handle more complicated flow conditions, such as the flow separation with high blade angle and the swirling flow in other types of swirlers.