Equation-Oriented Meanline Method for Axial Turbine Performance Prediction Under Choking Conditions

Meanline models play a crucial role in turbine design and system-level analyses, facilitating rapid evaluation of design concepts and prediction of off-design performance. Most of the existing meanline methods are inadequate in predicting turbine performance under choking conditions. These models either neglect the impact of losses on choking, or increases the computational complexity significantly. This limitation is addressed in this work, presenting a novel meanline model. The choking state at each cascade is determined by maximizing the mass flow rate, while taking into account the effect of losses. Leveraging the method of Lagrange multipliers, the optimization problems are transformed into a set of equations that seamlessly integrate with the rest of the meanline model. The resulting system of equations is then solved simultaneously using efficient root-finding algorithms, resulting in fast and reliable convergence. Validation against experimental data from three different turbines demonstrates the model's ability to accurately predict mass flow rate, torque, and exit flow angles across single- and multi-stage turbines, with errors typically within ±2.5 % and ±5.0 % for mass flow rate and torque respectively, and within ±5 degrees for flow angles. The proposed approach represents a significant advancement in meanline modeling, offering improved accuracy and computational efficiency.