Turbine cooling air estimation in thermodynamic simulations

Modern gas turbines utilize a high amount of the core mass flow rate for component cooling. Thus, a coherent thermodynamic gas turbine representation demands a well-modeled secondary air system, which is able to estimate mass flow rates depending on respective design decisions. In this paper, the focus is set on the estimation of turbine blade cooling air. For this purpose, five different methods are presented and analyzed. The described concepts can be split into empirical and semi-empirical approaches. The semi-empirical approaches, the Horlock [1], Jonsson [2] and the Halliwell [3] method, are able to predict the blade temperature based on a given cooling mass flow rate or the needed cooling air based on a given blade temperature. In contrast, the empirical methods, the Grieb [4] and the Walsh [5] method, can only predict the cooling air consumption. Due to the fully empirical approaches the field of application is limited to the considered engine structures. On the other hand, the empirical methods lead to a better convergence behavior in comparison to the semi-empirical approaches due to their relatively simple calculation methods. The selected cooling air estimations are implemented in the performance code DLRp2 [6–8]. Therefore, processes and methods are deployed that allow to estimate turbines with unlimited cooled stages. Additionally, an off-design procedure is proposed to consider the occurring stagnation temperature drop between stator and rotor based on a reference temperature offset. A simplified thermodynamic gas turbine model is used to analyze the different cooling air estimation methods. For this purpose, sensitivity analyses for the main cooling air parameters are carried out. Moreover, all methods that were developed for the most stressed operating point are compared. Finally, the simplified model is calibrated to NASA’s energy efficient engine [9].