Multistage Compressor and Turbine Modeling for the Prediction of the Maximum Turbine Speed Resulting From Shaft Breakage

A mathematical model for the prediction of the maximum speed of a high pressure turbine following a shaft failure event was developed. The model predicts the high pressure compressor and ducting system pre- and poststall behaviors such as rotating stall and surge after the shaft breakage. The corresponding time-dependent high pressure turbine inlet conditions are used to calculate the turbine maximum speed, taking into account friction and blade and vane tip clearance variations as a result of the rearward movement of the turbine and destruction of the turbine blading. The compressor and ducting system is modeled by a one-dimensional, stage-by-stage approach. The approach uses a finite-difference numerical technique to solve the nonlinear system of equations for continuity, momentum, and energy including source terms for the compressible flow through inlet ducting, compressor, and combustor. The compressor blade forces and shaft work are provided by a set of quasisteady state stage characteristics being valid for prestall and poststall operations. The maximum turbine speed is calculated from a thermodynamic turbine stand-alone model, derived from a performance synthesis program. Friction and blade and vane tip clearance variations are determined iteratively from graphical data depending on the axial rearward movement of the turbine. The compressor and ducting system model was validated in prestall and poststall operation modes with measured high pressure compressor data of a modern two-shaft engine. The turbine model was validated with measured intermediate pressure shaft failure data of a three-shaft engine. The shaft failure model was applied on a modern two-shaft engine. The model was used to carry out a sensitivity study to demonstrate the impact of control system reactions on the resulting maximum high pressure turbine speed following a shaft failure event.