An Efficient Prediction Method for the Azimuthal Migration of Combustion Inhomogeneity in Multi-Stage Cooled Turbines

The outlet temperature of combustor is commonly monitored by thermocouples at the turbine exhaust. In order to establish the corresponding relationship between the temperature measured by each thermocouple and the working state of each burner, the azimuthal migration of the combustion hot/cold streaks in the multi-stage turbines needs to be quantified. Experiments to measure this migration have high cost and considerable error. It is also difficult to quantify the migration under multiple working conditions. Three-dimensional full-annulus unsteady simulation can obtain this migration. But the unsteady simulation of a single working condition could take several weeks, which is too expensive for engineering usage. A method named Steady-state Computation of Azimuthal Migration (SCAM) is proposed in this paper. By establishing and solving the transport equation of the migration angle, the azimuthal migration of hot/cold streaks can be predicted by steady-state numerical simulation using the mixing plane at rotor-stator interface. The migration computed by this method is compared with the full-annulus unsteady simulation results in multiple working conditions. The results of SCAM method show good agreement with full-annulus simulations, while costing only 0.01% of the CPU hours. It is also found that the error of SCAM is mainly caused by the fixed boundary value at coolant source terms. The optimal spanwise location of the thermocouples at turbine exhaust is discussed based on the results. The method proposed could be applied to the fault diagnosis and precise repair of the combustors of gas turbines.