A mathematic model is proposed for predicting the effect of injected cooling air on cooled turbine performance.The model takes the gas flow as the mainstream flow and regards the cooling air as a consecutive source with continuous distribution in the flow field.A numerical method is presented for determining the intensity of the consecutive source.According to the model

the coupled aerothermodynamic equations reflecting the effect of the cooling air mixing in general form are derived in a relative coordinate system.As an example

the model is used in the throughflow calculation for the cooled turbine and the governing equations are derived along S 2 stream surface in a non orthogonal curvilinear coordinate system.By defining a quasi stream function which satisfies the continuity equation

a line relaxation calculation method is developed for the quasi stream function.It makes full use of the existed calculation method without considering the cooling air mixing and is easy to be programed.In accordance of the mathematic model a formula of entropy variation due to the cooling air mixing is derived in the light of the second law of thermodynamics.By means of the present calculation method

an air cooled gas turbine stage is analyzed.The results show the reasonableness of the mathematic model and the feasibility of the calculation method.