涡轮冷气掺混数学模型与计算方法的研究

本文建立了一个涡轮冷气掺混的数学模型并将其应用到气冷涡轮的 S2 流面计算中。根据该模型推导出了考虑冷气掺混时相对坐标系下的气动热力学方程组。通过掺混流函数的引入建立了计及冷气掺混的 S2 流面计算方法。计算结果表明了本文模型的合理性与算法的可行性

A MATHEMATIC MODEL AND A CALCULATION METHOD FOR COOLING AIR MIXING IN A TURBINE

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.