The influence of complicated interaction between the flow field and heat transfer in cooled turbines becomes more and more significant with the increasing turbine inlet temperature. However, classical through-flow methods did not take into account the influence of the interaction caused by air cooling. The aerodynamic design and cooling design of cooled turbines were carried out separately, and the iterations between the aerodynamic design and cooling design led to a long design period and raised the design cost. To shorten the design period and decrease the design cost, this paper proposes a concise aero-thermal coupled through-flow method for the design of cooled turbines, taking into account the influence of the complicated interaction between the flow field and heat transfer in cooled turbines. The governing equations, such as energy equation and continuity equation in classical through-flow method are re-derived theoretically by considering the historical influence of cooling with the same method that deals with viscous losses in this paper. A cooling model is developed in this method. The cooled blade is split into a number of heat transfer elements, and the heat transfer is studied element by element along both the span and the chord in detail. This paper applies the method in the design of a two-stage axial turbine, of which the first stator is cooled with convective cooling. With the prescribed blade temperature limitation and the knowledge of the flow variables of the mainstream at the turbine inlet, such as the total pressure, total temperature and mass flow rate, the convergence of the calculation is then obtained and the properties of the flow field, velocity triangles and coolant requirement are well predicted. The calculated results prove that the aero-thermal coupled through-flow method is a reliable tool for flow analysis and coolant requirement prediction in the design of cooled turbines.
