Abstract: In order to determine the reasonable range of reaction degree and accelerate the turbine design process and ameliorate the aerodynamic design system， the feasible region of the high-pressure turbine reaction degree considering the rotor inlet normalized relative total temperature and the reaction feasible region under multiple constraints were studied. The ??‘equivalent single-stage turbine’ method was used to derive the relationship between the reaction degree and the relative total temperature， the reaction feasible region calculation method under multi-constraints were established in the velocity triangle way. The studies show that the relative total temperature decreases as the reaction degree decreases at specified stage load factor and expansion ratio. The normalized relative total temperature reduces by 0.012 with the reaction reduces by 0.1. And the higher the total inlet temperature， the greater influence of the reaction degree on the relative total temperature. When the stage load factor is greater than a certain value or the expansion ratio is lower than a certain value， the reaction degree has a maximum value. To achieve an aerodynamic scheme with lower rotor inlet relative total temperature and higher efficiency， ??lower reaction degree and stage load factor should be selected when the expansion ratio is specified. Also， higher reaction should be selected for single stage turbine， while lower for a two-stage turbine. The multi-constrained reaction feasible region calculation comprehensively considers the constraints of turbine aerodynamics， heat transfer， strength and structure， which can determine the reaction feasible region quickly， and improve the design process. Finally， the reaction feasible region of a new high-speed aircraft low-pressure turbine was studied， which is 0.125 to 0.266. The further study shows that the maximum reaction degree is determined by the maximum allowed Mach number and the minimum allowed absolute flow angle at the outlet of the rotor.

Key words: Axial-flow turbine；Aerodynamics preliminary design；Reaction degree；Heat transfer design；Relative total temperature；Feasible region；Multiple constraints

摘要： 为快速确定反动度的合理取值范围，加快涡轮设计流程及完善气动设计体系，对考虑动叶进口相对总温的高压涡轮反动度可行域及多约束下反动度的可行域进行研究。采用“等效单级涡轮”的思路建立反动度与动叶进口无量纲相对总温之间的关系式以及采用速度三角形方法建立多约束条件下反动度可行域的计算方法。研究显示:当级负荷系数和膨胀比一定时，相对总温随反动度降低而降低。反动度降低0.1，则无量纲相对总温降低0.012。涡轮进口总温越高，反动度对相对总温影响幅度越大。当级负荷系数大于某值或膨胀比低于某值时，反动度均存在最大值。为保证气动方案具有较低值动叶进口相对总温和较高的效率，若膨胀比一定时，应选择较小的反动度和级负荷系数的设计思路，若级负荷系数一定时，对于单级涡轮反动度取值应较高，对于双级涡轮反动度取值应减小。建立考虑涡轮气动、传热、强度、结构方面的多约束可行域计算方法，可以快速确定反动度的可行域，完善涡轮气动方案设计并加快设计流程。以新型高速飞行器低压涡轮为分析对象，采用该方法确定其反动度可行域为0.125～0.266，并深入研究发现其反动度最大值由动叶出口最大允许马赫数和最小允许绝对气流角共同限制。

关键词: 轴流涡轮；气动方案设计；反动度；传热设计；相对总温；可行域；多约束