混流式水轮机转轮设计变量耦合强度分析

Variable coupling strength analysis of Francis turbine runner design

在开展混流式水轮机转轮的多学科优化时通常需要进行设计变量的学科耦合强度分析,以便为建立简洁、高效的多学科优化求解策略提供依据。该文提出了一种基于全局相对灵敏度的转轮设计变量耦合强度分析方法,该方法基于参数化全三维反问题设计理论实现对转轮几何的参数化控制,并通过改进后的MorrisOAT法进行各学科目标函数对转轮设计变量的全局相对灵敏度计算,然后以各设计变量的全局相对灵敏度集合为论域,引入模糊隶属度函数量化计算设计变量对各学科目标函数的隶属度。最后,以各设计变量的隶属度值为基础,提出了设计变量的耦合强度判定准则,为设计变量的耦合程度属性确定提供了参考。采用该文所提出的分析方法对某混流式水轮机模型转轮的设计变量开展了耦合强度分析,并根据变量的耦合强度分析结果开展了转轮的优化设计,优化后的转轮不仅使得水轮机在3个优化工况下的水力效率分别提高0.2%、0.82%和1.2%,同时叶片的空化和强度性能也得到改善,该结果表明该文所提出的混流式水轮机转轮设计变量耦合强度分析方法能可靠有效的界定各设计变量的耦合程度属性,从而验证了方法的可行性。

Hydropower is one of the most reliable source of green energy and is widely used to meet real-time electricity demand. The ever escalating energy demand and iterative development in hydropower have pushed the generation of hydropower towards a low lost-cost and more flexible state which can work in a wider hydrodynamic region without compromising its performance. So the research on multidisciplinary optimization of hydro turbine needs to be carried out. Francis-type turbine is attractive because the efficiency of the unit at its design point exceeds the other types. As mentioned above, with the needs of robust operation in wide region without compromising its performance, the Francis turbine runner has to be optimized under multidisciplinary constraints. Multidisciplinary optimization technology of Francis runners has always been a key point in the field of turbine research. The coupling strength of each variable is the basis for establishing a concise and efficient multidisciplinary optimization strategy. So in the multidisciplinary optimization of Francis runner, it is necessary to analyze the coupling strength of design variables. In this paper, based on the global relative sensitivity of design variables, a coupling strength analysis method of runner design variables has been presented. First, combing three-dimensional （3D） inverse design theory with curve parametric method, a parametric 3D inverse-design method has been developed to control the Francis runner geometry. According to this parametric 3D inverse-design method, the meridional flow passage and geometry of runner blade can be controlled by a set of discrete parameters. These parameters are treated as runner design variables. The hydraulic efficiency of turbine, the minimal pressure coefficient on runner blade and the maximum static stress of blade are selected as objective functions. Then the global relative sensitivity of each objective function to design variables is calculated by an improved Morris OAT method. Compared with the traditional Morris OAT method, an optimal Latin hypercube design technique is adopted in the improved method. The optimal Latin hypercube design technique has a better space filling property than the traditional one. So the sampling only needs to be done once, which reduces the time of global relative sensitivity analysis without compromising its precision. On the basis of the improved Morris OAT method, the speed of global relative sensitivity calculation is improved obviously. Secondly, the set which contains global relative sensitivity of design variables is treated as universe, and the semi-trapezoidal function in fuzzy mathematics is imported to quantify the membership of each variable to objective functions. After obtaining the membership of each variable, a judgment principle of variable’s coupling strength is presented in this paper. According to this judgment principle, the coupling strength property of each design variable can be defined as strong coupling, middle coupling and weak coupling. Finally, based on the coupling strength of each design variable, the multidisciplinary optimization strategy of Francis runner is established. And then the multidisciplinary optimization of Francis runner can be carried out. In order to validate the coupling strength analysis method, an application case is presented in the paper. In that case, the design variables of a Francis turbine runner with the head of 200 m are chosen as the analysis object. From the analysis result, it can be found that only the coupling strength property of maximum thickness is weak coupling, and the others are middle coupling. According to the result, a multidisciplinary optimization strategy is established and used in the optimization of Francis turbine runner. After optimization, both the hydraulic performance and strength property of the optimized runner are improved, demonstrating the effectiveness of the coupling strength analysis method. In conclusion, the method proposed in this paper can be adopted to analyze the coupling strength of design variables of Francis runner.