燃气轮机高温叶片随机不确定性量化的研究

The inevitable aleatory uncertainties such as geometrical variation in manufacturing process and fluctuation of operation conditions in operating process would lead to the design performance deviation of high temperature blades. The uncertainty representation methods for aleatory uncertainties of different sources will be investigated. The uncertainties of operation conditions will be derived by using the Bayesian approach, while the geometrical uncertainties will be depicted based on the non-stationary Gaussian stochastic process. Then, the uncertainty propagation analysis method for aleatory uncertainties will be established by coupling the techniques of non-intrusive polynomial chaos and sparse grid. The sensitivity analysis method for uncertainty parameters will also be developed according to the principles of data mining. Therefore, an efficient and accurate uncertainty qualification framework for high temperature blades will be proposed. The benchmark data for uncertainty qualification will be obtained by combining the physical experiment and Monte Carlo method, and an uncertainty qualification model for film cooling will be constructed for such purpose. Through uncertainty qualification of high temperature blades using proposed method, effects of geometric variation and fluctuation of operation conditions on flow field and heat transfer performance at endwall of high temperature blades will be researched. The mechanism behind will also be illustrated. To obtain endwall profile of excellent robustness and reliablity in aerodynamic and heat transfer performance, a multi-objective optimization of endwall will be conducted for maximizing the mean performance and reducing the performance sensitivity to uncertainties. The mathematical expressions for constraints and objective functions of optimization process will be researched and established accordingly.

加工和运行过程中必然存的几何、工况等随机不确定性将导致燃气轮机高温叶片性能偏离设计值。研究随机不确定性来源表征方法，采用贝叶斯逆推理获取工况不确定性，基于非平稳高斯随机过程描述几何不确定性；结合非嵌入多项式混沌方法和稀疏网格，建立随机不确定性传播分析方法；引入数据挖掘原理，发展不确定性参数敏感性分析方法；建立高效准确的高温叶片不确定性量化方法。结合蒙特卡洛方法和实验测量，构建气膜冷却问题不确定性量化模型，获得不确定性量化的基准数据。利用高温叶片不确定性量化方法，开展工况不确定性和几何不确定性对高温叶片端壁流动结构和换热性能影响的研究，阐明工况不确定性和几何不确定性对端壁流场形态和换热性能的作用机制。以提高平均性能和降低性能对不确定性的敏感程度为目标，建立约束条件和目标函数的数学表达式，开展端壁几何造型多目标优化设计，获得具有优秀气动鲁棒性和换热可靠性的端壁造型。

加工和运行过程中必然存的几何、工况等随机不确定性对燃气轮机高温叶片性能具有重要的影响。研究随机不确定性来源表征方法，采用贝叶斯逆推理获取工况不确定性，基于非平稳高斯随机过程描述几何不确定性；引入稀疏原则，采用格拉姆-施密特正交化求解多项式混沌的正交基底、最小角回归求解LASSO问题、贝叶斯优化寻找超参数，提出了稀疏多项式混沌展开模型，建立随机不确定性传播分析方法；发展了基于数据挖掘原理的参数全局敏感性分析方法，提出了一种基于稀疏多项式混沌展开的适用于任意输入的通用全局敏感性分析方法；构建了高效准确的高温叶片不确定性量化框架。搭建了平板气膜冷却试验台、带槽缝射流的扇形叶栅试验台，为高温叶片不确定性量化研究提供基础校验数据。利用高温叶片不确定性量化方法，开展工况不确定性和几何不确定性对高温叶片端壁流动结构和换热性能影响的研究，阐明工况不确定性和几何不确定性对端壁流场形态和换热性能的作用机制。揭示不确定性对不同类型端壁流动换热性能的影响规律，明确不确定性对端壁流动换热的影响程度，获取对不确定性因素不敏感的端壁几何造型。