涡轮动叶凹槽状叶顶传热特性和气动性能的不确定性量化研究

Uncertainty Quantification Analysis on Heat Transfer Characteristics and Aerodynamic Performance of Turbine Blade Squealer Tip

关键词:  涡轮动叶凹槽状叶顶  气膜冷却  传热特性  气动性能  不确定性量化

Key words:  Turbine blade squealer tip  Film cooling  Heat transfer  Aerodynamic performance  Uncertainty quantification

摘要:

第一级动叶叶顶是影响燃气涡轮气动性能和换热性能的关键区域。然而在叶顶的几何参数和运行环境往往存在着许多不确定性，这使得涡轮叶顶的实际气热性能明显偏离设计值。本文基于非嵌入式多项式混沌展开方法，结合Smolyak稀疏网格技术与Sobol Indic方法构建了涡轮动叶凹槽状叶顶传热特性和气动性能不确定性量化分析系统。研究并量化了叶顶间隙和主流进口总温与气膜冷却吹风比不确定性对涡轮动叶凹槽状叶顶气热特性的影响。不确定性分析结果表明：在考虑叶顶间隙与主流进口总温和吹风比不确定性的情况下，叶顶换热量Q_Tip基本符合正态分布。Q_Tip的统计均值相对于设计值增加13.56%，并且其偏离设计值10%的概率高达65.68%。相比叶顶尾缘区域，叶顶前缘部分的换热量对不确定性输入更加敏感。前缘区域的叶片壁面换热量Q_Blade的不确定性明显大于尾缘部分。在叶顶间隙与主流进口总温和吹风比不确定性的影响下，0~80%轴向弦长区域内叶顶总压损失系数存在微小偏差，但在80%轴向弦长以后区域总压损失系数的不确定性偏差会达到约50%。敏感度分析的结果表明，主流进口总温是叶片换热性能不确定性的主导变量，其对Q_Tip与Q_Blade不确定性的贡献分别为93.87%和98.32%。叶顶气动性能的不确定性则完全由叶顶间隙控制，其对叶顶总压损失系数不确定性的方差占比高达86.44%。与主效应相比，本文所研究的三个变量间的二阶交互效应对叶顶气热性能的影响几乎可以忽略不计。

Abstract:

The first-stage rotor squealer tip is a key area in the gas turbine for both aerodynamic performance and heat transfer characteristics， which should be carefully designed. However， there are many uncertainties in the geometrical parameters and operating environment of the blade tip， which makes the actual aerothermal performance of the turbine blade tip significantly deviate from the design value in actual use progress. The heat transfer characteristics and aerodynamic performance uncertainty quantification analysis system of the turbine blade squealer tip was established. The non-embedded polynomial chaos expansion method， integrated with Smolyak Sparse grid， Sobol Indic technology for the uncertainty quantification analysis system was developed. It was investigated and quantified that the effects of the tip clearance， mainstream inlet total temperature and blowing ratio uncertainty on the aerothermal performance of blade squealer tip. The uncertainty analysis results show that heat flux of squealer tip Q_Tip basically conforms to the normal distribution when considering the uncertainty of tip clearance， mainstream inlet total temperature and blowing ratio. The statistical mean value of the Q_Tip increased by 13.56% relative to the designed value and the probability of 10% deviation from the designed value is as high as 65.68%. The heat flux of squealer tip leading edge is more sensitive to uncertainty input by comparison to the trailing edge. The uncertainty of the heat flux on the blade surface Q_Blade near the leading edge region is obviously larger than that of the trailing edge area. The minor deviations of the total pressure loss coefficients at the squealer tip within 0~80% axial chord regions is observed considering the tip clearance， mainstream inlet total temperature and blowing ratio uncertainty inputs. However， the uncertainty error of the total pressure loss coefficient at the squealer tip after the 80% axial chord regions would reach about 50%. The sensitive analysis results show that the mainstream inlet total temperature is the dominant variable in the uncertainty of the blade heat transfer performance， and its contribution to the uncertainty of Q_Tip and Q_Blade is 93.87% and 98.32%， respectively. The uncertainty of the aerodynamic performance of the squealer tip is completely dominated by the tip clearance， and the uncertainty variance of it to the tip total pressure loss coefficient obtained as 86.44%. Compared with the main effect， the influence of the second-order interaction effect among the variables studied on the squealer tip aerothermal performance is almost negligible.