动叶凹槽状叶顶气膜冷却有效度和气动性能不确定性量化研究

Investigations on Uncertainty Quantification of Film Cooling Effectiveness and Aerodynamic Performance of Turbine Blade Squealer Tip

结合非嵌入式多项式混沌展开方法、稀疏网格技术、Sobol Indic敏感度分析方法以及RANS方程求解方法,提出了涡轮动叶凹槽状叶顶气热性能不确定性量化分析方法,数值模拟与实验数据吻合一致验证了本文方法预测凹槽状叶顶气热性能的有效性。在量化几何参数叶顶间隙和运行参数主流进口总温以及吹风比的不确定性的基础上,对GE-E 3动叶叶顶的气动以及换热性能进行不确定性量化,详细分析了不确定性输入量对平均气膜冷却有效度、间隙泄漏量以及下游总压损失系数的影响,并且通过Sobol Indic方法对各不确定性变量对叶顶气热性能不确定性的贡献进行量化研究。不确定性分析的结果表明:叶顶前缘区域的泄漏量对不确定性输入不敏感,但是尾缘区域泄漏量的不确定性偏差可达到25%;下游总压损失系数总体受不确定性波动的影响较小;在几何及工况不确定性的影响下,叶顶气膜冷却有效度的统计均值相比于设计值下降29.52%,并且其偏离设计值10%的概率高达91.83%。敏感度分析的结果表明:叶顶间隙的偏差是叶顶气动性能不确定性的主导变量,叶顶间隙偏差对泄漏量以及下游总压损失系数的方差占比分别达88.02%与85.31%;在叶顶传热特性的不确定性方面,3个研究变量对气膜冷却有效度不确定性的贡献均不可忽略。本文研究的3个变量中,叶顶间隙对凹槽状叶顶气动和气膜冷却有效度的综合影响最大,所以在叶片的加工装配过程中需要保证叶顶间隙的精度。

Combining the non-embedded polynomial chaotic expansion method,sparse grid,Sobol Indic technology and Reynolds-averaged Navier-Stokes(RANS)equation solving method,an uncertainty quantitative analysis method for the aerodynamic and heat transfer performance of the turbine blade squealer tip was proposed.Numerical simulations were consistent with experimental data,which verified the effectiveness of the numerical method for predicting the aerodynamic and heat transfer performance of the squealer tip.The aerodynamic and heat transfer performance of the GE-E 3 rotor blade tip was quantified on the basis of the uncertainties of the tip clearance,the total temperature of the mainstream inlet and the blowing ratio.The influences of the uncertain inputs on the average film cooling effectiveness,gap leakage and downstream total pressure loss coefficient were analyzed in detail.The Sobol Indic method was used to quantify the contribution of each uncertain variable to the uncertainty of the tip aerothermal characteristics.The results of the uncertainty analysis show that the leakage in the leading edge area of the blade tip is not sensitive to the uncertain input,but the uncertain deviation of the leakage in the trailing edge area can reach 25%.The downstream total pressure loss coefficient is generally less affected by uncertain fluctuations.Under the influence of the uncertainty of geometry and working conditions,the statistical mean value of the blade tip film cooling effectiveness is reduced by 29.52%compared with the design value,and the probability of 10%deviation from the design value is as high as 91.83%.The sensitivity analysis results show that the tip clearance deviation is the dominant variable in the uncertainty of the tip aerodynamic performance.The variances of the tip clearance deviation to the leakage and the total downstream pressure loss coefficient account for 88.02%and 85.31%,respectively.Among the three variables studied in this paper,tip clearance has the greatest comprehensive influence on the aerodynamic performance and film cooling effectiveness of the blade squealer tip,so the machining accuracy of tip clearance should be strictly guaranteed in the process of blade machining and assembly.