各向异性陶瓷基复合材料涡轮叶片概率性热分析方法

考虑陶瓷基复合材料等纤维增韧复合材料导热系数的各向异性及分散性，建立了基于概率统计的陶瓷基复合材料涡轮叶片热分析方法。研究中以Mark Ⅱ涡轮叶片冷却结构为例，综合利用有限元方法和蒙特卡洛方法，分析了应用陶瓷基复合材料后的温度场均值和波动特性。计算中将导热系数作为随机输入参数，分析了导热系数各向异性及其分散度对叶片前缘滞止点温度、尾缘温度以及高温区域（T>900K）面积的影响。计算中发现在本文的计算工况下,考虑导热系数存在正态波动情况时，叶片前缘滞止点、尾缘温度波动也满足正态分布。前缘滞止点温度在导热系数变异系数为01,导热系数比为2时其温度波动最大，相比12731K的均温，有16%的概率超温913K。尾缘温度在导热系数变异系数为01，导热系数比为10时波动最大，有16%的概率超过均值11529K达527K。计算结果表明:导热系数分散度所带来的波动，会导致叶片内部高温关注区域（T>900K）的面积增大，并且高温关注区域相对增加量ΔShot随导热系数变异系数α的增加而增加。计算结果表明，高温关注区域相对增加量最大发生在导热系数比为2，变异系数为0.1时，此时ΔShot=4.8%。 

Probabilistic thermal analysis of ceramic matrix composite turbine vane with anisotropic thermal conductivity

Considering the anisotropy and dispersion of thermal conductivity for ceramic matrix composites (CMC),a probabilistic thermal analysis model was established for predicting the temperature field of hot components made of CMC.Taking the cooling configuration of Mark Ⅱ turbine vane as an example,and assuming it was made of anisotropic CMC,the mean value and variation of the blade's temperature field by the finite element method coupled with Monte Carlo simulations was analyzed.In this work,anisotropic thermal conductivities were applied as the random input parameters,the effects of thermal conductivities' dispersion and anisotropy on the temperature field of CMC turbine vane were investigated.Furthermore the temperature fluctuations of leading edge stagnation point and trailing edge were studied,and the hot spot with temperature higher than 900 K (T＞900 K) was discussed.The temperatures of leading edge stagnation point and trailing edge were distributed normally,when the thermal conductivity exhibited a normal distribution.The maximum standard deviation of temperature of stagnation point appeared when the variation coefficient of thermal conductivity equaled 0.1,and the thermal conductivity ratio was 2.There was a probability of 16％ to exceed the mean value (1 273.1 K) by 9.13 K.Regarding the trailing edge,the maximum standard deviation was obtained,when the variation coefficient of thermal conductivity equaled 0.1 and the thermal conductivity ratio remained 10.There was a probability of 16％ to exceed the mean value (1 152.9K) by 5.27K.The results show that the dispersion of thermal conductivity leads to the increase of hot spot,and the relative rate of increment ΔShot rises with the increase of thermal conductivity's variation coefficient.In this study,the maximum/ΔShot was 4.8％,when the variation coefficient of thermal conductivity was 0.1,and the thermal conductivity ratio remained 2.