Abstract: A non-axisymmetric endwall contouring method based on parameterized ridge line was proposed to improve aerodynamic and heat transfer performance in cascade with low aspect ratio turbine vane by reducing cascade second loss and heat transfer level on endwall. Parametric contouring of non-axisymmetric endwall was formed by a ridge line close to pressure side of airfoil and several circumferential cosinusoidal curves，in order that the shape of endwall with high on pressure side but low on suction side could be predetermined. The multi-objective optimization，which adopt NSGA-Ⅱmulti-objective genetic algorithm，to minimize mass-averaged coefficient of secondary kinetic energy of cascade outlet and area-averaged heat transfer coefficient of endwall，was conducted to obtain the contouring of endwall. The optimization results indicated that，compared to flat endwall，mass-averaged coefficient of secondary kinetic energy and area-averaged heat transfer coefficient of non-axisymmetric endwall decreases by 27% and 6.9%，respectively. The main reason on the decrease in cascade secondary loss and endwall heat transfer is that the contouring of non-axisymmetric endwall reduces intensity of passage vortex and wall vortex by decreasing cross pressure gradient between airfoils and altering location of the secondary vortex system structure in cascade.

Key words: Non-axisymmetric endwall；Ridge line；Secondary loss；Heat transfer；Multi-objective optimization；Horseshoe vortex；Passage vortex

摘要： 为提高低展弦比涡轮叶片气动与换热性能，抑制叶栅二次损失并降低端壁换热水平，提出了一种基于参数化脊线的非轴对称端壁成型方法。非轴对称端壁参数化成型基于位于叶片压力侧的脊线及周向余弦曲线构成，预先保证了端壁压力侧较高、吸力侧较低的基本形状。以涡轮叶栅出口测量截面质量平均二次动能系数最小及端壁面积平均换热系数最小为优化目标，采用NSGA-Ⅱ多目标遗传算法进行气动与换热优化，得到非轴对称端壁造型。优化结果表明:与平端壁相比，非轴对称端壁涡轮叶栅出口测量截面的质量平均二次动能系数降低了27%，端壁面积平均换热系数降低了6.9%。非轴对称端壁造型通过平衡叶片间横向压力梯度，改变了马蹄涡与通道涡位置，通道涡和壁涡强度得到抑制，有效降低了涡轮叶栅二次损失及端壁换热。

关键词: 非轴对称端壁；脊线；二次损失；换热；多目标优化；马蹄涡；通道涡