基于伴随方法的叶片冷却通道导热优化研究  

Study on Adjoint-based Conduction Optimization Method for Blade Internal Cooling Passages

作　　者：阮有钢 刘战胜 丰镇平 RUAN You-Gang;LIU Zhan-Sheng;FENG Zhen-Ping(Institute of Turbomachinery,Shanxi Engineering Laboratory of Turbomachinery and Power Equipment,School of Energy and Power Engineering,Xi’an Jiaotong University,Xi'an 710049,China)

机构地区：[1]西安交通大学能动学院叶轮机械研究所,陕西省叶轮机械及动力装备工程实验室,西安710049

出　　处：《工程热物理学报》2021年第6期1431-1437,共7页Journal of Engineering Thermophysics

基　　金：国家自然科学基金资助项目(No.51876156)。

摘　　要：本文基于网格节点位置坐标变分技术,针对固体导热问题推导了导热伴随方程及其对应的边界条件,并应用有限体积法求解了导热与伴随方程。给出了固体域表面温度分布反设计问题和固体域平均温度正设计问题对应的目标泛函变分的具体表达式,应用拟牛顿算法构建了优化设计系统。针对空心圆环导热问题,计算了目标函数关于内径的梯度,并将计算结果与有限差分方法和理论值进行对比,验证了导热伴随系统的有效性。最后给出了空心圆柱内壁面形状反设计、空心叶片壁面厚度反设计的计算结果以及叶片型线保持不变,以降低叶片固体域平均温度为目标,对冷却通道隔板位置与厚度进行的优化设计结果。优化结构平均温度与初始结构相比降低了11.1 K。Heat conduction adjoint equation as well as corresponding adjoint boundary conditions were derived based on grid coordinate variation technique.The adjoint equation was solved adopting the finite volume method successfully.The formulas for the variation of augmented objective functions were induced in detail for surface temperature distribution inverse design and average temperature optimization problems.An optimization system was built based on quasi-newton methods.Derivatives of the objective function to the radius were calculated for conduction within a hollow cylinder.The values were compared with analytical and finite difference method gradients to validate the correctness of the method.Results of the inverse design cases for hollow cylinder inner wall shape and hollow blade thickness were given.Finally,the parameters of the cooling passage struts were designed for average temperature within the hollow blade.The average temperature of the optimal structure decreased 11.1 K compared to the original one.

关 键 词：内部冷却 连续伴随方法 反设计 导热优化 

分 类 号：TK472[动力工程及工程热物理—动力机械及工程]