叶轮机气弹耦合方程求解的时间推进方法评估  

Evaluation of Time-marching Method for Solving Aeroelastic Coupled Equations of Turbomachinery

作　　者：曹琳婷 王丁喜[1] 黄秀全[1] CAO Lin-ting;WANG Ding-xi;HUANG Xiu-quan(School of Power and Energy,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]西北工业大学动力与能源学院,西安710129

出　　处：《航空发动机》2022年第5期94-100,共7页Aeroengine

基　　金：国家科技重大专项(2017-Ⅱ-0009-0023)资助。

摘　　要：为了提高叶轮机颤振预测时的计算效率,同时兼顾求解的稳定性,有必要选取最适合的时间推进方法。基于降阶结构动力学方程的双向流固耦合方法常用于压气机气弹性能分析,针对气动弹性控制方程中结构动力学方程考查了多种时间推进方法对计算结果的影响。通过单自由度弹簧系统的数值求解探讨了不同时间推进方法的特点;选取实际压气机算例NASA Rotor 67进行颤振流固耦合分析,进行大量数值试验找到了各时间推进方法需要的最大时间步长,以此为依据对比出不同时间推进方法的计算效率。结果表明:采用单自由度弹簧系统和压气机颤振耦合求解得出的结论基本一致,说明时间推进方法的性能更多地与方法本身的数学性质有关,但是流固耦合求解时流场和结构的信息交互会带来一定影响。以实际颤振算例叶片瞬态响应振幅的对数衰减率作为衡量精度的标准,经典龙格-库塔方法是颤振耦合计算达到相同精度耗时最少的方法,其次是4阶隐式Adams方法和Newmark方法。In order to improve the computational efficiency of turbomachinery flutter prediction while considering the stability of solution,it is necessary to select the most appropriate time-marching method.The two-way fluid-structure coupling method based on the reduced order structural dynamics equation is often used to analyze the aeroelastic performance of the compressor.For the structural dynamics equation in the aeroelastic control equation,the influence of various time-marching methods on the calculation results was investigated.The characteristics of different time-marching methods were discussed through numerical solution of single degree of freedom spring system.NASA Rotor 67 was selected for flutter fluid-structure coupling analysis as a compressor case study,and a large number of numerical tests were carried out to find the maximum time step required by each time-marching method.Based on this,the calculation efficiency of different time-marching methods was compared.The results show that the conclusions obtained by using the single degree of freedom spring system and compressor flutter coupling solution are basically consistent,indicating that the performance of time-marching method is more related to the mathematical properties of the method itself,but the interaction of information between the flow field and the structure has a certain impact during a fluid-structure coupling solution.Taking the logarithmic decay rate of the blade transient response amplitude in the actual flutter calculation case as the measure of accuracy,the classical Runge-Kutta method is the least time-consuming method to achieve the same accuracy in flutter coupling calculation,followed by the 4th order implicit Adams method and Newmark method.

关 键 词：叶轮机 流固耦合 颤振 时域分析 经典龙格-库塔 航空发动机 

分 类 号：V215.34[航空宇航科学与技术—航空宇航推进理论与工程]