颤振数值模拟的时间步长选取方法研究  

A New Method for Obtaining Real-Time Step in Simulating Flutter Responses

作　　者：史爱明[1] 王刚[1] 杨永年[1] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国家重点实验室,陕西西安710072

出　　处：《西北工业大学学报》2005年第2期208-211,共4页Journal of Northwestern Polytechnical University

基　　金：航空基础科学基金(04A53006);航天创新基金资助

摘　　要：通过求解“简化”颤振方程,对颤振数值模拟中实时间步长的选取进行了分析研究;得到了一种在保证物理时间精度的前提下取得最大实时间步长的方法。在空间上,采用迎风的AUSM+-up格式;在时间上,采用双时间隐式进行时间推进数值求解了三维非定常Euler方程。利用非结构运动网格技术考虑三维机翼弹性变形,同时耦合多自由度结构运动方程数值模拟了跨音速标模算例AGARD445.6机翼的结构响应。研究结果表明:采用四步龙格-库塔方法求解结构方程,每个振荡周期内至少取20个时间点才能得到可靠的物理时间精度和可信的结构响应。A reasonable and efficient real-time step is important in simulating flutter response. A new method for obtaining a reasonable and efficient real-time step is presented. We first simplify the nonlinear dynamics equations which are used to describe the law of wing flutter to a linear system without damp.When the real-time step is 2.7×10^(-3) seconds, the simulation results of the linear system are wrong because of truncation error and rounding error of the real-time step. When the real-time step is 5.4×10^(-4) seconds, the simulation results of the linear system is right in the concerned period. In order to investigate the problem deeply, simulation of AGARD445.6 wing dynamic response in time domain is carried out. The unstructured dynamic mesh technique is introduced to simulate the movement of the wing. Full implicit dual-time temporal derivatives and upwind AUSM^+-up spatial derivatives are adopted to solve the Euler equations and to deal with the 3D unsteady aerodynamic problem. The dynamics equations of AGARD445.6 wing flutter is marched by Rung-Kutta method in the time domain. Comparisons between simulation results with wind tunnel experimental flutter characteristics show good agreement, giving confidence in the validity of the developed method. We draw the conclusion that at least twenty real-time steps are needed in an oscillation cycle in order to obtain good flutter dynamic responses.

关 键 词：颤振 双时间 AUSM^+-up格式 实时间步长 非定常Euler方程 

分 类 号：V211.47[航空宇航科学与技术—航空宇航推进理论与工程]