基于FTLE的激波捕获方法及其在背景波系下隔离段波系结构变化特性的应用研究

Shock-Capturing Method Based on Finite-Time Lyapunov Exponents and Its Applications to Analysis of Wave Structures in an Isolator with Background Waves

关键词:  高超声速流动  背景波系  拉格朗日拟序结构  激波捕获  突跳特性

Key words:  Supersonic flow  Background waves  Lagrangian coherent structure  Shock capture  Jumping behaviors

摘要:

将胀量梯度场作为粒子运动的“速度场”，使激波结构转变为排斥Lagrangian拟序结构（LCSs），并利用有限时间Lyapunov指数（FTLEs）进行捕获。通过设定虚拟积分时长，进一步地将此激波识别方法拓展到非定常流场波系结构的应用研究中。利用商业软件FLUENT数值模拟了背景波系下隔离段激波串的前移过程，求解了基于胀量梯度场的FTLEs并提取了FTLE脊，同时将FTLE方法与密度梯度法进行了对比，验证了FTLE方法的准确性与有效性。结合压力云图详细分析了激波串突跳前后的FTLE场，着重讨论了激波串内部波系结构的变化过程以及激波串的突跳机理。经分析发现，激波串的前移过程伴随着波系结构的延展和收缩，导致流场出现对称破缺。当对称破缺现象较为显著时，流场边界层分离加剧，激波串加速前移。研究显示，基于FTLE的激波捕获方法对边界层干扰剧烈以及激波强度差异较大的非定常流场有重要的应用价值。

Abstract:

Dilatation gradient was introduced to change shock waves into repelling Lagrangian coherent structures and further used as velocity field for virtual particles to calculate Finite-time Lyapunov exponents （FTLEs）， so that wave structures can be recognized clearly. Additionally， by taking virtual integration time into consideration， the shock-capturing method was extended to the study of unsteady flow fields， and applied to analysis of shock-train structures. At first， commercial software FLUENT was used to simulate the forward movements of isolator shock-train with background waves. Then the FTLEs were calculated by using dilatation gradient to replace velocity field and FTLE ridges were extracted. Furthermore， shock-capturing method based on density gradient was compared with FTLE method and the results show that FTLE method is valid and reliable. Finally， pressure distribution was combined with FTLE fields to analyze the changing of the shock-train structures and mechanism of sharp forward movements. As the results， it is shown that sharp forward movements are accompanied by stretch and shrink of the shock train， leading to symmetry-breaking. As there is a serious symmetry-breaking phenomenon in the isolator， the separation of boundary layer is intensified and high adverse pressure gradient is induced， pushing the shock-train forward. Following to the study， the shock-capturing method based on FTLE methods is of great importance to unsteady flow with intense shock wave/boundary layer interaction and large intensity differences of shock waves.