多稳态湍流尾流的特征：改进的状态识别在解析模型训练中的应用
Characterisation of a multistable turbulent wake: application of an improved regime identification with analytical model training
浏览论文内容
中文总结 AI 辅助
研究并排方柱尾流中多稳态射流，通过PIV测量速度场，利用射流位置和宽度表征多稳态。构建解析随机微分方程建模，用基于数据的方法平衡模型简单性与精度，可校正漂移并理解复杂多稳态下射流行为。
中文摘要 AI 辅助
本文介绍了在雷诺数\(R = U_\infty H/\nu = 10000\)（其中\(U_\infty\)为来流速度，\(H\)为方柱边长，\(\nu\)为运动粘度）下，对间距为\(G\)的并排两根方柱尾流中多稳态射流的实验研究和建模。通过二维二维分量粒子图像测速法（PIV）测量柱后速度场。利用射流的加权横向位置\(Y_m\)和射流宽度\(w\)来表征随着间隙比\(G/H\)增加的多稳态状态。可能存在三种主要的多稳态状态：三稳态、双稳态和单稳态。在风洞中，\(G/H\in [1.15,1.25]\)时观察到三稳态，\(G/H\in [1.5,2.65]\)时观察到双稳态，\(G/H\in [3.0,3.5]\)时观察到单稳态。在前两个\(G/H\)范围内，存在多稳态更复杂的间隙比。为了分析简单和复杂的多稳态状态以及从双稳态到单稳态的转变，针对每个间隙比构建了一个解析随机微分方程（SDE）对\(Y_m\)进行建模。这些SDE用多项式漂移和扩散表示。为此使用了一种基于数据的方法，该方法在模型的简单性（单项式数量较少）和精度之间找到权衡。使用基于数据的模型拟合方法的第一个关键优势是，当流动为三稳态、双稳态或单稳态时，能恢复分岔理论预期的漂移，还能用扩散表示的正确乘性噪声进行校正。第二个关键优势是，当多稳态状态复杂时，也能拟合非典型漂移表达式，有助于理解射流行为。
英文摘要
This article presents the experimental study and the modelling of the multistable jet in the wake of two side by side square bars separated by a distance $G$ at Reynolds number $R=U_\infty H/ν=10000$ (with $U_\infty$ the velocity of the incoming flow, $H$ the bar side and $ν$ the kinematic viscosity). The velocity field downstream of the bars is measured by means of two dimensional two components Particle Image Velocimetry (PIV). We use the weighted transverse position of the jet $Y_m$ and the jet width $w$ to characterise the regimes of multistability as the gap ratio $G/H$ is increased. Three main regimes of multistability are possible: tristability, bistability, and monostability. In our wind tunnel, tristability is observed for $G/H\in [1.15,1.25]$, bistability is observed for $G/H\in [1.5,2.65]$ and monostability is observed for $G/H\in [3.0,3.5]$. Within the first two ranges of $G/H$, there exists gap ratios for which multistability is more complex. In order to analyse the simple and complex multistability regimes as well as the transition from bistable to monostable, we construct an analytical stochastic differential equation (SDE) modelling $Y_m$ for each gap ratio. These SDEs are written with polynomial drift and diffusion. For this matter we use a data based method that finds an trade--off between simplicity of the model (smaller number of monomials) and precision. A first key advantage of the use of the data-based model fitting method is that when the flow is tristable, bistable or monostable, we recover the drifts expected from the theory of bifurcations, but we are now able to correct it with the right multiplicative noise expressed by the diffusion. The second key advantage is that we can also fit atypical drift expressions when the multistability regime is complex that help us make sense of the jet behaviour.
