论文标题
部分可观测时空混沌系统的无模型预测
Effect of ambient gas on cavity formation for sphere impacts on liquids
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Formation of a splash crown and a cavity following the impact of a sphere on a body of liquid is a classical problem. In the related problem of a droplet splashing on a flat surface, it has been established that the properties of the surrounding gas can influence the splashing threshold. At lower impact speeds, this is due mainly to the influence of gas kinetic effects, since the height of the gas lubrication film which is displaced during dynamic wetting is often comparable to the mean free path of the gas. At higher Weber and Reynolds numbers, on the other hand, inertial effects dominate and the density of the gas becomes important in determining whether a splash occurs. In this article, sphere impacts on a liquid body are investigated in a rarefied atmosphere using high-speed photography. It is found that the threshold entry speed for cavity formation is influenced by the density of the surrounding gas, whereas changing the mean free path of the gas has no effect. We attribute this phenomenon to the gas slowing the sealing of the thin crown sheet behind the sphere. This assertion is supported with experimental measurements of the liquid sheet thickness. In the range of parameters considered, the splash crown influences the movement of the contact line, an effect not previously observed.
