旋转流体多边形自由表面形成机理的实验和数值研究

开放圆柱形容器中的不可压缩牛顿流体，在旋转底盘驱动下产生自由表面变形。在特定底盘转速和液面初始高度条件下，大变形自由表面呈现旋转多边形模态。本项目旨在通过实验和数值相结合的方法，从根源上解释该旋转流体自由表面旋转多边形的生成和演化机理。实验上，采用傅立叶变换轮廓术，实时精准测量自由表面非定常演化，并通过粒子图像测速技术，对旋转流场结构实时观测；数值上，采用气液两相流直接数值仿真代码，对自由表面流进行三维非定常计算。该项对奇特旋转多边形不稳定性机理的研究，不仅能促进相关高效数值方法和精确测量技术的开发和利用，而且对探索涡动学、自由表面及流动稳定性等学术问题具有重要意义，相关研究方法和理论成果亦具有较高的工程应用价值。

A disk rotating at the bottom of an open cylindrical container partially filled with an incompressible Newtonian fluid generates a rotating flow with deformed free surface. At certain disk speeds and initial fluid heights, the largely deformed free surface takes the form of rotating polygons. This project aims to find the formation and evolution mechanisms of this free surface instability, with experimental and numerical approaches. Experimentally, the unsteady evolution of the free surface is accurately measured in real time using Fourier transform profilometry, and the flow velocity field through particle image velocimetry; Numerically, a two-phase flow solver is used to perform three-dimensional unsteady calculations of the free surface flow. This research on the mechanism of the peculiar rotating polygonal instability, not only promotes the development and use of numerical methods and accurate measurement techniques, but also has important significance for exploring academic problems such as the vorticity dynamics, free surface and flow stability. The methods and expected results can also be applied in engineering practice.