涡面场理论与应用

Theory and applications of the vortex-surface field

综述了涡面场理论与应用研究的主要进展.基于拉格朗日观点,涡面场提供了涡状流动结构识别、定量表征及建模的系统研究框架.在理论方面,涡面场将涡量矢量场简化表示为标量场,其等值面为由涡线组成的涡面.通过引入虚拟环量保持速度,亥姆霍兹涡量定理与Ertel定理在一定条件下可推广于一般流动.这保障了固定阈值涡面场等值面在不同时刻间的强相干性,使涡面场可用于流动结构追踪.作为普适的流动诊断工具,在任意给定流场中,可求解涡量驱动的伪时间演化方程构造涡面场数值解.进一步通过局部优化和边界约束算法可提高涡面场数值解的光滑性和收敛效率.然后利用双时间算法可计算涡面场的时间演化过程.结合大规模数值模拟数据,涡面场方法适用于分析含重要涡动力学过程的湍流与转捩等复杂流动机理.如涡面场揭示了各向同性湍流中交织为复杂网络的纠缠涡管结构,阐明了传统涡识别方法因无法展示完整涡管,故呈现出视觉上的破碎结构;涡面场演化统一框架揭示了不同类型壁流动转捩中普适且有序的流动结构以及相应动力学演化过程,无需在转捩的不同阶段人为切换结构识别方法并调整等值面阈值;基于涡面场的定量化研究,阐释了多物理耦合流动中涡面与激波、火焰或电磁场之间的相互作用机理.在涡面场定量刻画流动机理后,可进一步建模标量统计特征与工程应用中关键物理量之间的统计关联.例如,基于实验二维平面标量图像中的小尺度结构壁面倾角信息,可构造转捩摩擦阻力系数模型.此外,本文展望了涡面场未来研究方向与亟待解决的问题.

We review the progress on the theory and applications of the vortex-surface field(VSF). The VSF provides a systematic Lagrangian-based framework for the identification, characterization, and modeling of flow structures. From the theoretical perspective, the vorticity is simplified to a scalar field as the VSF. The VSF isosurface is a vortex surface consisting of vortex lines. By introducing the virtual circulation-preserving velocity, the Helmholtz theorem and the Ertel theorem are extended to some non-ideal flows, so that the VSF evolution equation can be expressed in a Lagrangian conservation form.Thus the VSF isosurfaces of the same threshold at different times have strong coherence, facilitating the tracking of vortex surfaces.As a general flow diagnostic tool, the numerical VSF solution can be constructed in arbitrary flow fields by solving a pseudo-transport equation driven by the frozen, instantaneous vorticity. In addition, the local optimization method and the boundary-constraint method can further improve the smoothness and convergence of VSF solutions. Then the two-time method is developed for calculating the temporal evolution of VSFs.From post-processing of large-scale database of numerical simulations, the VSF elucidates mechanisms in the flows with essential vortex dynamics, such as turbulence and transition. For example, the VSF reveals the complex network of tangling vortex tubes in isotropic turbulence, consistent with the vorticity equation and dynamics. In addition, Eulerian vortex-identification criteria cannot identify complete vortex tubes, so the visual "breakdown" of worm-like structures were often reported in the literature. The universal framework of the VSF evolution illustrates an ordered evolution process of coherence structures in transitional flows, in which it is no need to ad hoc change the structure-identification method and isocontour threshold. Moreover, the quantitative VSF study elucidates the interaction between the vortex surface and the shock wave, flame, or electromagnetic field in multi-physics coupled flows.Based on the characterization of VSFs, we seek robust statistical features, and then determine and model correlations between the features and critical quantities to be predicted in engineering applications. For example, we develop a predictive model of the skin-friction coefficient in boundary-layer transition based on the small-scale inclination angle in experimental images.Some open problems in the VSF study are discussed, including the regularization for the breakdown of virtual conservation theorems at vorticity nulls and the speedup of the numerical construction and evolution of VSFs.