AI 中文总结
该研究将POD子空间视为流动状态，通过扩散映射和Grassmann秩1更新算法，在翼型绕流实验中验证了可在线跟踪其低维演化，为流动状态估计与控制提供基础。
AI 中文摘要
在流体力学中，将宽范围流动参数和控制输入下的流动状态表示在低维状态空间中是一项核心挑战。本研究未将瞬时流场表示为前导本征正交分解（POD）模态张成的固定子空间，而是将POD子空间本身视为每种流动条件下的流动状态。与各流动条件关联的POD子空间集合定义了Grassmann流形上的状态空间。扩散映射识别POD子空间族的固有低维结构，而Grassmann秩1更新子空间估计算法在线跟踪POD子空间的时间演化。该框架通过翼型绕流实验验证：从麦克风阵列测量的壁面压力波动中提取不同攻角和不同控制输入下的POD子空间，发现这些子空间位于Grassmann流形的一维子流形上；此外，等离子体作动器诱导的分离流到附着流的转变，遵循与统计定常流动数据识别的同一子流形上的可复现轨迹，且子空间的时间演化与粒子图像测速观测的流场瞬态演化一致。结果表明，POD子空间可作为代表性流动状态，能基于壁面压力波动在低维空间中在线跟踪其跨宽范围流动条件的时间演化，为实时流动状态估计和反馈控制提供基础。
英文摘要
Representing flow states over a wide range of flow parameters and control inputs in a low-dimensional state space is a central challenge in fluid mechanics. Rather than representing the instantaneous flow field in a fixed subspace spanned by the leading proper orthogonal decomposition (POD) modes, this study regards the POD subspace itself as the flow state at each flow condition. The set of POD subspaces associated with flow conditions defines a state space on the Grassmann manifold. Diffusion maps identify the intrinsic low-dimensional structure of the family of POD subspaces, while Grassmannian rank-one update subspace estimation tracks the temporal evolution of a POD subspace online. The framework is experimentally demonstrated for flow around an airfoil. POD subspaces are extracted from wall-pressure fluctuations measured by a microphone array over a range of angles of attack and under different control inputs. The subspaces are found to lie on a one-dimensional submanifold of the Grassmann manifold. Moreover, the transition from separated to attached flow, induced by a plasma actuator, follows a reproducible trajectory along the same submanifold identified from statistically stationary flow data. The temporal evolution of the subspace is consistent with the transient evolution of the flow field observed using particle image velocimetry. These results show that POD subspaces can serve as representative flow states, enabling their temporal evolution across a wide range of flow conditions to be tracked online in a low-dimensional space based on wall-pressure fluctuations. This low-dimensional representation provides a basis for real-time flow-state estimation and feedback control.
