Wall-bounded turbulent flows can be challenging to measure within experiments due to the breadth of spatial and temporal scales inherent in such flows. Instrumentation capable of obtaining time-resolved data (e.g., hot-wire anemometers) tends to be restricted to spatially localized point measurements; likewise, instrumentation capable of achieving spatially resolved field measurements (e.g., particle image velocimetry) tends to lack the sampling rates needed to attain time resolution in many such flows. In this study, we propose to fuse measurements from multi-rate and multi-fidelity sensors with predictions from a physics-based model to reconstruct the spatiotemporal evolution of a wall-bounded turbulent flow. A “fast” filter is formulated to assimilate high-rate point measurements with estimates from a linear model derived from the Navier–Stokes equations. Additionally, a “slow” filter is used to update the reconstruction every time a new field measurement becomes available. By marching through the data both forward and backward in time, we are able to reconstruct the turbulent flow with greater spatiotemporal resolution than either sensing modality alone. We demonstrate the approach using direct numerical simulations of a turbulent channel flow from the Johns Hopkins Turbulence Database. A statistical analysis of the model-based multi-sensor fusion approach is also conducted.

由于此类流动固有的空间和时间尺度的广度，在实验中测量壁面湍流可能具有挑战性。能够获得时间分辨数据的仪器（例如，热线风速计）往往仅限于空间局部点测量；同样，能够实现空间分辨场测量（例如，粒子图像测速）的仪器往往缺乏在许多此类流中获得时间分辨率所需的采样率。在这项研究中，我们建议将来自多速率和多保真度传感器的测量与基于物理模型的预测相融合，以重建壁面湍流的时空演化。一个“快速”滤波器被公式化，以通过从 Navier-Stokes 方程导出的线性模型的估计来同化高速率点测量。此外，每次有新的现场测量可用时，都会使用“慢”滤波器来更新重建。通过在时间上向前和向后遍历数据，我们能够以比单独的任何一种传感模式更高的时空分辨率重建湍流。我们使用来自约翰霍普金斯湍流数据库的湍流通道流的直接数值模拟来演示该方法。还对基于模型的多传感器融合方法进行了统计分析。通过在时间上向前和向后遍历数据，我们能够以比单独的任何一种传感模式更高的时空分辨率重建湍流。我们使用来自约翰霍普金斯湍流数据库的湍流通道流的直接数值模拟来演示该方法。还对基于模型的多传感器融合方法进行了统计分析。通过在时间上向前和向后遍历数据，我们能够以比单独的任何一种传感模式更高的时空分辨率重建湍流。我们使用来自约翰霍普金斯湍流数据库的湍流通道流的直接数值模拟来演示该方法。还对基于模型的多传感器融合方法进行了统计分析。