Model-based multi-sensor fusion for reconstructing wall-bounded turbulence

Abstract: 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.