Sensor placement for data assimilation of turbulence models using eigenspace perturbations

Abstract

We present an approach to sensor placement for turbulent mean flow data assimilation in the context of Reynolds-averaged Navier–Stokes (RANS) simulations. It entails generating a spatial uncertainty map through the eigenspace perturbations (ESPs) of the baseline turbulence model (e.g., the k−ω shear stress transport model) to quantify the epistemic structural errors in the model. A novel greedy search algorithm is proposed to place sensors targeting regions of highest uncertainty in the spatial uncertainty map generated from ESP. The algorithm is computationally efficient (e.g., computational cost negligible compared to a RANS solution) and is both easy to implement and tune. It involves two hyper-parameters (a constraint to avoid sensor clustering and the number of sensors) which we investigate in-depth. A variational (adjoint-based) data assimilation approach is used for flow reconstruction. The proposed strategy was tested on three two-dimensional wall-bounded flows (Reynolds number ranging 5.6×103–9.36×105) involving flow separation and reattachment. For the wall-mounted hump case, we found that data assimilation using 33 sensors with our proposed sensor placement algorithm reduced the average velocity prediction error by 60% vs 38% with a simple uniform placement of sensors. Furthermore, we found that we could achieve 61% error reduction using our algorithm with only three sensors. Notably, in all tested cases, the error reduction using our method for sensor placement was close in accuracy to the instances where the entire flow field data were used for flow reconstruction, which involved two to three orders of magnitude more data points than the placed sensors.