Efficient assimilation of sparse time-averaged data for the optimization of URANS-based turbulent wake flow simulations

Data assimilation (DA) plays a crucial role in extracting valuable information from flow measurements in fluid dynamics problems. Often, only time-averaged data is available, which poses challenges for DA of unsteady flow problems. Recent works have shown promising results in optimizing Reynolds-averaged Navier-Stokes (RANS) simulations of stationary flows using sparse data through variational data assimilation, enabling the reconstruction of mean flow profiles.

In this study, we perform variational data assimilation (3D-Var) of sparse time-averaged data into an unsteady RANS (URANS) simulation by means of a stationary divergence-free forcing term in the URANS momentum equations. The efficiency and speed of our method are enhanced by employing coarse URANS simulations and leveraging the stationary discrete adjoint method for time-averaged URANS equations.

Our results demonstrate that data assimilation of sparse time-averaged velocity measurements not only enables accurate mean flow reconstruction but also improves the flow dynamics, specifically the vortex shedding frequency. To validate the efficacy of our approach, we apply it to turbulent flows around cylinders of various shapes at Reynolds numbers ranging from 3000 to 22000. Our findings indicate that data points near the cylinder play a crucial role in improving the vortex shedding frequency, while additional data points further downstream are necessary to also reconstruct the time-averaged velocity field in the wake region.