Flow Reconstruction of Urban Wind Fields for Wind-Based Path Planning

Three-dimensional Reynolds-Averaged Navier-Stokes simulations are performed to calculate the wind field of a full-size urban district of 1 km \(^2\) around the campus of Technical University of Berlin with the inlet wind direction as a parameter. Two-dimensional snapshots of the simulation data set are used for model reduction by proper orthogonal decomposition (POD) to reduce the complexity of the system. The POD modes are then used to estimate a high resolution wind field from sparse velocity sensor measurements by using the Gappy POD as a data reconstruction method. The sensor measurements are taken from a simulation test case that is not included in the snapshot basis. The sensor placement problem that needs to be solved to find effective sensor locations is investigated using two different methods. The performance of the data reconstruction is then assessed by calculating the least-squares reconstruction error. An application of the estimated urban wind field is demonstrated by finding a wind-based minimum-energy path from a start to a final location for an operation of unmanned aerial vehicles. The wind-based path is compared to the shortest path for a reduced order model taking only 5 sensor measurements. An overall mean energy reduction of 5.5 \(\%\) was calculated by the full-order model and of 3.9 \(\%\) by the reduced order model. This suggests that trajectory planning may be performed on inexpensive reduced-order models of the urban wind field.