CFC 2025

Sparse sensor placement for turbulent flow field reconstruction based on mean-flow-linearized dynamics

  • Kracht, Erick (University of Chile)
  • Brunton, Steven (University of Washington)
  • McKeon, Beverley (Stanford University)
  • Herrmann, Benjamin (University of Chile)

Please login to view abstract download link

Data-driven methods are improving our capability to predict, control and understand turbulent flows. However, these techniques often rely on having access to complete flow field measurements, which are difficult to acquire due to the multi-scale nature of turbulence. Fortunately, velocity field data may be reconstructed from measurements of a few “strategically placed” point sensors. [1] In recent work, we achieved this by combining a greedy sensor selection algorithm with a low-rank representation of the flow in terms of the leading empirical orthogonal functions (EOFs) that arise from the mean flow linearization [2]. Here, we include an eddy viscosity model in our linearized equations to compute eddy EOFs to investigate if they offer a more efficient low-rank representation for coherent perturbations of the mean flow. We test our method on data from numerical simulations of turbulent flow in a minimal channel at Reτ = 185. The flow reconstruction performance and sensor locations are investigated and compared with those obtained using a data-driven sensor placement strategy based on proper orthogonal decomposition modes. Moreover, we study how the wall-normal integrated reconstruction error is distributed in wavenumber-frequency space using the spectral proper orthogonal decomposition [3]. Our equation-based framework proves to be an attractive alternative, since it performs similarly to the data-driven approach, but it does not require data snapshots and relies only on knowledge of the mean flow. REFERENCES [1] Manohar, K., Brunton, B. W, Kutz, J. N. & Brunton, S. L. 2018 Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns. IEEE Control Systems Magazine 38 (3), 63–86. [2] Herrmann, B., Baddoo, P. J., Dawson, S. T., Semaan, R., Brunton, S. L. & McKeon, B. J. 2023 Interpolatory input and output projections for flow control. Journal of Fluid Mechanics 971, A27. [3] Towne A., Schmidt O. T. & Colonius T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis, J. Fluid Mech. 847, 821