Modeling the flow around a cylinder using sensitivity analysis and reduced spaces. - Patiño Ramirez, Gustavo Alonso (2018)
This thesis concerns the wake control and flow dynamic analysis for a flow around a circular cylinder at different Reynolds numbers using reduced models. The wake control and dynamics in the reduced space were addressed using the sensitivity theory and the adjoint method. In the case of wake control, it was possible to predict the physical parameters of the active and passive controllers on the wake of the main cylinder. On the other hand, in the construction of the reduced space, a new shift mode calculated from a perturbation of the mean flow was proposed using the sensitivity to base flow modifications. The mathematical basis of the reduced space was constructed using a Fourier modal decomposition of the flow enriched by the shift mode. The proposed reduced space made possible the recomposition of the flow and the comparison with the physical parameters calculated in the physical space. Additionally, using the reduced space, it was possible to determine the transition dynamics between the equilibrium point of the Navier Stokes equation and the non-linear saturation state using the Landau coefficients obtained in the reduced model, opening the possibility of solving the flow around a 2D and 3D cylinder with low computational cost.