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Sensitivity analysis applied for a flow around spring-mounted cylinder

Last modified: 2018-04-19

#### Abstract

Calculations of sensitivities for a flow around spring-mounted cylinder free to oscillate in the cross stream direction are introduced. In this work, the state vector of the fluid-structure interaction (FSI) problem is given by a base flow plus a perturbation, in which the base flow is steady and the displacement of the cylinder is given by a perturbation. The goal is to identify what regions of the domain originate the instabilities on the perturbation field. This region, called of

*wavemaker*, are given by the sensitivity to external forcing at specific cases in which the external forcing is proportional to the perturbation field. The mathematical expression for the sensitivity calculation is obtained by considering an optimization problem. The*wavemaker*region is determined in two cases: at subcritical Reynolds number Re=33 and supercritical Reynolds number Re=60. We observed that the*wavemaker*region changes with the variation of the natural frequency and presented differences if compared with the*wavemaker*region of the fixed cylinder at Re=33. However, for the flow past fixed and spring-mounted cylinders the*wavemaker*regions are similar at Re = 60. In the numerical simulations, the Spectral/*hp*element was used for spatial discretization and the linear adjoint FSI system was solved by considering a generalized eigenvalue problem, in which the Arnoldi method was employed.#### Keywords

Sensitivity; adjoint; spring-mounted cylinder

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