Polynomial chaos assessment of design tolerances for vortex-induced vibrations of two cylinders in tandem

The presence of aerodynamics loadings makes the design of some classes of elastic structures, as, for instance, marine structures and risers, very challenging. Moreover, capturing the complex physical interaction between the structure and the fluid is challenging for both theoretical and numerical models. One of the most important phenomena that appear in these situations is vortex-induced vibrations. The picture is even more complicated when multiple elastic elements are close enough to interact by modifying the fluid flow pattern. In the present work, we show how the common design practice for these structures, which is entirely based on deterministic simulations, needs to be complemented by the uncertainty quantification analysis. The model problem is a structure constituted by two elastically mounted cylinders exposed to a two-dimensional uniform flow at Reynolds number 200. The presence of a manufacturing tolerance in the relative position of the two cylinders, which we consider to be a source of uncertainty, is addressed. The overall numerical procedure is based on a Navier-Stokes immersed boundary solver that uses a flexible moving least squares approach to compute the aerodynamics loadings on the structure, whereas the uncertainty quantification propagation is obtained by means of a nonintrusive polynomial chaos technique. A range of reduced velocities is considered, and the quantification, in a probabilistic sense, of the difference in the performances of this structure with respect to the case of an isolated cylinder is provided. The numerical investigation is also complemented by a global sensitivity analysis based on the analysis of variance.