We study the stabilization of a fluid-structure interaction system around an unstable stationary solution. The system consists of coupling the incompressible Navier-Stokes equations, in a two dimensional polygonal domain with mixed boundary conditions, and a damped Euler-Bernoulli beam equations located at the boundary of the fluid domain. The control acts only in the beam equations. The feedback is determined by stabilizing the projection of the linearized model onto a finite dimensional invariant subspace. Here we have resolved two important challenges for applications in this field. One is the fact that we prove a stabilization result around a non zero stationary solution, which is new for such fluid-structure interaction systems. The other one is that the feedback laws that we determine do not depend on the Leray projector used to get rid of the algebraic constraints of partial differential equations. This is essential for numerical aspects.

A new parameterized CFD solver Turb’Opty™ has been developed based on a Taylor series expansion to high order derivatives of the solutions of the discretized Navier-Stokes equations. The method has been successfully applied to the laminar compressible flow field of the T106 turbine blade cascade. Comparisons with the classical CFD results have validated the accuracy of the parameterized solutions obtained by a simple polynomial reconstruction around a reference solution. The CPU efficiency has been emphasized by quickly computing the performance maps (power and losses) of this blade cascade. Wide industrial perspectives of turbomachinery global optimization are finally demonstrated by coupling this method with a simple genetic algorithm.

The newly developed parameterized CFD solver Turb’Opty™, based on a Taylor series expansion to high order derivatives of the solutions of the discretized Navier-Stokes equations, has been successfully applied to the turbulent incompressible flow field of an engine cooling fan blade cascade. Comparisons with the classical CFD results have validated the accuracy of the parameterized solutions obtained by a simple polynomial reconstruction around a reference solution with respect to two different flow parameters for two different cases: a fifth order expansion with respect to these coupled parameters for a frozen turbulence and a first order expansion with respect to each parameter for a variable turbulence. The latter is found to have a better accuracy and a larger range of application. Starting from a reference solution obtained with another commercial code has also been successfully tested. Finally, further industrial perspectives of turbomachinery global optimization are finally demonstrated by coupling this method with a simple genetic algorithm.