A cost-effective algorithm for the co-simulation of unsteady and non-linear aeroelastic phenomena

Increasingly flexible structures force engineers and scientists to improve simulation capabilities incorporating an adequate description of non-linear phenomena. Furthermore, many critical operating conditions of aeronautical and civil structures are associated with unsteady phenomena, which makes it necessary to tackle this kind of problems. A critical aspect to be analyzed is the stability of the system: the determination of, not only the critical flutter speed, but also the post-critical behavior, is fundamental to guarantee the safety of designs and determine mitigation strategies. In this work, a numerical technique that allows simulating the non-linear and unsteady behavior of highly flexible structures immersed in a fluid at high Reynolds numbers is presented. This problem is addressed using a co-simulation approach, coupling the Unsteady Vortex Lattice Method (as the aerodynamic model) with the Finite Element Method using non-linear beams and rigid bodies (as the structural dynamics model). The coupling is achieved through a weak interaction algorithm. The resulting method has a very good compromise between versatility and computational cost, and is not restricted to periodic motions or linear equations of motion. Nonlinearity is included through the possibility to represent large displacements and rotations of the structure, a visco-elastic material behavior, and a nonlinear relation between the aerodynamic loads and the incidence of the incoming flow. The domains considered in the submodels and the temporal and spatial discretizations used for each one are essentially different; the interaction process must take into account these aspects. The computational implementation is carried out by combining a general-purpose structural dynamics code with an aerodynamic tool oriented to the analysis of three-bladed horizontal axis wind turbines. Examples to validate the code and show the potential of the proposed method are presented in the Results section.