Abstract
This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.
Highlights
There are many technical or scientific applications in a wide range of technical disciplines, where the mathematical modelling of fluid-structure interaction (FSI) problems is important
The elastic axis was located at 40 percent of the airfoil chord measured from the leading edge of the airfoil, x f = 0.4c = 0.12 m and the center of gravity of the airfoil was located at 37 percent of the airfoil, i.e. xcg = 0.37c
This paper described two possible strategies of solution of an classical aeroelastic problem
Summary
There are many technical or scientific applications in a wide range of technical disciplines, where the mathematical modelling of fluid-structure interaction (FSI) problems is important. The mathematical modelling of FSI problems in general is much more complicated, because one needs to consider the viscous possibly turbulent flow which is in the interaction with the nonlinear behavior of the elastic structure. In applications the FSI problems are usually solved with the aid of the so-called partitioned or de-coupled approach, which approximates the fluid flow and structure motion by different solvers. One of the most popular methods is the finite element method, but in its application for numerical simulation of incompressible flow problem one must overcome several sources of instabilities. The paper is organized as follows: first the mathematical model is presented, the weak form suitable for application of the finite element method is introduced, the numerical approximation is presented and the numerical results are shown
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