Computational Strategies and Numerics for High-Fidelity Finite Element Models with Application to Aero-Engine Design

Due to the availability of enormous computational power and decreasing CPU costs, finite element models are becoming more and more complex in all fields of engineering. In this context, also aero-engine manufacturers try to model the thermo-mechanical behavior of their engines as accurately as possible. In the past, this was done by simplified Whole Engine models (classical WEM’s), but nowadays high-fidelity Whole Engine Models are currently being developed. These models contain no simplifications or idealizations as used in classical WEM’s, which leads on the one hand to the possibility of getting more accurate results in terms of displacements and stresses, but on the other hand causes a bunch of challenges with respect to the modeling strategy and numerics. Some of these challenges and numerical problems will be addressed and possible solution strategies will be eveloped.
In commercial finite element codes many different finite element formulations are available. Most of these standard elements work well for “normal” applications. But, for example, for poor aspect ratios the choice of the finite element formulation is essential to prevent unwanted phenomena like locking or hourglassing.
Since there are almost no simplifications or idealizations in high fidelity WEM’s, all types of nonlinearity are present (material, geometrical and contact nonlinearities). Especially the contact behavior is a major challenge in models with high complexity such as aero engines. For this reason, it is important to understand the different algorithms and principles of contact mechanics. Also the time-step size of numerical integration is influenced significantly by the chosen contact algorithm which has a direct impact on the overall computational time. If there should be no simplifications or idealizations, special attention has to be given to parts like bearings of the engine rotor. Here, we will answer the question about the necessary mesh density for such parts depending on the used contact formulation.
For the solution of the equations of motion of a thermo-mechanical system, numerical timeintegration schemes are necessary. There exist basically two different approaches for numerical integration, implicit and explicit schemes. The latter are suited in particular for highly dynamic processes, but could also be used for long term computations. This might be advantageous because of the simplicity and stability of explicit time-integration. On the other hand there is a need of extremely small time steps of these integration algorithms. Implicit time-integration is more complex, but allows for much bigger time-steps which, however, can cause difficulties with respect to contact problems. In this work both possibilities of timeintegration are discussed in detail with all advantages and disadvantages especially in the context of rotating flexible structures.
Typical high-fidelity Whole Engine Models have millions of degrees of freedom, which leads to very high computational costs. There are different possibilities of “model reduction” techniques aiming at reducing the number of degrees of freedom while keeping the accuracy as high as possible. One of these techniques will be discussed and finally its capabilities for academic examples as well as for the example of a Dummy Whole Engine Model will be investigated.