Influence of Different Parametrizations on the Optimum Design of a High Pressure Turbine Blade Firtree
Authors: Wagner Frank , Kühhorn Arnold , Weiss Thomas , Otto Dierk 
Published: September 2016

Today the design processes in the aero industry face many challenges. Apart from automation itself, a suitable parametric geometry setup plays a significant role in making workflows usable for optimization. At the same time there are tough requirements against the parametric model. For the lowest number of possible parameters, which should be intuitively ascertainable, a high flexibility has to be ensured. Within the parameter range an acceptable stability is necessary. Under these constraints the creation of such parametric models is a challenge, which should not be underestimated especially for a complex geometry.
In this work different kinds of parametrization with different levels of complexity will be introduced and compared. Thereby several geometry elements will be used to handle the critical regions of the geometry. In the simplest case a combination of lines and arcs will be applied. These will be replaced by superior elements like a double arc construct or different formulations of b-splines. There will be an additional focus on the variation of spline degree and control points. To guarantee consistency a set of general parameters will be used next to the specific ones at the critical regions. The different parameter boundaries have a influence on the possible geometries and should therefore be tested separately before an optimization run.
The analysis of the particular parametrization should be compared against the following points:
• effort for the creation of the parametrization in theory
• required time for the implementation in the CAD software
• error-proneness/robustness of the parametrization
• flexibility of the possible geometries
• accuracy of the results
• influence of the number of runs on the optimization
• comparison of the best results
Even though this assessment matrix is only valid for the considered case, it should show the general trend for the creation of these kinds of parametric models.
This case takes a look at a firtree of a high pressure turbine blade, which is a scaled version of the first row from a small to medium aero engine. The failure of such a component can lead to a critical engine failure. For that reason, the modeling/meshing must be done very carefully and the contact between the blade and the disc is of crucial importance. It is possible to use scaling factors for three dimensional effects to reduce the problem to a two dimensional problem. Therefore the contact description is shortened from face-to-line to line-to-point.
The main aim of the optimization is the minimization of the tension (notch stress) at the inner bends of the blade respectively at the outer bends of the disc. This has been the limiting factor in previous investigations. At this part of the geometry the biggest improvement are expected from a superior parametrization. Another important constraint in the optimization is the pressure contact (crushing stress) between blade and disc. Additionally the geometry is restricted with measurements of the lowest diameter at specific fillets to fulfill manufacturing requirements.