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Exact and Adaptive Modeling and Simulation of the Air Passage of Aircraft Engines

Final Report Summary - EXAMPLE (Exact and Adaptive Modeling and Simulation of the Air Passage of Aircraft Engines)


EXAMPLE improved the design and analysis processes for the air passage of aircraft engines by enhancing the existing mathematical technology using the new approach of Isogeometric Analysis (IGA). The first part of the project has been devoted to advanced volume parameterization techniques that are suitable for a particular class of complicated free form volumes, namely for the air passage of aircraft engines. The work in this part has contributed to achieve five specific objectives:

1.1 Techniques for generating a volumetric air passage parameterization. We defined a completely new air passage modelling methodology, based on a volume parameterization, to build up an efficient design-through-analysis process.

1.2 Validation of the created parameterizations. We validated the capability of the new parameterization with respect to various criteria: suitability for CFD analysis; computational time, robustness and efficiency; potential for automatic air passage optimization.

1.3 Optimization of parameterizations based on well-established quality criteria of the meshing community.

1.4 Investigation of the capabilities of an automatic design optimization for the air passage with respect to certain aerodynamic objectives.

1.5 Incorporation of adaptive and multi-level techniques.

The second part of EXAMPLE was concerned with the foundations by studying adaptive multilevel spline representations on three-dimensional domains. We obtained results addressing the following four specific topics:

2.1 Definition of hierarchical bases for trivariate multi-level tensor-product splines and investigation of their properties.

2.2 Algorithms and data structures for trivariate multi-level tensor-product splines. This is needed in order to prepare the ground for applications of the hierarchical spline technology in practice.

2.3 Applications to volume parameterization. We will use the adaptive spline spaces to enhance the volume parameterization techniques.

2.4 Application to numerical simulation in isogeometric analysis. Beside applications to volume parameterization we will also investigate the potential of our trivariate adaptive splines for isogeometric simulation.


The volumetric air passage modeling technology developed in EXAMPLE is ready for its commercial use to optimize the most critical blade geometries of modern aircraft engines, such as the mid turbine frame. Therefore, all tools and interfaces are set up to an entire optimization process for volume parameterization, mesh generation and deformation, computational fluid dynamics and post processing. The new approach is significantly faster which leads to an improvement of the overall design-to-product time. Furthermore, the new approach is more robust with respect to the overall algorithm failure rate which leads to more profound design results. Hence, EXAMPLE gained a significant and prompt impact to real engine development.

In addition, the integration of advanced spline technology has improved the product development process for sensible parts aircraft engines at MTU. Therefore, it was demonstrated that the THB-splines can significantly decrease the number of necessary coefficients compared to existing tensor-product spline technologies while maintaining the geometric quality.

The mathematical foundations of the multivariate adaptive spline technology have made substantial progress. Properties such as algebraic completeness, approximation power and linear independence are well understood, thereby providing a firm basis for applications in industry and in the emerging field of isogeometric analysis. The scientific results of the EXAMPLE project have been disseminated in a substantial number of scientific publications, which have appeared in leading journals in the field.

Besides the work on the mathematical foundations, the project has also focused on scientific software development. The THB-spline technology has been made available as part of the open source G+Smo library and is ready to use. The implementation is dimension-independent and versatile.

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G+Smo web page:


EXAMPLE improved the current product development process for some of the most critical aircraft engine parts. By bringing a brand-new developed technologies like adaptive splines and volumetric air passage modeling from its theoretical basis to a real industrial application, the mind-set of MTUs engineering department and management was encouraged to trust in the power of research projects like EXAMPLE. Moreover, the results prepared the ground for further technological developments in the wider field of shape modeling and isogeometric simulation.

The EXAMPLE project opened new perspectives and career opportunities for the participating fellows. The EXAMPLE scientific events and the participation in various international conferences and workshops provided the opportunity to establish many new scientific contacts for all EXAMPLE fellows. During the stay at MTU, as a global industrial player, the mathematical research oriented fellows also built up their network with the engineering communities and their concepts, problems and way of thinking. This greatly improves the understanding of each other to tackle interdisciplinary challenges in today's engineering world. Furthermore, this also increases the flexibility of their future career.