Category Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics

Identification of Sources of Error Induced by Geometry and Discretisation

The grid developer has many tools at his disposal. These methods range from manual procedures to fully automated ones, which allow the operator to mesh com­plex geometries like complete aircraft configurations including wings, tail planes, flaps and engines, by setting only a few parameters. However, these fully automated

E. Mazlum • R. Radespiel

Institute of Fluid Mechanics, Technische Universitat Braunschweig Hermann-Blenk-Str. 37, D-38108 Braunschweig, Germany e-mail: {e. mazlum, r. radespiel}@tu-bs. de

B. Eisfeld et al. (Eds.): Management & Minimisation of Uncert. & Errors, NNFM 122, pp. 3-28. DOI: 10.1007/978-3-642-36185-2_1 © Springer-Verlag Berlin Heidelberg 2013

meshing tools generally offer only very limited control on the exact topology of the generated grid. To efficiently analyse the uncertainties in the flow solution caused by the topology of the grid, a grid generation tool is needed which allows the user to shape the grid freely.

Especially for analysing the wake discretization, a grid generation tool is needed which gives the operator full control over the grid generation process. A suited grid generator is Gridgen V15 [1] which is why it was used as the preferred tool in this work. In Gridgen grids are generated manually by creating "connectors", "domains" and "blocks". This approach gives many design options for the shape of the grid in the wake region.

Furthermore, Gridgen allows the generation of hybrid grids. Hybrid grids are a combination of fully structured hexahedral layers, and semi or fully unstructured prism or tetrahedral layers, respectively.

Methods and Strategies for the Detection and Management of Grid Induced Uncertainties in Numerical Aerodynamics

Continuous development of numerical methods over the last decades together with increasing available computer power has made Computational Fluid Dynamics (CFD) a key technology in modern aircraft development. The results obtained over the last decades give rise to the vision that future aircraft design may almost entirely rely on numerical simulations. This shift in paradigm will not only dramatically change the engineering process in itself, but also the requirements on the simulation data. In particular, safe estimates of the errors and uncertainties of the simulation results will have to be provided, similar to error bars in experimental data from the windtunnel.

In order to meet such future needs, the collaborative research project MUNA – Management and Minimisation of Errors and Uncertainties in Numerical Aerody­namics – has been initiated within the 4th German Aeronautics Research Program (Luftfahrtforschungsprogramm). Following the predecessor projects ME­GAFLOW and MEGADESIGN, altogether 12 partners from industry (Airbus, Cas – sidian, Eurocopter), research organisations (DLR, Institute of Aerodynamics and Flow Technology) and universities (RWTH Aachen: Institute of Aerodynamics and Institute of Computational Analysis of Technical Systems; TU Berlin: Institute of Fluid Mechanics and Technical Acoustics; TU Braunschweig: Institute of Fluid Mechanics, Institute of Aircraft Design and Lightweight Structures and Institute of Scientific Computing; University Stuttgart: Institute of Aerodynamics and Gas – dynamics; University Trier: Department of Mathematics) have been developing and applying methods, addressing errors and uncertainties of various kind, typically en­countered in CFD simulations. For this purpose, the DLR TAU code was provided as major simulation tool.

In a first step the partners jointly collected possible sources of errors and uncer­tainties, where the computational grid, turbulence modeling, the numerical accuracy and geometrical issues in the context of coupled multidisciplinary simulations have been identified as important. Consequently, the research activities of the first project phase have been concentrating on the respective areas, which is also reflected by the organisation of the book.

In the second phase of the project, stochastic uncertainties, also called aleatory, have been addressed. Therefore the final part of the book is devoted to various activ­ities towards efficiently computing statistical output quantities due to uncertainties in the input parameters, including methods for the robust design under geometrical uncertainties.

The results of the project have been presented to the public during two Work­shops held on March 23th and 24th 2010 and on October 25th 2012. The current book documents the results achieved by the partners.

The editor is indebted to all co-workers of the project, in particular to the mem­bers of the steering committee, Holger Barnewitz (Airbus), Willy Fritz (Cassidian) and Prof. Dr. Frank Thiele (TU Berlin), for their contributions and inevitable sup­port in making MUNA a success. Furthermore the editor wants to thank the general editor of the Springer series “Notes on Numerical Fluid Mechanics and Multidiscip­linary Design”, Prof. Dr. W. Schroder, and the staff of the Springer-Verlag for the opportunity to publish the technical results of the MUNA project.

Finally the funding of the partner activities by the German Ministry of Economics within the 4th German Aeronautics Research Program is gratefully acknowledged.

Braunschweig Bernhard Eisfeld

November 2012

E. Mazlum and R. Radespiel

Abstract. For the numerical simulation of complex aircraft configurations discret­isation errors around wings and tailplanes as well as in their wakes are a key source of computational uncertainties. Both simplifications and uncertainties in the geo­metry description as well as improper numerical grids have an influence on the pre­diction of lift and drag coefficients, whereas the error magins are not well known. For this reason, the Institute of Fluid Mechanics systematically analysed and quan­tified grid induced uncertainties in the frame of the projekt MUNA. Based on this, strategies and tools have been developed for error detection and improvement of im­properly discretised grid regions. For the detection of dicrestization errors, a method based on the artificial dissipation of central schemes has been developed. Further­more, two methods have been developed for local grid improvement which follow two different grid manipulation strategies. These strategies are the local deforma­tion of grids and the local refinement of hexahedra. The developed methods and tools have been verified on different test cases.