Contributed Papers

1. M. Delanaye, F. Lani, I. Lepot, Cenaero asbl, Gosselies, Belgium:

CAD-centric multidisciplinary optimisation for industrial aeronautics design

The aim of the present contribution is to present innovative methodologies used to tackle challenging multi-disciplinary designs in the aeronautics and transport industries. Those include the design of complex turbomachinery blading for high-efficiency engines or cost-effective composite parts including geometry, material and manufacturing optimisation. The paper will present Cenaero in-house optimisation platform Minamo and the way it has been embedded in fully automated computational optimisation loops to carry on this complex design problems in a CAD-centric approach.

Minamo implements powerful mono- and multi-objective variants of genetic algorithms tuned and accelerated by robust and efficient coupling with surrogate models and is easily coupled with any CAE software in order to allow successful completion of multi-disciplinary shape optimisation for complex parts accounting for multiple engineering disciplines including manufacturing processes aspects and cost. As CAD systems have become an integral and critical part of the design process in various fields, it is of prime importance to exploit the native CAD system and CAD model directly within the design loop in order to avoid translation, manipulation and/or regeneration errors resulting from different geometry kernels. Direct and native CAD access based on the CAPRI middleware hence also constitutes a corner stone of the developed solutions.

Challenging industrial aeronautics and more particularly turbomachinery state-of-the-art applications will be presented in order to highlight the different innovative aspects of the developed methodologies. On the one hand, the robust multi-point non-axisymmetric hub design[1] of a High Pressure Compressor rotor blade will be detailed, highlighting the performance gain achieved while satisfying the stability constraints. On the other hand, an aero-acoustics optimisation of a contra-rotating open rotor including structural constraints carried out in the frame of the DREAM FP7 project will be described. The multi-objective optimisation specification first consisted in maximizing the global efficiency at Top-of -Climb and minimizing the acoustic level at Take-Off, while respecting thrust and power split constraints for each operation point. Both 2D profiles shape and 3D modifications, with variable pitch adjustment, were carried out based on 3D steady RANS evaluations with mixing plane approach. This first phase provided interesting trends, with an estimated 10dB noise reduction at Take-Off, but also essentially allowed to gain clear knowledge and understanding of the behavior of the chosen cost and constraints functions, among which the critical acoustic cost function implemented focusing on interaction noise.

Optimisation of manufacturing processes [2,3] shall help engineers to design and produce the best parts with both the objectives of reducing the cost and improving the mechanical performances of the structures. Applications of composite parts optimisation including performance of the part, manufacturing aspects and cost will be presented. First, a computational optimisation chain which supports the design and the development of parts made by injection of a thermoplastic resin reinforced with short carbon fibers will be presented. The investigated component is part of an assembly located inside a low pressure compressor of an aero-engine. The part is aimed to be optimised in order to achieve a minimal mass while maintaining the mechanical performance of its metallic counterpart. The optimisation chain includes as essential variability the position of injection ports. Challenges include the validation of the predictions in terms of fibers orientations, the prediction and minimization of the thermal shrinkage and deformation, the automatic generation of optimal meshes for structural analysis, based for instance on the analysis of hot spots in the structure and on ‘a posteriori’ error evaluation. Second, a new optimisation loop that is capable of optimising the draping of a composite part to increase the mechanical response and decrease the manufacturing cost will be described. Indeed, engineers and researchers are nowadays familiar with virtual testing approaches at different levels of the building block approach, from coupons to large components. However, current methods usually involve only the consideration of traditional objectives such as static, dynamic and buckling margins coupled with a maximum admissible mass constraint. Recent trends in the design of composite structures involve global approaches, integrating the consideration of manufacturing processes in a procedure aiming at the optimisation of the design and the draping process, both technically and economically. Today the majority of the aircraft and aerospace parts are based on preimpregnated carbon fibers plies delivered on rolls of prepreg tape. The part is then manufactured by applying a defined set of plies onto a tool thanks to a manual procedure (Hand Lay-up) or an automated method (Automated Tape Lay-up). During this process, the plies are shaped to form a structure of a complex geometry. The deflection involved in the process is necessary because this is the core of the composites forming methodology. Nevertheless, this deflection has an important impact on the mechanical properties as it entails the misalignment of the fibers. Hence, if the fibers angle of the part is different from the design fibers angle used in the computation to predict the final mechanical behavior, then the part’s in-service response and performance are compromised. The draping process is characterized by its dependence on the geometry, the location of the draping initiation (seed point), the draping direction (seed curve), the deformation property of the ply and in the case of prepregs, the mechanical properties of the whole laminate. The objectives are the minimization of the shear angle, the minimization of the scrap as well as the assessment of the manufacturability. The challenge of this work is to make the design procedures as robust as possible so that the virtual prototype can be transferred into the production line without any downstream problems.

References

1. Design optimisation of a HP compressor blade and its hub endwall, V. Iliopoulou, I. Lepot and P. Geuzaine, Paper GT2008-50293, to appear in the Proceedings of the ASME Turbo Expo 2008 Conference (Power for Land, Sea and Air), 2008.
2. Multi-disciplinary optimization of aerospace and aircraft components including draping process aspects, X. Mencaglia, D. Goode, F. Lani, Proceedings of the WCSMO8, 8th World Congress on Structural and Multidisciplinary Optimization, 2009.
3. CAD-centric technical-economical optimization of composite structures using feature-based cost models, X. Mencaglia, Ch. Friebel, H. Kato, F. Lani, in Proceedings of the Composites2009, 2nd ECCOMAS Thematic Conference on the Mechanial Response of Composites, 2

2. C. Hinterberger, M. Olesen, Faurecia, Augsburg:

Application of a Continuous Adjoint Flow Solver for Geometry Optimisation of Automotive Exhaust Systems

Meeting backpressure and flow uniformity requirements within severe packaging constraints presents a particular challenge in the layout of catalyst inlet cones. In these cases, a parameterized optimisation of the potentially complex cone geometries is inefficient (and inappropriate). Even assuming that a parameterization of the complex surface forms is possible, the choice of parametric shapes invariably affects the achievable results. Additionally, the long computation time for solving the flow fields limits the number of shape parameters that can be considered.

To overcome these restrictions, an optimisation tool has been developed at Faurecia Emissions Control Technologies [1] that is based on the continuous adjoint formulation derived and implemented by C. Othmer et al [2, 3]. The open source CFD toolbox OpenFOAM® is used as the platform for the implementation. Since the geometry itself is modelled using an immersed boundary method, no geometry parametrisation is required. The method allows computation of the sensitivity of flow uniformity and energy dissipation (or other target quantities) based on the instantaneous geometry. After the calculated surface sensitivities are combined and corrected for manufacturing and topological constraints, the location of the immersed boundary is automatically adjusted. It is thus possible to automatically determine a feasible catalyst cone geometry starting from an amorphous box (representing the packaging constraints) that is supplemented by definitions of inflow boundaries (for the flow coming from different manifold runners) and the outflow boundary (the catalyst surface). The calculation time associated with the process is on the same order of magnitude as the solution of the RANS equations itself. The optimisation tool and some practical results will be presented.

References:

1. C. Hinterberger, M. Olesen, “Automatic geometry optimisation of exhaust systems based on surface sensitivities computed by a continuous adjoint CFD method in OpenFOAM”, SAE 2010-01-1278
2. C. Othmer, E. de Villiers and H.G. Weller “Implementation of a continuous adjoint for topology optimisation of ducted flows”, AIAA-2007-3947
3. C. Othmer, “A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows”, Int. J. Num. Meth. Fluids, 2007

OpenFOAM® is a registered trademark of OpenCFD Ltd.

3. Jan Riehme¹, Uwe Naumann², University of Hertfordshire, Hatfield, and ²RWTH Aachen University, Aachen:

¹The differentiation-enabled NAG Fortran Compiler, ²RWTH Aachen University, Aachen

The development of the differentiation-enabled NAG Fortran Compiler is a joint effort of the University of Hertfordshire, UK, and the RWTH Aachen University, Germany. The target is the integration of current (or new) Automatic Differentiation technology into the industrial strength Fortran compiler of the Numerical Algorithm Group (NAG), Oxford, UK. The project is currently in the third period of funding by EPSRC.

Automatic Differentiation (AD) is a technique to enhance a given computer program in some high level programming language (more or less) automatically with code that computes sensitivities of outputs of the program with respect to inputs. Classically there are two basic types of AD-tools working on the source code of the program: Tools that exploit the overloading capabilities of programming languages (Fortran 90, C++), and source transformation tools. The latter approach yields a new source code augmented with statements computing derivatives (Tapenade, Open-AD, TAF, ...), but source transformation tools are compilers indeed. Thus their development, maintenance and extension is a very complex task. On the other hand, overloading tools (AD01, FadBad, Adol-C, Cpp-AD, ..) provides a new active datatype bundled with overloaded operators and intrinsic functions providing the necessary functionality to compute derivatives. Variables of the original program have to be activated by changing their data type from floating point to the new datatype, which has to be done by hand or by preprocessor macros. The development, maintenance, and extension of an overloading based AD-tool is much easier, but the calling an overloaded operator for every basic arithmetic operation can cause a serious runtime overhead.

The AD-enabled NAG Fortran Compiler utilizes a hybrid approach combining automatic datatype changes (source transformation) with overloading techniques. The compiler provides a number of differentiation modes (tangent linear, adjoint, tape based adjoint, second order adjoint, ... ), each one has its own private compad_module. Every compad_module exports a compad_type (and overloaded arithmetic operations, plus a number of support routines) used by the compiler to perform the datatype changes from floating point into compad_type automatically. Any detail of the AD-implementation of a specific module is hidden within the module, the compiler only rely on the existence of a compad_type. The original semantic analysis of the NAG Fortran Compiler resolves operations on compad_type by inserting calls of overloaded operators from the chosen module.

Although the overloaded approach of the AD-enabled NAG Fortran Compiler is very robust and gives good performance already, the compiler can be used to generate differentiated code: in this pure source transformation mode all calls of overloaded operators are replaced by corresponding differentiated code that is inserted into the internal representation directly. Thus all overhead of calling a subroutine for every single arithmetic operations is eliminated, and the runtime factor between the differentiated and the original code tends towards its theoretical limit.

We present the AD-enabled NAG Fortran Compiler by applying various of its AD-modes to an example code showing the benefits of the hybrid approach.

4. S. Schmidt, V. Schulz, University of Trier:

Aerodynamic Design based on Shape Calculus

The talk focuses on large scale shape optimisation with application in fluid dynamics. By using the Hadamard form of the shape derivative, one can compute the sensitivity information for a deformation of the shape as a discretized boundary integral. Because this approach does not need so called "mesh sensitivities'', a very fine parametrization of the shape is possible such as using every surface node of the CFD mesh of an entire aircraft.

Also, by not using a shape parametrization based on few smooth ansatz functions, the shape Hessian of the problem can be studied by operator symbols. Using such a Hessian approximation, a very efficient shape-SQP optimisation scheme can be derived. When employed in a one-loop fashion, a shape specific one-shot method is created where the Hadamard form of the shape derivative is used as reduced gradients and the Hessian approximation is based on operator symbols.

5. P. Trontin, J. Peter, F. Renac: ONERA, Chatillon:

Discrete adjoint solver for design in aeronautics

Both discrete direct differentiation method and discrete adjoint method have been considered at ON ERA for the computation of the derivatives of the aerodynamic functions (Cp ,Cl ,...) with respect to design parameters. For industrial applications where the number of design parameters is larger than the one of functions of interest, the discrete adjoint method is more efficient since its complexity only depends on the number of functions. In this framework, the sensitivity of the objective function J (α) = J(W (α), X(α)) is computed from adjoint equations

Obviously, robustness, accuracy and compatibility with various mesh strategies are critical for industrial applications. To increase the robustness of iterative algorithm (1), two different techniques have been considered: the  addition of artificial dissipation and the use of recursive projection method (RPM) which allows to point out prevailing eigenmodes of the iteration matrix fatal for convergence. Concerning accuracy, most often, the classical “frozen μt ” assumption is made. The corresponding lack of accuracy has been carefully estimated and both (k − ǫ) or (k − ω) turbulence models were linearized. Besides, the compatibility between the discrete adjoint method and the various joins of structured multi-blocks meshes (matching, line-matching, plane-matching and chimera grids) was ensured .

The discrete adjoint method of the elsA code has been used by ON ERA and AIRBU S for several complex shape optimisations. For example, the pylon of a wing-body pylon nacelle configuration [2], wings of wing-body configurations and rotor blades [3] were optimised.

References

1. J. Peter and R. Dwight. Numerical sensitivity analysis for aerodynamic optimization: A survey of approaches. Comput. Fluids, 39:373-391, 2010.
2. I.Salah El Din, G. Carrier and S. Mouton. Discrete adjoint in elsA (part II): application to aerodynamic design optimization. ONERA-DLR Aerospace Symposium, Toulouse, 2006
3. A. Dumont, A. Le Pape, J. Peter and S. Huberson. Aerodynamic shape optimization of Hovering Rotors using a discrete adjoint of RANS equations. To appear in AHS Journal.