Large scale three dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities. Special attention is paid to the applicability to large scale three dimensional problems like the optimization of an Onera M6 wing or a complete blended wing-body aircraft. The actual optimization is conducted in a one-shot fashion where the tangential Laplace-operator is used as a Hessian approximation, thereby also preserving the regularity of the shape.

Large scale three dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities. Special attention is paid to the applicability to large scale three dimensional problems like the optimization of an Onera M6 wing or a complete blended wing-body aircraft. The actual optimization is conducted in a one-shot fashion where the tangential Laplace-operator is used as a Hessian approximation, thereby also preserving the regularity of the shape.

Numerical simulation is already an important cornerstone for aircraft design, although the application of highly accurate methods is mainly limited to the design point. To meet future technical, economic and social challenges in aviation, it is essential to simulate a real aircraft at an early stage, including all multidisciplinary interactions covering the entire flight envelope, and to have the ability to provide data with guaranteed accuracy required for development and certification. However, despite the considerable progress made there are still significant obstacles to be overcome in the development of numerical methods, physical modeling, and the integration of different aircraft disciplines for multidisciplinary analysis and optimization of realistic aircraft configurations. At DLR, these challenges are being addressed in the framework of the multidisciplinary project Digital-X (4/ 2012-12/2015). This paper provides an overview of the project objectives and presents first results on enhanced disciplinary methods in aerodynamics and structural analysis, the development of efficient reduced order methods for load analysis, the development of a multidisciplinary optimization process based on a multi-level/variable-fidelity approach, as well as the development and application of multidisciplinary methods for the analysis of maneuver loads.

Potential flow pressure matching is a classical inverse design aerodynamic problem. The resulting loss of regularity during the optimization poses challenges for shape optimization with normal perturbation of the surface mesh nodes. Smoothness is not enforced by the parameterization but by a proper choice of the scalar product based on the shape Hessian, which is derived in local coordinates for starshaped domains. Significant parts of the Hessian are identified and combined with an aerodynamic panel solver. The resulting shape Hessian preconditioner is shown to lead to superior convergence properties of the resulting optimization method. Additionally, preconditioning gives the potential for level independent convergence.

Aerodynamic design based on the Hadamard representation of shape gradients is considered. Using this approach, the gradient of an objective function with respect to a deformation of the shape can be computed as a boundary integral without any additional "mesh sensitivities" or volume quantities. The resulting very fast gradient evaluation procedure greatly supports a one-shot optimization strategy and coupled with an appropriate shape Hessian approximation, a very efficient shape optimization procedure is created that does not deteriorate with an increase in the number of design parameters. As such, all surface mesh nodes are used as shape design parameters for optimizing a variety of lifting and non-lifting airfoil shapes using the compressible Euler equations to model the fluid.

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Abstract:The use of high-speed radial impellers is very common in blowers for industrial application. It is also very common to manufacture these impellers using circular arc blades. The design process as well is almost always based on former impeller series and experimental data available. In this work, a method is presented to improve the efficiency of radial impellers with a combined analytical and numerical method. This method is based on an extended analytical formulation of the flow in radial impellers, allowing optimizing efficiency in the design stage. It is complemented by the mathematical implementation of a well-known qualitative principle of efficiency optimization according to Carnot. Finally, the torque-speed characteristic of the motor is included in the design stage. The blade shapes are computed using an inverse method. The design is then validated by means of computational fluid dynamics (CFD) computation with a commercial solver. Finally, a prototype was built and measurements were carried out in a test rig. It is also shown that the design method provided very good predictions leading to an efficiency increase of 13 per cent and a maximum flowrate increase of 11 per cent. The design point was also met. It is also shown that the numerical computations and measurements are in good agreement. An analysis of the CFD results is also presented, giving an insight view into the substantial flow information within the old and the new impellers. The method presented is a combined analytical and numerical method suited to design high-efficiency radial impellers considering also the torque-speed characteristic of the motor without the need of a previous impeller series or knowledge of experimental data.

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