J.6 COMPUTER-AIDED ENGINEERING
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Multidisciplinary optimizations (MDOs) encompass optimization problems that combine different disciplines into a single optimization with the aim of converging towards a design that simultaneously fulfills multiple criteria. For example, considering both fluid and structural disciplines to obtain a shape that is not only aerodynamically efficient, but also respects structural constraints. Combined with CAD-based parametrizations, the optimization produces an improved, manufacturable shape. For turbomachinery applications, this method has been successfully applied using gradient-free optimization methods such as genetic algorithms, surrogate modeling, and others. While such algorithms can be easily applied without access to the source code, the number of iterations to converge is dependent on the number of design parameters. This results in high computational costs and limited design spaces. A competitive alternative is offered by gradient-based optimization algorithms combined with adjoint methods, where the computational complexity of the gradient calculation is no longer dependent on the number of design parameters, but rather on the number of outputs. Such methods have been extensively used in single-disciplinary aerodynamic optimizations using adjoint fluid solvers and CAD parametrizations. However, CAD-based MDOs leveraging adjoint methods are just beginning to emerge.
This thesis contributes to this field of research by setting up a CAD-based adjoint MDO framework for turbomachinery design using both fluid and structural disciplines. To achieve this, the von Kármán Institute’s existing CAD-based optimization framework cado is augmented by the development of a FEM-based structural solver which has been differentiated using the algorithmic differentiation tool CoDiPack of TU Kaiserslautern. While most of the code could be differentiated in a black-box fashion, special treatment is required for the iterative linear and eigenvalue solvers to ensure accuracy and reduce memory consumption. As a result, the solver has the capability of computing both stress and vibration gradients at a cost independent on the number of design parameters. For the presented application case of a radial turbine optimization, the full gradient calculation has a computational cost of approximately 3.14 times the cost of a primal run and the peak memory usage of approximately 2.76 times that of a primal run.
The FEM code leverages object-oriented design such that the same base structure can be reused for different purposes with minimal re-differentiation. This is demonstrated by considering a composite material test case where the gradients could be easily calculated with respect to an extended design space that includes material properties. Additionally, the structural solver is reused within a CAD-based mesh deformation, which propagates the structural FEM mesh gradients through to the CAD parameters. This closes the link between the CAD shape and FEM mesh. Finally, the MDO framework is applied by optimizing the aerodynamic efficiency of a radial turbine while respecting structural constraints.