Research Fellows
Mladen Banovic
Early Stage Researcher 12 at Universität Paderborn
The Rolls-Royce in-house airfoil design and blade generation tool Parablading has been differentiated in forward mode of AD using the AD tools ADOL-C and Tapenade. The Parablading tool is written both in C++ and Fortran, and therefore comes the necessity for mixed-language algorithmic differentiation. ADOL-C is based on the operator-overloading concept and has been used to differentiate a large part of the sources written in C++. Tapenade is based on the source-transformation concept and has been used to differentiate the rest of the sources written in Fortran. Therefore, different parts of the differentiated Parablading sources are linked to correctly propagate the derivative information.
The derivatives have been successfully verified against finite differences, using a parametric model of the TU Berlin stator test-case. Figure below outlines the comparison of surface sensitivities evaluated with AD and FD w.r.t. one section design parameter. As visible in the figure shown below, both methods coincide to a very high extent.
The differentiated Parablading tool has been coupled with a discrete adjoint CFD solver that is part of the Rolls-Royce in-house HYDRA suite of codes, also produced by algorithmic differentiation. This differentiated design chain is used to perform gradient-based optimization of the TU Berlin TurboLab stator test-case w.r.t. minimize the total pressure loss and exit whirl angle deviation objectives.
The two contradicting optimization criteria are coupled using the weighted sum approach to a single-objective optimization problem. A computational grid of 1.9M nodes is used for the CFD simulation. The minimum is found after 22 limited-memory BFGS steps, where the augmented objective is decreased by 14.37%. The optimization was highly influenced by exit whirl angle deviation, which is reduced by 42.84%, keeping the total pressure losses almost constant (-0.45%). The comparison between the baseline (grey) and optimal (green) TUB blade geometry is displayed below.
The work was conducted in a form of three secondments of ESR 12 - Mladen Banovic (UPB) to RRD, in a total duration of four months. It was done in a collaboration with ESR 11 - Ilias Vasilopoulos (RRD).