A level-set topology optimization of drag and lift problems incorporating unsteady flow field information
Angka Bayu Putranto (Institut Teknologi Bandung)
Lavi Rizki Zuhal (Institut Teknologi Bandung)
Theodoros Michelis (TU Delft - Aerospace Engineering)
Pramudita Satria Palar (Institut Teknologi Bandung)
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Abstract
Previous studies on drag and lift topology optimization have only accounted for steady flow field information, despite the sufficiently high Reynolds number such that vortex shedding would occur which causes unsteadiness. This work investigates the incorporation of unsteady flow field information in the result of the topology optimization. To that end, we propose a topology optimization framework that combines Lattice Boltzmann Method (LBM) for unsteady incompressible flow simulation and the Level Set Method for a clear-boundary representation of the evolving topology. A continuous adjoint variational analysis is used to derive the optimization method, which includes the adjoint problem and the optimizer. Objective functions that are specific to LBM and level set are formulated and verified with results from Navier–Stokes optimizers. The Reynolds numbers treated here are 10, 20, 100, and 150, the first two being lower than the first critical value of an initial circular cylinder, while the last two being above. In both regimes, the optimizer results in geometries that stabilize the wake. Particularly for the case of lift maximization, stabilization is achieved through the appearance of trailing elements which, in combination with an elongated trailing edge, create a suction mechanism. The optimizer converges toward local optimized solutions depending on the averaging length and initial geometry. To verify that the proposed framework can handle and optimize truly unsteady flow phenomena, an optimization is carried out for a body in the wake of a cylinder, a region dominated by inherent vortex shedding. Unlike past lift-maximization results, rounder leading edges are found for the main structure of lift maximization, facilitating the reception of incoming vortices for larger production of time-averaged lift while adhering to the drag constraint. These results confirm that the proposed method successfully incorporates unsteady flow effects into the fluid topology optimization process.