Perpustakaan Digital ITB

Topology optimization is a method of optimization that allows for the optimization of holes within a structure, aside from the shape and the size, allowing greater design freedom than classical optimization methods counterparts. Existing methods of topology optimization on lift and drag problems have only accounted for steady-state solutions, even though the Reynolds numbers of previous studies could be sufficiently high such that vortex shedding can be expected. This research formulates a topology optimization of lift and drag problems which can incorporate unsteady flow field. Because of the unsteady nature of the solver, the Lattice Boltzmann Method (LBM) is chosen as the base of the optimization, integrated with the level-set method whose mathematics provide a non-trivial combination. The continuous adjoint method is chosen to be the basis for optimization due to its efficiency. Among the novelties of the present research are the formulation of suitable objective functions that incorporates the level function, and the proposition of continuous adjoint boundary conditions for the problem which do not suffer from numerical instabilities. The devised optimization framework is tested by putting it into practice for optimization at Reynolds numbers of 10, 20, 100 and 150 defined from a reference cylinder. Convergence criteria based on the negligible change in the objective function and design variables are adopted. Optimizations in the steady regime show good agreement with results from literature, verifying the optimizer. As for the unsteady regime, successful optimization yields topologies that prevent the creation of unsteady vortices, through body streamlining and the addition of trailing structures. The optimizer is further tested by tackling the problem of optimization inside the wake of a cylinder. Again, optimizations prove to be successful, with similar characteristics as previous cases. Differences can occur in the detail, such as during lift maximization, which exhibit thicker leading edge for better vortex reception.