Continuous Adjoint-Based Shape Optimization for Particle Transport Problems in Fluids

In this thesis, we investigate two shape optimization problems involving fluid transport. Firstly, we analyze a novel approach for the reduction of the fluid residence time in polymer distributors for industrial fiber spinning processes. In contrast to the previous indirect approach that is based on the wall shear stress, we solve a transport equation for the residence time and incorporate it into the cost functional. We study the influence of the counter-acting goals of reducing high residence times and minimizing the pressure energy drop on the optimized shapes. Secondly, we consider the transport of a fluid-particle suspension in a bended pipe segment. We demonstrate how the erosion caused by the impact of particles with different diameters on the walls can be reduced by slight changes of the bend that are obtained from an optimization towards a selected particle species. Starting from one-way coupled Eulerian flow descriptions, we compute the shape derivatives of the optimization problems with the continuous-adjoint approach and use them for the numerical solution of application oriented three-dimensional test cases with a mesh-based gradient descent method.