Computation of Topological Sensitivities in Fluid Dynamics: Cost Function Versatility

Topology optimization of fluid dynamical systems is still in its infancy, with its first academic realizations dating back to as late as three years ago. In this paper, we present two approaches to fluid dynamic topology optimization that are based on potential flows and adjoint states, respectively. Special emphasis is paid to the computation of topological sensitivities with discrete adjoints and its versatility with respect to changes of the cost function: After providing the proof of concept of a discrete adjoint-based methodology for the optimization of dissipated power, we compute sensitivities with respect to equal mass flow through different outlets, flow uniformity and also angular momentum of the flow in the outlet plane. 1 TOPOLOGY OPTIMIZATION IN FLUID DYNAMICS In structure mechanics, topology optimization is a well-established concept for design optimization with respect to tension or stiffness [1]. Its transfer to computational fluid dynamics (CFD), however, just began three years ago with the pioneering work of Borrvall and Petersson [2]. Starting point for fluid dynamic topology optimization is a volume mesh of the entire installation space. Based on a computation of the flow solution inside this domain, a suitable local criterion is applied to decide whether a fluid cell is “good” or “bad” for the flow in terms of the chosen cost function. Two lines of thought have developed on how to iteratively remove the identified bad cells from the fluid domain: The cells are either punished via a momentum loss term [2]-[6], or holes are inserted into the flow domain, with their positions being determined from an evaluation of the topological asymptotic [7, 8]. Obviously, topology optimization fits ideally into the common industrial design process of freeform geometries. It delivers an unbiased design from scratch and, since it starts from the feasible domain and only removes fluid cells, design domain restrictions are automatically fulfilled. Possible automotive applications are the optimization of air ducts