Topology optimization applied to the design of Tesla-type turbine devices

Abstract

Tesla-type turbine devices are turbine devices which convert fluid motion into the rotating motion of a rotor, but without the need of any blades. This is possible due to the interaction of the boundary layer with the rotating fluid motion. In order to successfully optimize this type of fluid flow device through the topology optimization method, some relevant aspects need to be considered. The first one is due to its unique configuration, meaning that the 2D swirl flow model may be considered, which is much less computationally expensive than considering a “full” 3D model. Moreover, since higher mesh resolutions may be necessary in the design of Tesla-type turbines from to the possible appearence of smaller disk-like structures, this may increase the overall optimization cost if the traditional Taylor-Hood elements (quadratic finite elements for the velocity) are considered. This additional computational cost may be reduced by considering MINI elements (linear finite elements with bubble enrichment for the velocity) instead. Another modification that may be useful in its design is augmenting the traditional Brinkman model used in topology optimization with an additional inertial term (Brinkman-Forchheimer model), which may lead to better optimized Tesla turbine designs. Another factor to be considered is the multi-objective function, which may be defined to minimize the relative energy dissipation and maximize the power transferred from the fluid. In such case, the power objective function may be augmented with an additional porosity (material model) term. Numerical examples are presented, taking into account some aspects of the design of Tesla-type turbine devices.