Topology optimization based on a two-dimensional swirl flow model of Tesla-type pump devices

Abstract

Tesla pumps are composed of rotating disks (without blades) and are based on the boundary layer effect (i.e., viscous friction forces acting on the fluid and Coandă effect). The Tesla pump has various applications, however, the efficiency of its operation is quite low, which makes room for the optimization of its design. This way, novel configurations of devices based on this working principle can be developed. Thus, in this work, a Topology Optimization formulation is proposed to optimize the rotor of a Tesla-type pump device by using a 2D swirl flow model, which is a specific model that presents an axisymmetric flow with (or without) flow rotation around the axisymmetric axis. The 2D swirl laminar fluid flow modeling is solved by using the finite element method. A traditional material model is adopted by considering nodal design variables, and is extended to take into account the fact that the optimization is performed in a rotating reference frame and the relative tangential velocity behaves differently than the other velocity components (since the 2D swirl flow model is axisymmetric). A multi-objective function is defined in order to minimize energy dissipation and vorticity. An extra term is proposed to the vorticity function to reduce the generation of grayscale results. An interior point optimization algorithm (IPOPT) is applied to solve the optimization problem. Numerical results taking into account different aspects of the design of the rotor of a Tesla-type device are presented.