Topology optimization method for screw-type pumping using a Multiple Reference Frame-based approach

Abstract

Screw-type pumping is one of the earliest types of pumping that have been explored. It has been later developed for various types of applications, including water, oil, cement, energy generation/recovery, labyrinth seals etc. Due to the screw shape, the flow is intrinsically three-dimensional, which makes it computationally expensive for the simulation. Adding to that, since the efficiency of the screw-type pumping is usually low, it may be necessary to consider optimization. When taking into consideration an optimization method with a high flexibility in the design (topology optimization), the computational cost becomes much more prohibitive, since there are usually various optimization iterations, there is a simulation for each optimization iteration, and the adjoint model has to be computed in each iteration as well. Therefore, this work formulates a simplified model for the topology optimization of screw-type devices, using a Multiple Reference Frame-based approach. This simplified model operates in a two-dimensional mesh, and makes some assumptions and approximations inside the screw zone, resulting in a similar tendency to the 3D configuration, which should be enough in terms of a design procedure, at least on a preliminary level. Two types of objective functions are considered: one that considers a pump-type operation, in which the flow performance needs to be improved, and one that considers a labyrinth seal-type operation, in which the leakage flow should be minimized. The design variable is pointwise linear, and optimized through an optimization algorithm based on integer programming. The fluid flow is taken as laminar or turbulent. Some of the numerical examples are presented for the topology optimization using the proposed model.