A topology optimization approach applied to laminar flow machine rotor design

Abstract

The design of flow machines is still a difficult task, mainly due to the large number of free geometrical parameters involved. Thus, design optimization techniques can be applied to obtain optimized designs of these machines. This work deals with optimization of radial flow machine rotors (pumps and turbine), where a novel methodology for the propeller design is proposed based on the topology optimization method which distributes fluid or solid in a design domain to extremize a defined objective function subjected to some constraints. The design objective is to optimize the shape of the channel between two blades of the rotor to minimize the energy dissipation and vorticity, and minimize or maximize the power in the case of a pump or turbine, respectively. These objective functions are combined in a multi-objective function. A two-dimensional finite element is derived in a rotating frame for modelling the rotor flow behaviour. The modelling predicts the flow field between relative two blades of a rotor without considering the influence of the volute. It is assumed that the fluid is flowing in an idealized porous medium subjected to a friction force, which is proportional to the fluid velocity and the inverse local permeability. A porous flow model is introduced with a continuous (grey) permeability design variable for each element that defines the local permeability of the medium and allows the transition between fluid and solid property. The design optimization problem is solved by using the method of moving asymptotes (MMA). Numerical examples are presented to illustrate this methodology.