Basic study on objective function for topology optimization of fluid machinery

Abstract

In this study, we propose a new representation of objective or constraint function for topology optimization of fluid machine which rotates in the constant angular velocity. First, the governing equations for the fluid problem is described and the formulation of topology optimization for fluid machine is briefly discussed. Then, the energy conservation law of the flow in fluid machine is derived from both the governing equations itself and the Brinkman model, and the explanation of each term of the equations are discussed. Next, in order to verify those representations, two-dimensional fluid analysis is conducted for both cases in which the blades of centrifugal fan model are expressed by mesh geometry and Brinkman model. The result shows that those expressions agree within numerical error. Finally, the possibility of the novel formulation for topology optimization of fluid machine, such as the maximizing energy efficiency under the lower bound constraint of energy gain by the fluid, is discussed.