TOPOLOGY OPTIMIZATION METHOD APPLIED TO DESIGN CHANNELS FOR NON-NEWTONIAN FLUID FLOW
Jacqueline de Miranda Kian1; Emilio Carlos Nelli Silva1; Juan Saenz Romero2
1 Department of Mechanical Engineering of Escola Politécnica at the University of São Paulo; 2 Department of Mechanical Engineering, Federal University of Espírito Santo
doi:10.20906/CPS/COB-2015-0775
Resumo
The present work proposes the study of design channels for steady, incompressible non-Newtonian flow, by using Topology Optimization Method. This study focusses on fluidic systems dealing with blood, and presents itself as relevant when applied to design of biomedical devices such as arterial bypass grafts. The fluid flow is modeled with the Navier-Stokes equations coupled with Carreau-Yasuda constitutive equation for the shear rate dependent dynamic viscosity to take into account the effects of non-Newtonian blood properties. The Topology Optimization Method distributes regions of solid and fluid, given a volume constraint, within a specified domain in order to obtain a geometry and layout that minimizes energy dissipation, by using the material pseudo-density as design variable. To apply this method to fluidic systems design, a fictional porous flow based on Darcy equation is introduced and material interpolation functions for the inverse permeability and dynamic viscosity are defined. The flow model is implemented in its discrete form by using Finite Element Method through the OpenSource platform FEniCS, applied to automate the solution of mathematical models based on differential equations, and the optimization problem is solved by using the platforms DOLFIN-adjoint and PyIpopt optimizer. Optimal topologies of bidimensional channels for non-Newtonian flow are presented to illustrate the proposed method.
Palavras-chave: Topology optimization; Non-Newtonian fluids; Blood flow