Topological derivatives applied to fluid flow channel design optimization problems

Autor(es)

Sa, L. F. N. ^[1] ; Amigo, R. C. R. ^[1] ; Novotny, A. A. ^[2] ; Silva, E. C. N. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Escola Politecn, Dept Mechatron & Mech Syst Engn, Ave Prof Mello Moraes 2231, BR-05508030 Sao Paulo - Brazil

^[2] Lab Nacl Comp Cient LNCC MCT, Ave Getulio Vargas 333, BR-25651075 Petropolis, RJ - Brazil

• Tipo de documento: Artigo Científico
• Fonte: STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION; v. 54, n. 2, p. 249-264, AUG 2016.
• Citações Web of Science: 10

Resumo

Topology optimization methods application for viscous flow problems is currently an active area of research. A general approach to deal with shape and topology optimization design is based on the topological derivative. This relatively new concept represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations, such as holes and inclusions. In previous topological derivative-based formulations for viscous fluid flow problems, the topology is obtained by nucleating and removing holes in the fluid domain which creates numerical difficulties to deal with the boundary conditions for these holes. Thus, we propose a topological derivative formulation for fluid flow channel design based on the concept of traditional topology optimization formulations in which solid or fluid material is distributed at each point of the domain to optimize the cost function subjected to some constraints. By using this idea, the problem of dealing with the hole boundary conditions during the optimization process is solved because the asymptotic expansion is performed with respect to the nucleation of inclusions - which mimic solid or fluid phases - instead of inserting or removing holes in the fluid domain, which allows for working in a fixed computational domain. To evaluate the formulation, an optimization problem which consists in minimizing the energy dissipation in fluid flow channels is implemented. Results from considering Stokes and Navier-Stokes are presented and compared, as well as two- (2D) and three-dimensional (3D) designs. The topologies can be obtained in a few iterations with well defined boundaries. (AU)

• Processo FAPESP: 13/24434-0 - Sistemas propulsores eletromagnéticos para coração artificial implantável e dispositivos de suporte circulatório mecânico
• Beneficiário: José Roberto Cardoso
• Modalidade de apoio: Auxílio à Pesquisa - Temático
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• Processo FAPESP: 15/15189-7 - Método de otimização topológica aplicado ao projeto de rotores de máquinas de fluxo radiais operando em escoamento laminar
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