Fiber bundle topology optimization for mass and heat transfer in laminar flows

Yongbo Deng, Jan G. Korvink

Published 2024-11-14Version 1

This paper presents fiber bundle topology optimization for mass and heat transfer in surface and volume flows in the laminar region, to optimize the matching between the pattern of a surface structure and the implicit 2-manifold on which the surface pattern is defined. The fiber bundle concept is used to describe the pattern of the surface structure together with the implicit 2-manifold as an ensemble defined on the preset base manifold. Topology optimization of the pattern of the surface structure for mass and heat transfer in fluid flow is then implemented on the variable curved surface expressed as the implicit 2-manifold. For surface flow, fiber bundle topology optimization for mass and heat transfer is implemented based on the porous medium model by using the material distribution method, where the material density is used to interpolate the impermeability of the porous medium filled on the implicit 2-manifold. For volume flow, fiber bundle topology optimization for mass and heat transfer is implemented based on the mixed boundary condition interpolated by the material density used to represent the pattern of thin walls defined on the implicit 2-manifold, which is embedded in the three dimensional domain occupied by the volume flow. For both cases, two sets of design variables are defined for the pattern of the surface structure and the implicit 2-manifold, which is defined on the preset base manifold by using a differentiable homeomorphism. The fiber bundle topology optimization problems are analyzed by using the continuous adjoint method to derive the gradient information of the design objectives and constraints. They are then solved by using the gradient based iterative procedures.