Topology optimization of 3D Stokes flow problems

Allan Gersborg-Hansen, Ole Sigmund, Martin P. Bendsøe

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The design of MEMS devices have benefitted from the topology optimization tool and complicated layout problems have been solved, see [1] for an overview. This research is aimed at micro fluidic devices known as micro-Total-Analysis-Systems (muTAS) where the main physical phenomena originate from fluid mechanics. In future practice a muTAS could be used by doctors, engineers etc. as a hand held device with short reaction time that provides on-site analysis of a flowing substance such as blood, polluted water or similar. Borrvall and Petersson [2] paved the road for using the topology optimization tool for micro fluidic design problems by considering design of energy efficient devices subjected to Stokes flow. Several researchers have elaborated on [2], however, this research has focused on 2D fluid modelling which limits the practical impact of the computed designs. This limitation is caused by the finite size domain used in topology optimization problems which ensures that the velocity components couples, even for Stokes flow [3]. Physically Stokes flow is an exotic inertia free flow, which in practice complicates mixing by passive devices. Passive mixing devices are relevant particular at micro scales since they are easily manufacturable and maintenance free. Here we consider topology optimization of 3D Stokes flow problems which is a reasonable fluid model to use at small scales. The presentation elaborates on effects caused by 3D fluid modelling on the design. Numerical examples relevant for optimal micro fluidic mixer design are shown where the design is planar - compliant with micro fabrication techniques - and where the designs are 3D. In addition issues related to the parallel solution of the linear algebra problems are discussed. The implementation uses the commercial COMSOL multiphysics programme which is sufficiently flexible to provide semi--automated analytical sensitivities. 1. M. P. Bendsoe and O. Sigmund, "Topology Optimization - Theory, Methods and Applications", Springer Verlag, Berlin Heidelberg, 2003. 2. T. Borrvall and J. Petersson, "Topology optimization of fluids in Stokes flow", Int. J. Num. Meth. Fluids v. 41, p. 77-107, 2003. DOI:10.1002/fld.426 3 E. Lauga, A. D. Stroock, and H. A. Stone, "Three-dimensional flows in slowly varying planar geometries", Physics of fluids v. 16(8), p. 3051-3062, 2004. DOI: 10.1063/1.1760105
Original languageEnglish
Publication date2006
Publication statusPublished - 2006
EventSeventh World Congress on Computational Mechanics - Century City, United States
Duration: 16 Jul 200622 Jul 2006
Conference number: 7


ConferenceSeventh World Congress on Computational Mechanics
Country/TerritoryUnited States
CityCentury City


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