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Topology optimization in fluid flow problems
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, the topic of topology optimization in fluids is studied. With emphasis on modeling aspects, the general framework for formulating such problems is presented through a derivation of a sample problem. A survey of the literature, summarizing the developments in the area, forms the first part of the thesis.

The second part consists of two new contributions to this field. In the first paper, the problem of finding the optimal topology of fluid channels in a permeable material is examined. Theoretical results include proof of existence of solutions, as well as conditions for obtaining completely discrete designs. Numerical examples are provided to demonstrate the method.

Using methodologies from topology opt imization, in paper two, a design method is proposed for creating optimal bottom profiles for shallow water flow systems. Although this is not a topology optimization problem, since a continuous solution is sought, several results carry over due to a close relation to the problem described in the first paper.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2006. , 35 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1278
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-41382Local ID: 55914ISBN: 91-85643-69-6OAI: diva2:262234
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-12-12
List of papers
1. Topology optimization of regions of Darcy and Stokes flow
Open this publication in new window or tab >>Topology optimization of regions of Darcy and Stokes flow
2006 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, Vol. 69, no 7, 1374-1404 p.Article in journal (Refereed) Published
Abstract [en]

This paper treats the topology optimization problem of obtaining an optimal layout of regions of Darcy and Stokes flow, where the objective is the total potential power functional representing average fluid pressure. It extends the work of Borrvall and Petersson, which concerned optimal layout of Stokes flow only. A generalization of Stokes' equations is derived and used as state constraints in the optimization problem. A proof of existence of solutions is provided, and it is seen that although the corresponding proof in Borrvall and Petersson does not need regularization, the present one does. It is also concluded that linear interpolations of state parameters will result in black and white (unfiltered) designs. The method is tested on an area-to-point flow problem of the type discussed by Bejan, where the influence of various parameters and numerical strategies on the design are studied.

Topology optimization, fluid mechanics, mixed Darcy-Stokes flow, finite element method
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:liu:diva-14851 (URN)10.1002/nme.1811 (DOI)
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2013-12-12
2. Optimization of bottom profile in shallow water flow
Open this publication in new window or tab >>Optimization of bottom profile in shallow water flow
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In t his paper, a design method for creating optimal bottom profiles in flow systems, described by the linear shallow water equations, is proposed. The method is based on techniques commonly found in the area of topology optimization of structures. The presentation includes a derivation of the linearand stationary shallow water equations, which are used as state equations in the optimizaton problem. The final problem definition is closely related to the Darcy-Stokes fluid flow topology optimization problem, from which many results are derived by analogy.

From the numerical examples, it is concluded that natural-like designs can be created for proper choices of parameter values.

National Category
Engineering and Technology
urn:nbn:se:liu:diva-102486 (URN)
Available from: 2013-12-12 Created: 2013-12-12 Last updated: 2013-12-12

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