SUMMARYThis paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection.

Numerical homogenization is an efficient way to determine effective macroscopic properties, such as the elasticity tensor, of a periodic composite material. In this paper an educational description of the method is provided based on a short, self-contained Matlab implementation. It is shown how the basic code, which computes the effective elasticity tensor of a two material composite, where one material could be void, is easily extended to include more materials. Furthermore, extensions to homogenization of conductivity, thermal expansion, and fluid permeability are described in detail. The unit cell of the periodic material can take the shape of a square, rectangle, or parallelogram, allowing for all kinds of 2D periodicities.

This review paper provides an overview of the literature for topology optimisation of fluid-based problems, starting with the seminal works on the subject and ending with a snapshot of the state of the art of this rapidly developing field. “Fluid-based problems” are defined as problems where at least one governing equation for fluid flow is solved and the fluid–solid interface is optimised. In addition to fluid flow, any number of additional physics can be solved, such as species transport, heat transfer and mechanics. The review covers 186 papers from 2003 up to and including January 2020, which are sorted into five main groups: pure fluid flow; species transport; conjugate heat transfer; fluid–structure interaction; microstructure and porous media. Each paper is very briefly introduced in chronological order of publication. A quantititive analysis is presented with statistics covering the development of the field and presenting the distribution over subgroups. Recommendations for focus areas of future research are made based on the extensive literature review, the quantitative analysis, as well as the authors’ personal experience and opinions. Since the vast majority of papers treat steady-state laminar pure fluid flow, with no recent major advancements, it is recommended that future research focuses on more complex problems, e.g., transient and turbulent flow.

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non-flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross-sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. TOPOLOGY OPTIMIZATION OF MICROFLUIDIC MIXERS 499 diffusive properties, one can alter the geometry such that the flow distributes the matter more evenly in the solvent. By doing so, convection of matter is used as a mechanism to enhance mixing which; however, comes at the cost of an increased pressure drop between inlet and outlet. Stroock et al. [2] presented a mixer that induces chaotic advection by sequencing asymmetric microchannel sections containing staggered herringbones. For the systematic design of such microchannel mixers, topology optimization could be useful since no prerequisites are taken with respect to the geometry, only a design domain and boundary conditions need to be specified a priori.The material distribution method for topology optimization was first presented by Bendsøe and Kikuchi [3] for solid mechanics problems. Since then, topology optimization has been introduced in several other branches of physics such as optics, acoustics and flows (see e.g. Bendsøe and Sigmund [4] for an overview of the subject).Optimal design in fluid mechanics has been studied long before topology optimization was invented and optimal shapes minimizing the dissipated power for different profiles subjected to Stokes flow were already determined analytically in the 1970s by Pironneau [5] using shape optimization. As opposed to shape optimization, however, topology optimization allows introduction of new boundaries as the optimization progresses. This allows the topology to change several times during the optimization, which is impossible in shape optimization where the topology (i.e. the number of boundaries and connectivity) is predetermined.In topology optimization the geometry is represented as a gray-scale image. The color in each pixel (finite element) represents a value of a physical parameter, e.g. permeability, such that black pixels represent small permeability (no-flow regions with 'solid-like' material) and white pixels represent large permeability (fluid regions). Computationally, the gray-scale in each element is a design variable. Based on repeated finite element analyses the design variables are updated using gradient driven math programming tools as described in e.g. [4].Topology optimization in fluid mechanics was introduced by Borrvall and Petersson [6] modeling 2D flow in a Brinkman med...

 Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.