The main problem in density-based two-fluid optimization is the fact that the two fluids often mix in optimal designs. Therefore, state-of-the-art two-fluid heat exchanger optimization includes non-mixing constraints. However, the current non-mixing constraints can only impose a constant wall-thickness between the two fluids. Depending on the optimization problem, the forming of a wall with a variable thickness is advantageous for the heat transfer in the heat exchanger. A non-mixing constraint that can only impose a constant wall-thickness cannot further improve the heat transfer objective in such an optimization problem, since a variable wall-thickness cannot be generated. In these optimization problems, a non-mixing constraint that allows a variable wall-thickness to be formed can generate heat exchangers with a higher efficiency. In the proposed optimization method, a non-mixing constraint is provided which guarantees a pre-defined minimum wall-thickness separating the two fluids, and also allows the optimizer to locally increase the wallthickness above the minimum wall-thickness. The advantage of the proposed non-mixing constraint is that
the minimum wall-thickness can be set based on a manufacturing limit, while the optimization algorithm can vary the wall-thickness based on advantageous heat transfer.
In this report a method is proposed for the design of a two-fluid heat exchanger with density-based topology optimization. The density-based topology optimization method has two design variables to distinguish between the two fluids and solid material. The first design variable distinguishes between the fluid and solid material regions and the second design variables distinguishes between the two fluids. The non-mixing constraint relies on a two design variable method combined with a two-step filtering and projection method to generate a variable wall-thickness. The two-step filtering and projection method is applied to the second design variable to guarantee a solid material region with the minimum wall-thickness; the non-mixing region. The first design variable can be used to generate additional solid material regions that are combined with the non-mixing region to form a variable wall-thickness.
The research question is : Can a non-mixing constraint for density-based two-fluid topology optimization be created that guarantees a minimum wall-thickness and also allows for a wall-thickness larger than the minimum implemented within a finite element computational framework?
The optimization problem formulation used in this project is a heat transfer objective that is maximized with two pressure drop constraints, one for each fluid channel. The proposed non-mixing constraint is applied to a variety of 2D optimization problems where different design domains, heat exchanger configurations, materials and parameter settings are used to investigate the influence on the optimization behaviour. The results show that the non-mixing constraint guarantees a pre-defined minimum wall-thickness and also allows for a wall-thickness larger than the minimum wall-thickness. In addition, a method to determine a suitable parameter continuation scheme fine-tuned based on the parameter settings is provided. The proposed optimization method allows for two-fluid heat exchangers with identical and different fluids. A variety of material parameters is used to show the effect on the material interpolation and the optimization behaviour. Depending on the initial design and design domain, the optimization algorithm generates an optimal design with a constant wall-thickness or variable wall-thickness. Finally, to illustrate the possibilities with the proposed non-mixing constraint two 3D optimization problems are computed and one of the optimal designs is post-processed and manufactured.

Power electronic systems are reaching higher efficiencies as their technology advances, which often results in components of smaller size with higher power densities. Cooling these components becomes increasingly challenging as high power densities require cooling with large heat fluxes. Topology optimization (TO) of thermo-fluids can be used to find cooling interface geometries which achieve high heat transfer with realistic pumping power. However, current methods for thermo-fluid TO show several issues. Firstly, the fluid models used for thermo-fluid TO show weaknesses that cause deviating behavior compared to conventional fluid models, which can result in large under- or overestimation of heat transfer especially when applied to turbulent flow. Secondly, although this deviating behavior is known to result in inferior modeling accuracy, the achievable accuracy of thermo-fluid TO has never been quantified. Lastly, TO currently requires many modeling parameters to be specified manually. Since these parameters largely affect the accuracy of the thermo-fluid solver, tedious parameter tuning is part of the TO design process. This thesis firstly presents a framework which allows quantitative analysis of the modeling accuracy achievable with density-based thermo-fluid models in 2D. The framework reveals several effects causing errors in turbulent flow, as well as a predictability of density-based boundary layer flows. Secondly, a method is tested which minimizes errors of the density-based thermo-fluid models by meta-optimizing the modeling parameters. Applied to a test-case with turbulent flow, this method achieves up to 27% reduction of the modeling error compared to a parameter sweep. When applied to a laminar TO, it achieves similar accuracy as a manually tuned TO without needing any tuning. A second mitigation method which adjusts the thermal conductivity of porous solid material to compensate for erroneous convective heat transfer is infeasible, as it provides less accurate results than the first method. Lastly, a post-processing method which uses the meta-optimized data is tested and found to provide better accuracy than a conventional post-processing method.