Adjoint optimization of a liquid-cooled heat sink

Sammanfattning: Improving the design of flow channels in a liquid-cooled heat sink is critical for boosting the capabilities of electronic components as well as reducing energy usage by the pump. This work explores the use of topology optimization to minimize the pressure difference across a heat sink and consequently, the energy used to supply the liquid. Topology optimization involves solving mathematical equations to obtain the optimal design for a defined cost function, here the total pressure difference between the inlet and outlet. A design variable called the porosity is defined for each cell in the mesh. The porosity features in a sink term in the momentum equation, which 'solidifies' cells by velocity suppression when deemed to be counterproductive to the cost function. The adjoint method of topology optimization, in particular, is a well-established tool for use in flow network problems and includes non-physical parameters such as the adjoint velocity and pressure. The method isn't without its drawbacks, such as the numerical instability of the adjoint equations, and the absence of boundary layers or wall functions at the interface of high and low porosity. The strength of the adjoint method lies in the ease with which it calculates the gradient of the cost function with respect to the porosity. When applied to the geometries in this work, it is observed that the problem is non-convex and results in multiple optimums with similar cost values. Thus the objective becomes seeking solutions with the simplest shape and at the same time having a minimized pressure difference. Interesting techniques are tested, namely an interpolation function, a velocity tolerance, and a volume constraint. The work is accomplished by modifying an existing adjoint optimization solver in the open-source CFD software, OpenFOAM.