In general, the cooling phase of the high-pressure die casting process is based on complex physical phenomena: so-lidification of molten material; heat exchange between cast part, die and cooling fluid; turbulent flow inside the cooling channels that needs to be considered when computing the heat flux; interdependency of properties and temperature of the cooling liquid. Intuitively understanding and analyzing all of these effects when designing HPDC dies is not feasible. A remedy that has become available is numerical design, based for example on shape optimization methods. However, current computing power is not sufficient to perform optimization while at the same time fully resolving all physical phenomena. But since in HPDC suitable objective functions very often lead to integral values, e.g., average die temperature, this paper identifies possible simplifications in the modeling of the cooling phase. As a consequence, the computational effort is reduced to an acceptable level. A further aspect that arises in the context of shape optimization is the evaluation of shape gradients. The challenge here is to allow for large shape deformations without remeshing. In our approach, the cooling channels are described by their center lines. The flow profile of the cooling fluid is then estimated based on experimental data found in literature for turbulent pipe flows. In combination, the heat flux throughout cavity, die, and cooling channel can be described by one single advection-diffusion equation on a fixed mesh. The parameters in the equation are adjusted based on the position of cavity and cooling channel. Both results contribute towards a computationally efficient, yet accurate method, which can be employed within the frame of shape optimization of cooling channels in HPDC dies.
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