# Lattice Structure for Improving Cooling Uniformity in HPDC Mould Corners
## 2 Computation Domain Description  
The heat transfer process in high-pressure die casting is complex, unsteady, and involves phase change. However, for this study, cycle-specific details are not considered. It is assumed that the heat transfer process reaches a steady state after several cycles, with the time average mould temperature remaining constant. In the design phase, it is common to optimise the cooling system using steady-state simulations without explicitly solving the solidification process [17, 18, 19]. Instead, the solidification energy is approximated as an average volumetric heat source, distributed over the mould cavity surface. While steady-state assumptions simplify the analysis, they do not capture transient effects, such as thermal shock or solidification rates, which may be significant during the solidification process. These assumptions are deemed suitable for the objective of this work, which is to introduce a new method for improving the uniformity of the temperature distribution across the cavity surface.  
The steady-state model was developed to analyse the heat transfer rate and to identify the temperature distribution while internally cooling an aluminium alloy profile with 90-degree-angled corners with and without lattice structures. The computational domain is divided into three distinct regions: the fluid region (water pipe), the aluminium cast region (treated as a continuous heat generation source), and the mould, which uses the properties of H13 steel.  
Three different lattice structure sleeves surrounding the cooling pipe were generated and modelled as solid regions with the equivalent physical and thermal properties of three lattice structures: Body-Centred Cubic Cell (BCC), Face-and-Body-Centred Cubic Cell with Z-axis struts (BCCZ), and Face-Centred Cubic Cell with Z-axis struts (FBCC) [15]. Figure 1 illustrates the general layout and schematic of the corner cooling channel, where the cast is positioned at the external side of the mould corner with a single cooling channel passing through the mould cavity. The mould block dimension is 80 \(\times\) 80 mm with a depth of 18 mm. The cooling channel diameter is 6 mm, and the pitch distance between the bottom surface of the pipe and the mould/cast interface is maintained at 9 mm.  
Figure 1: Sketch showing the three computational regions and the lattice structure sleeves around the cooling pipe.  
Table 1 presents the properties of these three regions and lattice structures. These properties have been identified experimentally using those lattice structures in stagnant air.  
A polyhedral mesh with near-wall prism layers was employed to accurately capture the boundary layer near the walls for accurate evaluation of heat flux at the interface and cooling pipe surface. Various mesh sizes were used within the domain, with finer mesh regions applied to the fluid flow area and near the interface walls, as shown in Figure 2. The control volume method implemented in the STAR-CCM+ CFD package was used to discretise the governing equations. A mesh convergence study was performed to ensure that the results were independent of mesh resolution. The simulation employed a total cell count of approximately 450,000, with an overall mesh quality of 98.71%, based on evaluations of mesh validity and skewness angle. To address the near-wall viscous transitional sublayer, the all Y+ wall treatment model was used, accommodating different boundary layer mesh densities.