A simple approach to transient-state modeling of nitrogen cooling in the extrusion of light-alloy complex profiles

Nitrogen cooling has become a popular solution to reduce heat flux between the die and the profile in the hot extrusion process. However, designing effective cooling channels for complex-shape profiles poses challenges, especially when the phase transition of nitrogen significantly impacts heat transfer with solid bodies. To this end, the ability to model both the liquid and the gas phase is instrumental in devising design strategies, yet it should be combined with low computational complexity for industrial applications. The present work is aimed at employing the homogenous-flow approach as a simple, yet representative methodology to consider both phases in the simulations. One-dimensional model of nitrogen was combined with a three-dimensional extrusion model to perform the transient analysis of the whole process, mostly focused on the transition from fully gaseous to fully liquid flow. Validation using extrusion tests on seventeen AA6060 billets demonstrates the model's predictability in comparison with a fully liquid model. The average error associated with Homogeneous Flow Model was evaluated as below 10%, whereas the fully liquid approach yielded 25%. That proved the ability of the proposed model to reproduce the cooling effect, thus supporting the design of the cooling subsystem within the context of the whole extrusion tooling.