Multi-scale lumped modeling of micro-channels cooling structure for W7-X divertor unit target module

A novel concept for the cooling system of the W7-X divertor unit target module has been proposed, which in- volves tiles equipped with parallel arrays connected by hundreds of sub-millimeter rectangular micro-channels (MCs), obtained using Additive Manufacturing techniques. The structural material proposed for the heat sink substrate is galvanized copper, while the plasma facing material is tungsten. To reduce the high computational cost of thermal-hydraulic simulations of the tiles, a multi-scale lumped modeling approach has been built in previous studies. This involves replacing a group of hydraulic parallel MCs with a porous strip (PS), suitably calibrated to reproduce similar thermal-hydraulic behavior of the MCs. The aim of the current work is to verify that the PS-model is also suitable for the thermo-mechanical stress evaluation, comparing the results from arrays with MCs and PS. Since the heat sink and plasma-facing tiles are bonded, the interfacial delamination and shear stresses are analyzed, being crucial for structural integrity. The analyses, carried out in the elastic regime, show that the PS model returns conservative results when compared to the MCs model, with an overestimation of the delamination and shear stresses at the free edge. Results from both models reveal nearly identical interfacial stress predictions at the free surface edge. Moreover, it is found that both MCs and PS blocks, located near the bond interface, contribute to high-stress fluctuations that could lead to the delamination of the bond interface, suggesting that the distance of the microchannel from the interface should be increased. The PS model can reliably be used to design and verify the most convenient series/parallel connection of the tiles in the divertor unit target module, taking operational constraints into consideration.