Modelling of heat transfer and pressure drop during flow boiling of CO$_2$ in a horizontal tube with periodic open cellular inserts

During flow boiling in horizontal tubes, highly porous inserts can improve the wetting of the tube wall and the convective boiling. The literature focuses on solid sponge structures with irregular cell geometries. Hence, in this work the local heat transfer and pressure drop during flow boiling of CO$_2$ in periodic open cellular structures with cubic and Kelvin cell geometry were investigated. A strong influence of the cell geometry on the heat transfer and pressure drop was found. By combining the Forchheimer term with a two-phase flow method (homogeneous model, drift flux model) a new pressure drop model is proposed. The model has a mean absolute percentage error (MAPE) of 12% . Regarding the heat transfer, high-speed video recordings and an evaluation of the local heat transfer were used to test the tube segments for complete wetting. Thereafter, the convective boiling contribution was extracted from the local data of completely wetted tube segments by subtracting the nucleate boiling contribution. A separate model of the convective boiling is proposed for each cell type. The models have a MAPE of 20% . Finally, the circumferentially averaged heat transfer coefficient was found to follow a superposition of the heat transfer of the liquid and vapor phase.