A porous medium analogy for the helium flow in CICCs

Cable-in-Conduits are superconducting conductors that consist of a bundle of cabled strands enclosed in a leak-tight pipe, the jacket. Helium flows inside the jacket, in a meandrous flow path defined by the intersticial space among the cabled strands, or in specific passages introduced by design to reduce pressure drop. The main advantage of this design is to bring the coolant in close thermal contact with the superconductor, thus enhancing the heat removal as well as its thermal stability. To date, however, the details of the flow and heat transfer mechanism in this complex geometry are not well understood. We propose to use an analogy between the bundle of strands in the cable and a porous media. The analogy provides simple correlations for pressure drop and heat transfer prediction that contain explicitly permeability, drag factor and thermal dispersion. We use published pressure drop data to show that the range of permeability of a CICC is within the expected values for a porous medium with the same equivalent particle diameter, while the drag factor is consistently lower than what expected from the theory of particle beds, which will require further work to produce a satisfactory explanation. Experimental data for the internal heat transfer obtained from a short ITER conductor sample are in good agreement with the expected contribution of thermal dispersion, which supports or proposal.