A FRACTAL MODEL OF PERMEABILITY FOR THE LIQUID HELIUM FLOW IN CABLE-IN-CONDUIT CONDUCTORS

Abstract

The heat removal capability and the coolant pumping costs in the design of cable-in-conduit conductors are depend on the thermo-hydraulics of the liquid helium flow. Therefore, the accurate knowledge of the thermo-hydraulics of the flow is significant for the design of the cables, especially for permeability. In this paper, the fractal method is proposed to describe the cable cross-section and an approximate expression is derived. Then, a fractal permeability model for helium flow in CICCs is presented based on a porous medium analogy. The feasibility and validity of this model is verified by the comparison of the predicted values and the experimental values. The fractal model indicates that permeability of cables is determined by the cable geometric parameters, such as the effective porosity, the average cabling angle, the average diameter of strands and the pore area fractal dimension of the cable cross-section. This model does not contain any empirical constants or fitting constants and can be used to explain the mechanism and to predict the permeability of the helium flow in CICCs. Furthermore, the effects of cable geometric characteristics on the presented fractal permeability model are also analyzed and simulated. The results imply that permeability of cables decreases with increasing the cabling angle, increases with the effective porosity, the pore fractal dimension and the average diameter of the strands increase. These results are consistent with the physical situations.