Study On Thermo-hydraulic Characteristics Of Cable-in-conduit Conductors Based On Fractal Theory In Porous Media

Cable-in-Conduit Conductors(CICCs)is widely used in large superconducting magnet system for its characteristics of supporting high current,generating high magnetic field and maintaining the lowest energy loss,such as in the International Thermonuclear Experiemntal Reactor(ITER)magnet system.Generally,the low temperature environment of magnet system is realized by forced cooling of liquid helium in the conductor,which is inevitably affected by various thermal disturbance in the environment.Any kind of thermal disturbance is very likely to cause the quench and structural damage,threatening the safe operation of the superconducting magnet system.Therefore,it is of great significance to analyze the thermo-hydraulic characteristics of helium flows in CICCs,and design the conductor configuration with optimal thermal stability and cooling efficiency.In this paper,based on the porous media analogy of superconducting cable,fractal theory is used to describe the pore distribution on the cross section of superconducting cable,and fractal method is used to study the thermo-hydraulic characteristics of CICC conductor with two channels.Firstly,based on the method of superconducting cable analogy as a porous medium and the fractal permeability model of porous media,a fractal permeability prediction model of superconducting cable is established by combining the structural characteristics of superconducting cable.Compared with other superconducting cable permeability models in the literature,the model proposed in this paper does not contain any empirical constants or fitting constants,and the predicted values are closer to the experimental values.The fractal prediction model shows that permeability of superconducting cable is related to its porosity,average cabling angle of superconducting strands,fractal dimension of pores on cable cross section and average tortuosity of liquid helium flow paths.In addition,the influence of cable design paramters on permeability shows that the permeability of superconducting cables decreases with the increase of average cabling angle,and increases with the increase of pore fractal dimension.Secondly,based on the method of superconducting cable analogy as a porous medium and the mass,momentum and energy macroscopic governing equations of fluid in a porous media,a two-dimensional axisymmetric period model of dual channel CICCs is established.The characteristic parameters of superconducting cable in this model determined according to the fractal prediction model proposed in this paper.On this basis,the thermo-hydraulic characteristics of the dual-channel CICCs are studied,the effects of spiral geometric sizes and cable design parameters on pressure drop and equivalent transverse heat transfer coefficient are analyzed.The results of analysis show that when the Reynolds number is given,the pressure drop and equivalent transverse heat transfer coefficient increase with the increase of the ratio of thickness to inner diameter,the ratio of gap width to pitch,the average cabling angle of superconducting strands,decrease with the increase of pore fractal dimension.Thirdly,based on the method of superconducting cable analogy as a porous medium and fractal theory in porous media,fractal prediction models of pressure drop and friction factor of superconducting cable are established.Compared with the theoretical models in other literatures,the fractal model can predict the pressure drop and friction factor of the superconducting cable in ITER magnet more accurately.The fractal prediction model shows that pressure drop and friction factor of the superconducting cable are functions of the porosity,the average cabling angle of superconducting strand and the pore fractal dimension of cable cross section.In addition,the influence of superconducting cable design parameters on pressure drop and friction factor analyzed.The analysis results show that pressure drop and friction factor both increase with the increase of average cabling angle,and decrease with the increase of pore fractal dimension of cable cross section.Finally,based on the heat transfer mechanism of series thermal resistances,a modified model of equivalent transverse heat transfer coefficient of dual channel CICCs is established.The predicted values are in good agreement with the experimental data,which verifies the validity of the modified model.The comparison between the modified model and several prediction models in the literature shows that the modified model has wider applicability.In addition,the results of modified model show that pressure drop and equivalent transverse heat transfer coefficient of dual channel CICCs increase with the increase of average cabling angle of superconducting strand,and decrease with the increase of pore fractal dimension of cable cross section,which is consistent with the conclusions obtained by numerical calculation in this paper.