Experimental and Numerical Studies for Hydraulic Performance Evaluation of Cable-in-Conduit Conductor in Superconducting Magnet Applications

Abstract

Alternative energy sources, such as nuclear fusion, are needed to fulfil future energy demands due to rising energy consumption, depleting fossil fuel resources, and the fact that nuclear fission is not an intrinsically safe technique of energy generation. Scientists and engineers are interested in nuclear fusion because of its benefits, despite significant technological challenges in replicating the fusion process in laboratories. The most significant requirement for magnetic confinement-based fusion is the demand for a strong magnetic field to contain the hot plasma. Such a strong magnetic field, of the order of 10 Tesla, is produced using large superconducting (SC) magnets, which need efficient cryogenic cooling techniques to maintain the required low temperatures for the superconducting state. Because of their very high current carrying capacities as well as high and stable magnetic field, SC magnets are also a favorite option and sometimes the only choice in applications, other than magnetic confinement based fusion devices, such as magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), particle accelerators, and mass spectrometry. In order to maintain its compactness, the SC magnets are generally cooled through forced flow cooling as compared to bath type cooling, and hence, employ Cable in Conduit Conductor (CICC) windings which are internally cooled by the forced flow of helium at ~4 K temperature (for low temperature superconductors, LTS) to maintain the required superconducting state. The recent development of high temperature superconductors (HTS) has also opened up the possibility of CICC made of HTS which requires cooling typically between 20 K and 100 K. The cryogenic thermal stability of the CICC is of prime importance for the safe, stable, and reliable operation of SC magnets. The prediction of the thermal and hydraulic behavior of the CICC in large SC magnets is difficult due to the complex geometry involved, the variation in fluid properties, various heat in-flux incidences over the long length of the CICC, and a complex heat transport phenomenon. A few correlations for the friction factors in CICC have been proposed, mostly based on the analogy with either smooth pipes, a system of parallel capillaries, pebble beds, and porous media. A common objective of hydraulic studies is to obtain the most V reliable predictive correlation for friction factor in CICC geometries and to reduce the dependency on the experiment. So far, only the void fraction and Reynolds number have been considered in the predictive correlations in an explicit way. All the correlations have been derived based on the experimental results and best fit curve and are thereby proposed either as a function of Reynolds number (Re) or as a function of Re and porosity (or void fraction, ) both. Recent studies have provided the theoretical basis using the porous media analogy, but still, the key parameters for porous media, i.e., permeability (K) and drag coefficient ( ) are not known priori and presented as a function of only based on the best fitting curve method with the best accuracy up to ±17%. In the present work, a detailed literature review has been carried out highlighting the major gaps in the prediction of the hydraulic behavior of the CICC and a combination of experiment and numerical analysis approach was proposed to attend the same. In this novel approach, the pressure drop as a function of velocity was derived with the extraction of linear and quadratic coefficient terms of the Darcy-Forchheimer equation, based on the room temperature experiment performed on a CICC sample. The coefficients were applied as empirical values in the numerical analysis of fluid flow through the CICC with a definition of a porous medium to obtain the pressure drop simulation results at other operating conditions relevant to the actual operations. The value of permeability (K) as 3.6 x 10-6 m2 and the coefficient ( ) as 1121m-1 were obtained from the room temperature measurement, which are the geometrical properties. The results obtained with the present approach are found to be ±18% accurate when compared with the experimental results for 100 < Re < 2000. Furthermore, the numerical simulations were carried out to study the effects of various tortuosity ( , which is an inherent geometrical parameter due to CICC construction, on different cabling patterns and attempted to correlate the effect of , in the friction factor of the CICC. The CICC twisting pattern with 6+1 bundles or petals (solid conductor in the present study) with different twisting pitches was modeled for numerical simulation in 1.08 and a correlation for friction factor, f The proposed friction factor correlation is found to be most suitable for the Reynold number range of 100 < Re < 3000. VI The present study has usefulness for better prediction of the friction factor for the CICC with less reliance on the experiment for the pressure drop prediction and to ensure proper cooling of the CICC. This novel approach for the CICC hydraulic performance prediction using numerical simulation and empirical data from the CICC sample can be useful for a given CICC geometry involving the dense matrix of superconducting strands (porous medium). Using the High Performance Computing (HPC) machines, it is possible to conduct the hydraulic performance study for the entire SC magnet made from CICC.