A review of thermal-hydraulic issues in ITER cable-in-conduit conductors

Problems related to cable-in-conduit conductors (CICC) are intrinsically multi-physics involving coupled electro-magnetic/mechanical/thermal-hydraulic fields. Here we concentrate on the thermal-hydraulic issues because, although the CICC was first proposed for the low-T_C superconducting coils of the International Thermonuclear Experimental Reactor (ITER) many years ago, CICC thermal-hydraulics alone is less understood than could be expected. Some of the difficulties are due to the multi-channel nature of the ITER CICC, where strands containing the superconducting filaments are twisted in multi-stage sub-bundles (petals) delimited by wrappings and concentrated in an annular (porous-medium like) region, while a central channel, delimited by a spiral, provides lower hydraulic impedance and pressure relief to the flow of the supercritical helium coolant. Other difficulties are related to the multi-scale nature of this problem, with length scales relevant for thermal-hydraulics ranging from the strand diameter (<∼10⁻³ m), to the CICC length in a coil (up to several 10² m). On the other hand, taking advantage of this length-scale separation, the models presently used for CICC simulations are typically 1D (along the conductor) but they need constitutive relations (like friction and heat transfer coefficients) for the transverse mass, momentum and energy transport processes occurring between different conductor elements. The database for the transverse transport coefficients, unfortunately, does not appear complete, or free of internal contradictions, often because the smallness of the transverse scales makes even an experimental assessment of these processes difficult. Here we discuss these issues and possible strategies for overcoming some of the difficulties are proposed.     

The 4C code for the cryogenic circuit conductor and coil modeling in ITER

A new tool - the 4C code - has been developed, which allows the thermal-hydraulic simulation of the entire superconducting magnet system of the International Thermonuclear Experimental Reactor (ITER), with particular reference to: (1) the winding made of cable-in-conduit conductors (CICC), (2) the structures (the radial plates and the case of the toroidal field - TF - coils, for instance) and (3) the cooling circuits. In this paper the different components of the 4C code (1D 2-channel model of the CICC and of the structure cooling channels, 2D model of selected cross sections of the structures, 0D/1D model of the cryogenic circuit) are described in detail, together with the strategy adopted for the coupling between the different components and their integration in a single tool. The new tool is then applied to the modeling of two transients in an ITER TF coil: a simplified version of a cooldown of the coil and the response to a heat pulse applied in the winding.     

Using the Vincenta code to analyse pressure increases in helium during the quench of a superconducting magnet

The Vincenta code is used to simulate the pressure increases in helium in case of a quench in the superconducting coils. We focus on two classes of coil in which helium is in direct contact with the conductor: coils consisting of cable-in-conduit conductors (as in ITER or JT-60SA), in which supercritical helium is forced through long channels; and bath-cooled coils, in which static helium is confined in short channels perpendicular to the conductor and opening into a bath (as in Tore Supra or Iseult). Various physical phenomena are responsible for the pressure increases in helium, which is subjected to strong heat flux in the conductor during a quench: at the local level, i.e. in the heated channels, the inertial forces that must be overcome to expel the fluid and the friction forces due to the induced velocity; at the global level, i.e. throughout the cryogenic system, the adiabatic compression of non-heated volumes hydraulically connected to the heated channels. Here we analyse the thermohydraulic behaviour of helium to highlight the dominant phenomena, according to the geometry of the helium flow paths. The results are applied to numerical simulation of the pressure rise in case of quench in a JT-60SA cable-in-conduit conductor (CICC) and in the bath-cooled Iseult coil.     

Change of interstrand contact resistance and coupling loss in various prototype ITER NbTi conductors with transverse loading in the Twente Cryogenic Cable Press up to 40,000 cycles

The multistrand NbTi conductors for the Poloidal Field (PF) Coils of the International Thermonuclear Experimental Reactor (ITER) are subjected to heavy transverse loading due to the Lorentz forces in the coils. The current in the multistage Cable-In-Conduit Conductors (CICC) exceeds 50 kA and the magnetic field reaches up to more than 6 T for a few tens of thousands of pulses. The large transverse forces, accumulating from strand to strand over the cable cross-section, cause a severe deformation of the cable bundle inside the conduit and this goes along with electromagnetic, mechanical, and thermohydraulic effects. In order to study the electromagnetic and mechanical behaviour in more detail, a Cryogenic Cable Press is build to simulate the effect of the Lorentz forces on a conductor comparable to the present design for ITER in magnet operating conditions. The magnetisation of the conductor (and from this the coupling loss expressed in nτ) and the interstrand resistance (R_c) between various strands and strand bundles inside the cable can be measured along the loading history, starting at virgin condition and accordingly subjected to various loads. The results, all obtained on eight full-size ITER type NbTi conductor samples with a variety of cable strand layout and coatings, are reported here.A consistent correlation is found between the experimental AC loss and interstrand contact resistance (R_c) results. It is also observed that there is a strong impact of cyclic loading on the AC loss and R_c which may change up to orders of magnitude. The variation of the AC loss due to transverse cyclic loading of CICC conductors in ITER coils can be accomplished by reducing the void fraction. The results point out that cyclic loading with a significant number of cycles, sufficient to reach a saturation after having passed the peak transverse resistance, should be included in next tests on large NbTi CICC's and PF Model Coils as the AC loss and ability of current sharing among strands will vary along the loading history.     

Evaluation of thermal gradients and thermosiphon in dual channel cable-in-conduit conductors

In an effort to optimize superconductor cryogenics of large coils, dual channel cable-in-conduit conductors (CICC) have been designed. The qualitative and economic rationale of the conductor central channel is here justified but brings high complexity to the conductor cooling characteristics. Temperature gradients in the cable must be quantified to guarantee conductor temperature margin during coil operation under heat disturbance and set adequate inlet temperature. A simple one-dimensional thermal model, with neither fluid nor strand or jacket conduction, allows to better understand and quantify the steady state behavior of CICC central and annular channels. This thermohydraulic model with homogeneous central and annular temperatures and no jacket conduction is summarized with explicit thermal coupling equations. Local convection coefficients chosen proportional to friction factors lead to a model of global interchannel heat exchange coefficient serving the bithermal model. A first stationary experimental evaluation of the internal heat transfer coefficient using the interchannel heat exchange space constant at various heat loads and mass flow rates is illustrated on two full size samples tested at cryogenic temperatures. Annular heaters experiments with low distributed power achieve pertinent model correlation. Discrepancy between model and experimental data may be linked to the simplistic homogeneous annular temperature hypothesis, to the estimate of CICC mass flow distribution among channels, and to gravitational effects at high heat loads. Perturbation due to the thermosiphon generated between the two channels is considered since neither the experiments nor the expected applications are free of gravity.     

CFD model of ITER CICC. Part VI: Heat and mass transfer between cable region and central channel

Dual-channel cable-in-conduit conductors (CICC) are used in the superconducting magnets for the International Thermonuclear Experimental Reactor (ITER). As the CICC axial/transverse size ratio is typically ∼1000, 1D axial models are customarily used for the CICC, but they require constitutive relations for the transverse fluxes. A novel approach, based on Computational Fluid Dynamics (CFD), was recently proposed by these authors to understand the complex transverse thermal-hydraulic processes in an ITER CICC from first principles. Multidimensional (2D, 3D) Reynolds-Averaged Navier-Stokes models implemented in the commercial CFD code FLUENT were validated against compact heat exchanger and ITER-relevant experimental data, and applied to compute the friction factor and the heat transfer coefficient in fully turbulent spiral rib-roughened pipes, mimicking the central channel of an ITER CICC. That analysis is extended here to the problem of heat and mass transfer through the perforated spiral separating the central channel from the cable bundle region, by combining the previously developed central channel model with a porous medium model for the cable region. The resulting 2D model is used to analyze several key features of the transport processes occurring between the two regions including the relation between transverse mass transfer and transverse pressure drop, the influence of transverse mass transfer on axial pressure drop, and the heat transfer coefficient between central channel and annular cable bundle region.     

Heat transfer from plates to conductors: from toroidal field model coil tests analysis to ITER model

During a safety discharge of toroidal field type magnets, eddy currents and associated heat generation are induced in the plates. A model has been developed from the thermohydraulic code Gandalf with introduction of the equations of the heat diffusion from plates to conductors through the steel and insulation. The comparison of calculation and experimental results for the ITER toroidal field model coil is presented.Preliminary analysis for the ITER toroidal field coils is also presented, taking into account the conductor parameters, the magnetic field and the external hydraulic circuit. The possible quench of the magnetic system is discussed.     

Thermal-Electromagnetic Analysis for 14 kA Fast Discharge of a Model Coil

A model coil for 40-T hybrid magnet superconducting outsert magnet has been constructed and tested at the High Magnetic Field Laboratory, Chinese Academy of Sciences. The model coil was wound with Nb₃Sn cable-in-conduit conductor (CICC) cabled in a 316LN jacket cooled with supercritical helium. The model coil alone can produce about 4 T maximum magnetic field with an operating current of 14 kA. The model coil, in combination with 7.57-T NbTi background coil, can produce 11.5 T central field at 14 kA. During the test campaigns, a fast discharge was triggered by a dump resistor of 3.6 mΩ to evaluate the thermal-electromagnetic behavior of the model coil. In order to avoid a quench of the background coil, no current was exerted on the background coil through a power supply during the fast discharge of the model coil. The test results show that the central magnetic field is not scaled proportionally to the current decay of the model coil. The circuit model gives excellent results compared with the measured ones for the central magnetic field evolution as a function of time in this paper. For the thermal-hydraulic behavior during the fast discharge, the maximum temperature at the inlet simulated by the 1-D Gandalf code gives excellent agreement results compared with the measured ones with the conductor coupling time constant of 63 ms.     

JackPot: A novel model to study the influence of current non-uniformity and cabling patterns in cable-in-conduit conductors

JackPot is a new model that is used to analyse how and to what extend current non-uniformity among strands in a cable-in-conduit conductor (CICC) affects its performance. The joints at the extremities of the CICCs in coils and short samples introduce a non-uniform current distribution among the strands. A detailed and quantitative study down to strand level is required to explain the involved phenomena, to understand their implications on short sample and coil tests and to provide adequate solutions for improvements. The model can be used to evaluate the influence of the joint design and to define its baseline requirements for short-sample qualification testing, and for optimum magnet performance of for example the ITER coils.JackPot is an electrical network model that simulates the interaction between the superconducting strands in the cable (following their precise trajectories), the interstrand contact resistances, the conduit, and the cable’s connection to the joints. The backbone of JackPot is its cable geometry model, from which all relevant properties are derived. All parameters are derived from well defined experimental measurements on conductor sections and joints, except the axial strain for Nb₃Sn strands, which is the only free parameter in the model.The simulations demonstrate that the current non-uniformity is the source for a number of observed phenomena. Another conclusion is that completely filling the bottom joints and upper terminations of a short sample with solder, opposed to only (partly) soldering the cable surface, improves short-sample testing significantly for qualifying the ITER type CICCs. This paper describes the model and gives a few examples of applications for its validation.     

Effective thermal conductivity of the conductor insulation of the ITER toroidal field model coil at operation temperature

During current transients in the toroidal field model coil (TFMC), the radial plates carry eddy currents that generate Joule heat. The heat sink is the forced flow helium cooling of the conductor. Vice versa, during accidents, the radial plates act as a heat sink during the heat up of the conductor. In both cases, the time constant of heat transfer is given by the thermal conductivity of the insulation of the conductor. The code system MAGS (magnet system) is used to recalculate fast discharge experiments of the TFMC at the TOSKA facility. The model takes into account the transient magnetic field, the current in the conductor circuit, in the radial plates and coil case, the ac-losses in the conductor and the helium flow. The results clearly indicate that the power distribution in the radial plate should be taken into account and the thermal conductivity of the insulation is considerably lower than assumed up to now.     

Modelization of the thermal coupling between the ITER TF coil conductor and the structure cooling circuit

The ITER Toroidal Field (TF) coils are required not to quench during the most demanding event: a plasma disruption followed by a fast discharge of the Central Solenoid (CS), the Poloidal Field (PF) coils and the Correction Coils (CC). This event creates large heat deposition in the ITER magnet stainless steel structures in addition to the conductor AC losses. In order to prevent quench occurring in the TF conductor, cooling channels, implemented in the TF coil structure (TFCS), have to remove a large fraction of the heat deposited. The first integrated TF and structure mock-up has been manufactured and then tested in the HELIOS cryogenic test facility (CEA Grenoble) to determine the thermal coupling between the TFCS and the TF conductor, both actively cooled by supercritical helium at 4.4 K and 5 bar. It consists in a stainless steel casing, a cooling pipe glued with resin in the casing groove, winding pack (WP) ground insulation, a radial plate and a copper dummy cable-in-conduit-conductor (CICC). Steady state as well as transient thermal characterizations have been completed in May 2015. Simulation results by thermal hydraulic codes (VENECIA/SuperMagnet) and some of the experimental data are presented and discussed. The thermal coupling between the helium in the cooling tube and the TF coil structure is then modelled as an equivalent heat transfer coefficient in order to simplify the thermal hydraulic (TH) models. Comparison between simplified coupling and detailed coupling is presented.     

Thermo-hydraulic analysis of the gradual cool-down to 80 K of the ITER toroidal field coil

A time-dependent thermo-hydraulic simulation for an ITER toroidal field (TF) coil gradual cool-down to 80 K has been performed using a new FORTRAN code. The code is based on a 1D helium flow and 1D multi-region solid heat conduction model. The whole TF coil is simulated taking into account thermal conduction between winding pack and case, which are cooled down separately. To limit coil mechanical stresses and coolant pressure drop in the cooling channels, an improved cool-down mode has been developed based on the analysis. Typical and gradual cool-down temperature distributions of TF coil and case are presented. The results indicate that gradual cool-down to 80 K can be achieved in 3 weeks.     

管内电缆导体稳定性研究方法新探

管内电缆导体（ＣＩＣＣ）,是目前大型低温超导磁体的首选导体。随着超导技术的发展,ＣＩＣＣ在大型超导核聚变实验装置及超导储能磁体中的应用具有不可比拟的优越性。为降低导体成本而提出了在ＣＩＣＣ中采用的超导股线配以纯铜股线的设计方案,开展含纯铜股线ＣＩＣＣ稳定性机理及实验的研究,并开发ＣＩＣＣ优化设计软件,对ＣＩＣＣ在高科技术中的应用意义重大。     

Simulation of quench for the cable-in-conduit-conductor in HT-7U superconducting Tokamak magnets using porous medium model

A cable-in-conduit-conductor (CICC) consists of superconducting cable, copper, supercritical helium and conduit. To keep the operating temperature of superconducting cable lower than its current sharing temperature, the supercritical helium is forced flow through the CICC. The supercritical helium through the cable bundle has the complex directional changes due to the interaction between the supercritical helium and strands. The structure of CICC is characterized with the porous medium. The quench characteristics of CICC are analyzed by the model which the temperature difference between the strands and helium is assumed to be very small due to the heating induced flow to generate high heat transfer coefficient of supercritical helium. A moving mesh method is developed for the numerical solution of the problem with the steep drop for temperature and density of supercritical helium in the short front region of the normal zone. The computational mesh is obtained by equidistribution of a monitor function tailored for the functional variation of the arguments for density, temperature and velocity of supercritical helium. Existence and uniqueness of the discretised equations using a moving mesh are also established. The coupled equation for porous medium is solved using the finite element method with the artificial viscosity term. The validation of the code is tested by comparing it with the other codes with good accuracy. The converged properties of numerical solution due to quench in CICC are studied. We present preliminary estimates of the maximum conductor temperature rise and helium pressure during a quench in the inner layer of toroidal field (TF) magnet for HT-7U. The quench scenarios with different dump time constants of 6.25, 12, and 21.1 s are considered. The goal of such work is to guide the protection scheme and a detailed prediction of the quench evolution of magnet.     

Transverse heat transfer coefficients on a full size dual channel CICC ITER conductor

Dual channel Cable-In-Conduit Conductors (CICC) provide low hydraulic resistance and faster central channel circulation, limiting superconductors temperature rise. The Poloidal Field Insert Sample (PFIS) was tested in the SULTAN facility to evaluate the thermal coupling between the CICC channels upon an experimental heat transfer coefficient assessment. Simple assumptions on the flow – homogeneous central and annular temperatures, no jacket conduction, no steel inertia and diffusivity – lead to a one-dimensional thermal model fully solved in its transient response to a Heavyside temperature evolution at the inlet, using a Laplace transformation. Transient temperature step data fitted with the analytical resolution provide heat transfer coefficients as a function of mass flow rate, compared to crude predictions. The transient measurements provided consistent measurements on the full range of mass flow rate in both vertical flow directions, whereas steady state homogenization characteristic length measures pursuing the same goal suffer from annular isothermal assumption. Recommendations are made for the thermohydraulic instrumentation of future conductor samples.     

Electro-mechanical modeling of Nb3Sn CICC performance degradation due to strand bending and inter-filament current transfer

Performance degradation of Nb₃Sn cable-in-conduit conductors (CICCs) is a critical issue in large-scale magnet design such as the International Thermonuclear Experimental Reactor (ITER) and the series-connected hybrid (SCH) magnets currently under development at the National High Magnetic Field Laboratory (NHMFL). Not only the critical current is significantly lower than expectations but also the voltage-current characteristic is observed to have a much broader transition from a single strand to a CICC cable. The variation of conductor voltage-current characteristic as a result of cable electromagnetic, mechanical and thermal interactions is challenging to model. In this paper, we use a new numerical model, called the Florida electro-mechanical cable model (FEMCAM) benchmarked against 40 different conductor tests, to study the influence of bending strain and current non-uniformity on the critical current and n-value of Nb₃Sn strands and CICC cables. The new model combines thermal bending effects during cool-down, electromagnetic bending effects during magnet operation and current transfer in strands with filament fracture. The n-value of a strand under bending is derived from integration of filament critical current over strand cross-section for full and no current transfer. The cable n-value is obtained from the power law relation of cable electric field and critical current curve. By comparing numerical results with measurements of advanced Nb₃Sn strands and various CICC cables, we demonstrate that FEMCAM is self-consistent in modeling inter-filament current transfer. The new model predicts that I_c degradation of bent strands initially follows closely full current transfer but starts deviating and falls between full and no current transfer with an increasing bending strain. The results agree with recent TARSIS measurements for less than 1% bending strain mostly interested in practice. The strand n-value degradation from FEMCAM with no filament current transfer agrees better with measurements than that from full current transfer. Finally, FEMCAM simulated cable n-values are compared with various CICC measurements. The results imply that FEMCAM is a useful tool for the design of Nb₃Sn-based CICCs and both thermal bending and electromagnetic bending play important roles in CICC performance.     

Controlling for outer-diameter of superconducting cable for PF Cable-In-Conduit Conductor of ITER

Poloidal Field (PF) coils, made of CICC (Cable-In-Conduit Conductors), are the most important part of ITER (International Thermonuclear Experimental Reactor) superconducting magnet system. The structure of superconducting magnet system in ITER and the CICC are introduced. The main factors influenced the cabling of the superconducting cable for CICC is discussed. Analyzed the outer diameter controlling technique and the relationship between ac loss and structure parameters of the superconducting cable. The technique route of cabling has been established. Especially, the technique of dies setting for shaping + multi-rolling compacting dies + half-dies for diameter keeping is explained in detail, which can efficiently control the diameter and the cabling quality of the superconducting cable, without injury to strands line. The technical parameters for cabling is fixed and one 765 m long dummy cable and one 115 m long superconducting cable of CICC for PF coil is manufactured successfully for ITER the last.     

AC Loss Analysis of a Model Coil for a 40 T Hybrid Magnet

A model coil for a 40 T hybrid magnet was designed and manufactured at the High Magnetic Field Laboratory of the Chinese Academy of Sciences (CHMFL); the model coil was wound with Nb₃Sn cable-in-conduit-conductors (CICC) and cooled with 4.5 K supercritical helium. The performance of the model coil was tested, and the performance tests included a DC charging test, AC losses test, temperature margin test, cyclic load test, and fast discharge test. The AC losses produced in the different operation scenarios of the tests were simulated and analyzed by a modified Gandalf code. The simulated AC losses will be presented and compared with the test results in this paper.     

Electromagnetic analysis of a superconducting transformer for high current characterization of cable in conduit conductors in background magnetic field

A large cable-in-conduit-conductor (CICC) test facility has been designed and fabricated at the High Magnetic Field Laboratory of the Chinese Academy of Sciences (CHMFL) in order to meet the test requirement of the conductors which are applied to the future fusion reactor. The critical component of the test facility is an 80 kA superconducting transformer which consists of a multi-turn primary coil and a minor-turn secondary coil. As the current source of the conductor samples, the electromagnetic performance of the superconducting transformer determines the stability and safety of the test facility. In this paper, the key factors and parameters, which have much impact on the performance of the transformer, are analyzed in detail. The conceptual design and optimizing principles of the transformer are discussed. An Electromagnetic-Circuit coupled model built in ANSYS Multiphysics is successfully used to investigate the electromagnetic characterization of the transformer under the dynamic operation condition.     

Effect of self-field and current non-uniformity on the voltage-temperature characteristic of the ITER central solenoid insert coil by numerical calculations

For the optimisation of a magnet design with cable-in-conduit conductor (CICC) technology it is essential to comprehend the scaling of the critical current from the separate strand characteristics to the finally assembled cable performance in a coil. Several model coils have been tested in the framework of research for the International Thermonuclear Experimental Reactor (ITER). At present, the scaling of the critical current from the strand to the full cable performance and the apparent decrease of the n-index from strand to cable in the voltage-current curves is not understood. It is important to recognize the mechanisms behind this phenomenon in relation to the cost of the superconducting strand, which is significant in the manufacture of the magnets. Therefore, basic phenomena like the cable conductor self-field, the current unbalance introduced by the non-uniformity of the joints and a possible reversible or irreversible degradation of the voltage current characteristic of a strand during cable manufacture or electromagnetic loading of the magnet have to be considered. The voltage-current characteristic of the strand is extensively explored for the relevant range of magnetic field, temperature and axial strain space. Accordingly a numerical six-element network model is developed to simulate the conditions and behaviour of the last stage cable elements of a full-size ITER conductor. The experimental data, mainly in terms of voltage-current (VI) or -temperature (VT) characteristics, are obtained on the central solenoid insert coil (CSIC) experiment performed in Naka (Japan) in the framework of the research for ITER.The numerical model, which is briefly introduced, is used to study the cable performance by using experimentally obtained cable parameters like inter-strand (and bundle) contact resistance, strand critical current data as a function of magnetic field, temperature and applied axial strain, and external cable self-field measurements by Hall sensors for reconstruction of the current non-uniformity.The effect of a current redistribution due to the cable self-field on the voltage-temperature curve is calculated in correlation with the transverse resistance between the strands and last cabling stage bundles (petals). A realistic unbalanced current distribution is established by introducing non-uniform joints at the extremities of the CS-insert cable.It appears that the cable self-field effect hardly gives any change in the shape of the VT curve but merely a shift towards lower temperature giving a reduction of the current sharing temperature T_cs (10 μV/m) of <0.1 K. For typical CICCs with Cr-coated Nb₃Sn strands, there is practically no current redistribution due to the cable self-field, because of the high inter-strand contact resistance.An unbalanced current distribution also gives an earlier voltage rise in the VT curve, mainly at low levels of the electric field. At a 10 μV/m criterion practically no reduction of the T_cs (<0.1 K) is found by the numerical simulation. However, in the CSIC the experimentally obtained overall reduction in T_cs from strand to cable is 0.7 K for an operating current of 40 kA at 12.5 T background field.According to the results of the numerical simulation, the cable self-field effect and the non-uniform current distribution, which is unavoidably caused by the joints, cannot explain the early voltage rise and low n-index in the VT curve of the CS-insert coil. It is very likely that electromagnetic forces play a role in causing reversible degradation in critical current or even irreversible due to strand (filament) damage. Neither can it be excluded that strand deformation during cabling has an impact on the final conductor performance as well. Therefore additional effort is required in detailed 3D modeling of the possible strand deformations inside a cable and the impact it has on the strand performance by experimental verification on strand level.