4C

The confinement of high-temperature plasmas peculiar of nuclear fusion devices requires magnetic fields of several Tesla. In several fusion experiments (e.g., Tore Supra, KSTAR, EAST) as well as in future devices (e.g., ITER, W7-X, JT-60SA, EU DEMO) and most likely in a fusion reactor, these high fields are produced by superconducting (SC) coils, wound relying on the cable-in-conduit conductor (CICC) concept and carrying currents of several tens of kA each.

Due to the complexity of the magnet system and the large variety of transients that are expected to take place during a fusion reactor lifetime, together with the strict requirements for a safe and cheap operation of the cryoplant supplying the supercritical He (SHe) for the cooling of the SC coils, thermal-hydraulics (TH) has become a key issue in a fusion reactor design.

Since 2008, the Cryogenic Circuit Conductor and Coil (4C) code has been developed at the Energy Department of the Politecnico di Torino to allow the TH modeling of transients in the whole magnet system of fusion devices.

The 4C code is currently the state-of-the-art tool for this kind of modelling: it is flexible and easy-to-use in terms of geometry definition and model implementation and it has a modular structure. Each module, suitably coupled to the others, describes a sub-section of the magnet system:

-        Coil winding. This is an updated version of the Multi-conductor Mithrandir (M&M) code and analyzes the SC winding with its cooling paths. Each hydraulic channel is addressed as a 1D SHe flow in the conductor axial direction and is discretized with finite elements method. Mass, momentum and energy conservation equations are solved in each He region, coupled with transient conduction equations in the conductor and (separately) in the jacket.

-        Coil structures cooling channels. When the coil is encapsulated in bulky envelopes, additional casing cooling channels (CCC) are required. Each hydraulic channel is addressed as a 1D SHe flow in the CCC axial direction, is discretized with finite elements method and the solution of the mass, momentum and energy conservation equation for the cooling He results in the computation of He speed, temperature and pressure. The pipe wall can also be included in the model, solving a 1D heat conduction equation, coupled with the three He equations.

-        Coil structures. The thermal analysis of the bulky structures of the coil is performed computing the temperature map on a selected set of 2D azimuthal (poloidal) cross sections, approximating with finite elements the real 3D heat conduction problem.

-        Cryogenic circuit. The external cryogenic circuit(s) for the SHe is modeled using the object-oriented, equation based modeling language Modelica. The models of all the main cryogenic circuit components (pipes, valves, volumes, circulators, LHe bath, controllers, heat exchangers) are contained in the newly developed Cryogenics library, which is a suitable extension of the ThermoPower open-source library to the cryogenic operating conditions.

After the development of its core structure, the 4C code entered a long, detailed, successful (and never-ending) validation and benchmark campaign, exploiting experimental data from a wide range of transients and possible CICC configurations. The validation includes both the interpretative and predictive analysis of experimental data, so the tool is now ready for application to project design.

Research topics

• Superconducting magnets

Publications

1. Analysis of the cooldown of the ITER central solenoid model coil and insert coil
   Article
   

   Bonifetto, Roberto; Brighenti, Alberto; Isono, Takaaki; Martovetsky, Nicolai; Kawano, Katsumi; Savoldi, Laura; Zanino, Roberto
   SUPERCONDUCTOR SCIENCE & TECHNOLOGY
   Institute of Physics
   Vol.30 pp.17 ISSN:0953-2048 DOI:10.1088/0953-2048/30/1/015015

1. Development of a Thermal-Hydraulic Model for the European DEMO TF Coil
   Article
   

   Zanino, Roberto; Bonifetto, Roberto; Dicuonzo, Ortensia; Muzzi, Luigi; Nallo, GIUSEPPE FRANCESCO; Savoldi, Laura; Turtù, Simonetta
   IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY
   The IEEE Council on Superconductivity
   Vol.26 pp.6 ISSN:1051-8223 DOI:10.1109/TASC.2016.2523241

1. Verification of the Predictive Capabilities of the 4C Code Cryogenic Circuit Model
   Proceeding
   

   Zanino, Roberto; Bonifetto, Roberto; Hoa, C.; Savoldi, Laura
   AIP CONFERENCE PROCEEDINGS
   In: Advances in Cryogenic Engineering
   Cryogenic Engineering Conference (Anchorage (AK)) June 17-21, 2013
   Vol.1573 pp.8 (pp.1586-1593) ISSN:0094-243X ISBN:9780735412033 DOI:10.1063/1.4860896

2. Analysis of the Effects of the Nuclear Heat Load on the ITER TF Magnets Temperature Margin
   Article
   

   Savoldi, Laura; Bonifetto, Roberto; Bottero, U.; Foussat, A.; Mitchell, N.; Seo, K.; Zanino, Roberto
   IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY
   The IEEE Council on Superconductivity
   Vol.24 pp.4 ISSN:1051-8223 DOI:10.1109/TASC.2013.2280720

1. Validation of the 4C Thermal-Hydraulic Code against 25 kA Safety Discharge in the ITERToroidal Field Model Coil (TFMC)
   Article
   

   Zanino, Roberto; Bonifetto, Roberto; Heller, R.; Savoldi, Laura
   IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY
   IEEE
   Vol.21 pp.5 (pp.1948-1952) ISSN:1051-8223 DOI:10.1109/TASC.2010.2089771

1. The 4C Code for the Cryogenic Circuit Conductor and Coil modeling in ITER
   Article
   

   Savoldi, Laura; Casella, F; Fiori, B; Zanino, Roberto
   CRYOGENICS
   Vol.50 (pp.167-176) ISSN:0011-2275

1. M&M: Multi-Conductor Mithrandir Code for the Simulation of Thermal-Hydraulic Transients in Superconducting Magnets
   Article
   

   Savoldi, Laura; Zanino, Roberto
   CRYOGENICS
   Vol.40 (pp.179-189) ISSN:0011-2275

Total: 7