Within the framework of the International Thermonuclear Experimental Reactor (ITER) activities, tests of Nb3Sn-based cable-in-conduit conductors (CICC) for the ITER magnets have shown a hitherto unexplained decreasing performance (with respect to the measured single strand performance) at increasing thermo-mechanical load. This behaviour, which is rather ubiquitous as it affects both Model and Insert Coils and short straight samples as well, has been tentatively attributed, among other possible causes, to strand bending, not included in the ITER design criteria before the Model Coil tests. However, no quantitative verification of the idea has been presented so far and indeed, in order to reproduce the measured performance, ad-hoc fitting parameters in the form of a fictitious current-magnetic field (IxB) dependent average extra compression of the cable have been introduced. In this work we present a novel thermo-mechanical model suitably developed for Nb3Sn-based CICC. We study the behaviour of the conductor by means of a hierarchical multi-scale procedure. At the first level the strand can be modelled as a beam, defined by enriched kinematics to take into account its fibrous structure. At the following level, the behaviour of a triplet of strands is influenced by friction among strands, their pointwise contacts and the helicoidal geometry. The triplet is substituted with a single beam type element that can be suitably parameterised to work with different values of parameters in order to fit different cabling stages. We propose an algorithm for an automatic generation of parameters, depending on the geometry at each step of the hierarchy. In this way the performance of each cabling stage is analysed, making a recursive substitution of discrete models involving many beams with a single, continuous beam model, which characteristics are identified from the previous level. This chain of computations can be performed in a reasonable time when the effective properties are read as an output signal from a sufficiently trained Artificial Neural Network (ANN), which approximates the functional dependence of effective material properties on parameters describing the micro-structure. This procedure leads finally to the computation of the strain distribution inside the cable volume. The computed strain distribution is input to the critical current density jC scaling law for the single strand, together with the magnetic field distribution. The local electric field E, resulting from an empirical power law of the usual form E = EC (j/jC)n, is suitably averaged on the cable cross section and integrated along the CICC in order to obtain the voltage. Voltage-temperature and/or voltage-current characteristics for the CICC, as typically measured during DC performance tests, are then computed by the Mithrandir/M&M code for given reference scenarios. These characteristics are analyzed from the point of view of the IxB dependence and compared with measured ones, where available. Implications for the ITER design will also be discussed.

A novel thermo-mechanical approach to DC performance modelling of Nb3Sn superconducting cable-in-conduit conductors in ITER perspective

BOSO, DANIELA;SCHREFLER, BERNHARD
2006

Abstract

Within the framework of the International Thermonuclear Experimental Reactor (ITER) activities, tests of Nb3Sn-based cable-in-conduit conductors (CICC) for the ITER magnets have shown a hitherto unexplained decreasing performance (with respect to the measured single strand performance) at increasing thermo-mechanical load. This behaviour, which is rather ubiquitous as it affects both Model and Insert Coils and short straight samples as well, has been tentatively attributed, among other possible causes, to strand bending, not included in the ITER design criteria before the Model Coil tests. However, no quantitative verification of the idea has been presented so far and indeed, in order to reproduce the measured performance, ad-hoc fitting parameters in the form of a fictitious current-magnetic field (IxB) dependent average extra compression of the cable have been introduced. In this work we present a novel thermo-mechanical model suitably developed for Nb3Sn-based CICC. We study the behaviour of the conductor by means of a hierarchical multi-scale procedure. At the first level the strand can be modelled as a beam, defined by enriched kinematics to take into account its fibrous structure. At the following level, the behaviour of a triplet of strands is influenced by friction among strands, their pointwise contacts and the helicoidal geometry. The triplet is substituted with a single beam type element that can be suitably parameterised to work with different values of parameters in order to fit different cabling stages. We propose an algorithm for an automatic generation of parameters, depending on the geometry at each step of the hierarchy. In this way the performance of each cabling stage is analysed, making a recursive substitution of discrete models involving many beams with a single, continuous beam model, which characteristics are identified from the previous level. This chain of computations can be performed in a reasonable time when the effective properties are read as an output signal from a sufficiently trained Artificial Neural Network (ANN), which approximates the functional dependence of effective material properties on parameters describing the micro-structure. This procedure leads finally to the computation of the strain distribution inside the cable volume. The computed strain distribution is input to the critical current density jC scaling law for the single strand, together with the magnetic field distribution. The local electric field E, resulting from an empirical power law of the usual form E = EC (j/jC)n, is suitably averaged on the cable cross section and integrated along the CICC in order to obtain the voltage. Voltage-temperature and/or voltage-current characteristics for the CICC, as typically measured during DC performance tests, are then computed by the Mithrandir/M&M code for given reference scenarios. These characteristics are analyzed from the point of view of the IxB dependence and compared with measured ones, where available. Implications for the ITER design will also be discussed.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1555469
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