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Library
The CryoSoft library contains the on-line documentation for the SuperMagnet codes, as well as papers written by the CryoSoft team in collaboration with other researchers in the field. You are free to download, reference and distribute any of the notes found in this page. |
The on-line documentation for the SuperMagnet codes
| SUPERMAGNET | user's manual in Pdf format |
| CID | user's manual in Pdf format |
| THEA | user's manual in Pdf format |
| FLOWER | user's manual in Pdf format |
| POWER | user's manual in Pdf format |
| M'C | user's manual in Pdf format |
| GANDALF | user's manual in Pdf format |
| SOLIDS | thermophysical properties, user's manual in Pdf format |
| FLUIDS | thermophysical properties, user's manual in Pdf format |
| GX | interactive and PostScript graphics package, user's manual in Pdf format |
Papers from the on-line library
| CRYO-97-001 | AC Loss Calculation Algorithm |
| CRYO-97-003 | Analytical Calculation of Vector Potential in an Isoparametric Brick |
| CRYO-97-004 | Hydraulic Network Simulator Model |
| CRYO-97-005 | A Numerical Model for the Simulation of Quench in the ITER Magnets |
| CRYO-98-006 | Numerical Aspects in the Simulation of Thermohydraulic Transient in CICC's |
| CRYO-98-007 | The hydraulic solver Flower and its validation against the Quell experiment in SULTAN |
| CRYO-98-008 | Stability analysis of the ITER TF and CS conductors using the code Gandalf |
| CRYO-98-009 | Friction Factor Correlations |
| CRYO-98-010 | Heat Transfer Correlations |
| CRYO-98-011 | Kv-value and Head Loss Factor in Control Valves |
| CRYO-99-012 | Numerical Quenchback in Thermofluid Simulations of Superconducting Magnets |
| CRYO-99-013 | Stability and Protection of CICC's - An Updated Designer's View |
| CRYO-99-014 | Influence of Cable Conduction on Quench Propagation in Force-flow Cooled Conductors |
| CRYO-99-015 | Modelling Stability in Superconducting Cables |
| CRYO-99-016 | Costing Algorithm for Magnet Systems |
| CRYO-00-017 | Thermal, Hydraulic and Electric Analysis of Superconducting Cables: Model Description |
| CRYO-00-018 | Two-channel Analysis of QUELL Experimental Results |
| CRYO-01-019 | A General Model for Thermal, Hydraulic and Electric Analysis of Superconducting Cables |
| CRYO-02-020 | A theoretical Investigation on Current Imbalance in Flat Two Layer Superconducting Cables |
| CRYO-02-021 | Finite Element Simulation of Steady-State and Transient Forced Convection in Superfluid Helium |
| CRYO-02-022 | Predictive Quench Initiation Analysis of the ITER TF Model Coil |
| CRYO-02-023 | Conductor Analysis of the ITER FEAT Poloidal Field Coils During a Plasma Scenario |
| CRYO-02-024 | Application of the Code THEA to the CONDOPT Experiment in SULTAN |
| CRYO-02-025 | Transient Stability Analysis of the SeCRETS Experiment in SULTAN |
| CRYO-02-026 | Comparison between the predictions of the thermo-hydraulic code Gandalf and the results of a long length instrumented CICC module experiment |
| CRYO-02-027 | Critical Surface for BSCCO-2212 Superconductor |
| CRYO-02-028 | Inductance Calculation for Conductors of Arbitrary Shape |
| CRYO-02-029 | An Analytical Benchmark for the Calculation of Current Distribution in Superconducting Cables |
| CRYO-02-030 | Flower, a Model for the Analysis of Hydraulic Networks and Processes |
| CRYO-02-031 | Analysis of Electrical Coupling Parameters in Superconducting Cables |
| CRYO-02-032 | Analytical Solution for the Current Distribution in Multistrand Superconducting Cables |
| CRYO-03-033 | Influence of contact conductance longitudinal variations on current distribution in multistrand cables |
| CRYO-03-034 | MAGNUM - A FORTRAN library for the calculation of magnetic configurations |
We describe the calculation algorithm for AC loss calculation in superconducting cables presently implemented in M'C, version 2.5. The algorithm takes into account two loss components, hysteresis and coupling. Field penetration and screening are well approximated, allowing to deal with small and fast field cycles (minor loops).
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We describe the calculation algorithm for vector potential generated by an isoparametric brick with uniform current density. The calculation is fully analytic and stable inside and outside the brick.
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We describe here a model for the simulation of the hydraulic networks, dedicated especially to the simulation of time boundary conditions for superconducting cables cooling and quench simulation.
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A computational model describing the initiation and evolution of normal zone in the cable-in-conduit superconductors designed for the international thermonuclear experimental reactor (ITER) is presented. Because of the particular geometry of the ITER cables, the model treats separately the helium momenta in the two cooling channels and the temperatures of the cable constituents. The numerical implementation of the model is discussed in conjunction with the selection of a well-suited solution algorithm. In particular, the solution procedure chosen is based on an implicit upwind finite element technique with adaptive time step and mesh size adjustment possibilities. The time step and mesh adaption procedures are described. Examples of application of the model are also reported.
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This paper gives a brief description of the model commonly used to simulate thermohydraulic transients in Cable-in-Conduit Conductors (CICC's), in particular quench initiation and evolution. A discussion on the mathematical and physical characteristics of the system of equations is the starting point to assess the difficulties and advantages of the method used for the numerical solution of this class of problems. The crucial points in the simulation of quench are highlighted, they are associated with the fluid flow and the presence of moving boundaries. The implications for a selection of an optimally suited solution method are discussed.
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Knowledge of the hydraulic boundary conditions is a prerequisite for accurate estimates of the quench characteristics of superconducting magnets. A set of routines Flower has been designed and interfaced to the code Gandalf to provide a simplifed model of the hydraulic connections to a cryogenic plant of a coil using cable-in-conduit conductors with central cooling channel. The validation against experimental data provided by the Quench Experiment on Long Length (QUELL) in the CRPP facility SULTAN have shown that Flower is able to simulate the hydraulic boundary conditions within engineering limits of accuracy.
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The stability of the TF and CS cable-in-conduit conductors for the International Thermonuclear Experimental Reactor (ITER) has been analyzed with the code Gandalf. The energy margins, computed for a number of disturbance scenarios, are in the order of some 100mJ/ccst, well above the expected disturbances. A detailed convergence study is shown to be essential not only in principle but also in practice, e.g. dual stability was found in some cases, but disappeared when the integration time step was refined.
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We describe in this note the friction factor correlations implemented in the friction library.
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We describe in this note the heat transfer correlations implemented in the heattransfer library. The correlation are mainly focussed at describing heat transfer in helium.
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Cryogenic valves are usually characterised through design coefficients, indicated as Kv in DIN/IEC534. In this note we show how to use the Kv coefficient to compute the head loss factor for valves to be used in models of the type implemented in Flower.
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One of the most important thermofluid processes encountered in internally cooled superconducting magnets is that of quenching. Numerical simulation of the quench propagation involves accurately modeling a moving boundary layer at the quench front. Due to the highly non-linear nature of the quench process, slightest numerical errors can rapidly grow to unacceptable limits. The quench propagation in such a non-converged solution exhibits a very rapid propagation velocity which resembles a "quenchback" effect. Hence, the term "Numerical Quenchback" is used to characterize a numerically unstable solution of the governing quench model. This paper presents the underlying physical phenomena that causes a numerical discretization scheme to have error terms that increase exponentially with time, causing the numerical quenchback effect. Specifically, by analytically solving the equivalent differential equation of the numerical scheme, we are able to obtain closed form relations for the error terms associated with the propagation velocity. This allows us to define error criteria on the space and time steps used in the simulation. The reliability of the error criteria is proven by detailed convergence studies of the quench process.
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This paper gives un update on stability and protection of CICC's, with a main focus on simple analytical formulae to be used for cable design purposes. The status of the present understanding is reviewed, collecting the main results as far as possible into a consistent notation. Various additional aspects of present interest are briefly discussed, such as special cable configurations (hybrid cables, cables with additional cooling channels) and operation in superfluid helium. Some considerations on cable current distributions, and its effect on cable stability, are given
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This paper discusses the influence of thermal conduction along the cable on the propagation of normal zones in force-flow cooled conductors. It is shown that because of conduction in the cable, and because of a temperature gradient between cable and cooling helium, the normal zone always propagates faster than the speed of the helium being ejected from the normal zone: the normal front advances the heated helium slug. Expressions to estimate the front advance speed are given, and its influence on the global propagation speed is discussed
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Stability is one of the key issues in the design of a superconductor, and indeed deserves much attention in the magnet design and analysis. Stability-oriented design procedures and calculations involve the detailed knowledge of the response of the cable to thermal, fluid dynamic and electric transient phenomena that are difficult to tackle analytically in cables. This has justified a significant numerical modelling effort in the field. This paper reviews basic stability models and presents selected advances in the methods developed and results obtained. A unified, semi-continuum model is proposed for stability analysis of cables. The time scales of relevance during stability transients are identified and analysed.
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In this note we describe a costing algorithm for systems of magnets. The algorithm gives a good approximation to the magnet system cost, taking into account details of superconducting cable manufacture.
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This note describes a generic, multi-component and multi-channel model for general, consistent and simultaneous analysis of thermal, electric and hydraulic transients in superconducting cables. The model is devised for most general situations, but reduces in limiting cases to commonly known models without loss of efficiency. In the note we give details on the governing equations and describe the solution method used to deal with the high numerical complexity of the coupled field problem.
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We have improved the model presently used in the thermo-hydraulic code Gandalf, adapting it to cable-in-conduit conductors with central cooling channel such as those developed for the model coils of ITER. In particular the helium flow in an arbitrary number of parallel channels have now independent velocity and thermodynamic state (pressure and temperature). We demonstrate the capability of the new model by means of comparison to measurements taken during the QUELL experiment in SULTAN. We compare in particular data on heat slug at zero current and field in a broad range of energy inputs, as well as data on quench propagation, to simulation results obtained with the single channel approximation and the newly implemented two-channel model. The latter achieves a significantly better agreement with experimental data, in particular in the case of slow heating transients such as in heat slug propagation tests.
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In this paper we describe a generic, multi-component and multi-channel model for the analysis of superconducting cables. The aim of the model is to treat in a general and consistent manner simultaneous thermal, electric and hydraulic transients in cables. The model is devised for most general situations, but reduces in limiting cases to most common approximations without loss of efficiency. We discuss here the governing equations, and we write them in a matrix form that is well adapted to numerical treatment. We finally demonstrate the model capability by comparison with published experimental data on current distribution in a two-strand cable.
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A model for the simulation of current distribution in superconducting Rutherford cables is described. The model assumes that interstrand currents can flow continuously among the strands, as if the contact resistances were smeared along the cable length. The model is aimed at the simulation of the generation and development of long range current loops in the presence of time dependent magnetic fields. The results of the model are compared with those obtained through the lumped constants circuit model currently used to calculate the current distribution in Rutherford cables obtaining a good quantitative agreement. The model has also been applied to the study of current distribution in the Rutherford cable of a short LHC dipole magnet. The calculated values of current differences among the strands are in qualitative agreement with experimental data on the amplitude of the periodic oscillations of the magnetic field in the magnet bore.
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In this paper we discuss the solution of transient mass, momentum and energy balances in superfluid helium by means of a finite element algorithm. A simple linearization procedure is used for the non-linear pseudo-diffusion term in the energy balance arising because of the unique counterflow heat transport mechanism in superfluid helium. The linearization algorithm is analyzed for accuracy order and stability. We show in practical tests the reliability of the algorithm devised, comparing the numerical solutions to experimental data available in literature.
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In the ITER TF Model Coil, the experimental evaluation of the superconducting critical properties will only be possible by heating the helium upstream of the inner joint. The goal of this predictive heat slug propagation and quench initiation analysis is to assess if a quench will be initiated in the high field region of the conductor or in the joint. An instability of the cryogenic system occurs when only one pancake is heated. To avoid the unwanted quench in the joint the test must be performed with high helium mass flow rates and slow heating procedures.
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In the framework of the ITER (International Thermonuclear Experimental Reactor) FEAT (Fusion Energy Advanced Tokamak) project, a fully superconducting PF (Poloidal Field) system has been designed in detail. The Central Solenoid and the 6 equilibrium coils constituting the PF system provide the magnetic fields which develop, shape and control the 15 MA plasma during the 1800 s of a typical plasma scenario. The 6 PF coils will be wound two-in-hand from a 45 kA niobium-titanium CICC (Cable-In-Conduit-Conductor). These coils will experience severe heat loads specially during the 400 s of the plasma burn: nuclear heating due to the 400 MW of fusion power, thermal radiation and AC losses (30 to 300 kJ). The AC losses along the PF coil pancakes are deduced from accurate magnetic field computations performed with a 3D magnetostatic code, TRAPS. The nuclear heating and the thermal radiation are assumed to be uniform over a given face of the PF coils. These heat loads are used as input to perform the thermal and hydraulic analysis with a finite element code, GANDALF. The temperature increases (0.1 to 0.4 K) are computed, the margins and performances of the conductor are evaluated.
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The CONDOPT (CONDuctor OPTimization) experiment has been recently completed in SULTAN. The current sharing behaviour of Nb3Sn samples was assessed as a function of the number of cyclic loads experienced during current sweeps in a 10 T background field. We present here results of a computer analysis performed with the code THEATM (for consistent Thermal, Hydraulic and Electric Analysis) in support of the interpretation of the experimental results. We focus in particular on the critical current and current sharing temperature runs, providing details on the features and effects of current distribution among cable sub-stages.
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We present here the results of the analysis of the stability experiment SeCRETS, performed on two Nb3Sn cable-in-conduit conductors with the same amount of total copper stabilizer, but different degree of segregation. The model used for the analysis, including superconducting strands, conductor jacket and helium, is solved with the code GandalfTM. We obtain a qualitative agreement of simulation results and experimental values. The simulation results confirm that in the operation regime explored in the experiment the segregated copper is not effective for stability. The details of the current sharing and the approximation taken for the transient heat transfer are shown to be critical for the interpretation.
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Thermo-hydraulic modeling of cable in conduit conductors (CICC) contains one main uncertainty in the heat exchange coefficient used in the different possible fluid regimes. Nowadays validation of codes, by comparison with data from experiments involving long length instrumented conductors, is one of the main technique for assessing the design tools for the large magnets foreseen in the next generation fusion machines. To this purpose, a broad disturbance scenario has to be investigated to confirm the magnet's stability versus normal and off-normal working conditions. In this paper a comparison between the predictions of the code Gandalf and the data obtained from an instrumented NbTi conductor module is carried out.
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In this note we describe a simple parametrization for the calculation of the engineering critical current in BSCCO-2212. Typical parameters to be used for the material are reported. The critical surface is described as a function of applied field and operating temperature. Additional expressions are given for the critical temperature and field and current sharing temperature.
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In this note we describe a method for the numerical calculation of inductances among conductors of arbitrary shape. The conductor is discretized using isoparametric bricks with uniform current density. The calculation is numerically stable and automatically adaptive up to a predefined accuracy. A convergence acceleration based on the study of the numerical error properties is used to achieve fast and accurate results.
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The validation of numerical codes for the calculation of current distribution and AC loss in superconducting cables versus experimental results is essential, but could be affected by approximations in the electromagnetic model or incertitude in the evaluation of the model parameters. A preliminary validation of the codes by means of a comparison with analytical results can therefore be very useful, in order to distinguish among different error sources. We provide here a benchmark analytical solution for current distribution that applies to the case of a cable described using a distributed parameters electrical circuit model. The analytical solution of current distribution is valid for cables made of a generic number of strands, subjected to well defined symmetry and uniformity conditions in the electrical parameters. The closed form solution for the general case is rather complex to implement, and in this paper we give the analytical solutions for different simplified situations. In particular we examine the influence of different boundary conditions, the effect of a localised resistance in the middle of the cable such as in case of quench and the effects of localized time dependent magnetic fluxes acting on the cable.
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We have developed in the past years a model that describes hydraulic networks that are typical of the cryogenic interconnection of superconducting magnets. The original model, called Flower, was used mostly to provide consistent boundary conditions for the operation of a magnet. The main limitations were associated with the number and nature of modelling elements available, and to the maximum size of the model that could be solved. Here we present an improvement of the model largely relaxing the above limitations by the addition of new modelling elements, such as parallel flow heat exchangers, and by a significant improvement in the numerics of the solver, using sparse matrix storage and solution techniques. We finally show a typical application to the case of a magnet quench in the LHC string.
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The analysis of current distribution and redistribution in superconducting cables requires the knowledge of the electric coupling among strands, and in particular the interstrand resistance and inductance values. In practice both parameters can have wide variations in cables commonly used such as Rutherford cables for accelerators or Cable-in-Conduits for fusion and SMES magnets. In this paper we describe a model of a multi-stage twisted cable with arbitrary geometry that can be used to study the range of interstrand resistances and inductances that is associated with variations of geometry. These variations can be due to cabling or compaction effects. To describe the variations from the nominal geometry we have adopted a cable model that resembles to the physical process of cabling and compaction. The inductance calculation part of the model is validated by comparison to semi-analytical results, showing excellent accuracy and execution speed.
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Current distribution in multistrand superconducting cables can be a major concern for stability in superconducting magnets and for field quality in particle accelerator magnets. In this paper we describe multistrand superconducting cables by means of a distributed parameters circuit model. We derive a system of partial differential equations governing current distribution in the cable and we give the analytical solution of the general system. We then specialize the general solution to the particular case of uniform cable properties. In the particular case of a two-strand cable, we show that the analytical solution presented here is identical to the one already available in the literature. For a cable made of N equal strands we give a closed form solution that to our knowledge was never presented before. We finally validate the analytical solution by comparison to numerical results in the case of a step-like spatial distribution of the magnetic field over a short Rutherford cable, both in transient and steady state conditions.
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We discuss the consequence of a common approximation taken in the derivation of the transmission line model for the description of current distribution in multistrand cables. The approximation consists in considering the contact conductances matrix uniform along the cable length. We have selected a test case that is representative of a Rutherford cable close to a cable splice in a magnet, and we have compared the results obtained using the approximate equations to those obtained when the governing equations are derived in an alternative manner, taking into account possible longitudinal variations of the contact conductance.
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This note reports general formulae for the calculation of magnetic field generated by conductors in plane 2-D, axisymmetric 2-D and 3-D configurations, in the presence of current and magnetization sources. All formulae have been programmed in numerically stable routines, collected in a library named MAGNUM.
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