Investigation of suitability of the method of volume averaging for the study of heat transfer in superconducting accelerator magnet cooled by superfluid helium.

In the field of applied superconductivity, there is a growing need to better understand heat transfers in superconducting accelerator magnets. Depending on the engineering point of view looked at, either 0-D, 1-D, 2D or 3D modeling may be needed. Because of the size of these magnets, alone or coupled together, it is yet, impossible to study this numerically for computational reasons alone without simplification in the description of the geometry and the physics. The main idea of this study is to consider the interior of a superconducting accelerator magnet as a porous medium and to apply methods used in the field of por-ous media physics to obtain the equations that model heat transfers of a superconducting accelerator magnet in different configurations (steady-state, beam losses, quench, etc.) with minimal compromises to the physics and geometry. Since the interior of a superconducting magnet is made of coils, collars and yoke filled with liquid helium, creating channels that interconnect the helium inside the magnet, an upscaling method provides models that describe heat transfer at the magnet scale and are suitable for numerical studies. This paper presents concisely the method and an example of application for super-conducting accelerator magnet cooled by superfluid helium in the steady-state regime in considering the thermal point of view

Numerical Investigation of Thermal Counterflow of He II Past Cylinders

We investigate numerically, for the first time, the thermal counterflow of superfluid helium past a cylinder by solving with a finite volume method the complete so-called two-fluid model. In agreement with existing experimental results, we obtain symmetrical eddies both up- and downstream of the obstacle. The generation of these eddies is a complex transient phenomenon that involves the friction of the normal fluid component with the solid walls and the mutual friction between the superfluid and normal components. Implications for flow in a more realistic porous medium are also investigated

Superfluid Helium Flow in Porous Media

Superfluid helium is primarily used in the field of applied superconductivity. Given the complexity of the magnet geometry and the scales involved, a real 3D simulation of heat transfer in such devices at the micro-channel scale is very difficult, even impossible. However, the repeatability or even periodicity of the structure suggests the possibility of a macro-scale description following a porous medium approach. Which macro-scale model may be used? This largely remains an open field while some answers have been proposed based on experimental or theoretical work

Numerical Investigation of Heat Transfer in a Forced Flow of He II

In this paper, we use the complete two-fluid model to simulate transient heat transfer for a forced flow of He II at high Reynolds number following the setup of the experiments performed by Fuzier, S. and Van Sciver, S., “Experimental measurements and modeling of transient heat transfer in forced flow of He II at high velocities,” Cryogenics, 48(3–4), pp. 130 – 137, (2008). A particular attention has been paid to the heat increase due to forced flow without external warming. The simulation are performed using HellFOAM , the helium superfluid simulator based on the OpenFOAM technology. Simulations results are then compared to the experimental data

Refinement and application of a generic CFD toolkit covering the heat flows in combined solid-liquid systems to investigate thermal quench limits of superconducting magnets

The recently developed robust multiregion numerical toolkit for the modeling of heat flows in combined solid-liquid systems is extended to cover larger temperature domains, crossing the superfluid (HeII) to normal helium (HeI) phase transition, and to include NbTi cables that feature open electrical insulation, porous to superfluid helium. The aim is to probe the influence of thermal design details on the temperature margin of superconducting magnets. The model enhancements are discussed and the model is applied to analyze the results of a particle beam loss test in an LHC main dipole. We show and quantify the degree to which the build characteristics of the superconducting magnet, such as electrical insulation and interlayer fishbones, influence the local temperature margin and, hence, the quench level seen by the magnet

Development and application of a generic CFD toolkit covering the heat flows in combined solid–liquid systems with emphasis on the thermal design of HiLumi superconducting magnets

The main objective of this work is to develop a robust multi-region numerical toolkit for the modeling of heat flows in combined solid–liquid systems. Specifically heat transfer in complex cryogenic system geometries involving super-fluid helium. The incentive originates from the need to support the design of superconductive magnets in the framework of the HiLumi-LHC project (Brüning and Rossi, 2015) [1]. The intent is, instead of solving heat flows in restricted domains, to be able to model a full magnet section in one go including all relevant construction details as accurately as possible. The toolkit was applied to the so-called MQXF quadrupole magnet design. Parametrisation studies were used to find a compromise in thermal design and electro-mechanical construction constraints. The cooling performance is evaluated in terms of temperature margin of the magnets under full steady state heat load conditions and in terms of maximal sustainable load. We also present transient response to pulse heat loads of varying duration and power and the system response to time-varying cold source temperatures

Heat Extraction From the LHC Main Dipole, Main Quadrupole, and MQXA Superconducting Cables

The forthcoming operation of the CERN Large Hadron Collider (LHC) at 13-14 TeV requires a deep understanding of the heat transfer mechanisms in the most critical superconducting magnets. This is aimed at determining their steady-state quench limits and constitutes an input to compute the magnets stability in transient conditions as well, to prevent beam induced quenches. Heat extraction capability of the LHC Nb-Ti magnets relies on the significant contribution provided by superfluid helium (He II). Due to lack of knowledge of the He II distribution in the cable and in the compressed insulation, experimental investigations are necessary. In this work we present an experimental study aimed at reproducing the thermal behavior of superconducting coils using short length samples. With respect to previous studies, a new instrumentation technique was developed and an in-situ calibration of the thermocouples was performed. The study was conducted on different types of instrumented cables-stack reproducing the main bending dipole (MB), the main quadrupole (MQ), and the MQXA, which is one of the two low-β interaction region quadrupoles. The heat extraction was determined as a function of the cable temperature, of the bath temperature and of the beam loss scenario

A PISO-like algorithm to simulate superfluid helium flow with the two-fluid model

International audienceThis paper presents a segregated algorithm to solve numerically the superfluid helium (He II) equations using the two-fluid model. In order to validate the resulting code and illustrate its potential, different simulations have been performed. First, the flow through a capillary filled with Hell with a heated area on one side is simulated and results are compared to analytical solutions in both Landau and Gorter-Mellink flow regimes. Then, transient heat transfer of a forced flow of He Ills investigated. Finally, some two-dimensional simulations in a porous medium model are carried out