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

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

Thermal performances of a meter-scale cryogenic pulsating heat pipe

The combination of dry superconducting magnet using cryocooler as a cold source is becoming a standard. As the magnetic field highly decreases the cryocooler performances, the distance between the hot and cold spot is preferable to be higher than 1 m to maintain these performances. Thanks to their operation simplicity, compacity, lightness, and of course thermal performances, Pulsating Heat Pipes (PHP) are good candidates, as long two-phase thermal link, for these kind of systems. PHP can also work without gravity, in multiple orientations, with a small amount of liquid/gas and at a temperature around the saturation state of the working fluid inside. These devices are studied at different temperature to mostly cool down small electronic devices. At cryogenic temperature, PHPs have been studied in vertical and horizontal position filled with nitrogen, helium and neon mixtures. The longest one ever tested at these temperature is about 30 cm long. In this paper, we present the thermal performances of a 1 m long horizontal PHP made of 36 stainless steel parallel tubes. The tube internal diameter is 1.5 mm, close to the critical diameter (~1.7 mm) to maintain capillarity forces necessary to the PHP operation. Both evaporator and condenser section are copper made and are separated by an adiabatic section. Each section is 33 cm long and 40 cm large. This PHP has been studied with nitrogen with the condenser temperature maintained at 75 K. Several pressure and temperature sensors placed in the three different sections allow to monitor the thermodynamic behavior of the PHP. The maximum equivalent thermal conductivity measured is about 150 kW/(m.K) with a liquid ratio of 0,7 inside the PHP. This system can transfer a maximum heat power of 30 W before reaching its operation limit

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

Steady-State heat transfer through micro-channels in pressurized He II

The operation of the Large Hadron Collider superconducting magnets for current and high luminosity future applications relies on the cooling provided by helium-permeable cable insulations. These insulations take advantage of a He II micro-channels network constituting an extremely efficient path for heat extraction. In order to provide a fundamental understanding of the underlying thermal mechanisms, an experimental setup was built to investigate heat transport through single He II channels typical of the superconducting cable insulation network, where deviation from the macro-scale theory can appear. Micro-fabrication techniques were exploited to etch the channels down to a depth of ~ 16 μm. The heat transport properties were measured in static pressurized He II and analyzed in terms of the laminar and turbulent He II laws, as well as in terms of the critical heat flux between the two regions

Heat-balance integral method for heat transfer in superfluid helium

The heat-balance integral method is used to solve the non-linear heat diffusion equation in static turbulent superfluid helium (He II). Although this is an approximate method, it has proven that it gives solutions with fairly good accuracy in non-linear fluid dynamics and heat transfer. Using this method, it has been possible to develop predictive solutions that reproduce analytical solution and experimental data. We present the solutions of the clamped heat flux case and the clamped temperature case in a semi-infinite using independent variable transformation to take account of temperature dependency of the thermophysical properties. Good accuracy is obtained using the Kirchhoff transform whereas the method fails with the Goodman transform for larger temperature range

Preliminary heat deposition model for a dipole Nb3_{3}Sn model magnet

This report presents the thermal modeling of the Nb$_{3}$Sn magnet under development within the EuCARD project. We will cover the geometry and the materials that are currently considered for the magnet, knowing that these parameters will be adjusted for the optimization of the magnet. The thermal modeling is described with the mesh structure, the physics and the boundary conditions taken into account. This first model does not include liquid helium cooling channels since this issue was not known at the time of this report. Calculations are performed for two base temperatures of 1.9 K and 4.2 K

Superfluid helium forced flow in the Gorter-Mellink regime

A dimensional study of the momentum equations of superfluid helium is presented together with a parametric analysis of newly derived dimensionless numbers. The study is performed with a focus on the role of forced flows in the Gorter-Mellink regime. The dimensionless numbers are derived in such a way they become dependent solely on the total fluid velocity, heat flux, and thermophysical properties in order to facilitate their application to engineering problems where the velocity of the single fluid components might be difficult to measure directly. With a similar approach, a novel form of the superfluid Reynolds number is obtained. This form takes into account the velocity of a forced flow and allows to make considerations about the contribution of both forced flow and heat flux to the establishment of the ordinary turbulence in the normal fluid component. It is also presented a formula for a channel critical dimension at which the critical heat flux for the onset of superfluid turbulence causes ordinary turbulence too. •The role of forced flow in the Gorter-Mellink regime of He II is investigated.•Novel dimensionless numbers are derived as a function of macroscopic quantities only.•The pressure drop term becomes comparable to the mutual friction force in forced flow.•A novel superfluid Reynolds number is derived to include both forced and counter-flow.•A formula for critical characteristic dimension for the onset of turbulence is derived.A dimensional study of the momentum equations of superfluid helium is presented together with a parametric analysis of newly derived dimensionless numbers. The study is performed with a focus on the role of forced flows in the Gorter-Mellink regime. The dimensionless numbers are derived in such a way they become dependent solely on the total fluid velocity, heat flux, and thermophysical properties in order to facilitate their application to engineering problems where the velocity of the single fluid components might be difficult to measure directly. With a similar approach, a novel form of the superfluid Reynolds number is obtained. This form takes into account the velocity of a forced flow and allows to make considerations about the contribution of both forced flow and heat flux to the establishment of the ordinary turbulence in the normal fluid component. It is also presented a formula for a channel critical dimension at which the critical heat flux for the onset of superfluid turbulence causes ordinary turbulence too