g acceleration of gravity ≈9.81 m/s2
Nomenclature xix
R gas constant 8.314472J/(mol.K)
Acronyms
APT Absolute Pressure Transducer BV Buffer Volume
CFD Computational Fluid Dynamics FFT Fast Fourier Transform
FR Filling Ratio %
MLI Multi-Layer Insulation
NHMFL National High Magnetic Field Laboratory NTC Negative Temperature Coefficient
CEA Atomic Energy Commission
DACM Accelerators, Cryogenics and Magnetism Department HTS High Temperature Superconductors
MRI Magnetic Resonance Imaging PHP Pulsating Heat Pipe
PHPs Pulsating Heat Pipes
PTC Positive Temperature Coefficient
SR2S Space Radiation Superconductive Shield VOF Volume of Fluid
UDF User-Defined Function VP Vacuum Pump
Nomenclature xx
Introduction
Cryogenics is the area of physics covering the production of low temperature environment and study of physical effects at these temperatures. Its use cover a wide range of appli-cations in electronics, medicine, physics, rocketry, levitation and high magnetic field pro-duction. It is indispensable for revealing in certain materials their superconducting state, only attainable at cryogenic temperatures. In fact, below a certain critical temperature (Tc), the superconductivity phenomenon appears in materials (known as superconductors), allowing the circulation of electrical current without any resistance or energy loss. Con-sequently, in the case of superconducting magnets, this lack of electrical resistance allows the generation of huge magnetic fields used, for example, in Magnetic Resonance Imaging (MRI) for medical applications or to deviate and focalize particles in accelerators.
Nowadays, research efforts on superconductivity focus on developing new materi-als with high critical temperature, known as High Temperature Superconductors (HTS), avoiding the use of helium as cryogenic cooling fluids. This allows to deal with repetitive helium scarcities by using other cryogenic fluids more affordable existing in large quantities on earth.
In addition, the interest in superconducting technologies for space applications is demanding new cryogenic technologies able to work without gravity, as studied in the project Space Radiation Superconductive Shield (SR2S) [3,4]. Funded by the European Commission, the objective of this scientific project was to develop technologies to protect the astronauts during deep space travel missions from overexposure to harmful radiation, which increases the probability of developing serious diseases, such as cancer. During this project, active shielding solutions have been studied involving superconducting magnets surrounding the space shuttles and using the magnetic field to deflect particles by chang-ing their trajectory as the geomagnetic field does on earth. The project succeeded in demonstrating the potential of key technologies needed for the development of such an active magnetic shield. As a member of this project, the Accelerators, Cryogenics and Magnetism Department (DACM) of the CEA Paris - Saclay, worked on the cryogenic cooling technology for this superconducting space magnet. The DACM developed meter-scale cryogenic Pulsating Heat Pipes (PHPs), one of the longest created so far, as a novel technology for space applications.
Introduction 2 Invented by Akachi in the 90’s, pulsating heat pipes have been widely studied at room temperature by Khandekar [5], for example, and developed in multiple sizes for different applications, such as electronics cooling [6] or thermal storage [7,8]. In the cryogenic field, pulsating heat pipes have been mostly studied for cooling superconducting magnets. For example, a PHP of a few centimeters long has been tested by Mito et Natsume [9–12]
using different cryogenic working fluids. At the same time, in the meter-scale, a 1 m long vertical cryogenic PHP has been studied by Fonseca [13] using helium as working fluid. The literature reveals that pulsating heat pipes working in no-gravity conditions are comparable to the ones working in horizontal position on earth [14]. However, no horizontal meter-scale cryogenic PHP able to work with different fluids has been developed until now. Concerning numerical simulations related to the physical phenomena occurring in pulsating heat pipes, the main numerical codes have been developed in one dimension by Shafii et Zhang [15, 16] and later by Mameli et al. [17] and Nikolayev et al. [18–
20]. Nowadays, there is no effective method to predict PHPs behavior and a completed numerical model of a PHP would be a step towards a predictive tool for future PHPs designs. The development of 2D numerical models would represent the first step for a future simulation of an entire PHP. To summarize, the chaotic behavior of the pulsating heat pipes makes them unpredictable and a more fundamental comprehension, guided by experimental and numerical tests, is needed for the development of future cryogenic pulsating heat pipes design applications.
For these reasons, the objective of the present work consists in characterizing the thermohydraulic behavior of the meter-scale horizontal cryogenic PHPs as a cooling solu-tion for superconducting magnets.
In chapter 1 the role of cryogenics and the superconductivity phenomenon are de-fined. The main existing superconducting magnet cooling techniques are exposed and a detailed definition followed by a literature review on pulsating heat pipes is given. Finally, the motivation and contribution of this work are provided.
Chapter 2 is dedicated to the description of the cryogenic experimental facility, composed of three horizontal one-meter long pulsating heat pipes.
The following chapters focus on the experimental and numerical results collected during the present research project. In chapter 3, experimental results obtained using nitrogen as working fluid during a progressive heat load test are presented. The thermo-dynamic characteristics of the fluid are defined based on the temperature and pressure evolution of the evaporator, adiabatic and condenser parts. Thermal performance and circulation modes are also provided. This test will be considered as the “reference” to compare with other experimental results in the following chapters.
Chapter4is dedicated to a comparison of the experimental results from progressive heat load and fixed heat load tests using three different working fluids, which are nitrogen,
Introduction 3 neon and argon. Physical parameters of the different working fluid are compared to un-derstand differences in the fluid’s behavior. Moreover, the influence of the buffer volume connection to the PHP during experimental tests is analyzed.
Specific tests to determine the influence in the thermal performance of the start-up conditions and the temperature of the condenser have also been performed. These experimental results are presented in chapter5. This chapter also focuses on the influence of the number of turns in the thermal performance of the system. Finally, results of tests of a sudden increase of heat load are discussed. These tests are supposed to simulate the heat load submitted during the quench of a superconducting magnet to help comprehend the transient behavior of such heat pipes.
Chapter 6is dedicated to the numerical work developed during the present research project. Firstly, the experimental reference model of a single-branch cryogenic PHP is defined. Secondly, the 2D axisymmetric numerical model with assumptions and limiting conditions is presented. Then, the numerical results are shown and explained with respect to the literature findings.
Finally, the last part of this document reviews the findings of this work and identifies potential investigations to solve new questions concerning the operating mode of pulsating heat pipes.
Introduction 4