This work is concerned with the design, development and performance evaluation of an inertance Pulse Tube Cryocooler (PTC). The main components of a PTC are the compressor, regenerator, pulse tube and inertance tube coupled to a reservoir. The inertance tube is a key component that affects the pressure and mass flow and phase shift between them and hence the performance. In conjunction with the compressor, it also plays a strong role in determining the frequency of operation. The PTC is designed based on system level numerical models (SAGE and DeltaE), component level thermo-acoustic models (DeltaE) of inertance tube and regenerator and experimental data of earlier fabricated Stirling coolers. As a starting point, an inertance tube with a diameter of 3 mm and 3.1 m long was chosen through component level analysis that provides phase shift of around 50 degrees at a pressure ratio of 1.1 for an acoustic power of about 4 W (in order to achieve 1 W of net cooling at 80 K) at 25 bar mean pressure and 60 Hz. From this inertance tube geometry, an estimate of the mass flow rate at the cold heat exchanger is obtained. Based on this mass flow rate, the initial dimensions of the pulse tube and regenerator are arrived at. A parametric study using system level model is carried out to obtain the maximum COP by varying inertance tube length and regenerator diameter. A flexure bearing compressor consisting of moving coil linear motor coupled to a piston is designed for the above cold head. Based on the above design considerations, the PTC compressor and cold head are fabricated and assembled. The PTC is charged with helium at mean pressure of 25 bar and instrumented with pressure and position transducers, temperature sensors and a skin-bonded heater for simulating the heat load on the cold head. Experimental data for the PTC were obtained with two different inertance tube lengths for different frequencies of operation. The cold head temperature exhibited a minimum with respect to the frequency. This optimum frequency shifts towards lower frequency with increased length of the inertance tube. The experimental data clearly shows that with different inertance tube lengths the optimum frequency locates itself for obtaining zero phase shift at the middle of the regenerator. It is observed that the optimum frequency is closely linked to the natural frequency of the pressure wave in the inertance tube suggesting a standing wave within the inertance tube with the pressure node at the reservoir. Thus the inertance tube is found to be analogous to a quarter wave resonator in a thermo-acoustic device. It may thus be possible to pre-fix an operating frequency for a given PTC cold head by choosing an inertance tube length close to quarter wave resonator length. This study has given insights on the phase shift between pressure and mass flow rate governed by the inertance tube and the connection between the optimum and natural frequencies which can be used for better design of PTCs.

Certaines missions d'astrophysique embarquent des détecteurs infrarouges ou X qui sont refroidis à des températures subkelvin via un système cryogénique qui comporte soit un bain d'hélium (comme pour Herschel), soit un réfrigérateur Joule-Thomson (comme pour Planck) pour le pré-refroidissement de l'étage subkelvin. Un doigt froid à tube à gaz pulsé ayant les mêmes performances qu'un Joule-Thomson pourrait offrir un certain nombre d'avantages pour les futures chaines cryogéniques (pas de pré-refroidissement nécessaire, simplicité d'intégration, fiabilité accrue).L'objectif de cette thèse concerne l'étude et la réalisation d'un doigt froid à tube à gaz pulsé 4K qui pourrait remplacer une machine Joule-Thomson. Deux principaux axes d'étude ont été menés parallèlement : des études sur les matériaux régénérateur et des études de performances. Des développements technologiques portant sur le régénérateur (étude et mise en forme de différents matériaux ayant des anomalies de chaleur spécifique à basse température) ont été menés afin d'améliorer les performances d'un doigt froid à tube à gaz pulsé haute fréquence (30Hz) travaillant avec de l'hélium 4.Cette thèse a permis d'obtenir la meilleure performance mondiale en terme de température limite en utilisant de l'hélium 4 et avec un pré-refroidissement à 20K. Une température limite de 3,86K a été obtenue et une puissance froide de 25mW est disponible à 5K. Cette thèse a également permis d'étudier l'effet du gaz réel sur le comportement de la machine, en particulier grâce à des mesures de profils de température du régénérateur. Cinq configurations différentes de régénérateur (variation de la répartition de chaleur spécifique le long du régénérateur froid) ont été testées. Elles ont permis de mieux comprendre le rôle de la répartition de la chaleur spécifique dans le régénérateur. Ces différentes mesures ont été complétées avec des études de fluctuations de températures pariétales réalisées à l'aide d'une centrale d'acquisition rapide (toutes les millisecondes). / Some astrophysics missions embark infrared or X detectors which are cooled down to subkelvin temperatures using a cryogenic cooling system that features helium bath (like for the Herschel satellite) or a Joule-Thomson cryocooler (like for the Planck satellite) for the precooling of the subkelvin cooling stage. A pulse tube cold finger which would have the same performances as a Joule-Thomson cryocooler could offer some advantages for future cryogenic chains (no need of precooling, simplicity of integration, increased reliability).The goal of this PhD is the making and the study of a pulse tube cold finger working at temperature around 4K which could replace a Joule-Thomson cryocooler. Two main lines have been worked on simultaneously : studies on materials for the cold regenerator and studies on the cold finger performances. Technological developments on the cold regenerator (including study and shaping of different materials with specific heat anomalies at low temperature) have been performed to enhance the performances of a cold finger working at high frequency (30Hz) with helium 4.The work done during this PhD led to the best no-load temperature never achieved using helium 4 and with a precooling of 20K. A no-load temperature of 3.86K has been obtained and 25mW of cooling power are available at 5K. In addition the effect of real gas on the cryorefrigerator operation has been studied in particular thanks to the measurement of regenerator thermal profiles. Five configurations with different regenerator fillings (variation of the distribution of the specific heat along the cold regenerator) have been tested. These five tests led to a better understanding of the role of the distribution of the specific heat in the regenerator. These measurements have been completed with studies of regenerator wall temperature fluctuations recorded thanks to a fast data acquisition system (each millisecond).

Cryocoolers are closed cycle devices which produce cooling below 120 K. Usually, one or two linear motors are used to drive one pulse tube cryocooler. Cryocoolers are used for various applications like, cooling of infra red detectors, cryo surgical knife, cryogen recondenser etc. In this thesis the design development and testing of Twin Pulse Tube Cryocooler (TPTC) are discussed. TPTC consists of two pulse tubes driven by dual piston head linear compressor. This dual piston linear compressor is operated using single linear motor. Using this configuration, cooling power is doubled with reduced cost of compressor. The design, fabrication and testing of Linear Moving Magnet Synchronous Motor (LMMSM) based dual piston head linear compressor are carried out indigenously. Finite Element Method (FEM) analysis is used for estimating eddy current loss and flux distribution pattern in various mover configurations of the linear motor. The developed fabrication and assembly procedure of linear motor are discussed in detail. The mover of linear motor is supported by using a pair of cross armed C – type flexures. These flexures are designed using FEM and are fabricated indigenously. The flexure pairs are tested for 108 cycles with ± 3 mm stroke length of linear motor before assembling compressor. Linear motor is usually required to be operated at different frequencies. Thus, a variable frequency and variable voltage Pulse Width Modulated (PWM) based power supply is designed using analog circuits like Op-Amps. This cost effective power supply is capable of delivering 27 A at 100 V with frequency range of 25 Hz to 80 Hz continuously. Sage software was used to carry out 1-D simulation and obtain dimensions of various Pulse Tube Cryocooler (PTC) components. Various pulse tube configurations like Joint Twin PTC, Twin PTC with buffer volume and single PTC with buffer volume were carried out. A Computational Fluid Dynamics (CFD) Fluent 2-D analysis was carried out for single PTC with buffer volume. The fabrication and assembly procedure of PTC is discussed in detail. A novel method of heat exchanger fabrication was developed and analyzed using FEM and its performance is tested experimentally. The twin PTC is operated at 34 bar and 48 Hz. A light weight High Temperature Superconductor (HTS) based level sensor is developed to monitor the cryogen level. The developed sensor was calibrated against discrete diode array and pre-calibrated continuous capacitance type level sensor. The calibrations were carried out in indigenously designed and fabricated 4-wall cryostat using Liquid Nitrogen (LN2) and LOX as cryogen. LabVIEW software based data acquisition was designed for testing, recording and monitoring the performance of twin PTC and level sensors during experiments.