The performance evaluation and parametric studies of an Inertance Tube Pulse Tube Refrigerator (IPTR) are performed for different length-to-diameter ratios, with the Computational Fluid Dynamics (CFD) package FLUENT. The integrated model consists of individual models of the components, namely, the compressor, compressor cooler, regenerator, cold heat exchanger, pulse tube, warm heat exchanger, inertance tube and the reservoir. The formulation consists of the governing equations expressing the conservation of mass, momentum and energy with axi-symmetry assumption and relations for the variable thermophysical properties of the working medium and the regenerator matrix, and friction factor and heat transfer coefficients in oscillatory flows. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of heat exchangers and the regenerator which are treated as porous zones. In addition, the wall thickness of the components is also accounted for. Dynamic meshing is used to model the compressor zone. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the overall performance. The thermal non-equilibrium results in a higher cold heat exchanger temperature due to inefficiencies. The dynamic characteristics of pulse tube are analyzed by introducing a time constant. The study is extended to other types of PTRs, namely, the Orifice type Pulse Tube Refrigerator (OPTR), Double Inlet type Pulse Tube Refrigerator (DIPTR) and a PTR with parallel combination of inertance tube and orifice (OIPTR). The focus of the second phase of analysis is the pulse tube region. The oscillatory flow and temperature fields in an open-ended pipe driven by a time-wise sinusoidally varying pressure at one end and subjected to an ambient-to-cryogenic temperature difference across the ends, is numerically studied both with and without the inclusion of buoyancy effects. Conjugate effects arising out of the interaction of oscillatory flow with heat conduction in the pipe wall are taken into account by considering a finite thickness wall with an insulated exterior surface. Parametric studies are conducted with frequencies in the range 5-15 Hz for an end-to-end temperature difference of 200 K. As the pressure amplitude increases, the temperature difference between the wall and the fluid decreases due to mixing at the cold end. The pressure amplitude and the frequency have negligible effect on the time averaged Nusselt number. The effect of buoyancy is studied for hot side up and cold side up configurations. It is found that the time averaged Nusselt number does not change significantly with orientation or Rayleigh number. Sharp changes in Nusselt number and velocity profiles and an increase in energy transfer through solid and gas were observed when natural convection comes into play with hot end placed down. Cooldown experiments are conducted on a preliminary experimental setup. Comparison of the numerical and experimental cooldown curves disclosed a number of areas where improvement is required, primarily the leakage past the piston and the design of the heat exchangers. The setup is being improved to bring out a second and improved version for attaining the lower cold heat exchanger temperature.

No description available.

A single-stage pulse tube cryocooler was designed and fabricated to provide cooling at 50 K for a high temperature superconducting (HTS) magnet, with a nominal electrical input frequency of 50 Hz and a maximum mean helium working gas pressure of 2.5 MPa. Sage software was used for the thermodynamic design of the pulse tube, with an initially predicted 30 W of cooling power at 50 K, and an input indicated power of 1800 W. Sage was found to be a useful tool for the design, and although not perfect, some correlation was established. The fabricated pulse tube was closely coupled to a metallic diaphragm pressure wave generator (PWG) with a 60 ml swept volume. The pulse tube achieved a lowest no-load temperature of 55 K and provided 46 W of cooling power at 77 K with a p-V input power of 675 W, which corresponded to 19.5% of Carnot COP. Recommendations included achieving the specified displacement from the PWG under the higher gas pressures, design and development of a more practical co-axial pulse tube and a multi-stage configuration to achieve the power at lower temperatures required by HTS.

The operation of pulse tube cryocoolers (PTCs) is based on complicated and poorly-understood solid-fluid interactions involving periodic flows of a cryogenic fluid in a flow loop that includes components filled with micro porous structures. CFD simulation is the current trend in modeling of pulse-tube cryocoolers. Such simulations can only be meaningful if correct closure relations are available. The objective of this investigation is to measure and empirically correlate the axial hydrodynamic parameters for two widely used cryocooler regenerator structures. A test section will be designed, constructed and instrumented for the measurements. Porous structures tested will include 325 and 400-Mesh stainless screens, each at two different porosities. Tests will be performed with helium as the working fluid, over a wide range of parameters. The longitudinal permeabilities and Forchheimer s inertial coefficients will then be obtained in an iterative process where agreement between the data and the predictions of detailed CFD simulations for the entire test sections and their vicinity are sought. Empirical correlations representing the longitudinal permeability and Forchheimer s coefficient in terms of relevant dimensionless parameters will then be developed.

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.

L'4He et l'3He sont des systèmes modèles pour comprendre les propriétés quantiques de la matière fortement corrélée. C'est pour cette raison que plusieurs études ont été consacrées à la compréhension de leur dynamique. A basses températures où les effets quantiques jouent un rôle essentiel, les excitations élémentaires dans l'4He sont décrites par un mode collectif d'excitations: phonon-roton. Par contre pour un système d'3He la description est plus complexe, le spectre d'excitation a deux composantes: un mode collectif (zéro-son) et un continuum d'excitations incohérentes de type particule-trou. Les deux sont bien décrites par la théorie de Landau des liquides de Fermi qui trouve sa validité pour des petits vecteurs d'onde. Jusqu'à présent, on supposait que la dynamique dans les liquides de Fermi à vecteurs d'onde élevés était essentiellement incohérente. Cette thèse porte sur l'exploration, par diffusion inélastique de neutrons, des excitations collectives dans l'3He liquide 2D adsorbé sur un substrat de graphite. Un tel travail expérimental requiert trois ingrédients essentiels : un réfrigérateur à dilution afin de travailler à basses températures, un spectromètre temps de vol afin de mesurer le facteur de structure dynamique du système et un substrat solide (graphite exfolié ZYX) pour la préparation de films d'3He-2D par physisorption. Nos expériences sur ces films d'3He déposés en deuxième couche sur de l'4He solide adsorbé sur le graphite nous ont permis de faire les observations suivantes : à petit vecteur d'onde, le zéro-son est plus proche de la bande particule-trou que celui observé dans le cas de l'3He massif, tandis qu'à fort vecteur d'onde le mode collectif entre dans le continuum et réapparait de l'autre côté. Cette nouvelle branche, observée pour la première fois, est aujourd'hui décrite par la théorie dynamique à N-corps développée par nos collaborateurs de l'université Johannes Kepler de Linz, Autriche. Au cours de ce travail de thèse plusieurs techniques expérimentales ont été développées, en particulier, un réfrigérateur à dilution sans fluide cryogénique robuste adapté à des expériences de diffusion neutronique. Son optimisation a permis de réduire le temps de refroidissement de ce type de réfrigérateurs. / 4He and 3He are model systems for understanding quantum properties of strongly interacting matter. For this reason many studies have been devoted for the understanding of their dynamics. At low temperatures at which quantum effects play an essential role, the elementary excitations in 4He are described by a phonon-roton collective mode. For 3He, the physical description is more complicated, the spectrum has two components: collective excitations (zero-sound) and incoherent particle-hole excitations. Both are described by Landau's theory of Fermi liquids which is valid at low wave vectors. So far, it was thus believed that the dynamics at high wave vectors is essentially incoherent. This thesis is mainly concerned by exploring the collective excitations of a two dimensional 3He film adsorbed on graphite, using inelastic neutron scattering. Such an experiment has three main requirements: a dilution refrigerator in order to work at low temperatures, a time of flight spectrometer for measuring the dynamical structure factor of 3He and a solid substrate (exfoliated graphite ZYX) to obtain a two dimensional film by physical adsorption. Our investigations of the dynamics in two-dimensional 3He adsorbed on graphite preplated with 4He films have revealed important features: At low wave-vectors, the zero-sound mode is considerably depressed compared to bulk 3He. At higher wave vectors, the collective excitations branch enters the particle-hole continuum, and reappears at the lower energy branch of the continuum. This new branch, observed for the first time, is described by the dynamic many-body theory developed by our collaborators from Johannes Kepler University, Linz, Austria. During this work several low temperature techniques have been developed, in particular a robust, cryogen-free dilution refrigerator adapted to the demanding conditions of a neutron scattering experiments. Due to its efficient design, the cooling time has been considerably reduced compared to that of refrigerators of the same type developed in the past.

Ce travail a été effectué dans le cadre d’études de la miniaturisation d’un cryo-réfrigérateur de type tube à gaz pulsé (TGP) et particulièrement pour mieux comprendre l’écoulement et le transfert de chaleur dans un régénérateur, l’élément clé du TGP.Nous présentons les études numérique et expérimentale du facteur de frottement et du nombre de Nusselt pour les écoulements stationnaires et continus à nombre de Reynolds modéré O(1 − 100) au sein d’un régénérateur micro-fabriqué. L’influence de la porosité et de la géométrie est étudiée. La micro-structure précisément contrôlée représente des canaux incurvés de largeur de 10, 20 et 40 μm et de profondeur de 100 à 300 μm qui forment un réseau de colonnes ayant des profiles de losanges ou sinusoïdaux. Les micro-canaux sont gravés sur un substrat de silicium par la technologie DRIE. Une technologie d’implantation de thermomètres à l’intérieur de la micro-structure de régénérateur a été développée et mise en œuvre. Les performances des micro-régénérateurs ont été étudiées selon deux approches : la première se base sur le rapport des pertes de charges dans l’écoulement et de l’efficacité du transfert thermique (NPH/NTU) ; la deuxième, sur le coefficient de transfert de chaleur globale proposé par Bejan. L’étude numérique de ces deux critères montre tout le potentiel des micro-structures proposées. / This research is done in the framework of miniaturisation of pulse tube cryocoolers studies and especially to gain a better understanding of the mass flow and heat transfert in the regenerator, which is a crucial component of these type of cryocoolers.In this work we present a numerical and experimental study of the Darcy-Weisbach friction factor and Nusselt number for a continuous and steady flow at moderate Reynolds number O(1−100) in a micro-machined regenerators. The influence of porosity from 40 to 80 % and of the geometry parameters are studied. Well-controlled microstructures represent convoluted channels of 10, 20 or 40 μm width and 100 or 300 μm depth generated by rhombic- or sinusoidal-shaped columns.The channels are etched in Silicon wafers using DRIE MEMS technology. The thermometers are integrated inside the regenerator’s micro-structure to measure the temperature evolution. The efficiency of the regenerators is estimated using two different approaches : the first, as a ratio of pressure drop losses and heat transfer efficiency (NPH/NTU) ; the second, as a volumetric heat transfer density coefficient proposed by Bejan. The numerical study of the efficiency shows theinterest of proposed micro-structures.

Pulse Tube Cryocoolers (PTC) is widely used in aerospace and missile guiding systems where extreme reliability and ruggedness are crucial. PTCs, in particular, are a class of rugged refrigeration systems that are capable of maintaining temperatures as low as 4 K, without a moving part in their cold end. The operation of PTCs is based on complicated and poorly-understood solid-fluid interactions involving periodic flows of a cryogenic fluid in micro porous structures. Currently, PTCs is often modeled as one-dimensional flow fields using methods whose relevance to cryocoolers is at best questionable. Furthermore, recent CFD-based investigations have underscored the need for adequate closure relations representing periodic flows in anisotropic micro porous media, and have shown that multi-dimensional effects can be significant in PTCs. The objectives of this investigation were to experimentally measure and correlate the anisotropic hydrodynamic parameters for typical micro porous structures that are used in the regenerators of PTCs fillers; perform modeling and CFD-based simulations to elucidate the component and system-level thermo-fluidic processes in modern pulse tube cryocooler designs; and perform a preliminary CFD-based assessment of the effect of miniaturization on the thermal performance of a current PTC design. In the experiments, the measurement and correlation of the directional (axial and radial) permeabilities and Forchheimer s inertial coefficients of meshed screen, sintered mesh, foam metal, and stacked micro-machined plate regenerator fillers were of interest. Hydrodynamic parameters under steady-state conditions were addressed first. Pressure drops were measured for purely axial flow in cylindrical test sections and predominantly radial flows in annular test sections that contained regenerator fillers of interest, under steady-state conditions. The permeabilities and Forchheimer s inertial coefficients were then obtained in an iterative process where agreement between the data and the predictions of detailed CFD simulations addressing the entire test sections and their surroundings were sought. Periodic flows were then addressed. Using high frequency pressure transducers and hot wire anemometry, instantaneous pressures and mass fluxes are measured under periodic purely axial flow conditions. CFD simulations of the experiments were then performed, whereby permeabilities and Forchheimer coefficients that bring about agreement between data and simulation results were calculated.

Pulse tube refrigerators (PTR) are robust, rugged cryocoolers that do not have a moving component at their cold ends. They are often employed for cryogenic cooling of high performance electronics in space applications where reliability is paramount. Miniaturizing these refrigerators has been a subject of intense research interest because of the benefits of minimal size and weight for airborne operation and because miniature coolers would be an enabling technology for other applications. Despite much effort, the extent of possible PTR miniaturization is still uncertain. To partially remedy this, an investigation of the miniaturization of pulse tube refrigerators has been undertaken using several numerical modeling techniques. In support of these models, experiments were performed to determine directional hydrodynamic parameters characteristic of stacked screens of #635 stainless steel and #325 phosphor bronze wire mesh, two fine-mesh porous materials suitable for use in the regenerator and heat exchanger components of miniature PTRs. Complete system level and pulse tube component level CFD models incorporating these parameters were then employed to quantitatively estimate the effects of several phenomena expected to impact the performance of miniature PTRs. These included the presence of preferential flow paths in an annular region near the regenerator wall and increased viscous and thermal boundary layer thicknesses relative to the pulse tube diameter. The effects of tapering or chamfering the junctions between components of dissimilar diameters were also investigated. The results of these models were subsequently applied to produce successively smaller micro-scale PTR models having total volumes as small as 0.141 cc for which sufficient net cooling was predicted to make operation at cryogenic temperatures feasible. The results of this investigation provide design criteria for miniaturized PTRs and establish the feasibility of their operation at frequencies up to 1000 Hz with dimensions roughly an order of magnitude smaller than those that have recently been demonstrated, provided that challenges related to their regenerator fillers and compressors can be addressed.

Les pulses tubes sont des cryoréfrigérateurs similaires aux machines Stirling mais sans pièce mobile à froid, ce qui diminue les vibrations et augmente leur fiabilité. Toutes ces caractéristiques sont les bienvenues pour les applications spatiales, un domaine où le poids et la taille de la machine sont critiques. C'est dans ce cadre qui s'insère la recherche sur la miniaturisation des pulses tubes ; pour le réussir, on peut diminuer le volume déplacé pendant un cycle de la machine, en augmentant simultanément la fréquence d'opération. Pour savoir quels sont les limitations à l'augmentation de fréquence, des simulations sur le comportement du régénérateur et l'inertance à très hautes fréquences ont été faits; une étude expérimentale sur les pertes thermiques dans le tube a été aussi élaborée; et, finalement, des prototypes de pulse tube ont été dimensionnés et caractérisés, l'un desquels satisfait les spécifications initialement données : 0.25 W à 120 K avec 20 W puissance mécanique, à 100 Hz. / Pulse Tubes are a kind of cryocoolers similar to Stirling refrigerators, apart from the cold mobile element, absent in the first, which lessens their exported vibrations and increases their reliability. Spatial applications seek these characteristics for the instruments embarked, along with small weight and size. These needs stimulate the research on pulse tube miniaturization; to achieve this reduction, one can decrease the swept volume per cycle, whilst increasing the frequency of operation. To understand the barriers to carry out very high frequency operation, simulations on the behavior of the regenerator and inertances were made, as well as an experimental study on the thermal losses of the expansion tube. Finally, several very high frequency pulse tube prototypes were built and benchmarked, one of which fulfills the requirements we had initially set : 0.25 W at 120 K, with 20 W of input power at 100 Hz.