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.

Pulse tube cryocoolers (PTCs) are among the most attractive choices of refrigerators for applications requiring up to 1 kW of cooling in the temperature range of 4-123 K as a result of the high relative efficiency of the Stirling cycle, the reliability of linear compressors, and the lack of cryogenic moving parts resulting in long life and low vibration signature. Recently, PTCs have been successfully used in applications in the 150 K range, extending the useful range of the device beyond the traditional cryogenic regime. A carefully designed cylindrical cavity referred to as the pulse tube replaces the mechanical expander piston found in a Stirling machine. A network consisting of the pulse tube, inertance tube, and surge volume invoke out-of-phase pressure and mass flow oscillations while eliminating all moving parts in the cold region of the device, significantly improving reliability over Stirling cryocoolers. Terrestrial applications of PTCs expose a fundamental flaw. Many PTCs only function properly in a narrow range of orientations, with the cold end of the pulse tube pointed downward with respect to gravity. Unfavorable orientation of the cold head often leads to a catastrophic loss of cooling, rendering the entire cryocooler system inoperable. Previous research indicates that cooling loss is most likely attributed to secondary flow patterns in the pulse tube caused by free convection. Convective instability is initiated as a result of non-uniform density gradients within the pulse tube. The ensuing secondary flow mixes the cryogen and causes enhanced thermal transport between the warm and cold heat exchangers of the cryocooler. This study investigates the nonlinear stabilizing effect of fluid oscillation on Rayleigh-Bénard instability in a cryogenic gas subject to misalignment between gravitational body force and the primary flow direction. The results are directly applicable to the flow conditions frequently experienced in PTCs. Research has shown that the convective component can be minimized by parametrically driven fluid oscillation as a result of sinusoidal pressure excitation; however, a reliable method of predicting the influence of operating parameters has not been reported. In this dissertation, the entire PTC domain is first fully simulated in three dimensions at various angles of inclination using a hybrid method of finite volume and finite element techniques in order to incorporate conjugate heat transfer between fluid domains and their solid containment structures. The results of this method identify the pulse tube as the sole contributor to convective instability, and also illustrate the importance of pulse tube design by incorporating a comparison between two pulse tubes with constant volume but varying aspect ratio. A reduced domain that isolates the pulse tube and its adjacent components is then developed and simulated to improve computational efficiency, facilitating the model’s use for parametric study of the driving variables. A parametric computational study is then carried out and analyzed for pulse tubes with cold end temperatures ranging from 4 K to 80 K, frequencies between 25-60 Hz, mass flow - pressure phase relationships of -30◦ and +30◦, and Stokes thickness-based Reynolds numbers in the range of 43-350, where the turbulent transition occurs at 500. In order to validate the computational models reported and therefore justify their suitability to perform parametric exploration, the CFD codes are applied to a commercially developed single stage PTR design. The results of the CFD model are compared to laboratory-measured values of refrigeration power at temperatures ranging from 60 K to 120 K at inclination angles of 0◦ and 91◦. The modeled results are shown to agree with experimental values with less than 8.5% error for simulation times of approximately six days using high performance computing (HPC) resources through Georgia Tech’s Partnership for Advanced Computing (PACE) cluster resource, and 10 days on a common quad-core desktop computer. The results of the computational parametric study as well as the commercial cryocooler data sets are compiled in a common analysis of the body of data as a whole. The results are compared to the current leading pulse tube convective stability model to improve the reliability of the predictions and bracket the range of losses expected as a function of pulse tube convection number. Results can be used to bracket the normalized cooling loss as a function of the pulse tube convection number NPTC. Experimental data and simulated results indicate that a value of NPTC greater than 10 will yield a loss no greater than 10% of the net pulse tube energy flow at any angle. A value of NPTC greater than 40 is shown to yield a loss no greater than 1% of the net pulse tube energy flow at all angles investigated. The computational and experimental study completed in this dissertation addresses static angles of inclination. Recent interest in the application of PTCs to mobile terrestrial platforms such as ships, aircraft, and military vehicles introduces a separate regime wherein the angle of inclination is dynamically varying. To address this research need, the development of a single axis rotating cryogenic vacuum facility is documented. A separate effects apparatus with interchangeable pulse tube components has also been built in a modular fashion to accommodate future research needs.

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.