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.

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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.

Low cost cryocoolers suitable for long term use in industrial environments are required for superconducting technologies to be competitive with copper based devices in real world applications. Industrial Research Limited is developing such cryocoolers, which use metal diaphragm based pressure wave generators to convert electrical energy to the gas volume displacement required. This project explores methods of increasing the volume displacement provided by the diaphragms while ensuring the components stay within the acceptable material limits. Various alternative diaphragm shapes are tested against the currently used shape through finite element analysis. In addition to testing alternative diaphragm shapes, each shape’s dimensions are optimised. It is concluded the currently used design can be improved by offsetting the piston rest position and slightly reducing the piston diameter. A more detailed analysis is carried out of the bend radii created during fabrication of the diaphragm, and physical testing is performed to verify unexpected calculated stress concentrations. High stresses are observed, however it is concluded unmodelled material features have a large effect on the final stress distribution. It is recommended advantageous shape changes calculated in the first part of the work be trialled to increase the efficiency of the cryocooler, and that investigation of the material behaviour during commissioning of the pressure wave generator be carried out to better understand the operational limits of the diaphragms.

A miniature centrifugal compressor is a key component of a reverse Brayton cycle cryogenic cooling system. The system is commonly used to generate a low cryogenic temperature environment for electronics to increase their efficiency, or generate, store and transport cryogenic liquids, such as liquid hydrogen and oxygen, where space limit is also an issue. Because of space limitation, the compressor is composed of a radial inlet guide vane, a radial impeller and an axial-direction diffuser (which reduces the radial size because of smaller diameter). As a result of reduction in size, in order to obtain the required static pressure ratio/rise, the rotating speed of the impeller is as high as 313 KRPM, if Helium is used as the working fluid. Two main characteristics of the compressor – miniature and high-speed, make it distinct from conventional compressors. Higher compressor efficiency is required to obtain a higher COP (coefficient of performance) system. Even though miniature centrifugal compressors start to draw researchers' attention in recent years, understanding of the performance and loss mechanism is still lacking. Since current experimental techniques are not advanced enough to capture details of flow at miniature scale, numerical methods dominate miniature turbomachinery study. This work numerically studied a high speed miniature centrifugal compressor. The length and diameter are 7 cm and 6 cm, respectively. The study was done on the same physical compressor but with three different combinations of working fluid and operating speed combinations: air and 108 KRPM, helium and 313 KRPM, and neon and 141 KRPM. The overall performance of the compressor was predicted with consideration of interaction between blade rows by using a sliding mesh model. It was found that the specific heat ratio needs to be considered when similarity law is applied. But Reynolds number effect can be neglected. The maximum efficiency observed without any tip leakage was 70.2% for air 64.8% for helium 64.9% for neon. The loss mechanism of each component was analyzed. Loss due to turning bend was found to be significant in each component, even up to 30%. Tip leakage loss of small scale turbomachines has more impact on the impeller performance than that of large scale ones. Use of 10% tip gap was found to reduce impeller efficiency from 99% to 90%. Because the splitter was located downstream of the impeller leading edge, any incidence at the impeller leading edge leads to poorer splitter performance. Therefore, the impeller with twenty blades had higher isentropic efficiency than the impeller with ten blades and ten splitters. Based on numerical study, a four-row vaned diffuser was used to replace a two-row vaned diffuser. It was found that the four-row vaned diffuser had much higher pressure recovery coefficient than the two-row vaned diffuser. However, most of pressure is found to be recovered at the first two rows of diffuser vanes. Consequently, the following suggestions were given to further improve the performance of the miniature centrifugal compressor. 1. Redesign inlet guide vane based on the numerical simulation and experimental results. 2. Add de-swirl vanes in front of the diffuser and before the bend. 3. Replace the current impeller with a twenty-blade impeller. 4. Remove the last row of diffuser.

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The study presents a systematic single and two-phase analysis of fluid flow and heat transfer in a liquid hydrogen storage vessel for both earth and space applications.The study considered a cylindrical tank with elliptical top and bottom. The tank wall ismade of aluminum and a multi-layered blanket of cryogenic insulation (MLI) has been attached on the top of the aluminum. The tank is connected to a cryocooler to dissipate the heat leak through the insulation and tank wall into the fluid within the tank. The cryocooler has not been modeled; only the flow in and out of the tank to the cryocooler system has been included. The primary emphasis of this research has been the fluid circulation within the tank for different fluid distribution scenario and for different level of gravity to simulate all potential earth and space based applications. The equations solved in the liquid region included the conservation of mass, conservation of energy, and conservation of momentum. For the solid region only the heat conduction equation was solved. The steady-state velocity, temperature and pressure distributions were calculated for different inlet positions, inlet opening sizes, inlet velocities and for different gravity values. The above simulations were carried out for constant heat flux and constant wall temperature cases. It was observed from single-phase analysis that a good flow circulation can be obtained when the cold entering fluid was made to flow in radial direction and the inlet opening was placed close to the tank wall. For a two-phase analysis the mass and energy balance at the evaporating interface was taken into account by incorporating the change in specific volume and latent heat of evaporation. A good flow circulation in the liquid region was observed when the cold entering fluid was made to flow at an angle to the axis of the tank or aligned to the bottom surface of the tank. The fluid velocity in the vapor region was found to be higher compared to the liquid region. The focus of the study for the later part of the present investigation was the conjugate heat transfer during a confined liquid jet impingement on a uniform and discrete heating source. Equations governing the conservation of mass, momentum, and energy were solved in the fluid region. In the solid region, the heat conduction equation was solved. The solid-fluid interface temperature shows a strong dependence on several geometric, fluid flow, and heat transfer parameters. For uniform and discrete heat sources the Nusselt number increased with Reynolds number. For a given flow rate, a higher heat transfer coefficient was obtained with smaller slot width and lower impingement height.The average Nusselt number and average heat transfer coefficient are greater for a lower thermal conductivity substrate. A higher heat transfer coefficient at the impingement location was seen at a smaller thickness, whereas a thicker plate or a higher thermal conductivity plate material provided a more uniform distribution of heat transfer coefficient. Compared to Mil-7808 and FC-77, ammonia provided much smaller solidfluid interface temperature and higher heat transfer coefficient whereas FC-77 provided lower Nusselt number. In case of discrete heat sources calculations were done for two different physical conditions, namely, when the total input power is constant and when the magnitude of heat flux at the sources are constant. There was a periodic rise and fall of interface temperature along the heated and unheated regions of the plate when the plate thickness was negligible. The average Nusselt number and average local heat transfer coefficient were highest for uniform heating case and it increased with number of heat sources during discrete heating.

The study considered development of a finite-element numerical simulation model for the analysis of fluid flow and conjugate heat transfer in a zero boil-off (ZBO) cryogenic storage system. A spherical tank was considered for the investigation. The tank wall is made of aluminum and a multi-layered blanket of cryogenic insulation (MLI) has been attached on the top of the aluminum. The tank is connected to a cryocooler to dissipate the heat leak through the insulation and tank wall into the fluid within the tank. The cryocooler has not been modeled; only the flow in and out of the tank to the cryocooler system has been included. The primary emphasis of this research has been the fluid circulation within the tank for different fluid distribution scenario and for different level of gravity to simulate all the potential earth and space based applications. The steady-state velocity, temperature, and pressure distributions were calculated for different inlet positions, inlet velocities, and for different gravity values. The simulations were carried out for constant heat flux and constant wall temperature cases. It was observed that a good flow circulation could be obtained when the cold entering fluid was made to flow in radial direction and the inlet opening was placed close to the tank wall. The transient and steady state heat transfer for laminar flow inside a circular microtube within a rectangular substrate during start up of power has also been investigated. Silicon, Silicon Carbide and Stainless Steel were the substrates used and Water and FC-72 were the coolants employed. Equations governing the conservation of mass, momentum, and energy were solved in the fluid region. Within the solid wafer, the heat conduction was solved. The Reynolds number, Prandtl number, thermal conductivity ratio, and diameter ranges were: 1000--1900, 6.78--12.68, 27--2658, and 300 µ m--1000 µ m respectively. It was found that a higher aspect ratio or larger diameter tube and higher thermal conductivity ratio combination of substrate and coolant requires lesser amount of time to attain steady state. It was seen that enlarging the tube from 300 µ m to 1000 µ m results in lowering of the fluid mean temperature at the exit. Nusselt number decreased with time and finally reached the steady state condition. It was also found that a higher Prandtl number fluid attains higher maximum substrate temperature and Nusselt number. A correlation for peripheral average Nusselt number was developed by curve-fitting the computed results with an average error of 6.5%. This correlation will be very useful for the design of circular microtube heat exchangers.

Stirling cryocoolers are required for a wide variety of applications, especially in military equipment, due to their small size, low weight, long lifetime and high reliability considering their efficiency. Thus, it is important to be able to investigate the operating performance of these coolers in the design stage. This study focuses on developing a computer program for simulating a Stirling cryocooler according to the second order analysis. The main consideration is to simulate thermodynamic, fluid dynamic and heat transfer behavior of Stirling cryocoolers. This goal is achieved by following the route of Urieli (1984), which was focused on Stirling cycle engines. In this research, a simulation for performance prediction of a Stirling cryocooler is performed. In addition to that, the effects of system parameters are investigated. This attempt helps to understand the real behavior of Stirling cryocoolers using porous regenerator material. Results implied that first order analysis methods give optimistic predictions where second order method provides more realistic data compared to first order methods. In addition to that, it is shown that regenerator porosity has positive effect on heat transfer characteristics while affecting flow friction negatively. As a conclusion, this study provides a clear understanding of loss mechanisms in a cryocooler. Performed numerical analysis can be used as a tool for investigation of effects of system parameters on overall performance.