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.

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.