B.J. Huang

System design of orifice pulse-tube refrigerator using linear flow network analysis

Abstract A linear flow network model was developed for the system analysis of an orifice pulse-tube refrigerator (OPT). The flow network analysis considers the pressure as the electric voltage and the mass flow as the electric current. The linear governing equations for the flow network are derived from the continuity and the momentum equations and are analytically solved simultaneously with the energy equation derived to account for the thermal effect in the flow network. The thermal performance calculation can thus be greatly simplified by solving the equivalent circuit of the OPT using a sinusoidal signal analysis. To minimize the analytical errors, an equivalent pulse tube temperature T ptm was introduced with a weighting factor W F which was determined experimentally. The linear flow network analysis provides a powerful tool for the system performance analysis of an OPT.

Effect of oversize in wire-screen matrix to the matrix-holding tube on regenerator thermal performance

Abstract A typical regenerator in a cryocooler is usually made by packing hundreds of fine-mesh but oversize wire screens into a small circular tube to provide better thermal performance. By the use of the oversize wire screens, the flow leakage around the inner circumference of the tube is significantly reduced. The oversize in the wire screen is the difference between the diameter of the wire screen and the inner diameter of the tube. In the present study a single-blow test method was used to investigate the effect of oversize on the thermal performance of regenerators. Heat transfer and pressure measurements were performed on three test regenerators. The value in oversize ranged from 0.05 mm to 0.55 mm. The average heat transfer rate of regenerators increases with oversize of wire screens. In addition, empirical relations are provided for the Nusselt number and friction factor versus the Reynolds number for each test regenerator.

Linear network analysis of regenerator in a cyclic-flow system

Abstract A linear dynamics model of Darcys form for a regenerator is first derived, from which a linear network analysis is employed to study the dynamic response of the regenerator in a cyclic-flow system. It is shown that the dynamic response of the regenerator is determined by the design of the load impedance Z2(s). The amplitude attenuation and phase shift between the mass flow and the pressure wave due to the effects of the regenerator configuration and the load impedance can be clearly seen from the present linear network analysis. It is found that introduction of load impedance will reduce the bandwith of a regenerator and increase the phase lag of the mass flow with respect to the pressure wave.

New techniques for the non-contact measurement of displacer motion of a miniature split-Stirling cryocooler

Abstract This paper proposes optional methods to calibrate the static sensitivity of the measurement of displacer motion inside the cold finger of a split-Stirling cryocooler. The relative displacement measurement method, as previously proposed, required that the regenerator matrix material should have such a high magnetic permeability that the linear variable-differential transformer (LVDT) could measure the displacer motion without large signal amplification. This would be impossible for low-permeability materials, e.g. stainless steel 316L and 304L, contained in the displacer. Therefore, three options are proposed for the calibration of static sensitivity: contact, purge or dynamic calibration methods. Temperature compensation is also found to be necessary to transfer the LVDT voltage to the true displacer displacement when performing the non-contact measurement of the displacer motion.

Split-type free-displacer Stirling refrigerator design using linear network analysis

A linear network analysis is developed for the system design of split-type free-displacer Stirling refrigerators. The dynamics models are derived to describe the input/output relation of each component by use of the governing equations in conjunction with linearization and approximation. By connecting the equivalent circuits of the components together, a linear network consisting of a fluid network and a displacer network is obtained. The fluid network accounts for the propagation of gas flow induced by the pressure wave; while the displacer network accounts for the displacer motion induced by the pressure force exerted on the displacer. Two transfer functions are further derived for the displacer motion and the gas pressure of the expansion space with respect to the piston motion. The system performance is then evaluated from the frequency response of the transfer functions by using the sinusoidal signal analysis. The performance prediction of a split-type free-displacer Stirling refrigerator using the linear network analysis is shown to be satisfactory.

Dynamic response of regenerator in cyclic flow system

Abstract The dynamic response of isothermal and cyclic flow in a regenerator is investigated. A basic transfer-function model for the regenerator is derived and used to study the system dynamics of a regenerator connecting a reciprocating piston and a reservoir using two models, G mm ( s ) and G mp ( s ). The frequency response of the mass flow rate at the reservoir side of the regenerator induced by pressure or mass flow rate waves at the piston side is shown to approach zero at high frequency, but to approach a constant value of gain at low frequencies. The cut-off frequency f cut and bandwidth depend on the regenerator design (wire mesh size, porosity, length, diameter, etc.). The criteria for the use of a quasi-steady approximation in regenerator modelling can then be determined by comparing the operating frequency with the regenerator bandwidth. It is also shown that attenuation of the mass flow rate fluctuation induced by the pressure waves is stronger for regenerators with a larger void volume and that the use of air or nitrogen as the working fluid will induce a stronger attenuation effect than helium.

System performance analysis of Gifford-McMahon cooler

Abstract System performance analysis of a Gifford-McMahon (GM) cooler was carried out using the half-cycle mean model of a regenerator and instantaneous solutions of the mass and momentum equations. A PC-based simulation package GMSYS was also developed for system design analysis of a single-stage GM cryocooler. It is shown experimentally that the predicted values agree very well with test results.

Linear network analysis of split-type stirling refrigerator

Abstract A linear network model is developed for split-type Stirling refrigerators. We obtain an equivalentnetwork and two transfer-function functions from which the system performance can be evaluated. Implementation of the linear network model in the system design analysis of split-type Stirling refrigerator is shown satisfactory.

A pulse-tube refrigerator using variable-resistance orifice

Abstract In the present study, we propose a new design of orifice pulse-tube refrigerator (VROPT) using a variable-resistance valve to replace the conventional orifice. The variable-resistance orifice (VRO) is basically a high-speed solenoidal valve similar to the fuel jet device widely used in automobile engines. By changing the frequency and periods of ON and OFF of the valve through an electronic device, we can change the flow resistance of the VRO. This thus provides a possibility for an OPT to be controlled on-line during operation. From the results obtained in the present study, we have shown that VROPT is able to achieve on-line control by regulating the duty cycle d or frequency f v of the VRO. We also show that VROPT will not loss its thermal performance as compared to conventional OPT.

Performance characteristics of pulse tube refrigerators

Abstract In the present study experiments were carried out to investigate the performance characteristics of pulse tube refrigerators. It was found that the cool-down time t c during the transient or start-up period is dominated by the time constant of the pulse tube wall τ pt and that the dynamics of a basic pulse tube (BPT) refrigerator approaches that of a first-order system. For steady state operation, the cold-end temperature T L was found to vary with τ pt , and the cooling load Q L increases monotonically with increasing τ pt . This indicates that heat pumped by the gas from the cold to the hot end increases with decreasing h pt (i.e. less energy exchange between the gas and wall). The process of heat storage or release of the pulse tube wall is thus shown to have a negative effect on the performance of a BPT refrigerator. It was thus found experimentally that the gas compression/expansion process inside the pulse tube, which is similar to a Brayton cycle but lies between isothermal and adiabatic, can explain the performance of BPT refrigerators. The present experiment also shows that the performance of a pulse tube refrigerator at transient and steady states is mainly dominated by the time constant of the pulse tube wall τ pt .