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Large-scale helium cryo-refrigerator is widely used in superconducting systems, nuclear fusion engineering, and scientific researches, etc., however, its energy efficiency is quite low. First, a 2 kW at 20.0 K helium Brayton cryo-refrigerator is built, and a series of tests have been systematically conducted to investigate the performance of the cryo-refrigerator. It is found that maximum heat conductance proportion (90.7%) appears in the heat exchangers of cold box rather than those of heat reservoirs, which is the main characteristic of the helium Brayton cryo-refrigerator/cycle different from the air Brayton refrigerator/cycle. Other three characteristics also lie in the configuration of refrigerant helium bypass, internal purifier and non-linearity of specific heat of helium. Second, a model of helium Brayton cryo-refrigerator/cycle is presented according to finite-time thermodynamics. The assumption named internal purification temperature depth (PTD) is introduced, and the heat capacity rate of whole cycle is divided into three different regions in accordance with the PTD: room temperature region, upper internal purification temperature region and lower one. Analytical expressions of cooling capacity and COP are obtained, and we found that the expressions are piecewise functions. Further, comparison between the model and the experimental results for cooling capacity of the helium cryo-refrigerator shows that error is less than 7.6%. The PTD not only helps to achieve the analytical formulae and indicates the working temperature of internal purifier, but also reflects the heat conductance distribution of heat exchangers in the cold box. Last, effects of the PTD on cooling capacity and COP of the helium cryo-refrigerator are investigated. In a word, this study provides a better understanding of energy conversion and utilization of the cycle and helps to optimize it.

The phase space method is used in studying a thermo-acoustic heat engine in this paper. The maximum Lyapunov exponent is used to quantify the phase space that is reconstructed from the pressure signal of the thermo-acoustic heat engine. For quantifying the system change, the maximum Lyapunov exponents of the reconstructed pressure phase space trails are calculated. The plot of the maximum Lyapunov exponents versus time is attained. Good agreement between the plot and the evolving process of the real physical phenomenum indicates that the maximum Lyapunov exponents can reflect the state changes of the thermo-acoustic heat engine.