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Exploring new technologies for the next generation pulse tube cryocooler below 2K

Periodic Reporting for period 1 - EngPTC2 (Exploring new technologies for the next generation pulse tube cryocooler below 2K)

Reporting period: 2019-09-02 to 2021-09-01

In this project, we aim to explore new technologies for the next generation pulse tube cryocooler(PTC) below 2K. Those technologies would have very important application in the areas of space exploration, quantum communicaton and quantum computing. To achieve this, we proposed to use helium3-helium4 mixtures as working gas in the state of the art 4K pulse tube cryocooler to extend its lowest cooling temperature. So theoretically, it need to build a model to to analysis the performance of pulse tube with helium3-helium4 mixtures, which requires the precise equation of state (EOS) and other thermodynamic properties (such as enthalpy, heat capacity, etc.) of the 3He-4He mixtures. And experimentally, it needs to build a experimental system to study and check its performance.
Finaly, after long time collectting the database of 3He-4He mixtures and studing the EOS model, we successfully build the first wide-range equation of state (EOS) for 3He-4He mixtures based on the reduced Helmholtz free energy multi-fluid approximations model. It covers the temperature range 2.17 K to 300 K, the pressure from the vapor pressures up to 3 MPa, for any given mixture 3He concentration. In the experiment, we built a small pulse tube cryocooler system. But there still has some problems to be solve and improve.
Since the project begin, there has two aspects of progerss. One is the study of the equation of state (EOS) for 3He-4He mixtures. Another is the building of experimental system.
For the EOS of 3He-4He mixtures, this project developed the first wide-range equation of state for 3He-4He mixtures based on the Helmholtz free energy, which is reliable for the temperature from 2.17 K to room temperature, pressure from vapor pressure to higher than 3 MPa. To obtain an accuracy calculation model, four different departure functions from KW0, 4He-Ne, 4He-Ar and Ne-Ar multi-fluid model are tested. For each of them, five parameters were optimized to find the minimum deviation from the available experimental data by using the Levenberg–Marquardt method. The results showed that the KW0 model was the best one to predict the thermophysical properties for 3He-4He mixtures. The comparison between the present model and the available experimental data shows that the present model has a good predictive performance not only on the liquid and gas ρpT relation but also on the vapor-liquid equilibrium properties of 3He-4He mixtures. For the most data of ρpT relation, saturated liquid density and speed of sound, the error of present EOS is less than 2 %. For the most data of bubble point pressure, dew point pressure, saturated vapor density and isochoric heat capacity, the error of present EOS is less than 5%, except some points near the critical region or λ point, the error of which can be higher than 8%. Although the present model gives a relatively poor prediction of the saturated heat capacity, it can be improved in the future if more accurate experimental data is available. Furthermore, by comparing with the virial EOS, it also shows that the current model has good extrapolation performance at temperatures above 20 K to room temperature. Based the present EOS, a software was developed by using MATLAB graphical user interfaces (GUI). One can use it to calculate the thermophysical properties at a given point. In addtion, the calculated tabulated database was built, which covers thermophysical properties of ρpT relation, entropy, enthalpy, heat capacity, volumetric thermal expansion, and compression factor at the pressure from saturated pressure up to 3 MPa, temperature from 2.2 K to 350 K, and 3He concentration from 0 to 1.
For the experimental system, in order to save the consumption of helium-3, a small pulse tube (D=5.5 mm) was built. The cold traps within a heater were used as the compressor. In the experiment, the cold trap was put into liquid nitrogen. By heating and removing the heating on the cold trap, a pressure wave can be generated. Meanwhile, another cold trap with some phase different heating can be used as phahe shifter. Theoretically, those two cold trap can generate a Stiling cycle. But unfortunatelly, this idea was failed because the frequency of this compressor can only be around 0.1 Hz, which is too low to generate a avilable cooling power.
In summary, the main output of this project is the first wide-range equation of state for 3He-4He mixtures. The results have been submitted to the J. Phys. Chem. Ref. Data (open access), in which a easy use database and software has been built as the Supplementary Material. It will be very useful for the design and optimization of ultra-low temperature refrigerators.
The main progress of this project is the developement of the first wide-range equation of state for 3He-4He mixtures based on the Helmholtz free energy. Using this EOS of 3He-4He mixtures can lead new research areas in the development of the next generation of space-borne 3He-4He 1K-class Vuilleumier Pulse Tube cooler. Objectives would be to decrease by half the mass of the 300K-1K cooling chain needed to operate space born sub-K cooler, while improving their reliability for long lasting missions. It can also be used to look at new insights in the fine design and operation of modern pulse-tube cooled 3He-4He dilution refrigerator with large cooling power down to 15mK, which interest lies in their increasingly use in the emergence of Quantum Computing.
Themalphysical properties calculator for 3He-4He mixtures