Peculiarities of superfluid helium boiling as a cryogenic agent on a flat heater inside a vertical channel

Objective. The aim of the work is to study heat and mass transfer processes during He–II boiling as a cryogenic agent on a flat heating surface inside a cylindrical channel at immersion depths comparable to its height.

Method. The study is based on the application of thermodynamic analysis methods, natural and computational modeling of processes and objects of cryogenic engineering.

Result. A schematic of the experimental cell, as well as the methodology for conducting the experiment and data processing, are presented. Attention is paid to the behavior of the interfacial surface depending on various experimental parameters: pressure above the liquid surface, specific heat load and the height of the liquid column above the heating element. A classification of boiling regimes in a vertical channel depending on the visual nature of the processes at the liquid-vapor interfacial surface is proposed. Dependences of the position of the liquid level in the channel on time are constructed. All series were compared, regularities between the interfacial surface velocity, the temperature difference in the liquid and the immersion depth of the heating element in superfluid helium were revealed. A heat balance for the evaporated liquid was compiled in order to estimate heat losses into free volume.

Conclusion. When developing and designing systems using superfluid helium as a cryogenic agent, one can assume the morphology of the interfacial surface and the corresponding operating mode of the system.

1. Takada S., Kobayashi H., Murakami M. and Kimura N. Comparative Study of Heat Transfer Performance and Visualization Images of Superfluid Helium Boiling in Narrow Two-dimensional channel. IOP Conf. Series: Materials Science and Engineering, 2020. № 012142.

2. Takada S., Kimura N., Pietrowicz S., Grunt K., Murakami M., Okamura T. Visualization of He II boiling process under the microgravity condition for 4.7 s by using a drop tower experiment. Cryogenics, 2017; 89: 157-162. № 897 012013

3. Puzina Yu.Yu. Kryukov A.P. Boiling modes of helium II on a cylindrical heater inside a porous structure. High temperature Thermophysics, 2023; 6 (4): 619-624.(In Russ)

4. Bondarenko V.L., Kupriyanov M.Yu., Verkhovny A.I., Kutsko A.G., and Sirota K.K. Influence of porous medium geometric parameters on superfluid 4he entropy filter operation. Chemical and Petroleum Engineering, 2022; 58.

5. Bondarenko V.L., Gafov A.P. Estimation of cost of He-3 isotope extraction from natural helium by cryogenic methods. Vestn. MGTU im. N. E. Baumana, Ser. Mashinostr., 2012; 8:54–61.

6. Allain H., Quintard M., Prat M., Baudouy B. Upscaling of superfluid helium flow in porous media. International Journal of Heat and Mass Transfer. 2010;53: 4852–4864.

7. Serebrov A.P., Lyamkin V.A., Fomin A.K., Onegin M.S. Source of ultracold neutrons based on superfluid helium for the PIK reactor. Journal of Technical Physics, 2022; 92(6). (In Russ)

8. Liming Zhu, Dajun Fan, Peng Zhang, Jun Wen, Yongping Hu, Xianjin Wang, Yugang Zhao, Yuxuan Wang, Junhui Zhang, Xiaofei Niu. Performance evaluation of plate heat exchangers with chevron-type corrugation pattern for the superfluid helium cryogenic system. Case Studies in Thermal Engineering, 2025, 106359.

9. Xin Zhang, Longyu Yang, Yixin Wang, Xueshuo Shang, Wendi Bao, Ziyi Li, Cheng Shao, Zheng Cui. Cryogenic helium flow in adiabatic capillary tubes: Numerical insights into choked flow and superfluid behavior in Joule-Thomson cryocoolers. Cryogenics, 2025; 147.

10. Shen Y, Liu D, Chen S, Zhao Q, Liu L, Gan Z. Study on cooling capacity characteristics of an open-cycle Joule-Thomson cryocooler working at liquid helium temperature. Appl Therm Eng, 2020; 166.

11. Qu Qianxi, Wang Liguo, Chen Huan, Dai Niannian, Jia Peng, Xu Dong, Li Laifeng. Study on flow characteristics of the cryogenic throttle valve for superfluid helium system. Cryogenics, 2024; 138.

12. Lisowski E, Filo G. CFD analysis of the characteristics of a proportional flow control valve with an innovative opening shape. Energ Conver Manage, 2016; 123: 15–28.

13. Jin Shang, Cui Lv, Jinzhen Wang, Huaiyu Chen, Sihao Liu, Ziwei Li, Linghui Gong, Jihao Wu. Development of cold compressors for a 500 W@2 K superfluid helium refrigeration system. Cryogenics, 2023; 123.

14. Durañona U., Abdel Maksoud W., Baudouy B., Berriaud C., Calvelli V., Dilasser G., Lorin C., Lottin J.-P., Pontarollo T., Stacchi F. Design of a magnet to study quench propagation in a Cable-In-Conduit-Conductor filled with stagnant superfluid helium. Cryogenics, 2022; 125.

15. Berriaud C, Maksoud WA, Calvelli V, Dilasser G, Juster F-P, Madur A. Conductor Design of the Madmax 9 T Large Dipole Magnet. IEEE Trans Appl Supercond, 2020; 30:1–5.

16. Caldwel A., Dvali G., Majorovits B., Millar A., Raffelt G., Redondo J., Reimann O., Simon F., Steffen F. Dielectric Haloscopes: A New Way to Detect Axion Dark Matter. Physical Review Letters, 2017;118

17. Vitrano A., Stepanov V., Authelet G., Baudouy B. Experimental study of three-phase helium mixtures in confined channels. Cryogenics, 2023; 135.

18. Vitrano A, Baudouy B. Double phase transition numerical modeling of superfluid helium for fixed nonuniform grids. Comput Phys Commun, 2022; 273.

19. Korolev P.V., Kryukov A.P. Calculation method of a phase separator with direct capillary channels for the separation of superfluid helium and its vapors. Bulletin of the MPEI, 2024; 4: 133-142.

20. Korolev P.V., Kryukov A.P., Puzina Y.Y. Experimental study of the boiling of superfluid helium (he-ii) in a porous body. Journal of applied mechanics and technical physics, 2017; 4: 679-686

21. Puzina Yu.Yu., Kryukov A.P. Recovery heat flux at superfluid helium boiling in a U-shape channel with a porous backfill. Cryogenics, 2024; 141: 103864.

22. Kryukov A.P., Van Sciver S.W. Calculation of the recovery heat flux from film boiling in superfluid helium. Cryogenics, 1981; 21.

23. Kryukov A.P., Mednikov A.F. Experimental study of HE-II boiling on a sphere. Journal of Applied Mechanics and Technical Physics, 2006; 47: 836–841.

24. Korolyov P.V., Kryukov A.P., Puzina Yu.Yu., Yachevsky I.A. The formation of a closed vapor film during the boiling of helium II on a cylindrical heater inside the porous structure. Journal of Physics: Conf. Series 1675 (2020) 012059 doi:10.1088/1742-6596/1675/1/012059.

25. Heat and mass transfer on the interfacial surfaces of condensate-steam. Kryukov A.P., Levashov V.Yu., Zhakhovsky V.V., Anisimov S.I. Successes of physical sciences, 2021;191:113–146. (In Russ)

26. Levashov V.YU., Kryukov A.P., Kusov A.L. Flow structure near an evaporation surface. Fluid Dynamics, 2024; 59(6): 1850-1859.