The world's first verification of agreement of the condensing heat-transfer to hydrogen with the Nusselt theory

　In the condensation and liquefaction of hydrogen, re-liquefaction of evaporated gas in the liquid hydrogen tank for the high-temperature SMES (Superconducting Magnetic Energy Storage) is assumed as illustrated in the above figure for the high-efficiency hydrogen energy system. In the case of liquid helium, certain types of medical-use MRI (Magnetic Resonance Imaging) equipment are already provided with the small refrigerator for re-liquefaction. Nevertheless, there has been very little experimental work on the condensing heat-transfer to cryogenic fluids.

　These re-liquefaction systems require high performance condensing heat exchangers (condenser), which are to have the high heat flux and small heat-transfer temperature difference across the condensate film. However, only few reliable experimental data are available on the condensing heat-transfer to cryogenic fluids such as hydrogen, deuterium, and helium.

　 In the world’s first demonstration of the hydrogen liquefaction experiment undertaken by means of the magnetic refrigeration (cf. Hydrogen liquefaction by magnetic refrigeration) [11. 12], it was necessary to design a experimental apparatus using a thermo-syphon type high-performance heat pipe operated at temperature difference ∆T of within 2 K (ΔT < 2 K), as shown in the above figure. To clarify the relationship between the condensing heat-transfer coefficient measured in previously reported experiments and the theoretical Nusselt eq., we did further experiments on the condensation of hydrogen and nitrogen, which is also important to develop a high-performance and compact heat exchanger (condenser) for liquefaction or re-liquefaction of hydrogen.

　 The process of film-condensation on a vertical wall is shown in the above figure. The well-known theoretical analysis of laminar film-condensation on the vertical wall was made by Nusselt W. The experimental investigations with nitrogen and oxygen have shown a good agreement, within experimental error, between experimental data and those predicted by the Nusselt eq. On the other hand, in the investigations with cryogenic fluids such as hydrogen, deuterium, and helium, the experimental condensing heat-transfer coefficients have fallen below those predicted by the Nusselt eq., and diverged with decreasing temperature difference ∆T across the condensate film, as illustrated in the figure below.

　The test apparatus using a G-M type small refrigerator (UCR31W made by MHI) to investigate the condensing heat-transfer for hydrogen is shown in the figure below. The hydrogen vapor, which is generated by continuously vaporizing liquid hydrogen in the reboiler by means of an electrical heater, flows up into the condensing tube, while the liquid condensate flows down the tube in annular film along the tube wall. Before the hydrogen experiments, we conducted the experiments with nitrogen to confirm the measurement accuracy of our test apparatus. Relationships between the condensation number Nu* and the film Reynolds number Re* for nitrogen are shown in the figure below, together with the experimental data for nitrogen and oxygen previously reported by Haselden et al. Also, calculation results (solid line) derived from the Nusselt eq. are shown for comparison, and the condensing heat-transfer coefficients for nitrogen are in good agreement with the Nusselt eq. within about ±20%.

　Our experimental condensing heat-transfer coefficients for hydrogen and the previously reported data by Drayer et al. are compared with the Nusselt eq. as shown in the figure below. Relationships between the condensation number Nu* and the film Reynolds number Re* for hydrogen as obtained from the present experiment are shown in the figure below. Also, the previously obtained experimental data for hydrogen and helium, and calculation results (solid line) derived from the Nusselt eq. are shown for comparison [6-8].

　We have firstly verified that the condensing heat-transfer coefficient for hydrogen are in good agreement with the Nusselt eq. within about ±20%.

　 The present study obtained in the experiments suggests that the condensing heat-transfer coefficients for deuterium and helium might also be obtained using the Nusselt eq. when their condensate liquid films are in laminar flow. This result is important in thermal and cryogenic engineerings such as the re-liquefaction of evaporated gas in the liquid hydrogen tank for the high-temperature SMES etc. and in the liquid helium tank for MRI equipments.