Numerical optimization on convergent geometries of helium supersonic nozzles.

The supersonic nozzle is a crucial component of supersonic two-phase expander, which is proposed as an innovative alternative to liquefy helium. To investigate helium flow process in supersonic nozzles with different convergent linetypes, the flows in supersonic nozzles whose convergent sections are Quintic polynomial curve, Bicubic parametric curve, Witoszynski curve, and Translation of Witoszynski curve, are respectively simulated by Fluent 19.0. The findings indicate that the supersonic nozzle designed by the Witoszynski curve has following advantages: (1) Both its outlet temperature and pressure is the lowest while the outlet Mach number is the highest, indicating the best expansion refrigeration effect among four supersonic nozzles. (2) The summit of nucleation rate is the highest, achieving 2.200 × 1022 m-3⋅s -1. Outlet droplet number reaches 1.154 × 1016 kg-1, higher than that of other nozzles. (3) This supersonic nozzle is also the first to undergo the condensation process among these four nozzles. (4) Its outlet liquid mass fraction is the highest at 16.03 % and its droplet radius is the smallest at 3.689 × 10–7 m. Therefore, it is recommended to utilize the Witoszynski curve to realize helium liquefaction.