Numerical studies of nitrogen spontaneous condensation flow in laval nozzles using varying droplet growth models

Spontaneous condensation of gas at transonic or supersonic flow is a great concerned phenomenon in many cryogenic engineering fields. An accurate model is of great significance to better understand the mechanism of such condensation and arising issues. In this paper, numerical studies for the effect of droplet growth model modification on the nitrogen condensation flow through Laval nozzles were performed in ANSYS CFX via user defined language. The used four profiles of Laval nozzle were designed with different expansion rate (3000, 5000, 7000 and 10000 s⁻¹) in Ji's experiment (Ji 1990). The throat size is 6.5 (height) × 3.2 (width) mm. Firstly, the classical nucleation model with non-isothermal correction was successful to accurately predict the location of condensation onset in experiment by the down calibration for nucleation rate. The supercooled degree is about 9 K and nucleation rate is at the order of 10²⁰ m⁻³·s⁻¹. Secondly, the simulations of condensation flow using different droplet growth models including Gyarmathy and Young models were accomplished. Based on the analysis of interphase heat and mass transfer, the influence mechanism caused by modification for droplet growth rate on two-phase flow fields was revealed. The results indicate that this modification has a considerable effect on the development of droplet size and relaxation time of gas back to equilibrium, but little influence on location prediction of condensation onset. Finally, the effect of inlet total pressure on two-phase flow parameters was also analyzed. At low pressure, a larger supercooled degree (∼11 K) is required to trigger the occurrence of spontaneous condensation. Correspondingly, the influence intensity resulting from the change of droplet growth model on the interphase mass transfer and thermal fields will obtain some enhancement, but still inappreciable compare to the expansion effect.