Flow behavior of expanding ytterbium vapor jet through rectangular nozzles in the transition regime

The sublimation and expansion behavior of metallic ytterbium (Yb) vapor through rectangular nozzles with converging, straight, and diverging cross sections were studied in the transition flow regime for the Knudsen number range of 0.05 ≤ Kn ≤ 5 using direct simulation Monte Carlo (DSMC) method. The DSMC solver was validated with in-house experimental data for mass flow rate and mass flux distribution. It was observed that the mass flow rate from the converging nozzle was limited by evaporation and sonic choking while it was in agreement with the Hertz–Knudsen equation for the straight nozzle. Gas flow diode effect was observed for these finite nozzles with linearly varying cross section with an L/H ratio of 2.8, which disappears in the free molecular flow regime. The effect was found to be increasing with increasing nozzle angle before decreasing after a certain angle due to back-streaming. Among the three nozzles, converging nozzle showed maximum divergence of vapor beam in the radial direction while minimum spread was observed in the diverging nozzle. The divergence of the vapor beam increased with increasing Knudsen number for the converging nozzle, but the opposite was observed for the diverging geometry. This was attributed to the difference in the reflection pattern of the vapor atoms from the nozzle walls. The divergence went through a minima before increasing again for the straight nozzle with increasing Knudsen number. The opposing effects of lower collisional frequency and higher nondirectional velocities due to reflections from the nozzle surface were identified as the reason. Axis-switching phenomenon was identified in the transition regime for Kn = 0.4 and was attributed to the anisotropic expansion of Yb vapor, resulting in steep pressure gradient in the minor axis. The axis-switching was observed at an X/D value of nearly 12 and 18 for converging and straight nozzles, respectively. No axis-switching was observed for diverging nozzle upto an X/D value of 35. The novelty of the current study lies in identifying the gas flow diode effect in finite macroscopic nozzles and the axis switch phenomenon in rarefied gas in a physical vapor deposition system.