Modeling viscous effects on boundary layer of rarefied gas flows inside micronozzles in the slip regime condition

Abstract

The present work provided a numerical investigation of the supersonic flow of rarefied gas into a planar micronozzle characterized by small depth and long divergent section. 2D and 3D computational fluid dynamics (CFD) computations were performed using the continuum Navier-Stokes equations in combination with partial slip conditions at walls, based on a the establishment of the slip regime related to a Knudsen number ranging between 1 x 10-3 and 1 x 10-1. Different partial slip conditions were considered, i.e. the ideal case of pure slip conditions and the full viscous case with Maxwellian slip conditions on sidewalls and planar walls, as well as the case of Maxwellian slip just on sidewalls. The Maxwell slip model was set with a tangential accommodation coefficient equal (TMAC) to 0.8. Comparisons were based on the estimation of the global performance of the micronozzle in terms of thrust force, specific impulse, discharge coefficient and Isp-efficiency.It resulted that when the nozzle depth was neglected, 3D simulations led to the same solution obtained by means of 2D computations inside the micronozzle. The boundary layer thicknesses experienced a linear growth on the sidewalls, and the viscous losses produced a reduction of the performance of about the 95%. Significant differences were found in the prediction of the jet plume, which took the typical bell-shape form in cases involving 2D computations, yet 3D simulations estimated a plume characterized by the succession of oblique shock waves and expansion fan waves. Instead, when the nozzle depth was considered, 3D simulations underlined a completely different behavior of the flow because of the establishment of the nozzle blockage and a viscous heating. The performance suffered an intense degradation of about the 47%, and the analysis of the jet plume highlighted the formation of the Mach disk followed by the typical diamond-shaped subsonic recirculation region.