An Experimental and Numerical Analysis of the Influence of Surface Roughness on Supersonic Flow in a Nozzle Under Atmospheric and Low-Pressure Conditions

The ongoing research in Environmental Scanning Electron Microscopy (ESEM) is contributed to in this paper. Specifically, this study investigates supersonic flow in a nozzle aperture under low-pressure conditions at the continuum mechanics boundary. This phenomenon is prevalent in the differentially pumped chamber of an ESEM, which separates two regions with a significant pressure gradient using an aperture with a pressure ratio of approximately 10:1 in the range of 10,000 to 100 Pa. The influence of nozzle wall roughness on the boundary layer characteristics and its subsequent impact on the oblique shock wave behavior, and consequently, on the static pressure distribution along the flow axis, is solved in this paper. It demonstrates the significant effect of varying inertial-to-viscous force ratios at low pressures on the resulting impact of roughness on the oblique shock wave characteristics. The resulting oblique shock wave distribution significantly affects the static pressure profile along the axis, which can substantially influence the scattering and loss of the primary electron beam traversing the differential pumping stage. This, in turn, affects the sharpness of the resulting image. The boundary layer within the nozzle plays a crucial role in determining the overall flow characteristics and indirectly affects beam scattering. This study examines the influence of surface roughness and quality of the manufactured nozzle on the resulting flow behavior. The initial results obtained from experimental measurements using pressure sensors, when compared to CFD simulation results, demonstrate the necessity of accurately setting roughness values in CFD calculations to ensure accurate results. The CFD simulation has been validated against experimental data, enabling further simulations. The research combines physical theory, CFD simulations, advanced experimental sensing techniques, and precision manufacturing technologies for the critical components of the experimental setup.