Sensors (Dec 2023)
Comparative Analysis of Supersonic Flow in Atmospheric and Low Pressure in the Region of Shock Waves Creation for Electron Microscopy
Abstract
This paper presents mathematical-physics analyses in the field of the influence of inserted sensors on the supersonic flow behind the nozzle. It evaluates differences in the flow in the area of atmospheric pressure and low pressure on the boundary of continuum mechanics. To analyze the formation of detached and conical shock waves and their distinct characteristics in atmospheric pressure and low pressure on the boundary of continuum mechanics, we conduct comparative analyses using two types of inserted sensors: flat end and tip. These analyses were performed in two variants, considering pressure ratios of 10:1 both in front of and behind the nozzle. The first variant involved using atmospheric pressure in the chamber in front of the nozzle. The second type of analysis was conducted with a pressure of 10,000 Pa in front of the nozzle. While this represents a low pressure at the boundary of continuum mechanics, it remains above the critical limit of 113 Pa. This deliberate choice was made as it falls within the team’s research focus on low-pressure regions. Although it is situated at the boundary of continuum mechanics, it is intentionally within a pressure range where the viscosity values are not yet dependent on pressure. In these variants, the nature of the flow was investigated concerning the ratio of inertial and viscous flow forces under atmospheric pressure conditions, and it was compared with flow conditions at low pressure. In the low-pressure scenario, the ratio of inertial and viscous flow forces led to a significant reduction in the value of inertial forces. The results showed an altered flow character, characterized by a reduced tendency for the formation of cross-oblique shockwaves within the nozzle itself and the emergence of shockwaves with increased thickness. This increased thickness is attributed to viscous forces inhibiting the thickening of the shockwave itself. This altered flow character may have implications, such as influencing temperature sensing with a tipped sensor. The shockwave area may form in a very confined space in front of the tip, potentially impacting the results. Additionally, due to reduced inertial forces, the cone shock wave’s angle is a few degrees larger than theoretical predictions, and there is no tilting due to lower inertial forces. These analyses serve as the basis for upcoming experiments in the experimental chamber designed specifically for investigations in the given region of low pressures at the boundary of continuum mechanics. The objective, in combination with mathematical-physics analyses, is to determine changes within this region of the continuum mechanics boundary where inertial forces are markedly lower than in the atmosphere but remain under the influence of unreduced viscosity.
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