Application of Prandtl's Theory in the Design of an Experimental Chamber for Static Pressure Measurements

CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures

This paper deals with CFD analyses of the difference in the nature of the shock waves in supersonic flow under atmospheric pressure and pressure conditions at the boundary of continuum mechanics for electron microscopy. The first part describes the verification of the CFD analyses in combination with the experimental chamber results and the initial analyses using optical methods at low pressures on the boundary of continuum mechanics that were performed. The second part describes the analyses on an underexpanded nozzle performed to analyze the characteristics of normal shock waves in a pressure range from atmospheric pressure to pressures at the boundary of continuum mechanics. The results obtained by CFD modeling are prepared as a basis for the design of the planned experimental sensing of density gradients using optical methods, and for validation, the expected pressure and temperature courses from selected locations suitable for the placement of temperature and pressure sensors are prepared from the CFD analyses.

Mathematical-Physics Analyses of the Nozzle Shaping at the Aperture Gas Outlet into Free Space under ESEM Pressure Conditions

The paper presents a methodology that combines experimental measurements and mathematical-physics analyses to investigate the flow behavior in a nozzle-equipped aperture associated with the solution of its impact on electron beam dispersion in an environmental scanning electron microscope (ESEM). The shape of the nozzle significantly influences the character of the supersonic flow beyond the aperture, especially the shape and type of shock waves, which are highly dense compared to the surrounding gas. These significantly affect the electron scattering, which influences the resulting image. This paper analyzes the effect of aperture and nozzle shaping under specific low-pressure conditions and its impact on the electron dispersion of the primary electron beam.

Mathematical Physics Analysis of Nozzle Shaping at the Gas Outlet from the Aperture to the Differentially Pumped Chamber in Environmental Scanning Electron Microscopy (ESEM)

A combination of experimental measurement preparations using pressure and temperature sensors in conjunction with the theory of one-dimensional isentropic flow and mathematical physics analyses is presented as a tool for analysis in this paper. Furthermore, the subsequent development of a nozzle for use in environmental electron microscopy between the specimen chamber and the differentially pumped chamber is described. Based on experimental measurements, an analysis of the impact of the nozzle shaping located behind the aperture on the character of the supersonic flow and the resulting dispersion of the electron beam passing through the differential pumped chamber is carried out on the determined pressure ratio using a combination of theory and mathematical physics analyses. The results show that nozzle shapes causing under-expanded gas outflow from the aperture to the nozzle have a worse impact on the dispersion of the primary electron beam. This is due to the flow velocity control. The controlled reduction in the static pressure curve on the primary electron beam path thus causes a significantly higher course of electron dispersion values than variants with shapes causing over-expanded gas outflow.

Comparative Analysis of Supersonic Flow in Atmospheric and Low Pressure in the Region of Shock Waves Creation for Electron Microscopy

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.

Impact of Supersonic Flow in Scintillator Detector Apertures on the Resulting Pumping Effect of the Vacuum Chambers

The article describes the combination of experimental measurements with mathematical-physics analyses in flow investigation in the chambers of the scintillator detector, which is a part of the environmental scanning electron microscope. The chambers are divided with apertures by small openings that keep the desirable pressure differences between three chambers: The specimen chamber, the differentially pumped intermediate chamber, and the scintillator chamber. There are conflicting demands on these apertures. On the one hand, the diameter of the apertures must be as big as possible so that they incur minimal losses of the passing secondary electrons. On the other hand, it is possible to magnify the apertures only to a certain extent so the rotary and turbomolecular vacuum pump can maintain the required operating pressures in separate chambers. The article describes the combination of experimental measurement using an absolute pressure sensor and mathematical physics analysis to map all the specifics of the emerging critical supersonic flow in apertures between the chambers. Based on the experiments and their tuned analyses, the most effective variant of combining the sizes of each aperture concerning different operating pressures in the detector is determined. The situation is made more difficult by the described fact that each aperture separates a different pressure gradient, so the gas flow through each aperture has its own characteristics with a different type of critical flow, and they influence each other, thereby influencing the final passage of secondary electrons detected by the scintillator and thus affecting the resulting displayed image.

Slip Flow Analysis in an Experimental Chamber Simulating Differential Pumping in an Environmental Scanning Electron Microscope

This paper describes the combination of experimental measurements with mathematical-physical analysis during the investigation of flow in an aperture at low pressures in a prepared experimental chamber. In the first step, experimental measurements of the pressure in the specimen chamber and at its outlet were taken during the pumping of the chamber. This process converted the atmospheric pressure into the operating pressure typical for the current AQUASEM II environmental electron microscope at the ISI of the CAS in Brno. Based on these results, a mathematical-physical model was tuned in the Ansys Fluent system and subsequently used for mathematical-physical analysis in a slip flow regime on a nozzle wall at low pressure. These analyses will be used to fine-tune the experimental chamber. Once the chamber is operational, it will be possible to compare the results obtained from the experimental measurements of the nozzle wall pressure, static pressure, total pressure and temperature from the nozzle axis region in supersonic flow with the results obtained from the mathematical-physical analyses. Based on the above comparative analyses, we will be able to determine the realistic slip flow at the nozzle wall under different conditions at the continuum mechanics boundary.