Modelling and Simulation of a Velocity Field within Supersonic Flows in Low-Pressure Areas

et al. 2021

Sensors

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Pumping in vacuum chambers is part of the field of environmental electron microscopy. These chambers are separated from each other by a small-diameter aperture that creates a critical flow in the supersonic flow regime. The distribution of pressure and shock waves in the path of the primary electron beam passing through the differentially pumped chamber has a large influence on the quality of the resulting microscope image. As part of this research, an experimental chamber was constructed to map supersonic flow at low pressures. The shape of this chamber was designed using mathematical–physical analyses, which served not only as a basis for the design of its geometry, but especially for the correct choice of absolute and differential pressure sensors with respect to the cryogenic temperature generated in the supersonic flow. The mathematical and physical analyses presented here map the nature of the supersonic flow with large gradients of state variables at low pressures at the continuum mechanics boundary near the region of free molecule motion in which the Environmental Electron Microscope and its differentially pumped chamber operate, which has a significant impact on the resulting sharpness of the final image obtained by the microscope. The results of this work map the flow in and behind the Laval nozzle in the experimental chamber and are the initial basis that enabled the optimization of the design of the chamber based on Prandtl’s theory for the possibility of fitting it with pressure probes in such a way that they can map the flow in and behind the Laval nozzle.

Section: Flow Analyzes In the Experimental Chambermentioning

confidence: 99%

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

Šabacká

Neděla

et al. 2021

Sensors

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“…From the presented data, it follows that the mass flow rate of the gas in the direction towards the aperture PLA 2 decreases as the distance between the apertures PLA 1 and PLA 2 increases. It comes out that, for all the models, a bigger angle delivers a better result due to the detached shock wave, behind which a bigger pressure loss occurs [10][11][12]. The difference in the character of the shock wave being formed behind the aperture PLA 2 becomes obvious from Fig.…”

Section: Fig 10 Graphic Of Probability Of Electron Dispersion Of Eacmentioning

confidence: 87%

Analysis of Impact of Conic Aperture in Differentially Pumped Chamber

Hlavatá

Vyroubal

2019

AiMT

The paper focuses on the simulation of medium dynamics in the environmental scanning electron microscope. In particular, the paper examines the conical aperture location effect in the differentially pumped chamber and the width of the pumping channel in this chamber. The solution is based on the Taylor-Maccoll theory about the impact of the shock wave and was obtained by the use of continuum and finite volume methods in the ANSYS Fluent system.

“…Recently, an experimental chamber simulating the pumping conditions in an environmental electron microscope was fabricated, where two chambers with a large pressure gradient were separated by a small deferentially pumped region with a Laval nozzle-shaped opening [ 3 , 10 ]. Typically, in practice, a pressure of 2000 Pa is used in the specimen chamber (further denoted as P1), and a pressure of approximately 100 Pa is used in the differentially pumped chamber (further denoted as P2).…”

Section: Introductionmentioning

confidence: 99%

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

Šabacká

Bayer

et al. 2022

Sensors

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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.