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

Pavla Šabacká,Vilém Neděla,Jiří Maxa,Robert Bayer

doi:10.3390/s21206849

Abstract

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.

Highlights

The Department of Electrical and Electronic Engineering of the Brno University of Technology in cooperation with the Institute of Instrumentation Technology of the Academy of Sciences of the Czech Republic in Brno is conducting research on environmental electron microscopy with a focus on the field of vacuum pumped chambers, and on differentially pumped chambers and chambers for samples that are separated by a small diameter aperture, which causes a critical flow in the supersonic regime ending in a shock wave
The environmental scanning electron microscope (ESEM) is one of the most promising tools for studying plant [4,5,6] and polymer [7,8] samples using special signal electron detectors [9], which were developed based on gas flow simulations
Use of a Membrane Pressure Difference Sensor for Low Pressures Measurements Using the mathematical and physical analyses above, it was found that the pressure distribution in the two chambers separated by the Laval nozzle corresponds to the pressure distribution in the nozzle itself

Summary

Introduction

The experimental chamber is currently being completed This experimental chamber has been designed to simulate the flow condition in the aperture region between the sample chamber and the differentially pumped chamber, between which there is normally a pressure difference of 100 Pa to 2000 Pa. It was necessary to perform mathematical and Sensors 2021, 21, 6849. For the investigated case, the chamber behind the nozzle was designed in such a way that the supersonic flow was not affected in any way and the subsequent mathematical and physical analyses showed no effect of even reflected sshuobcskeqwuaevnetsmoanththeemgaatiscfalloawndinpthhyespicaathl aonfatlhyesepsritmheanrysheloewcterdonnboeeafmfe.ct of even reflected shock waves on the gas flow in the path of the primary electron beam.

Use of a Membrane Pressure Difference Sensor for Low Pressures Measurements

Conclusions