# Application of a Total Pressure Sensor in Supersonic Flow for Shock Wave Analysis Under Low-Pressure Conditions

## TL;DR

This paper describes a sensor for measuring total pressure in supersonic flows to study shock waves under low-pressure conditions.

## Contribution

A novel total pressure sensor is applied to analyze shock waves in low-pressure supersonic flows, with implications for electron microscopy environments.

## Key findings

- The sensor successfully characterized total pressure downstream of a nozzle with normal shock waves.
- CFD models were validated and calibrated for low-pressure regimes near continuum limits.
- Entropy increase across shock waves was quantified due to molecular behavior at low pressures.

## Abstract

This study examines the design and implementation of a sensor developed to measure total pressure in supersonic flow conditions using nitrogen as the working fluid. Using a combination of absolute and differential pressure sensors, the total pressure distribution downstream of a nozzle—where normal shock waves are generated—was characterized across a range of low-pressure regimes. The experimental results were employed to validate and calibrate computational fluid dynamics (CFD) models, particularly within pressure ranges approaching the limits of continuum mechanics. The validated analyses enabled a more detailed examination of shock-wave behavior under near-continuum conditions, with direct relevance to the operational environment of differentially pumped chambers in Environmental Scanning Electron Microscopy (ESEM). Furthermore, an entropy increase across the normal shock wave at low pressures was quantified, attributed to the extended molecular mean free path and local deviations from thermodynamic equilibrium.