Mathematical modelling of dynamic processes in pressure measurement systems in gas-liquid media

Ulyanovsk State Technical University, Ulyanovsk, 432027, Russia

^* Corresponding author: velmisov@ulstu.ru

Abstract

The object of the study is a mathematical model of a system for monitoring pressure changes in the combustion chamber of an aircraft engine, the components of which are a pipeline and a sensor. In the course of the study, the problem is reduced to a linear equation with a deviating argument. The objective of the work is to construct solutions to the equation with a deviating argument and apply them in an application to the problem of studying the dynamics of an elastic element of a pressure sensor interacting with a gas or liquid. By introducing a small parameter, an approximate equation is obtained that relates the deformation of the elastic element of the sensor and the law of change in pressure of the working environment in the engine. For this equation, a program has been developed in the Mathematica system that allows obtaining graphs of the deformation of the elastic element of the sensor in cases of rigid clamping and hinged fastening for different values of the system parameters. A numerical method for studying the equation based on the Runge-Kutta method is also proposed. The conducted study provides an opportunity to determine the optimal values of the parameters of mechanical pressure measurement systems at the design stage.