Investigation of mathematical model of pressure measurement system in~aircraft engines

P. A. Velmisov ; A. V. Ankilov ; Yu. V. Pokladova

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 4, pp. 567-577

Résumé

A mechanical system consisting of a pipeline connected at one end to the combustion chamber of an aircraft engine, and with a sensor designed to measure the pressure in the combustion chamber at the other end is investigated in the work. The sensitive element of the sensor, which transmits information about pressure, is an elastic plate. A mathematical model of a pressure measurement system, taking into account the transfer of heat flow through a pipeline with a working medium (gas or liquid) from the engine to the elastic element, is proposed. To describe the vibrations of the sensitive element of the sensor, a linear model of a solid deformable body is considered, taking into account the temperature distribution over the thickness of the elastic element. Using the small parameter method, a coupled system of asymptotic partial differential equations was obtained that describes the joint dynamics of the gas-liquid medium in the pipeline and the elastic sensitive element of the pressure sensor. The cases of hinged and rigid fastening of the ends of the sensing element were studied. Based on the Bubnov – Galerkin method, the problem is reduced to the study of a coupled system of ordinary differential equations. Using the computer algebra system Mathematica 12.0, numerical experiments were carried out for specific parameters of the mechanical system.