Middle Volga Mathematical Society Journal

DOI 10.15507/2079-6900.23.202104.461–471

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 35Q35, 35Q74, 65M06

Investigation of dynamic processes in pressure measurement systems for gas-liquid media

Yu. A. Tamarova, P. A. Velmisov, N. D. Aleksanin, N. I. Nurullin

Ulyanovsk State Technical University (Ulyanovsk, Russian Federation)

Abstract. Initial-boundary value problems for systems of differential equations are considered, which are mathematical models of the mechanical system "pipeline - pressure sensor". In such a system, to mitigate the effects of vibration accelerations and high temperatures, the sensor is located at a certain distance from the engine and is connected to it via a pipeline. The "pipeline - pressure sensor" system is designed to measure pressure in gas-liquid media, for example, to control the pressure of the working medium in the combustion chambers of engines. On the basis of the proposed models, the joint dynamics of the sensitive element of the pressure sensor and the working medium in the pipeline is studied. To describe the motion of the working medium, linear models of fluid and gas mechanics are used, to describe the dynamics of a sensitive element, linear models of the mechanics of a deformable solid are applied. Analytical and numerical methods for solving initial-boundary value problems under study are presented. The numerical study of the initial-boundary value problem was carried out on the basis of the Galerkin method. In analytical study using the introduction of averaged characteristics, the solution of the original two-dimensional problem is reduced to the study of a one-dimensional model, whose further study made it possible to reduce the solution of the problem to the study of a differential equation with a deviating argument. Also, a numerical experiment is carried out and an example of calculating the deflection of the sensor’s moving element is presented.

Key Words: differential equations, aeroelasticity, elastic element, pressure sensor, dynamics, pipeline

For citation: Yu. A. Tamarova, P. A. Velmisov, N. D. Aleksanin, N. I. Nurullin. Investigation of dynamic processes in pressure measurement systems for gas-liquid media . Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 23:4(2021), 461–471. DOI: https://doi.org/10.15507/2079-6900.23.202104.461–471

Submitted: 09.09.2021; Revised: 25.11.2021; Accepted: 16.11.2021

Yuliya A. Tamarova, Postgraduate Student, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), ORCID: http://orcid.org/0000-0001-6408-1573, kazakovaua@mail.ru

Petr A. Velmisov, Head of the Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), D. Sci. (Physics and Mathematics), ORCID: https://orcid.org/0000-0001-7825-7015, velmisov@ulstu.ru

Nikolai D. Aleksanin, Postgraduate Student, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), ORCID: https://orcid.org/0000-0002-9586-6506, nickx73@yandex.ru

Nail I. Nurullin, Postgraduate Student, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), ORCID: https://orcid.org/0000-0002-7095-426X, yehekkbyy@mail.ru

All authors have read and approved the final manuscript.

Conflict of interest: The authors declare no conflict of interest.