Труды Института механики им. Р.Р. Мавлютова

ISSN 2542–0380

Электронный научный журнал | Electronic Scientific Journal

Proceedings of the Mavlyutov Institute of Mechanics

Shayakhmetova R.F. The compression of gas followed by expansion Proceedings of the Mavlyutov Institute of Mechanics. 2017. 12(2). 195–198.

2017. Vol. 12. Issue 2, Pp. 195–198
URL: http://proc.uimech.org/uim2017.2.029,en
DOI: 10.21662/uim2017.2.029

The compression of gas followed by expansion

Shayakhmetova R.F.

Mavlyutov Institute of Mechanics, Ufa

Abstract

We consider the system of gas dynamics equations with the state equation of the monatomic gas. The system admits a group of transformations with a 14-dimensional Lie algebra. A projective operator is specific to this algebra. We consider the invariant submodel on two-dimensional subalgebra containing the projective operator. For the vorticity-free motions, the submodel is reduced to an overdetermined system of three equations. A particular solution is found for it, physical interpretation is given, and trajectories of gas particles are depicted. The solution gives the gas compression followed by expansion.

Keywords

monatomic gas,
invariant solution,
vorticity-free motion

Article outline

Problem: To consider the invariant submodel on two-dimensional subalgebra containing a projective operator for the 14-dimensional Lie algebra admitted by the equations of motion of the monatomic gas. To consider the condition of vorticity-free motion.

Methods: The methods of the theory of differential equations and group analysis are used.

In a study was determined:

1. For vorticity-free motion, the submodel is reduced to an overdetermined system of three equations.

2. For vorticity-free motion, a particular solution is found and its physical interpretation is given.