|
Article information
2020 , Volume 25, ¹ 5, p.55-65
Bautin S.P., Nikolaev I.V.
Numerical solution of the problem of the gas compression from rest to rest
There is a flat, cylindrical or spherical layer homogeneous polytropic gas. One-dimensional and isentropic flows described by solutions of a system of gas dynamics. Let the gas be homogeneous at the initial moment of time with the density 1, and the gas velocity equal to 0 (state 1). At the final point in time the gas is again homogeneous with density large then 0 and rests (state 2). Purpose: It is need to find the gas flows that occur when a one-dimensional gas layer is shock-free compressed from the state 1 to the state 2. Methodology. In [1] was prove the existence of a solution to the problem of compression from rest to rest. To do this, the task is reduced to three initial boundary value problems. For this task the existence and uniqueness theorems of the solution are proved. In the proof of the theorems in particular, it is found that the solution has a feature on the compression piston in the final moment of compression, which at the point itself is described by the centered formula Riemann waves, and in its vicinity a generalization of the centered Riemann wave. Thus in theorems received a positive answer to the question about the existence of a solution (it can be written out in the form of an infinite series) in some area. However, theorems was not give answer about size of the solution area: no specific mass and density values were specified gas that can be compressed in the appropriate shock-free manner. In [2], the problem was solved numerically for the case of shock-free compression one-dimensional gas layer when the compression piston moves from the outside towards the axis or center symmetries. Findings. In the current work, the problem is numerically solved for the case of compression by a moving piston from inside to external stationary wall. The solution is obtained using its known properties and the method of characteristics. When numerical constructing there were no intersections of characteristics of the same family, which allows us to assert that the absence of shock waves in compression-induced flows. For specific mass values and the gas density trajectory of the compression piston was obtained in the form of table dependencies.
[full text]
Keywords: shock-free compressed of the gas, method of characteristics, one-dimensional flow
doi: 10.25743/ICT.2020.25.5.005
Author(s):
Bautin Sergey Petrovich
Dr. , Associate Professor
Position: Professor
Office: Snezhinsk Institute of Physics and Technology National Research Nuclear University MEPhI
Address: 456776, Russia, Snezhinsk, Komsomol str., 8
Phone Office: (343) 221 25 49
E-mail: SPBautin@mail.ru
SPIN-code: 4343-3821Nikolaev Iurii Vladimirovich
PhD. , Associate Professor
Position: person working for doctors degree
Office: Snezhinsk Institute of Physics and Technology National Research Nuclear University "MEPhI"
Address: 456776, Russia, Snezhinsk, Komsomolskaya str., 8
E-mail: ynikolaev@list.ru
SPIN-code: 5263-0161 References:
1. Dolgoleva G.V., Zabrodin A.V. Kumulyatsiya energii v sloistykh sistemakh i realizatsiya bezudarnogo szhatiya [Cumulation of energy in layered systems and implementation of shock-free compression]. Moscow: Fizmatlit; 2004: 72. (In Russ.)
2. Invention RU 2432627, Int. C1 G21B 1/19(2006.01). Mishen’ dlya polucheniya termoyadernykh reaktsiy [Target for producing thermonuclear reactions] / Bautin S.P. Application 2010113417/07 from 06.04.2010. Publication 27.10.2011. Bulletin No. 30. (In Russ.)
3. Krayko A.N. Variational problem of the one-dimensional isentropic compression of an ideal gas. Prikladnaya matematika i mekhanika. 1993; 57(5):35–51. (In Russ.)
4. Bautin S.P. Matematicheskoe modelirovanie sil’nogo szhatiya gaza [Mathematical Modelling of Strong Gas Compression]. Novosibirsk: Nauka; 2007: 312. (In Russ.)
5. Rozhdestvenskiiy B.L., Yanenko N.N. Sistemy kvazilineynykh uravneniy i ikh prilozheniya k gazovoy dinamike [Systems of quasilinear equations and their applications to gas dynamics]. Moscow: Nauka; 1978: 687. (In Russ.)
6. Nikolaev Yu.V. About numerical solution of A.N. Kraiko problem. Computational Technologies. 2005; 10(1):90–102. (In Russ.)
7. Nikolaev Yu.V. On numerical solution of the problem on shock-free compression of one-dimensional gas layers. Computational Technologies. 2001; 6(2):104–109. (In Russ.)
8. Bautin S.P., Nikolaev Yu.V. A method for calculating shockless powerful compression of unidimensional gas layers. Computational Technologies. 2000; 5(4):3–12. (In Russ.)
9. Novakovskiy N.S. Analytical and numerical reconstruction of generalized central compression wave’s sound characteristics. Mathematical Structures and Modeling. 2017; 2(42):94–104. (In Russ.)
10. Novakovskiy N.S. The combined numerical method for solving the one-dimensional ideal gas shockfree strong compression problem in R. Mises configuration. Mathematical Structures and Modeling. 2017; 1(41):92–101. (In Russ.)
11. Novakovskiy N.S. One-dimensional math modeling of ideal gas strong compession in R. Mises configuration. Mathematical Structures and Modeling. 2016; 3(89):93–109. (In Russ.)
12. Mises R. Matematicheskaya teoriya techeniy szhimaemoy zhidkosti [Mathematical theory of flows of compressible fluid]. Moscow: Izdatel’stvo inostrannoy literatury; 1961: 588. (In Russ.)
Bibliography link:
Bautin S.P., Nikolaev I.V. Numerical solution of the problem of the gas compression from rest to rest // Computational technologies. 2020. V. 25. ¹ 5. P. 55-65
|
