ISSN 2658–5782

DOI 10.21662

DOI 10.21662

Electronic Scientific Journal

2019. Vol. 14. Issue 2, Pp. 82–88

URL: http://mfs.uimech.org/mfs2019.2.012,en

DOI: 10.21662/mfs2019.2.012

URL: http://mfs.uimech.org/mfs2019.2.012,en

DOI: 10.21662/mfs2019.2.012

Non-stationary process characteristics of the gas outflow into a liquid

Alekseev M.V.^{∗}, Vozhakov I.S.^{∗,∗∗}, Lezhnin S.I.^{∗,∗∗}

A numerical simulation of the process of the outflow of gas under pressure into a closed container partially filled
with liquid was carried out. For comparative theoretical analysis, an asymptotic model was used with assumptions about the adiabaticity of the gas outflow
process and the ideality of the liquid during the oscillatory one-dimensional motion of the liquid column. In this case, the motion of the liquid column
and the evolution of pressure in the gas are determined by the equation of dynamics and the balance of enthalpy. Numerical simulation was performed in
the OpenFOAM package using the fluid volume method (VOF method) and the standard

gas outflow,

high pressure chamber,

OpenFOAM,

gas injection into water,

gas injection into liquid lead

**Problem:** Analytical and numerical study of the process of outflow of gas under pressure into a closed container with liquid. Obtaining characteristic process parameters and comparing the calculation results by the asymptotic model and the results of numerical simulation.

**Methods:** For the theoretical analysis, an asymptotic model was used, in which assumptions were made about the adiabatic process of gas outflow and fluid ideality during oscillatory motion of the liquid column, and the movement of the liquid column and the evolution of pressure in the gas are determined by the dynamics equation and the enthalpy balance. As a numerical method for solving a system of model differential equations in partial derivatives, a finite-difference scheme was chosen, based on the use of the Euler method in the OpenFOAM package. The resolution of the interphase surface was carried out by the volume of fluid method (VOF method).

**In a study was determined:**

- The dynamics of pulsations in the gas cavity arising during the flow of gas into the closed region substantially depends on the physical properties of the liquid in the volume. In the case of water, the growth of a slug occurs vertically displacing the liquid and compressing the gas volume in the upper region. At a time of 5 ms, the compression of the gas volume ceases and then the expansion phase follows. The movement of the liquid forms a compression of the gas shell in its central part in the radial direction (8 ms). In the case of lead, the growth of a slug occurs both in the radial and vertical directions. At the same time, the shape of the gas shell takes on a “bell-shaped” appearance. Liquid displacement by compression of the upper gas volume ends in 12 ms. Then there is a return motion of the liquid and compression of the slug. A cumulative jet is formed at the upper boundary, which, when moving downward, breaks down from the oncoming gas stream inside the slug, and the interphase boundary of the slug becomes unstable, leading to the separation of small bubbles from the slug and the formation of jets and drops inside the slug.
- The difference in the numerical calculation of pressure from the asymptotic model during the injection of gas into water is characterized by uneven pulsations. This non-uniformity is because, when injected into water, a gas stream is formed that passes through the liquid column. In this case, an unsteady gas-dynamic structure of pressure surges is formed inside the gas shell. When the gas flows into the water “at the first pulsation”, the pressure near the nozzle is always lower than the critical pressure, which characterizes the possible blocking of the flow. In the numerical calculation of gas injection into the lead, the jet gas flow is not observed. Calculation of the pressure at the first pulsation of the slug is in good agreement with the pressure obtained from the asymptotic model.

- Vozhakov I.S., Lezhnin S.I., Alekseev M.V., Bogomolov A.R., Pribaturin N.A.
Gas outflow modeling into the high density environment // Vestnik of Kuzbass State Technical University. 2016. No. 5. C. 86–92. (in Russian)

https://journals.kuzstu.ru/article/3120.pdf - Alekseev M.V., Vozhakov I.S., Lezhnin S.I., Pribaturin N.A., The effect of interphase friction on the two-phase mixture outflowing characteristics into a high density medium //
Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy. 2016. Т. 2, No 3. C. 49–62. (in Russian)

DOI: 10.21684/2411-7978-2016-2-3-49-62 - Lezhnin S.I., Alekseev M.V., Vozhakov I.S., Pribaturin N.A.
Simulating gas (vapor) outflow into a liquid // Journal of Physics: Conference Series. 2018. Vol. 1105, No 1. PP. 012081. IOP Publishing

DOI: 10.1088/1742-6596/1105/1/012081 - Nigmatulin R.I. Dynamics of Multiphase Media: v. 1. Hemisphere Publ. Corp New York, United States, 1990. 507 p.
- Boris J.P., Landsberg A.M., Oran E.S., Garder J.H. LCPFCT - Flux-Corrected Transport Algorithm for Solving Generalized Continuity Equations. NRL/MR/6410-93-7192

https://pdfs.semanticscholar.org/250a/7bd3e46de18e0af13d43011956f31a0880af.pdflT - The OpenFOAM Foundation. Open Source Computational Fluid Dynamics (CFD) Toolbox. 2019. openfoam.org.

https://cfd.direct/openfoam/user-guide/ - Brackbill J.U., Kothe D.B., Zemach C. A continuum method for modeling surface tension // Journal of Computational Physics. 1992. Vol. 100. P. 335–354.

DOI: 10.1016/0021-9991(92)90240-Y - Alekseev M.V., Vozhakov I.S., Lezhnin S.I. Pressure pulsations while gas injection into a liquid- filled closed vessel at high pressure drop // Thermophysics and Aeromechanics. 2019. Vol. 26, No 5 (in press).
- Bolotnova R.Kh. Study the dynamics of hollow jet formation under vaporoutflow from the supercritical state // Multiphase Systems. 2018. V. 13, No 4. P. 73–78

DOI: 10.21662/mfs2018.4.011 - Bolotnova R.Kh., Gainullina E.F. Supercritical steam outflow through a thin nozzle: forming a hollow jet // Thermophysics and Aeromechanics. 2018. No 5. P. 751–757.

https://www.sibran.ru/journals/issue.php?ID=174876 - Alekseev M.V., Vozhakov I.S., Lezhnin S.I., Pribaturin N.A. [Three-Dimensional modeling of gas injection into an open, liquid-filled pipe region]Trehmernoe modelirovanie inzhekcii
gaza v otkrytuju, zapolnennuju zhidkost’ju trubnuju oblast’ // [Abstracts of the XXXV Siberian Thermophysical Seminar dedicated to the 75th anniversary of doctor of technical
Sciences, Professor V.I. Terekhov.] Tezisy Dokladov XXXV Sibirskogo Teplofizicheskogo Seminara, posvjashhjonnyj 75-letiju d.t.n., professora V.I. Terehova. 27–29 August 2019,
Novosibirsk, Russia, P. 104. (in Russian)

http://www.itp.nsc.ru/conferences/sts35/files/STS35_abstracts.pdf - Alekseev M.V., Vozhakov I.S., Lobanov P.D., Svetonosov A.I., and Mohan V.K., Lezhnin S.I., Pribaturin N.A.
Numerical simulation of pulsed gas-to-liquid injection modes using open source CFD software package OpenFoam //
Journal of Physics: Conference Series. 2018. Vol. 1105. No 1. P=012085., IOP Publishing

DOI: 10.1088/1742-6596/1105/1/012085 - Lezhnin S.I., Mosunova N.A., Savchenko I.V. Recommendations on adopting the values and correlations for calculating the thermophysical and kinetic properties of liquid lead //
Thermal Engineering. 2015. Vol. 62, No 6. P. 434–437.

DOI: 10.1134/S0040363615060077