Preview

Herald of Dagestan State Technical University. Technical Sciences

Advanced search

INTEGRATION OF THE NUMERICAL SOLUTION MODULE OF THE KINETIC EQUATION INTO THE CFD PACKAGE FOR THE VOLUME CONDENSATION PROBLEM OF THE VAPOR-GAS MIXTURE FLOW THROUGH A NOZZLE

https://doi.org/10.21822/2073-6185-2021-48-1-65-75

Abstract

Objective. Integrating the numerical solution module of the kinetic equation for the droplet size distribution function in a CFD package. Application of the module to volumetric condensation at the supersonic flow of a vapor-gas  mixture through a nozzle in a two-dimensional formulation, comparison of  the results with experimental data of third-party authors.

Methods. In this  paper, the problem of volume condensation in the supersonic flow of a vapor-gas mixture through a nozzle is solved by finite element methods in a two-dimensional formulation using user-defined functions.

Results. A module for the numerical solution of the kinetic equation for the droplet size distribution function is presented as a user-defined function integrated into the calculated CFD package.

Conclusion. The module application to volumetric condensation for a vapor-gas mixture flow through the nozzle gave a qualitative agreement in all areas and a quantitative agreement in the area of intense condensation with  measurement data. The distributions of temperatures, pressures, and  the degree of supersaturation are presented both along the central axis and  on the plane bounded by the contour of the computational domain. It is shown that the module does not depend on the solver type (stationary or non-stationary).

About the Authors

A. A. Sidorov
National Research University «MPEI»
Russian Federation
Graduate Student

14 Krasnokazarmennaya St., Moscow 111250, Russia



A. K. Yastrebov
National Research University «MPEI»
Russian Federation
Cand. Sci. (Technical), Assoc. Prof., Department of Low temperatures

14 Krasnokazarmennaya St., Moscow 111250, Russia



References

1. Sternin L.Ye. Osnovy gazodinamiki dvukhfaznykh techeniy v soplakh. M.: Mashinostroyeniye, 1974. [Sternin L.Ye. Fundamentals of gas dynamics of two-phase flows in nozzles. Moscow: Mechanical Engineering, 1974. (In Russ)]

2. Sidorov A.A., Yastrebov A.K. Vliyaniye geometricheskikh kharakteristik kanala i svoystv parogazovoy smesi na ob"yemnuyu kondensatsiyu pri techenii v sople // Teploenergetika. 2018. № 1. S. 68-76. [Sidorov A.A., Yastrebov A.K. Influence of the geometric characteristics of the channel and the properties of the vapor-gas mixture on the volumetric condensation during the flow in the nozzle // Teploenergetika. 2018.No. 1.pp. 68-76. (In Russ)]

3. H. Pathak, K. Mullick, S. Tanimura, B. E. Wyslouzil. Nonisothermal Droplet Growth in the Free Molecular Regime. //Aerosol Science and Technology, 47:1310–1324, 2013. [H. Pathak, K. Mullick, S. Tanimura, B. E. Wyslouzil. Nonisothermal Droplet Growth in the Free Molecular Regime. // Aerosol Science and Technology, 47: 1310–1324, 2013. (In Russ)]

4. Crabtree A. Thermophysical Properties of Saturated Light and Heavy Water for Advanced Neutron Source Applications. Oak Ridge National Laboratory, ORNL / TM-12322, 1993.

5. Herrig S., Thol M. A Reference Equation of State for Heavy Water // J. Phys. Chem. Ref. Data, Vol. 47, No. 4, 2018.

6. Vargaftik N.B. Handbook on the thermophysical properties of gases and liquids. M., 1972, 720 pages.

7. N.M. Kortsenshteyn, A.K. Yastrebov. Interphase heat transfer during bulk condensation in the flow of vapor - gas mixture // International Journal of Heat and Mass Transfer. 2012. Vol. 55. P. 1133 - 1140.

8. Pope S. B. Turbulent Flows. Cambridge University Press, 2000, 771 pp.

9. Landau L. D., Lifshits Ye. M. Gidrodinamika. Izdaniye 6-ye. M.: Fizmatlit, 2015. 728 s. (Teoreticheskaya fizika, t. VI). [Landau L.D., Lifshits EM Hydrodynamics. Edition 6. Moscow: Fizmatlit, 2015.728 p. (Theoretical physics, vol. VI). (In Russ)]

10. Fluent Theory guide 14, https://www.ansys.com/Products/Fluids/ANSYS-Fluent. Labuntsov D.A., Yagov V.V. Mechanics of two-phase systems: Textbook for universities - Moscow: MPEI Publishing House, 2000, 374 pp.

11. Labuntsov D.A., Yagov V.V. Mekhanika dvukhfaznykh sistem: Uchebnoye posobiye dlya vuzov – M.: Izdatel'stvo MEI, 2000, 374 str. [Labuntsov D.A., Yagov V.V. Mechanics of two-phase systems: Textbook for universities - Moscow: MPEI Publishing House, 2000, 374 pp. (In Russ)]

12. Kortsenshteyn N.M., Samuylov Ye.V., Yastrebov A.K. Novyy metod modelirovaniya ob"yemnoy kondensatsii peresyshchennogo para // Teplofizika vysokikh temperatur, 2009, tom 47, №1, s. 1-12. [Kortsenstein N.M., Samuilov E.V., Yastrebov A.K. A new method for modeling the volumetric condensation of supersaturated steam // Thermophysics of high temperatures, 2009, Vol 47, no. 1-12. (In Russ)]

13. Kirillin V.A., Sychev V.V., Sheyndlin A.Ye. Tekhnicheskaya termodinamika. M.: Izdatel'skiy dom MEI, 2008. S. 271-294. [Kirillin V.A., Sychev V.V., Sheindlin A.E. Technical thermodynamics. M .: Publishing house MEI, 2008.S. 271-294. (In Russ)]

14. I.N. Shishkova, A.K. Yastrebov. Raschet potoka massy para pri izotermicheskoy kondensatsii na sfericheskikh kaplyakh v shirokom diapazone chisel Knudsena na osnove resheniya kineticheskogo uravneniya Bol'tsmana // Kolloidnyy zhurnal, 2016. T. 78, № 5. S. 660 – 667. [I. N. Shishkova, A.K. Yastrebov. Calculation of the vapor mass flow during isothermal condensation on spherical drops in a wide range of Knudsen numbers based on the solution of the Boltzmann kinetic equation // Colloid Journal, 2016. V. 78, No. 5. pp. 660 - 667. (In Russ)]

15. 15. I.N. Shishkova, A.K. Yastrebov. Issledovaniye ispareniya i kondensatsii v prisutstvii nanochastits // Kolloidnyy zhurnal. 2015. T. 77. № 5. S. 669 – 675. [I.N. Shishkova, A.K. Yastrebov. Investigation of evaporation and condensation in the presence of nanoparticles // Colloid journal. 2015.Vol. 77.No. 5.pp. 669 - 675 (In Russ)]

16. Xuewen C., Yang L., Xuerui Z., Dan G. Jiang B. Supersonic refrigeration performances of nozzles and phase transition characteristics of wet natural gas considering shock wave effects // Case Studies in Thermal Engineering Vol.24, 100833.

17. Giesen, A. Kowalik & P. Roth (2004) Iron-atom condensation interpreted by a kinetic model and a nucleation model approach, Phase Transitions: A Multinational Journal, 77:1-2, 15-129.

18. Shishkova I.N., Kryukov A.P., Levashov V.Y. Vapour–liquid jointed solution for the evaporation–condensation problem // International Journal of Heat and Mass Transfer Volume 141, October 2019, pp.9-19.

19. Pathak, K. Mullick, S. Tanimura, B. E. Wyslouzil. The structure of D2O-nonane nanodroplets // The Journal of Chemical Physics 140, 224318 (2014);

20. H. Pathak, S. Tanimura, B. E. Wyslouzil. Binary nucleation rates for ethanol/water mixtures in supersonic Laval nozzles: Analyses by the first and second nucleation theorems// The Journal of Chemical Physics 139, 174311 (2013).


Review

For citations:


Sidorov A.A., Yastrebov A.K. INTEGRATION OF THE NUMERICAL SOLUTION MODULE OF THE KINETIC EQUATION INTO THE CFD PACKAGE FOR THE VOLUME CONDENSATION PROBLEM OF THE VAPOR-GAS MIXTURE FLOW THROUGH A NOZZLE. Herald of Dagestan State Technical University. Technical Sciences. 2021;48(1):65-75. (In Russ.) https://doi.org/10.21822/2073-6185-2021-48-1-65-75

Views: 458


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2073-6185 (Print)
ISSN 2542-095X (Online)