Abstract
The working fluid entering a turboexpander under actual operating conditions may contain some impurities that affect the flow characteristics, the resulting temperature at the outlet of the turboexpander unit (TEU) stage, and the service life of its flow path. The presence of impurities often causes erosive damage to the TEU impeller blades due to their bombardment by droplets of the formed condensate. Modern standard methods for calculating the effects of cavitation and volume condensation either cannot take into account the presence of these effects and the extent of their influence on the flow characteristics and the TEU flow path at the design stage or they have a poor accuracy and are only a tool for probabilistic prediction of the effects of cavitation and volume condensation. Thus, modern refrigeration equipment and the overall turbomachine building industry require such a tool that would be free from these disadvantages. The problem of volume condensation during the expansion of a vapor-gas mixture in the flow path of a specific TEU stage was solved for the first time using a condensation model, which is based on the kinetic equation for the droplet size distribution function in a nonstationary 3D formulation. The model was implemented as a special module integrated into the CFD-package. Three-dimensional nonstationary predictions are used as the basis for a comparative analysis of the effect of condensation on the thermogasdynamics of the process of expansion of an incondensable gas carrier and a condensable impurity in the flow path of a stage in a specific TEU model. Regions where volume condensation may occur are localized. Their location is used as the basis for an analysis of the potential consequences (whether this will have any effect on thermogasdynamics and whether regions susceptible to erosive wear will appear). In this paper, we propose a method for calculating the expansion of multicomponent mixtures in the flow path of the TEU stage with or without condensation.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS0040601522090063/MediaObjects/11509_2022_1416_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS0040601522090063/MediaObjects/11509_2022_1416_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS0040601522090063/MediaObjects/11509_2022_1416_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS0040601522090063/MediaObjects/11509_2022_1416_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS0040601522090063/MediaObjects/11509_2022_1416_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS0040601522090063/MediaObjects/11509_2022_1416_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS0040601522090063/MediaObjects/11509_2022_1416_Fig7_HTML.png)
Similar content being viewed by others
REFERENCES
A. A. Sidorov and A. K. Yastrebov, “Numerical simulation of the gas expansion process in a turboexpander unit by the finite volume method,” Therm. Eng. 68, 604–611 (2021). https://doi.org/10.1134/S0040601521070089
M. E. Deich and G. A. Filippov, The Gas Dynamics of Two-Phase Media, 2nd ed. (Energoizdat, Moscow, 1981) [in Russian].
M. E. Deich and G. A. Filippov, Two-Phase Flows in Thermal Power Equipment Components (Energoatomizdat, Moscow, 1987) [in Russian].
D. I. Plachendovskii, Study of Two-Phase Operation Regimes of Cryogenic Turboexpanders, Candidate’s Dissertation in Engineering (Moscow, 1981).
N. M. Kortsenshtein, E. V. Samuilov, and A. K. Yastrebov, “New method of simulation of volume condensation of supersaturated vapor,” High Temp. 47, 83–94 (2009).
N. M. Kortsenshtein and A. K. Yastrebov, “Bulk condensation in a dusty vapor–gas flow with regard to dust particle size distribution,” Colloid J. 78, 472–477 (2016). https://doi.org/10.1134/S1061933X16040104
N. M. Kortsenshteyn and A. K. Yastrebov, “Interphase heat transfer during bulk condensation in the flow of vapor–gas mixture,” Int. J. Heat Mass Transfer 55, 1133–1140 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2011.09.059
S. Tanimura, Y. Zvinevich, B. E. Wyslouzil, M. Zahniser, J. Shorter, D. Nelson, and B. McManus, “Temperature and gas-phase composition measurements in supersonic flows using tunable diode laser absorption spectroscopy: The effect of condensation on the boundary-layer thickness,” J. Chem. Phys. 122, 194304 (2005). https://doi.org/10.1063/1.1900084
G. Lamanna, On Nucleation and Droplet Growth in Condensing Nozzle Flows, PhD Thesis (Eindhoven Univ. of Technology, Eindhoven, The Netherlands, 2000). https://doi.org/10.6100/IR539104
I. Gad-el-Hak, A. E. Hussin, A. M. Hamed, and N. A. Mahmoud, “3D numerical modeling of zeotropic mixtures and pure working fluids in an ORC turbo-expander,” Int. J. Turbomach. Propul. Power 2, 2 (2017). https://doi.org/10.3390/ijtpp2010002
A. A. Sidorov and A. K. Yastrebov, “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,” Vestn. Dagest. Gos. Tekh. Univ., Tekh. Nauki 48, 65–75 (2021). https://doi.org/10.21822/2073-6185-2021-48-1-65-75
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Fizmatlit, Moscow, 2015; Elsevier, 2013).
Fluent Theory Guide 14. https://www.ansys.com/ Products/Fluids/ANSYS-Fluent
D. A. Labuntsov and V. V. Yagov, Mechanics of Two-Phase Systems: Textbook (Mosk. Energ. Inst., Moscow, 2000) [in Russian].
D. C. Wilcox, “Formulation of the k-ω turbulence model revisited,” AIAA J. 46, 2823–2838 (2008). https://doi.org/10.2514/1.36541
V. V. Sychev, A. A. Vasserman, F. D. Kozlov, G. A. Spiridonov, and V. A. Tsymarnyi, Thermodynamic Properties of Nitrogen (Izd. Standartov, Moscow, 1977) [in Russian].
GOST R 8.974-2019. Gas Analysis. Conversion of Gas Mixture Composition Data (2019).
L. E. Sternin, Fundamentals of Gasdynamics of Two-Phase Nozzle Flows (Mashinostroenie, Moscow, 1974) [in Russian].
I. N. Shishkova and A. K. Yastrebov, “Calculation of vapor mass flux upon isothermal condensation on spherical droplets in a wide range of Knudsen numbers based on the solution of the Boltzmann kinetic equation,” Colloid J. 78, 722–729 (2016). https://doi.org/10.1134/S1061933X16050173
W. Wagner, IUPAC Thermodynamic Tables Project Centre, “A new correlation method for thermodynamic data applied to the vapour pressure curves of argon, nitrogen and water,” Cryogenics 18, 122 (1978). https://doi.org/10.1016/0011-2275(78)90125-X
A. A. Sidorov and A. K. Yastrebov, “Effect of channel geometry and properties of a vapor–gas mixture on volume condensation in a flow through a nozzle,” Therm. Eng. 65, 57–64 (2018). https://doi.org/10.1134/S0040601518010068
A. Van Itterbeek and O. Verbeke, “Density of liquid nitrogen and argon as a function of pressure and temperature,” Physica 26, 931–938 (1960). https://doi.org/10.1016/0031-8914(60)90042-2
D. Stansfield, “The surface tension of liquid argon and nitrogen,” Proc. Phys. Soc. 72, 854–866 (2002). https://doi.org/10.1088/0370-1328/72/5/321
J. E. Jensen, W. A. Tuttle, R. B. Stewart, H. Brechna, and A. G. Prodell, Selected Cryogenic Data Notebook (Brookhaven National Laboratory, Upton, N.Y., 1980).
Y. A. Cengel and M. A. Boles, Thermodynamics: An Engineering Approach, 5th ed. (McGraw-Hill, Boston, Mass., 2006).
A. A. Sidorov and A. K. Yastrebov, “CFD-calculation of influence of impurities on the characteristics of a helium turboexpander,” J. Phys.: Conf. Ser. 1683, 022052 (2020). https://doi.org/10.1088/1742-6596/1683/2/022052
O. A. Mart’yanov and V. I. Merkulov, “Overview of the problem of moist air flow in turboexpanders,” Izv. MGTU MAMI 8 (4-1), 51–55 (2014).
Funding
The study was financially supported by the Russian Foundation for Basic Research (project no. 19-38-90247).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by T. Krasnoshchekova
Rights and permissions
About this article
Cite this article
Sidorov, A.A., Yastrebov, A.K. Simulation of Bulk Condensation during Expansion of a Vapor-Gas Mixture in the Flow Path of a Stage of a Turboexpander Unit. Therm. Eng. 69, 806–815 (2022). https://doi.org/10.1134/S0040601522090063
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040601522090063