# Mathematical modeling of the heating process in a vortex tube at the gas distribution stations

2019;
: pp. 311–319

Revised: May 04, 2019
Accepted: June 20, 2019

Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 311–319 (2019)

1
Department of Heat, Gas Supply and Ventilation, Institute of Building and Environmental Engineering, Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Department of Heat, Gas Supply and Ventilation, Institute of Building and Environmental Engineering, Lviv Polytechnic National University
4
Department of Heat, Gas Supply and Ventilation, Institute of Building and Environmental Engineering, Lviv Polytechnic National University

In all sectors of the national economy of Ukraine, issues of energy efficiency and saving of fuel and energy resources are important.  Legislative changes in the branches and scientific developments of scientists allow reducing the energy dependence of Ukraine on imported fuels.  One of the energy-saving measures for the transportation of natural gas is the use of a vortex tube for heating natural gas at gas distribution stations.  Natural gas is heated before the process of reducing it in the gas pressure regulator to prevent the formation of crystalline hydrates within the gas pressure regulator.  The complexity of the implementation of such a measure is the explosion of the fire hazard of natural gas, which makes it impossible to conduct a sufficient number of experimental studies to determine the required characteristics of the vortex tube for operation at the gas distribution station.  Therefore, for the wide introduction of a vortex tube at gas distribution stations, a generalized mathematical model should be developed that would allow describing the process of heating the vortex tube of a working gas with different thermophysical parameters.  In this paper, the thermodynamic and physical bases of the process of heating the compressed gases in the vortex tube are considered and the main parameters that influence the operation of the vortex tube are determined.  The mathematical model of the process of heating the natural gas in a vortex tube is scientifically substantiated and improved.  To improve the mathematical model of the natural gas heating process in the vortex tube, loss of dynamic pressure was determined on each characteristic section of the vortex tube and the degree of heating therein.  Moreover, the mathematical model proposed by the authors allows us to determine the thermal power of the vortex tube and the amount of heat needed to heat the working gas in the vortex tube.

1. Sevastyanov R. V., Kalitina Ya. Yu.  Energy efficiency of industrial enterprises of Ukraine and barriers to its implementation.  Economic Bulletin of the Zaporizhzhya State Engineering Academy. 7, 144--154 (2014), (in Ukrainian).
2. Analysis of the efficiency of energy use in developed foreign countries and dependence on their imports.  Kyiv, Ministry of Energy and Coal Industry of Ukraine, NEC "Ukrenergo", Scientific and Technical Center for Electricity, 2015 (in Ukrainian).
3. Voznyak O. T.  Influence of interaction of jets on air distribution in the room.  Bulletin of the Lviv Polytechnic National University "Heat Power Engineering. Environmental engineering. Automation'". 432, 27--31 (2001), (in Ukrainian).
4. Labay V., Dovbush O., Yaroslav V., Klymenko H.  Mathematical modeling of a split-conditioner operation for evaluation of exergy efficiency of the R600A refrigerant application.  Mathematical Modeling and Computing. 5 (2), 169--177 (2018).
5. Zhelykh V., Kozak Ch., Savchenko O.  Using of Thermosiphon Solar Collector in an air Heating System of Passive House.  Pollack Periodica. 11 (2), 125--133 (2016).
6. Zhelykh V., Savchenko O., Pashkevych V., Matusevych V.  The geothermal ventilation of passive house. Budownictwo o zoptymalizowanym potencjale energetycznym. 2 (16), 145--150 (2015).
7. Dombrovskyi O., Korsakaite D., Geletukha G., Savchuk S.  What can bioenergy do to overcome gas crises. March 27, 2018(in Ukrainian).
8. Savchenko O., Zhelykh V., Yurkevych Yu., Shapoval S., Kozak Kh.  Using vortex tube for decreasing losses of natural gas in engineering systems of gas supply.  Pollack Periodica. 13 (3), 241--250 (2018).
9. Rattanongphisat W.  The Development of Ranque-Hilsch Vortex Tubes: Computational Models.  Industrial Technology Journal, Lampang Rajabhat University. 32, 40--51 (2010).
10. Smith Eiamsa-ard, Pongjet Promvonge.  Review of Ranque--Hilsch effects in vortex tubes.  Renewable and Sustainable Energy Reviews. 12 (7), 1822--1842 (2008).
11. Carrascal E., Sala J. M.  Mass, energy, entropy and exergy rate balance in a Ranque--Hilsh vortex tube.  Journal of technology and science education. 3 (3), 122--131 (2013).
12. Balinsky I. S., Koval R., Banakhevych Yu., Kashina O.  Patent of Ukraine for invention, №43673A, Gas distribution station, 17 December 2001, Bulletin No. 11 (in Ukrainian).
13. Vortex tube and its use in the technique of separation of gas mixtures.  Chemical and petroleum engineering. (Overview).  Moscow, TsINTIHIMneftemash, 1983 (in Russian).
14. Rudnik A. A., Kolomeyev V. M., Rozonyuk V. V., Grigil M. А. et al.  Operation and Maintenance of Gas Distribution Stations of Main Gas Pipelines: Reference.  Kyiv, Rоstоk (2003), (in Ukrainian).