DOI: 10.17587/prin.16.143-155

Application of Three-Parametric Differential RANS-Model of Turbulence for Solving the Problems of Gas Flow Energy Separation

V. G. Lushchik, Leading Scientist, vgl_41@mail.ru, S. S. Popovich, Senior Research Scientist, pss@imec.msu.ru, A. M. Chaika, Leading Programmer, chaika.anya@gmail.com, Lomonosov Moscow State University, Institute of mechanics, Moscow, 119192, Russian Federation

Corresponding author: Sergey S. Popovich, Senior Research Scientist, Lomonosov Moscow State University, Institute of mechanics, Moscow, 119192, Russian Federation, E-mail: pss@imec.msu.ru

The paper describes the numerical study technique for problems of external compressible gas flow around permeable surfaces applying a three-parameter RANS turbulence model. Numerical study of energy separation in the boundary layer on an impermeable and permeable plate with gas injection/suction in the range of Prandtl numbers Pr from 0.05 to 5 showed that temperature stratification increases with decreasing Pr number. Gas injection into a supersonic flow reduces temperature stratification compared to an impermeable plate, while suction increases the effect. The influence of the Prandtl and Mach numbers of the external flow on the value of temperature stratification, which is largely determined by the value of the suction intensity and, consequently, the total flow rate of the sucked gas, is studied. Temperature stratification is most pronounced for gases with small Prandtl numbers. It has been established that with intensive gas suction in the boundary layer on the section of the impermeable plate following the permeable part, the wall temperature drops sharply. The reason for the formation of a zone with a lower wall temperature is the laminarization of the boundary layer on the permeable wall with intensive suction resulting in the asymptotic suction mode. The conducted numerical study confirmed a significant decrease in the wall temperature compared to the temperature of the injected gas for both laminar and, to a lesser extent, a turbulent boundary layer with foreign injection of helium into xenon with a Prandtl number variable along the length compared to a uniform gas injection with a constant Prandtl number. The results of numerous numerical studies of the main elements of the working process in the energy separation device were obtained, which served as a justification for the possibility of energy separation of the gas flow.

Keywords: RANS turbulence model, compressible boundary layer, gas injection/suction through the permeable wall

pp. 143—155

For citation:
Lushchik V. G., Popovich S. S., Chaika A. M. Application of Three-Parametric Differential RANS-Model of Turbulence for Solving the Problems of Gas Flow Energy Separation, Programmnaya Ingeneria, 2025, vol. 16, no. 3, pp. 143—155. DOI: 10.17587/prin.16.143-155 (in Russian)

The work was carried out within the framework of research financed by the state budget AAAA-A19-119012990115-5.

References:

1. Leont'ev A. I. Gas-dynamic method of energy separation of gas flows, High Temperature, 1997, vol. 35, no. 1, pp. 155—157 (in Russian).
2. Leont'ev A. I. Gas-Dynamic Methods of Temperature Stratification (a Review), Fluid Dynamics, 2002, vol. 37, no. 4, pp. 512—529. DOI: 10.1023/A:1020629000437.
3. Leont'ev A. I. Temperature stratification of supersonic gas flow, Physics. Doklady, 1997, vol. 42, no. 6, pp. 309—311 (in Russian).
4. Popovich S. S., Zditovets A. G., Kiselev N. A., Makarova M. S. Application of supersonic machine-free energy separation method in pressure reduction of natural gas, Thermal processes in engineering, 2019, vol. 11, no. 1, pp. 2—15 (in Russian).
5. ZditovetsA. G., Leontiev A. I., Vinogradov U. A., Strongin M. M., Popovich S. S. Method of gas temperature stratification, Patent no. RU 2672457 C1, 2018.11.14 (in Russian).
6. Popovich S. S., Leontiev A. I., Vinogradov U. A., Kiselev N. A., Makarova M. S., Medvetskaya N. V., Strongin M. M. Method of natural gas pressure reduction, Patent no. RU 2713551C1, 2020.05.02 (in Russian).
7. Zditovets A. G., Vinogradov Yu. A., Strongin M. M. Experimental study of machine-free energy separation of air flows in a Leontiev tube, Thermal Processes in Engineering, 2015, vol. 7, no. 9, pp. 397—404 (in Russian).
8. Popovich S. S. Experimental Automation and Data Processing Features for Supersonic Heat Transfer Research, Programmnaya Ingeneria, 2018, vol. 9, no. 1, pp. 35—45. DOI: 10.17587/prin.9.35-45 (in Russian).
9. Leontiev A. I., Popovich S. S., Vinogradov U. A., Strongin M. M. Experimental research of supersonic aerodynamic cooling effect and its application for higher energy separation efficiency, Proceedings of the l6hInternational Heat Transfer Conference IHTC-16, Beijing: Begell House Inc., 2018, pp. 2987—2994. DOI: 10.1615/IHTC16.cov.021244.
10. Leontiev A. I., Lushchik V. G., Makarova M. S., Popovich S. S. The Temperature Recovery Factor in a Compressible Turbulent Boundary Layer, High Temperature, 2022, vol. 60, no. 3, pp. 409—431. DOI: 10.1134/S0018151X22030117.
11. Lushchik V. G., Makarova M. S., Yakubenko A. E. Application of the Three-Parameter Model of Shear Turbulence for Solving Problems of External Flowing on Permeable Surfaces by a Compressible Gas Flow, Programmnaya Ingeneria, 2017, vol. 8, no. 12, pp. 563—574. DOI: 10.17587/prin.8.563-574 (in Russian).
12. Lushchik V. G., Pavel'ev A. A., Yakubenko A. E. Three-parameter model of shear turbulence, Fluid Dynamics,1978, vol. 13, no. 3, pp. 350-360. DOI: 10.1007/BF01050525.
13. Lushchik V. G., Pavel'ev A. A., Yakubenko A. E. Three-parameter model of turbulence: Heat transfer calculations, Fluid Dynamics, 1986, vol. 21, no. 2, pp. 200—211. DOI: 10.1007/BF01050170.
14. Ginevsky A. S., Ioselevich V. A., Kolesnikov A. V. et al. Methods for calculating the turbulent boundary layer, in: Itogi Nauki i Tekhniki. Ser. Mechanics of fluid and gas, 1978, vol. 11, pp. 155— 304 (in Russian).
15. Volchkov E. P., Makarov M. S. The gas-dynamic temperature stratification in a supersonic flow, Izv. Ross. Akad. Nauk, Energ., 2006, no. 2, pp. 19—31 (in Russian).
16. Vigdorovich I. I., Leont'ev A. I. Theory of the energy separation of a compressible gas flow, Fluid Dynamics, 2010, vol. 45, no. 3, pp. 434—440. DOI: 10.1134/S0015462810030105.
17. Leont'ev A. I., Lushchik V. G., Yakubenko A. E. Injection/suction effect on energy separation of compressible flows, Fluid Dynamics, 2011, vol. 46, no. 6, pp. 935—941. DOI: 10.1134/ S001546281106010X.
18. Leontiev A. I., Lushchik V. G., Yakubenko A. E. Compressible turbulent boundary layer on a permeable plate with injection of foreign gas, High Temperature, 2007, vol. 45, no. 4, pp. 488—496. DOI: 10.1134/S0018151X07040086.
19. Leont'ev A. I., Lushchik V. G., Makarova M. S. Temperature stratification under suction of a boundary layer from a supersonic flow, High Temperature, 2012, vol. 50, no. 6, pp. 739—743. DOI: 10.1134/S0018151X12060065.
20. Leontiev A. I., Lushchik V. G., Yakubenko A. E. Compressible turbulent boundary layer on a permeable plate with injection of foreign gas, High Temperature, 2007, vol. 45, no. 4, pp. 488—496. DOI: 10.1134/S0018151X07040086.
21. Leontiev A. I., Lushchik V. G., Yakubenko A. E. A heat-insulated permeable wall with suction in a compressible gas flow, Int. J. Heat and Mass Transfer, 2009, vol. 52, pp. 4001—4007. DOI: 10.1016/j.ijheatmasstransfer.2008.10.029.
22. Leont'ev A. I., Lushchik V. G., Makarova M. S. Features of heat transfer on a permeable surface in a compressible-gas flow, Doklady Physics, 2018, vol. 63, no. 9, pp. 371—374. DOI: 10.1134/ S1028335818090033.
23. Lushchik V. G., Makarova M. S. Distinctive features of heat transfer on a permeable plate in supersonic flow under injection of extraneous gas, Fluid Dynamics, 2020, vol. 55, no. 5, pp. 636—639. DOI: 10.1134/S0015462820050109.
24. Leontiev A. I., Lushchik V. G., Makarova M. S. The temperature recovery factor in a boundary layer on a permeable plate, High Temperature, 2017, vol. 55, no. 2, pp. 246—252. DOI: 10.1134/S0018151X17020080.