Experimental and numerical modeling of the supersonic jets expanding into a rarefied medium. Part 1: non-condensing flows




This work presents the first part of a study aimed at developing methods for experimental and numerical modeling of jet flows with significant rarefaction effects. To carry out experimental measurements of flow parameters in jets expanding into a vacuum or highly rarefied medium on the modern gas-dynamic complex LEMPUS-2, the electron beam diagnostic (EBD) method was used for dimensional visualization of flows and measurements of absolute values of local flow density. For numerical simulation of a stationary axisymmetric nitrogen jet expanding through a sonic nozzle into rarefied medium, a hybrid approach was employed: gas parameters in the dense flow region are determined using the solution of the Navier-Stokes equations, and in the rarefied flow region with the direct simulation Monte Carlo method. A comparison of experimental and numerical methods was carried out for this problem under conditions of insignificant condensation effects. The results of numerical calculations and experiments were compared with each other and with published theoretical data. The good agreement of the results confirms the high predictive ability of the methods used for the outflow of a non-condensable gas from sonic nozzles into a rarefied medium.

rarefied gas dynamics, numerical modeling, electron beam diagnostics, verification, sound nozzle, density of rarefied gas

Alexandr Zarvin, Kirill Alexeevich Dubrovin, Yevgeniy Alexandrovich Bondar, Lev Yarkov, Alexandr Zaitsev, Valery Vladimirovich Kalyada, Alexander Yaskin

Volume 25, issue 2, 2024 year


Экспериментальное и численное моделирование истечения сверхзвуковых струй в разреженную среду. Часть 1: течения без влияния конденсации

Настоящая работа представляет собой первую часть исследования, направленного на развитие методов экспериментального и численного моделирования струй в условиях существенного вляния эффектов разреженности. Для проведения экспериментальных измерений параметров течения в струях, истекающих в вакуум или сильно разреженное пространство, на современном газодинамическом комплексе ЛЭМПУС-2 использован метод электронно-пучковой диагностики (ЭПД), включающий размерную визуализацию потоков и измерения абсолютных значений локальной плотности потока. Для численного моделирования стационарной осесимметричной струи, истекающей через звуковое сопло в разреженное пространство, использован гибридный подход: параметры газа в области плотного течения определяются с использованием решения уравнений Навье-Стокса, а в разреженной – на основе метода прямого статистического моделирования. Сравнение экспериментальных и численных методов моделирования выполнено для задачи истечения струи азота в разреженную среду для условий, когда влияние конденсации несущественно. В работе представлено сравнение результатов численных расчетов и экспериментов в одинаковых условиях между собой и с известными теоретическими данными. Хорошее совпадение результатов подтверждает высокую предсказательную способность используемых методов для условий истечения неконденсирующегося газа из звуковых сопел в разреженное пространство.

динамика разреженных газов, численное моделирование, электронно-пучковая диагностика, звуковое сопло, плотность разреженного газа

Alexandr Zarvin, Kirill Alexeevich Dubrovin, Yevgeniy Alexandrovich Bondar, Lev Yarkov, Alexandr Zaitsev, Valery Vladimirovich Kalyada, Alexander Yaskin

Volume 25, issue 2, 2024 year



1. Kislyakov N.I., Rebrov A.K., Sharafutdinov R.G. Diffusion processes in the mixing zone of a low-density supersonic jet // PMTF. 1973. No. 1. P. 121-131.
2. Gerasimov Yu.I., Yarygin V.N. Flow of jets of ideal and real gases from axisymmetric nozzles. Questions of similarity. 1. Flow of jets into vacuum // Physicochemical kinetics in gas dynamics. 2012. 2012. T. 13, issue. 1. http://chemphys.edu.ru/issues/2012-13-1/articles/295/.
3. Gerasimov Yu.I., Yarygin V.N. Flow of jets of ideal and real gases from axisymmetric nozzles. Questions of similarity. 2. Outflow into a flooded space // Physicochemical kinetics in gas dynamics. 2012. T. 13, issue. 2. http://chemphys.edu.ru/issues/2012-13-2/articles/315/.
4. Zarvin A.E., Kalyada V.V., Madirbaev V.Zh., Korobeishchikov N.G., Khodakov M.D., Yaskin A.S., Khudozhitkov V.E., Gimelshein S.F. Condensable supersonic jet facility for analyzes of transient low-temperature gas kinetics and plasma chemistry of hydrocarbons // IEEE Transact. Pl. Sci. 2017. V. 45. Iss. 5. P. 819-827. DOI: 10.1109/TPS.2017.2682901.
5. Zarvin A.E., Yaskin A.S., Kalyada V.V. The influence of condensation on the sizes of strongly underexpanded jets when expiring into a rarefied flooded space // Journal of PMTF. 2018. T. 59. No. 1. P. 99-106. DOI: 10.15372/PMTF20180111
6. Yaskin A.S., Zarvin A.E., Dubrovin K.A., Kalyada V.V. Bifurcation of a liquid micro-jet in a vacuum // Vacuum. 2022. V.198, N.4. P.110904. doi: 10.1016/j.vacuum.2022.110904.
7. Avtaeva S.V., Yakovleva T.S., Kalyada V.V., Zarvin A.E. The electron beam diagnostic of the clustered supersonic nitrogen jets // IOP Conf. Series: Journal of Physics: Conf. Series. 2017. V.927. P.012005. doi: 10.1088/1742-6596/927/1/012005.
8. Khudozhitkov V.E., Zarvin A.E., Kalyada V.V. Generation of a low-temperature plasma in a nozzle to initiate ion-cluster reactions in jets of mixtures of methane with a buffer gas // E3S Web of Conferences. 2023. V.459. P.01007. doi: 10.1051/e3sconf/202345901007.
9. Khudozhitkov V.E., Kalyada V.V. Registration of protoned argon and helium in a clustered gas flow of argon-hydrogen and helium-hydrogen mixtures // AIP Conference Proceedings. 2021.V.2351. P.040003. doi: 10.1063/5.0052014.
10. Dubrovin K.A., Zarvin A.E., Kalyada V.V., Yaskin A.S., Dering E.D. Application of electron beam diagnostics for the study of rarefied clustered gas flows // Vacuum. 2023.V.218. P.112652. doi: 10.1016/j.vacuum.2023.112652.
11. Zarvin A.E., Madirbaev V.Z., Dubrovin K.A., Kalyada V.V. On the mechanism of ionic-cluster excitation of argon levels in molecular gas mixtures // Plasma Chem Plasma Process. 2022. V.42. P.247–265. doi:10.1007/s11090-021-10214-2.
12. Gochberg A. Electron beam fluorescence methods in hypersonic aerothermodynamics. Prog. Aerospace Sci. 1997. V. 33, P. 431-480. DOI:10.1016/S0376-0421(97)00002-X.
13. Muntz E.P., Abel S.J., Maguire B.L. Nhe electron beam fluorescence probe in experimental gas dynamics // Aerospace Technical Conference and Exhibit. Houston, Texas. Suppl. IEEE Trans. Aerospace AS-3. 1965. V. 2. P. 210.
14. Lee H.F., Petrie S.L. Electron beam visualization in hypersonic air flows // 7th Aerodynamic Testing Conference. 1972. P. 1017. https://doi.org/10.2514/6.1972-1017.
15. Belan M., De Ponto S., Tordella D. Determination of density and concentration from fluorescent images of a gas flow // Exp. Fluids. 2007. V. 45. No. 3. Source arXiv. DOI: 10.1007/s00348-008-0493-5
16. Shpenik O.B., Bulgakova A.I., Zavilopulo A.N., Erdevdi N.M., Bandurin Yu.A. Excitation of valine molecules by electron impact in the gas phase // PZhTP. 2021. T. 47. Issue. 14. pp. 30-34.
17. Ieshkin A.E., Danilov A.V., Chernysh V.S., Ivanov I.E., Znamenskaya I.A. Visualization of supersonic flows with bow shock using transversal discharges // J. Viz. 2019. V. 22. P. 741-750. https://doi.org/10.1007/s12650-019-00565-6.
18. Yarygin V.N., Gerasimov Yu.I., Krylov A.N., Mishina L.V., Prikhodko V.G., Yarygin I.V. Gas dynamics of spacecraft and orbital stations (review) // Teplofiz. Aerodin. 2011. T. 18. No. 3. P. 345-372.
19. Zarvin A.E., Yaskin A.S., Kalyada V.V., Ezdin B.S. On the structure of a supersonic jet under conditions of developed condensation. PZhTF. 2015. T.41. Vol. 22. pp. 74-81.
20. Dubrovin K.A., Zarvin A.E., Rebrov A.K. Features of the process of formation of supersonic jets of rarefied gases under conditions of developed condensation // Prikl. 2023. No. 5. P. 70-83. DOI: 10.15372/PMTF202315325.
21. Zarvin A.E., Yaskin A.S., Dubrovin K.A., Kalyada V.V.. Visualization of low-density gas-dynamic objects in full-scale processes modeling on small experimental plants // Vacuum. V. 2021. 191(9). 110409. https://doi.org/10.1016/j.vacuum.2021.110409.
22. Borzenko B.N., Karelov N.V., Rebrov A.K., Sharafutdinov R.G. experimental study of the population of rotational levels of molecules in a free nitrogen stream // Prikl. 1976. No. 5. P. 20-31.
23. Smith J.A., Driscoll J.F. The electron-beam fluorescence technique for measurements in hypersonic turbulent flows // J. Fluid Mech. 1975. V. 72. Part 4. P. 695-719.
24. Sukhinin G.I., Sharafutdinov R.G. Determination of the effective probabilities of rotational transitions during electron impact excitation of the N2+B2Σ state from the ground state of nitrogen // Technological Physics. 1983. T. 53. No. 2. P. 333-340.
25. Ashkenas H.Z., Sherman F.S. The structure and utilization of supersonic free jets in low density wind tunnels // Rarefied Gas Dynamics (Proceedings of the 4th RGD Symposium, Academic Press, New York). 1966. V. 2. P. 84.
26. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994.
27. Ivanov M. S., Kashkovsky A. V., Gimelshein S. F., et al. SMILE system for 2D/3D DSMC computations // Rarefied gas dynamics: Proc. of the 25th Intern. symp., Saint-Petersburg (Russia), 21–28 July 2006 / Ed. by M. S. Ivanov, A. K. Rebrov. S.-Petersburg: Siberian Branch of Russ. Acad. of Sci., 2007. P. 539–544.
28. M. S. Ivanov, S. V. Rogazinsky, “Economic schemes for direct statistical modeling of rarefied gas flows”, Matem. Modeling, 1:7 (1989), 130–145
29. Ivanov, M. S.; Bondar, Ye. A. ; Markelov, G. N.; Gimelshein, S. F.; Taran, J. -P. Study of the Shock Wave Structure about a Body Entering the Martian Atmosphere. RAREFIED GAS DYNAMICS: 23rd International Symposium. AIP Conference Proceedings, Volume 663, pp. 481-488 (2003). doi: 10.1063/1.1581585
30. Kashkovsky A.V., Vashchenkov P.V., Shevyrin A.A., Shkredov T.Y., Bondar Y.A., Krylov A.N. Aerothermodynamics of the Federation crew module at high-altitude reentry. 31st International Symposium on Rarefied Gas Dynamics (RGD 2018). AIP Conference Proceedings, Volume 2132, Issue 1, id.100014 (2019). doi: 10.1063/1.5119609
31. Bondar E.A., Gimelshein S.F., Markelov G.N., Ivanov M.S. Direct statistical modeling of the structure of a shock wave in a dissociating gas. Thermophysics and aeromechanics. 2006. T. 13. No. 2. P. 257-274.
32. Kashkovsky, A. V.; Bondar, Ye. A.; Krylov, A. N.; Rodicheva, A. A. Multi-zone kinetic-continuum simulation of an orbit correction thruster back flow around a space station. Proc. of 32nd symposium on rarefied gas dynamics. AIP Conference Proceedings, Volume 2996, Issue 1, id.080010. Doi: 10.1063/5.0187374
33. Shoev G.V., Bondar E.A., Khotyanovsky D.V., Kudryavtsev A.N., Maruta K., Ivanov M.S. Numerical study of the entry and propagation of a shock wave in a microchannel. Thermophysics and aeromechanics. 2012. T. 19. No. 1. P. 19-34.
34. Khotyanovsky D.V., Bondar Y.A., Kudryavtsev A.N., Shoev G.V., Ivanov M.S. Viscous Effects in Steady Reflection of Strong Shock Waves. AIAA Journal. 2009. Vol. 47. No. 5. P. 1263-1269. https://doi.org/10.2514/1.40539
35. Ivanov I.E., Timokhin M.Y., Kryukov I.A., Bondar Y.A., Kokhanchik A.A., Ivanov M.S. Study of the shock wave structure by regularized Grad's set of equations. 28th International Symposium on Rarefied Gas Dynamics 2012. AIP Conference Proceedings, Volume 1501. AIP Conference Proceedings, Volume 1501, Issue 1, p.215-222. Doi: 10.1063/1.4769507
36. Zeitoun D.E., Graur I.A., Burtschell Y., Ivanov M.S., Kudrayvtsev A.N., Bondar Ye.A. Continuum and Kinetic Simulations of Shock Wave Propagation in Long MicroChannel. Rarefied Gas Dynamics: Proceedings of the 26th International Symposium. AIP Conference Proceedings 1084. Conference Location and Date: Kyoto, Japan, 20-25 July 2008. Published December 2008., p.464-469. Doi: 10.1063/1.3076523
37. Gimelshein S., Wysong I., Bondar Y., Ivanov M. Accuracy analysis of DSMC chemistry models applied to a normal shock wave. 28th International Symposium on Rarefied Gas Dynamics 2012. AIP Conference Proceedings, Volume 1501. AIP Conference Proceedings, Volume 1501, Issue 1, p.637-644. Doi: 10.1063/1.4769602
38. Yevgeniy Bondar, Anatoly Trotsyuk and Mikhail Ivanov. DSMC Modeling of the Detonation Wave Structure in Narrow Channels. AIAA Paper 2009-1568 (2009). doi: https://doi.org/10.2514/6.2009-1568
39. Yevgeniy Bondar and Mikhail Ivanov. DSMC Study of an H2/O2 Detonation Wave Structure. AIAA Paper 2010-4504 (2010). doi: https://doi.org/10.2514/6.2010-4504
40. Bondar Y.A., Ivanov M.S., Maruta K. Hydrogen-Oxygen Detonation Study by the DSMC Method. 27TH INTERNATIONAL SYMPOSIUM ON RATED GAS DYNAMICS. AIP Conference Proceedings, Volume 1333, pp. 1209-1214 (2011). doi: 10.1063/1.3562808
41. Borgnakke C., Larsen P.S. Statistical collision model for Monte Carlo simulation of polyatomic gas mixture // J. Comput. Phys. 1975. V. 18. P. 405-420.
42. Bird G. A. Breakdown of continuum flow in freejets and rocket plumes // Rarefied gas dynamics: Proc. of the 12th Intern. symp., Charlottesville (USA), July 7–11, 1980. S. l.: AIAA, 1980. P. 681–693.
43. Skovorodko P.A.; Ramos A.; Tejeda G.; Fernández J.M.; Montero S. Experimental and numerical study of supersonic jets of N2⁠, H2⁠, and N2+H2 mixtures // AIP Conf. Proc. 2012. V. 1501. P 1228–1235. https://doi.org/10.1063/1.4769682