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DOI 10.21662
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Bolotnova R.Kh., Korobchinskaya V.A. The formation features of supercritical steam-water jets (review). Multiphase Systems. 17 (2022) 1–2. 27–37 (in Russian).
2022. Vol. 17. Issue 1, Pp. 27–37
DOI: 10.21662/mfs2022.1.003
The formation features of supercritical steam-water jets (review)
Bolotnova R.Kh., Korobchinskaya V.A.∗,∗∗
Mavlyutov Institute of Mechanics, UFRC RAS, Ufa, Russia
∗∗Bashkir Sate University, Ufa, Russia


The review of works on study of dynamics formation of water fluid jet of supercritical parameters outflowing from a high-pressure chamber through a thin nozzle has been carried out. The system of model equations describing the dynamics of outflow processes in both single-phase and multiphase gas-vapor-liquid media is considered. It based on the laws of conservation of mass, momentum and energy of phases in accordance with single-pressure, single-speed and two-temperature approximations with the allowance for contact-type heat transfer and mass transfer for evaporation and condensation under equilibrium conditions. The numerical realization of model representations is carried out by the method of movable Lagrangian grids and using modified solvers of the OpenFOAM package. The analysis of the features initial stage of the formation of a steam-water jet at outflow through a thin nozzle is given based on the results of numerical simulation by the Lagrangian method in the case of a two-dimensional axisymmetric formulation. The problems about the study of the evolution a forming jet during the outflow of a single-phase flow of water-steam and a boiling jet of supercritical state parameters are considered, by the numerical realization in the OpenFOAM package. The features the formation of Mach disk, accompanied by the appearance of a cavity inside the jet, are noted. It is shown that during the outflow of a boiling steam-water jet, the vortex zones are formed near the axis of symmetry and periodic pulsations of pressure and mass velocity are generated, which subsequently lead to acoustic oscillations preceding the main jet flow observed in experiments. The justification of reliability the applied numerical method realized by the new OpenFOAM solvers is given on the example of comparing numerical and analytical solutions to L.I. Sedov’s problem of a point explosion in two-phase gas-drop mixture and comparing the results of numerical solution and experimental photography of supersonic nitrogen jet outflowing through cylindrical nozzle from high-pressure vessel.


thin nozzle,
boiling water outflow,
mathematical and numerical modeling,
OpenFOAM package

Article outline

Purpose. Review of studies about the processes of formation of boiling steam-water jets under different regimes of outflowing from thin nozzles with a description of the most important results obtained over the past few years.

Methodology. The numerical modeling of the studied outflow regimes the equations of dynamics of a gas-liquid mixture in a three-dimensional Cartesian coordinate system were used, including the laws of conservation of mass, momentum and energy of each phase in accordance with single-pressure, single-speed and two-temperature approximations with the allowance for contact-type heat transfer and mass transfer for evaporation/condensation. In the studies considered, the simulation was performed using the method of movable Lagrangian grids and modified solvers of the OpenFOAM package

Findings. At the initial stage of studies of the processes of spatial outflow of a steam-water mixture, the numerical method of the shock-capturing method on movable Lagrangian grids deformed in time was used. The intensive expansion of the gas flow is observed in the calculations, as in the experiment of Reshetnikov A.V. et al. (2012). Over time, the supersonic outflow mode saved, further expansion the flow occurs along the lateral boundaries with large values of the vy component of the velocity in these areas compared to the axial zone, which is accompanied by the formation of a parabolic jet.

In further the process of steam-water outflow from a thin nozzle was carried out using the sonicFoam solver of the OpenFOAM library package with the Peng-Robinson equation of state of steam-water. Along the boundary of the expanding supersonic jet, a barrel shock is generated, when him reflected from the axis of symmetry, a normal shock is formed in the calculations.

Interaction of high-speed flow with adjacent low disturbed zone leads to curving of gas motion trajectories and development of Kelvin-Helmholtz instability, which is followed by the formation and growth of vortex zones. The main vortex supports the supersonic velocity of flow at the outer section of jet. The weaker vortex formed near the symmetry axis in the gas surrounding the jet due to the direction of gas flow towards the jet movement contributes to the shifts the central zone of the Mach disk towards the nozzle, which leads to the generation of a hollow jet.

The continuation of researches was carried out with additional consideration in the model of a gas-vapor-liquid mixture of heat and mass transfer processes occurring of evaporation and condensation. The process of forming a series of toroidal vortices contributes to the swirling of the jet, its expansion and further leads to flow turbulization is showed. Over time, in the near zone of symmetry axis the forming regime outflow generates local regions of periodically oscillating pressure and mass flow velocity in the jet. The regime of jet flow considered above is the source of acoustic periodic oscillations with radially spreading; they exist in the initially undisturbed gas zone in front of the main jet, which were observed in experiments.


The review presents the results of theoretical studies about features of the formation of axisymmetric jets during the outflow of boiling liquids through a thin nozzle from a high-pressure vessel.

The equations of model describing the dynamic of a gas-vapor-liquid medium during the formation of multiphase jet flows taking into account heat and mass transfer processes are given.

Numerical modeling methods used in solving the considered problems are indicated. The development of model representations and applied numerical methods in research of the studied processes with visualization of the results is shown.

At the first stages of studies of the initial stage of jet formation process, it is shown that at the initial supercritical temperature, a supersonic flow regime is formed with a slight condensation of the vapor phase and the formation of a parabolic jet.

Further numerical studies using modifications of solvers from the OpenFOAM package revealed the conditions for the formation of a barrel shock in the jet, a Mach disk and vortex zones that swirling the jet towards the outer zone. The development of the jet flow is accompanied by the formation of a group of toroidal vortices that form dynamic local zones of periodic pulsations pressure and mass velocity in the near zone of the axis of symmetry of jet, which are sources of acoustic pulsations in the gas zone preceding the main flow.

The reliability of numerical method used is based on the comparison of numerical and analytical solutions of test problem. Satisfactory agreement of the simulated process of formation a supersonic nitrogen jet with experimental data is shown.


  1. Ishii R., Fujimoto H., Hatta N., Umeda Y. Experimental and numerical analysis of circular pulse jets // J. Fluid Mech. 1999. V. 392. Pp. 129–153.
    DOI: 10.1017/S0022112099005303
  2. Reshetnikov A.V., Busov K.A., Mazheiko N.A., Skokov V.N., Koverda V.P. Transient behavior of superheated water jets boiling // Thermophysics and Aeromechanics. 2012. V. 9, No. 2. Pp. 329–336.
    DOI: 10.1134/S0869864312020151
  3. Reshetnikov A.V., Mazheiko N.A., Skokov V.N., Begletsov V.N., Koverda V.P. Pulsation dynamics during explosive boil-up of overheated water jets // Techn. Phys. Letters. 2007. V. 33, No. 9. Pp. 732–737.
    DOI: 10.1134/S1063785007090052
  4. Busov K.A., Reshetnikov A.V., Mazheiko N.A., Kapitunov O.A. Effect of a passive swirler on the superheated liquid flow // J. Applied Mech. Techn. Phys. 2019. V. 60, No. 1. Pp. 53–58.
    DOI: 10.1134/S0021894419010085
  5. Anufriev I.S., Shadrin E.Yu., Kopyev E.P., Sharypov O.V., Leschevich V.V. Liquid fuel spraying by a high-speed steam jet // Thermophysics and Aeromechanics. 2020. V. 27, No. 4. Pp. 627–630.
    DOI: 10.1134/S0869864320040162
  6. Alekseev M.V., Lezhnin S.I., Pribaturin N.A., Sorokin A.L. Generation of shockwave and vortex structures at the outflow of a boiling water jet // Thermophysics and Aeromechanics. 2014. V. 21, No. 6. Pp. 763–766.
    DOI: 10.1134/S0869864314060122
  7. Alekseev M.V., Vozhakov I.S., Lezhnin S.I., Pribaturin N.A. Wave processes at outflow of water coolant with initial supercritical parameters // Thermophysics and Aeromechanics. 2017. V. 24, No. 5. Pp. 799–802.
    DOI: 10.1134/S0869864317050158
  8. Alekseev M.V., Vozhakov I.S., Lezhnin S.I. Pressure pulsations during gas injection into a liquid-filled closed vessel with a high pressure drop // Thermophysics and Aeromechanics. 2019. V. 26, No. 5. Pp. 781–784.
    DOI: 10.1134/S0869864319050159
  9. Senachin P.K., Kiryushin I.I., Samarin A.V., Senachin A.P., Ulrich S.A. Numerical simulation of the dynamics of a non-stationary liquid jet // Thermophysics and Aeromechanics. 2020. V. 27, No. 6. Pp. 811–824.
    DOI: 10.1134/S0869864320060025
  10. Bolotnova R.Kh., Korobchinskaya V.A. Boiling water jet outflow from a thin nozzle: spatial modeling // Thermophysics and Aeromechanics. 2017. V. 24, No. 5. Pp. 761–771.
    DOI: 10.1134/S0869864317050110
  11. Bolotnova R.Kh., Buzina V.A. (Korobchinskaya V.A.), Galimzyanov M.N., Shagapov V.Sh. Hydrodynamic features of boiling liquid outflow // Teplofizika i Aeromekhanika [Thermophysics and Aeromechanics]. 2012. V. 19, No. 6. Pp. 719–730 (in Russian).
    eLIBRARY ID: 18198246
  12. Nigmatulin R.I., Bolotnova R.Kh. Wide-range equation of state of water and steam: Simplified form // High Temperature. 2011. V. 49, No. 2. Pp. 303–306.
    DOI: 10.1134/S0018151X11020106
  13. Bolotnova R.Kh., Gainullina E.F. Supercritical steam outflow from a thin nozzle: forming a hollow jet // Thermophysics and Aeromechanics. 2018. V. 25, No. 5. Pp. 751–757.
    DOI: 10.1134/S0869864318050116
  14. Bolotnova R.Kh., Korobchinskaya V.A., Faizullina E.A. Analysis the dynamic formation of a vapor supersonic jet under outflow from thin nozzle // J. Physics: Conference Series. 2021. V. 2103. Pp. 012219–1–012219-6.
    DOI: 10.1088/1742-6596/2103/1/012219
  15. Bolotnova R.Kh., Korobchinskaya V.A. Modeling of dynamics of supercritical water jet outflowing from a thin nozzle // Thermophysics and Aeromechanics. 2022. Vol. 29, № 3. Pp. 347–355.
    DOI: 10.1134/S0869864322030039
  16. Nigmatulin R.I. Dynamics of Multiphase Media. Hemisphere, New York, 1990.
  17. Landau L.D., Lifshitz E.M. Fluid Mechanics. Vol. 6. Pergamon Press, Oxford, 1987.
  18. OpenFOAM. The Open Source Computational Fluid Dynamics (CFD) Toolbox. (дата обращения: 31.10.2022)
  19. Sedov L.I. Similarity and Dimensional Methods in Mechanics. CRC Press, Boca Raton, 1993.
    DOI: 10.1201/9780203739730
  20. Orescanin M.M., Austin J.M., Kieffer S.W. Unsteady high-pressure flow experiments with applications to explosive volcanic eruptions // J. of Geophysical Research. 2010. V. 115. Pp. B06206-1-B06206-18.
    DOI: 10.1029/2009JB006985
  21. Abramovich G.N. Applied Gas Dynamics. Foreign Technology Div Wright-Patterson AFB, OH, 1973.