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Modeling of dynamics of supercritical water jet outflowing from a thin nozzle

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Thermophysics and Aeromechanics Aims and scope

Abstract

The fluid dynamics of a water fluid jet with supercritical state parameters outflowing from a high-pressure vessel through a thin nozzle is investigated. The numerical modeling of the jet was carried out using a system of equations for a gas-vapor-liquid mixture which includes the conservation laws for mass, momentum, and energy formulated in one-pressure, one-velocity, and two-temperature approximation. The simulation takes into account the contact heat and mass transfer processes of evaporation and condensation under equilibrium condition using a modified solver reactingTwoPhaseEulerFoam within the OpenFOAM free open package. The process of barrel shock formation in a supersonic boiling jet with developing the Mach disk is demonstrated. It was found that the outflow process is accompanied by the formation of vortex zones near the jet symmetry axis and this induces periodic pulsations in pressure and mass velocity inside the jet. Finally, this generates the acoustic pulses series preceding the main jet flow.

Justification of reliability for the applied numerical method implemented through the OpenFOAM package solver is offered through comparing the numerical and analytical solutions for the Sedov problem of a strong point explosion in a two-phase gas-droplet mixture (for the planar case). The comparative analysis of simulation and the experimental photography for the supersonic nitrogen jet ejected from a cylindrical nozzle of a high-pressure reservoir is presented. The numerical results obtained with the OpenFOAM package demonstrate a satisfactory agreement with analytical solution and experimental data.

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Abbreviations

x, y, z :

Cartesian coordinates, m

t :

time, s

α i, α i0 :

current and initial volume fraction for the ith phase

ρ i, ρ i0, ρ′, ρ′0, ρ :

current and initial densities for the ith phase, gas-droplet mixture, kg/m3

k :

constant describing the gas-droplet mixture density

γ :

adiabatic exponent of gas-droplet mixture

\({c_{{p_i}}},{c_{{V_i}}},c\) :

isobaric and isochoric heat capacity for the ith phase, particle heat capacity, J/(kg·K)

p, p 0, p′:

current and initial pressure for the gas-droplet mixture, Pa

E :

explosion energy, J

\({\vec v}\) :

vector of mass velocity m/s

x h, y h :

length and radius of a high pressure reservoir, m

x s, y s :

length and radius of nozzle, m

x M :

distance from the nozzle outlet to the Mach disk

d c, d e, h c, h e :

calculated and experimental values for the Mach disk diameter and barrel height, m

δ x, δ d :

relative accuracy, %

τ i :

viscous stress tensor for the ith phase, Pa

γ i, δ i, eff :

thermal diffusivity and effective thermal diffusivity, m2/s

T i :

temperature, K

K i, e i :

kinetic and internal energy for the ith phase, J/kg

h i, L i :

enthalpy and latent heat of vaporization/condensation, J/kg

K ht :

heat-exchange coefficient, kg/(K·s3)

Γi :

mass transfer rate, kg/(m3·s)

I :

unit tensor

μ i :

dynamic viscosity for the ith phase, kg/(m·s)

\({\vec v}\) :

frequency, kHz

\({\vec T}\) :

period of pulsation, μs

m l :

mass fraction of water

i = l, g:

subscripts describing the liquid and vapor phases.

References

  1. R. Ishii, H. Fujimoto, N. Hatta, and Y. Umeda, Experimental and numerical analysis of circular pulse jets, J. Fluid Mech., 1999, Vol. 392, P. 129–153.

    Article  ADS  Google Scholar 

  2. A.V. Reshetnikov, K.A. Busov, N.A. Mazheiko, V.N. Skokov, and V.P. Koverda, Transient behavior of superheated water jets boiling, Thermophysics and Aeromechanics, 2012, Vol.19, No. 2, P. 329–336.

    Article  ADS  Google Scholar 

  3. A.V. Reshetnikov, N.A. Mazheiko, V.N. Skokov, V.N. Begletsov, and V.P. Koverda, Pulsation dynamics during explosive boil-up of overheated water jets, Techn. Phys. Letters, 2007, Vol. 33, No. 9, P. 732–737.

    Article  ADS  Google Scholar 

  4. K.A. Busov, A.V. Reshetnikov, N.A. Mazheiko, and O.A. Kapitunov, Effect of a passive swirler on the superheated liquid flow, J. Applied Mech. Techn. Phys., 2019, Vol. 60, No. 1, P. 53–58.

    Article  ADS  Google Scholar 

  5. I.S. Anufriev, E.Yu. Shadrin, E.P. Kopyev, O.V. Sharypov, and V.V. Leschevich, Liquid fuel spraying by a high-speed steam jet, Thermophysics and Aeromechanics, 2020, Vol. 27, No. 4, P. 627–630.

    Article  ADS  Google Scholar 

  6. M.V. Alekseev, S.I. Lezhnin, N.A. Pribaturin, and A.L. Sorokin, Generation of shockwave and vortex structures at the outflow of a boiling water jet, Thermophysics and Aeromechanics, 2014, Vol. 21, No. 6, P. 763–766.

    Article  ADS  Google Scholar 

  7. M.V. Alekseev, I.S. Vozhakov, S.I. Lezhnin, and N.A. Pribaturin, Wave processes at outflow of water coolant with initial supercritical parameters, Thermophysics and Aeromechanics, 2017, Vol. 24, No. 5, P. 799–802.

    Article  ADS  Google Scholar 

  8. M.V. Alekseev, I.S. Vozhakov, and S.I. Lezhnin, Pressure pulsations during gas injection into a liquid-filled closed vessel with a high pressure drop, Thermophysics and Aeromechanics, 2019, Vol. 26, No. 5, P. 781–784.

    Article  ADS  Google Scholar 

  9. P.K. Senachin, I.I. Kiryushin, A.V. Samarin, A.P. Senachin, and S.A. Ulrich, Numerical simulation of the dynamics of a non-stationary liquid jet, Thermophysics and Aeromechanics, 2020, Vol. 27, No. 6, P. 811–824.

    Article  ADS  Google Scholar 

  10. R.Kh. Bolotnova and V.A. Korobchinskaya, Boiling water jet outflow from a thin nozzle: spatial modeling, Thermophysics and Aeromechanics, 2017, Vol. 24, No. 5, P. 761–771.

    Article  ADS  Google Scholar 

  11. R.Kh. Bolotnova, V.A. Buzina (V.A. Korobchinskaya), M.N. Galimzyanov, and V.Sh. Shagapov, Hydrodynamic features of boiling liquid outflow, Teplofizika & Aeromekhanika, 2012, Vol. 19, No. 6, P. 719–730.

    Google Scholar 

  12. R.Kh. Bolotnova and E.F. Gainullina, Supercritical steam outflow from a thin nozzle: forming a hollow jet, Thermophysics and Aeromechanics, 2018, Vol. 25, No. 5, P. 751–757.

    Article  ADS  Google Scholar 

  13. R.Kh. Bolotnova, V.A. Korobchinskaya, and E.A. Faizullina, Analysis the dynamic formation of a vapor supersonic jet under outflow from thin nozzle, J. Physics: Conference Series, 2021, Vol. 2103, P. 012219–1–012219–6.

    Google Scholar 

  14. L.I. Sedov, Similarity and Dimensional Methods in Mechanics, CRC Press, Boca Raton, 1993.

    Google Scholar 

  15. OpenFOAM. The Open Source Computational Fluid Dynamics (CFD) Toolbox. 2021. Available: http://www.openfoam.com.

  16. M.M. Orescanin, J.M. Austin, and S.W. Kieffer, Unsteady high-pressure flow experiments with applications to explosive volcanic eruptions, J. Geophys. Research, 2010, Vol. 115, P. B06206–1–B06206–18.

    ADS  Google Scholar 

  17. G.N. Abramovich, Applied Gas Dynamics, Foreign Technology Div Wright-Pattersonafb, OH, 1973.

    Google Scholar 

  18. R.I. Nigmatulin, Dynamics of Multiphase Media, Hemisphere, New York, 1990.

    Google Scholar 

  19. L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Vol. 6, Pergamon Press, Oxford, 1987.

    Google Scholar 

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Authors and Affiliations

  1. Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia

    R. Kh. Bolotnova & V. A. Korobchinskaya

  2. Bashkir State University, Ufa, Russia

    V. A. Korobchinskaya

Authors
  1. R. Kh. Bolotnova
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  2. V. A. Korobchinskaya
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Correspondence to R. Kh. Bolotnova.

Additional information

Research was supported by federal budget for the state assignment 0246-2019-0052.

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Bolotnova, R.K., Korobchinskaya, V.A. Modeling of dynamics of supercritical water jet outflowing from a thin nozzle. Thermophys. Aeromech. 29, 347–355 (2022). https://doi.org/10.1134/S0869864322030039

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  • DOI: https://doi.org/10.1134/S0869864322030039

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