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Atomization and Sprays

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NUMERICAL SIMULATION OF SUPERCRITICAL AND SUBCRITICAL INJECTION OF CRYOGENIC NITROGEN BASED ON THE HOMOGENEOUS EQUILIBRIUM MODEL OF TWO-PHASE FLOW

Volume 32, Issue 1, 2022, pp. 91-113
DOI: 10.1615/AtomizSpr.2021039106
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ABSTRACT

Multidimensional numerical simulations of the outflow of the dense turbulent jet of cryogenic nitrogen into a chamber filled with nitrogen at normal temperature are performed using the homogeneous equilibrium model of the two-phase flow and the new accurate analytical equation of state (EOS) of real gas for nitrogen. The applicability of the new EOS is verified in a wide range of density (from 0 to the liquid density in the triple point) and temperature (from 100 K to 5000 K). The results of calculations are compared with available experimental data on nitrogen density variation in the jets. The satisfactory agreement of the results is obtained. The developed EOS allows the identification of two-phase flow regions and the mass fractions of liquid and gas based on the local instantaneous values of density and temperature in the jet without using the two-fluid flow model.

Figures

  • Nitrogen saturation line plotted based on the tabulated data of Span et al. (2000) (crosses) and
Eq. (5) (curve)
  • Nitrogen saturation line calculated by Eq. (21) (curve) and taken from tables of Span et al. (2000)
(symbols). 1 stands for gas; 2 stands for liquid.
  • Self-similar dependence of Eq. (24) (curve) and the tabulated data of Span et al. (2000) (symbols)
for isotherms. 1: T = 300 K; 2: T = 400 K; 3: T = 500 K; 4: T = 600 K; 5: T = 700 K; 6: T = 800 K.
  • Calculated (curves) and tabulated (symbols, Span et al., 2000) values of the specific heat of nitrogen
Cv versus density in the region of supercritical fluid on several isotherms. 1: T = 300 K; 2: T = 400 K; 3:
T = 800 K; 4: T = 1000 K; 5: T = 1200 K.
  • Computational domain: (a) side view; (b) enlarged view from the side of the nozzle channel
  • (a) Cp(T ); (b) ρ(T ); (c) E(T ); (d) ρ(T ); and (e) ρ(T ) dependences for nitrogen at isobar 3.98
MPa: (1) calculated and (2) taken from Lemmon et al. (2021)
X/D = 10 and X/D = 20, the calculation underestimates the density at the jet periphery. This
latter effect can be associated with the presence of large eddies in the jet structure, which are not
resolved by the turbulence model used.
  • Calculated stabilized fields of nitrogen density in the longitudinal section of the computational
domain obtained for sets of conditions (a) I and (b) II
  • Calculated (curves) and measured (symbols, Mayer et al., 2003) stabilized profiles of nitrogen
density along the axis of symmetry of the jet for sets of conditions (a) I and (b) II
  • Calculated (curves) and measured (symbols, Mayer et al., 2003) stabilized distributions of the
dimensionless density of nitrogen ρ+ on the dimensionless radius r/r1/2 at different distances from the
nozzle exit X/D for a set of conditions I. 1: X/D = 1.2; 2: X/D = 5; 3: X/D = 10; 4: X/D = 15; 5:
X/D = 20; 6: X/D = 25
  • (a) Cp(T ); (b) ρ(T ); (c) E(T ); (d) ρ(T ); and (e) ρ(T ) dependences for nitrogen at isobar 3.1
MPa: (1) calculated and (2) taken from Lemmon et al. (2021)
et al. (2021) on the isobar P = 3.1 MPa at 100 ≤ T ≤ 300 K. Comparison shows that all the
thermophysical parameters of the problem, obtained by the proposed EOS and by Eqs. (28) and
(29), are in excellent agreement with the data of Lemmon et al. (2021)
  • (a) Calculated stabilized field of nitrogen density and (b) the two-phase region (shown in black)
in the longitudinal section of the computational domain obtained for the set of conditions III
  • Calculated profiles of (a) density and (b) temperature of cryogenic nitrogen along the axis of
symmetry of the jet for the set of conditions III at different times after the start of injection
  • Calculated stabilized distributions of (a) density and (b) temperature of cryogenic nitrogen on the
dimensionless radius r/r1/2 at different distances from the nozzle exit, X/D, for the set of conditions III.
1: X/D = 1.2; 2: X/D = 5; 3: X/D = 10; 4: X/D = 15; 5: X/D = 20; 6: X/D = 25.
(ρ2) density on the isobar P = 3.1 MPa. The interval ρ2 ≤ ρ ≤ ρ1 corresponds to the two-phase
region.
REFERENCES
  1. Abudour, A.M., Mohammad, S.A., Robinson, R.L., Jr., and Gasem, K.A.M., Volume-Translated Peng- Robinson Equation of State for Saturated and Single-Phase Liquid Densities, Fluid Phase Equilibr., vol. 335, pp. 74-87,2012. DOI: 10.1016/j.fluid.2012.08.013. DOI: 10.1016/j.fluid.2012.08.013

  2. Ashgriz, N., Ed., Handbook of Atomization and Sprays: Theory and Applications, New York: Springer, 2011. DOI: 10.1007/978-1-4419-7264-4. DOI: 10.1007/978-1-4419-7264-4

  3. AVL FIRE, Computational Fluid Dynamics for Conventional and Alternative Powertrain Development, https://www.avl.com/fire (retrieved on April 20,2021).

  4. Battistoni, M., Magnotti, G.M., Genzale, C.L., Arienti, M., Matusik, K.E., Duke, D.J., Giraldo, J., Ilavsky, J., Kastengren, A.L., Powell, C.F., andMarti-Aldaravi, P., Experimental and Computational Investigation of Subcritical Near-Nozzle Spray Structure and Primary Atomization in the Engine Combustion Network Spray D, SAE Tech. Paper 2018-01-0277,2018. DOI: 10.4271/2018-01-0277. DOI: 10.4271/2018-01-0277

  5. Blokkeel, G., Barbeau, B., and Borghi, R., A 3D Eulerian Model to Improve the Primary Breakup of Atomizing Jet, SAE Tech. Paper 2003-01-0005, 2003 SAE World Congress, Detroit, Michigan, March 3-6,2003. DOI: 10.4271/2003-01-0005. DOI: 10.4271/2003-01-0005

  6. Chehroudi, B. and Talley, D., The Fractal Geometry of a Cryogenic Nitrogen Round Jet Injected into Sub- and Super-Critical Conditions, Atomization Sprays, vol. 14, pp. 81-91, 2004. DOI: 10.1615/AtomizSpr.v14.i1.50. DOI: 10.1615/AtomizSpr.v14.i1.50

  7. Clerc, S., Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows, J. Comput. Phys, vol. 161, pp. 354-375,2000. DOI: 10.1006/jcph.2000.6515. DOI: 10.1006/jcph.2000.6515

  8. De Lorenzo, M., Lafon, P., Di Matteo, M., Pelanti, M., Seynhaeve, J.-M., and Bartosiewicz, Y., Homogeneous Two-Phase Flow Models and Accurate Steam-Water Table Look-Up Method for Fast Transient Simulations, Int. J. Multiphase Flow, vol. 95, pp. 199-219, 2017. DOI: 10.1016/ j .ijmultiphaseflow.2017.06.001.

  9. Desantes, J.M., Garcla-Oliver, J.M., Pastor, J.M., Olmeda, I., Pandal, A., and Naud, B., LES Eulerian Diffuse-Interface Modeling of Fuel Dense Sprays Near- and Far-Field, Int. J. Multiphase Flow, vol. 127, Article ID 103272,2020. DOI: 10.1016/j.ijmultiphaseflow.2020.103272. DOI: 10.1016/j.ijmultiphaseflow.2020.103272

  10. Dubrovskii, A.V, Kuznetsov, N.M., and Frolov, S.M., Approximation of Thermodynamic Properties of Acetylene, Combust. Explos., vol. 8, no. 1, pp. 215-228,2015a. (in Russian).

  11. Dubrovskii, A.V, Kuznetsov, N.M., and Frolov, S.M., Approximation of Thermodynamic Properties of Ammonia, Combust. Explos, vol. 8, no. 1, pp. 198-214,2015b. (in Russian).

  12. Ferziger, J.H. andPeric, M., Computational Methods for Fluid Dynamics, New York: Springer, 1996. DOI: 10.1007/978-3-319-99693-6. DOI: 10.1007/978-3-319-99693-6

  13. Frolov, S.M., Kuznetsov, N.M., and Krueger, C., Real-Gas Properties of N-Alkanes, O2, N2, H2O, CO, CO2, and H2 for Diesel Engine Operation Conditions, Rus. J. Phys. Chem. B, vol. 3, no. 8, pp. 1191-1252,2009. DOI: 10.1134/S1990793109080090. DOI: 10.1134/S1990793109080090

  14. Frolov, S.M., Ivanov, V.S., Tukhvatullina, R.R., Frolov, F.S., Kuznetsov, N.M., and Basara, B., Numerical Simulation of the Operation Process in a Diesel Engine with the Real-Gas Equation of State, Combust. Explos., vol. 12, no. 1,pp. 73-83,2019. DOI: 10.30826/CE19120109. DOI: 10.30826/CE19120109

  15. Garcia-Oliver, J.M., Pastor, J.M., and Pandal, M., Diesel Spray CFD Simulations Based on the E-Y Eu- lerian Atomization, Atomization Sprays, vol. 23, no. 1, pp. 73-95, 2013. DOI: 10.1615/AtomizSpr.2013007198. DOI: 10.1615/AtomizSpr.2013007198

  16. Hanjalic, K., Popovac, M., and Hadziabdic, M., A Robust Near-Wall Elliptic Relaxation Eddy-Viscosity Turbulence Model for CFD, Int. J. Heat Fluid Flow, vol. 25, pp. 897-901, 2004. DOI: 10.1016/j .ijheatfluidflow. 2004.07.005.

  17. Jarczyk, M. and Pitznery, M., Large Eddy Simulation of Supercritical Nitrogen Jets, AIAA Paper No. 2012-1270, 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition January 9-12, 2012, Nashville, Tennessee, 2012. DOI: 10.2514/6.2012-1270. DOI: 10.2514/6.2012-1270

  18. Jemison, M., Sussman, M., and Arienti, M., Compressible, Multi-Phase Semi-Implicit Method with Moment of Fluid Interface Representation, J. Compt. Phys, vol. 279, pp. 182-217, 2014. DOI: 10.1016/j.jcp.2014.09.005. DOI: 10.1016/j.jcp.2014.09.005

  19. Kuznetsov, N.M. and Shvedov, K.K., Equation of State of the Detonation Products of RDX, Combust. Explos. Shock Waves, vol. 2, no. 4, pp. 52-58,1966. DOI: 10.1007/bf01261517. DOI: 10.1007/bf01261517

  20. Kuznetsov, N.M., Water-Steam Two-Phase Mixture. The Equation of State, Sound Velocity, Isentropes, Dokl. Akad. Nauk SSSR, vol. 257, no. 4, pp. 858-860,1981.

  21. Kuznetsov, N.M., The Equation of State and Phase Equilibrium Curve for the Liquid-Vapor System, Dokl. Akad. Nauk SSSR, vol. 266, no. 3, pp. 613-616,1982.

  22. Kuznetsov, N.M., Aleksandrov, E.N., and Davydova, O.N., Analytical Representation of the Curves of Liquid-Vapor Phase Equilibrium for Saturated Hydrocarbons, High Temp, vol. 40, pp. 359-363,2002. DOI: 10.1023/A:1016055822514. DOI: 10.1023/A:1016055822514

  23. Kuznetsov, N.M., Dubrovskii, A.V., Frolov, S.M., and Gubin, S.A., Analytical Approximation of Thermal and Caloric Equations of State for Real Gases in a Wide Range of Density and Temperature, Combust. Explos, vol. 3, pp. 83-89,2010. (in Russian).

  24. Kuznetsov, N.M., Dubrovsky, A.V., and Frolov, S.M., Analytical Approximation of the Thermal and Caloric Equations of State for Real Gases over a Wide Density and Temperature Range, Rus. J. Phys. Chem. B, vol. 5, no. 7, pp. 1084-1105,2011a. DOI: 10.1134/S1990793111070050. DOI: 10.1134/S1990793111070050

  25. Kuznetsov, N.M., Dubrovskii, A.V., and Frolov, S.M., Analytical Approximation of Equations of State of Real Gases in an Extended Range of Pressure and Density, Combust. Explos, vol. 4, pp. 68-74,2011b.

  26. Lemmon, E.W. and Jacobsen, R.T., Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air, Int. J. Thermophys., vol. 25, no. 1, pp. 21-69, 2004. DOI: 10.1023/B:IJOT. 0000022327.04529.f3. DOI: 10.1023/B:IJOT.0000022327.04529.f3

  27. Lemmon, E.W., McLinden, M.O., and Friend, D.G., Thermophysical Properties of Fluid Systems, in NIST Chemistry Webbook, NIST Standard Reference Database Number 69, P.J. Linstrom and W.G. Mallard, Eds., Gaithersburg, MD: National Institute of Standards and Technology, 2021. DOI: 10.18434/T4D303. DOI: 10.18434/T4D303

  28. Li, C., Crua, C., and Vogiatzaki, K., Effect of the Scale Resolution on the Two-Phase Coupling Characteristics of High Speed Evaporating Sprays Using LES/Eulerian-Lagrangian Methodologies, Int. J. Multiphase Flow, vol. 120, Article ID 103060,2019. DOI: 10.1016/j.ijmultiphaseflow.2019.06.013. DOI: 10.1016/j.ijmultiphaseflow.2019.06.013

  29. Magnotti, G.M. and Genzale, C.L., Detailed Assessment of Diesel Spray Atomization Models Using Visible and X-Ray Extinction Measurements, Int. J. Multiphase Flows, vol. 97, pp. 33-45, 2017. DOI: 10.1016/j. ij multiphaseflow.2017.08.002.

  30. Mayer, W., Tellar, J., Branam, R., Schneider, G., and Hussong, J., Raman Measurement of Cryogenic Injection at Supercritical Pressure, Heat Mass Transf., vol. 39, pp. 709-719,2003. DOI: 10.1007/s00231-002-0315-x. DOI: 10.1007/s00231-002-0315-x

  31. Oschwald, M., Smith, J.J., Branam, R., Hussong, J., Schik, A., Chehroudi, B., and Talley, D., Injection of Fluids into Supercritical Environments, Combust. Sci. Technol., vol. 178, nos. 1-3, pp. 49-100, 2006. DOI: 10.1080/00102200500292464. DOI: 10.1080/00102200500292464

  32. Peng, D.Y. and Robinson, D.P., A New Two-Constant Equation of State, Ind. Eng. Chem. Fund, vol. 15, no. 1,pp. 59-64,1976. DOI: 10.1026/l160057a011. DOI: 10.1026/l160057a011

  33. Ries, F., Obando, P., Shevchuck, I., Janicka, J., and Sadiki, A., Numerical Analysis of Turbulent Flow Dynamics and Heat Transport in a Round Jet at Supercritical Conditions, Int. J. Heat Fluid Flow, vol. 66, pp. 172-184,2017. DOI: 10.1016/j.ijheatfluidflow.2017.06.007. DOI: 10.1016/j.ijheatfluidflow.2017.06.007

  34. Rutland, C.J., Large-Eddy Simulations for Internal Combustion Engines-A Review, Int. J. Engine Res, vol. 12, no. 5, pp. 421-451,2011. DOI: 10.1177/1468087411407248. DOI: 10.1177/1468087411407248

  35. Sierra-Pallares, J., Garcia del Valle, J., Garcia-Carrascal, P., and Castro Ruiz, F., Numerical Study of Supercritical and Transcritical Injection Using Different Turbulent Prandtl Numbers: A Second Law Analysis, J Supercrit. Fluid, vol. 115, pp. 86-98,2016. DOI: 10.1016/j.supflu.2016.05.001. DOI: 10.1016/j.supflu.2016.05.001

  36. Span, R., Lemmon, E.W., Jacobsen, R.T., Wagner, W., and Yokozeki, A., A Reference Equation of State for the Thermodynamic Properties ofNitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa, J Phys. Chem. Ref. Data, vol. 29, no. 6, pp. 1361-1433,2000. DOI: 10.1063/1.1349047. DOI: 10.1063/1.1349047

  37. Sweby, P.K., High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws, SIAM J. Numer. Anal., vol. 21, no. 5, pp. 995-1011,1984. DOI: 10.1137/0721062. DOI: 10.1137/0721062

  38. Vargaftik, N.B., Tables on the Thermophysical Properties of Liquids and Gases, 2nd ed., New York: Halsted Press, 1975. DOI: 10.1002/aic.690210636. DOI: 10.1002/aic.690210636

  39. Zong, N. and Yang, V., Cryogenic Fluid Jets and Mixing Layers in Transcritical and Supercritical Environments, Combust. Sci. Technol, vol. 178, pp. 193-227,2006. DOI: 10.1080/00102200500287613. DOI: 10.1080/00102200500287613

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