Published 12 issues per year
ISSN Print: 1044-5110
ISSN Online: 1936-2684
Indexed in
NUMERICAL SIMULATION OF SUPERCRITICAL AND SUBCRITICAL INJECTION OF CRYOGENIC NITROGEN BASED ON THE HOMOGENEOUS EQUILIBRIUM MODEL OF TWO-PHASE FLOW
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
-
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
-
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
-
AVL FIRE, Computational Fluid Dynamics for Conventional and Alternative Powertrain Development, https://www.avl.com/fire (retrieved on April 20,2021).
-
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
-
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
-
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
-
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
-
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.
-
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
-
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).
-
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).
-
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
-
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
-
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
-
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
-
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.
-
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
-
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
-
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
-
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.
-
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.
-
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
-
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).
-
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
-
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.
-
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
-
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
-
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
-
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.
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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