Research Papers

A Physically Based, One-Dimensional Two-Fluid Model for Direct Contact Condensation of Steam Jets Submerged in Subcooled Water

[+] Author and Article Information
David Heinze

Mechanical Engineering,
Kernkraftwerk Gundremmingen GmbH,
Dr.-August-Weckesser-Str. 1, 89355 Gundremmingen, Germany
e-mail: david.heinze@partner.kit.edu

Thomas Schulenberg

Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology,
Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
e-mail: schulenberg@kit.edu

Lars Behnke

Mechanical Engineering,
Kernkraftwerk Gundremmingen GmbH,
Dr.-August-Weckesser-Str. 1, 89355 Gundremmingen, Germany
e-mail: lars.behnke@kkw.rwe.com

1Corresponding author.

Manuscript received June 12, 2014; final manuscript received December 17, 2014; published online March 24, 2015. Assoc. Editor: Milorad Dzodzo.

ASME J of Nuclear Rad Sci 1(2), 021002 (Mar 24, 2015) (8 pages) Paper No: NERS-14-1012; doi: 10.1115/1.4029417 History: Received June 12, 2014; Accepted December 17, 2014; Online March 24, 2015

A simulation model for the direct contact condensation of steam in subcooled water is presented that allows determination of major parameters of the process, such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin–Helmholtz and Rayleigh–Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations, which is solved by means of the explicit Runge–Kutta–Fehlberg algorithm. The simulation results are in good qualitative agreement with published experimental data over a wide range of pool temperatures and mass flow rates.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Cattadori, G., Galbiati, L., Mazzocchi, L., and Vanini, P., 1995, “A Single-Stage High Pressure Steam Injector for Next Generation Reactors: Test Results and Analysis,” Int. J. Multiphase Flow, 21(4), pp. 591–606. 10.1016/0301-9322(94)00086-Y
Deberne, N., Leone, J. F., and Lallemand, A., 2000, “Local Measurements in the Flow of a Steam Injector and Visualisation,” Int. J. Thermal Sci., 39(9–11), pp. 1056–1065. 10.1016/S1290-0729(00)01194-7
Dumaz, P., Geffraye, G., Kalitvianski, V., Verloo, E., Valisi, M., Méloni, P., Achilli, A., Schilling, R., Malacka, M., and Trela, M., 2005, “The DEEPSSI Project, Design, Testing and Modeling of Steam Injectors,” Nuclear Eng. Des., 235(2–4), pp. 233–251. 10.1016/j.nucengdes.2004.08.058
Chan, C., and Lee, C., 1982, “A Regime Map for Direct Contact Condensation,” Int. J. Multiphase Flow, 8(1), pp. 11–20. 10.1016/0301-9322(82)90003-9
Song, C. H., and Kim, Y. S., 2011, “Direct Contact Condensation of Steam Jet in a Pool,” Adv. Heat Transfer, 43, pp. 227–288. 10.1016/B978-0-12-381529-3.00003-7
Song, C. H., Cho, S., and Kang, H. S., 2012, “Steam Jet Condensation in a Pool: From Fundamental Understanding to Engineering Scale Analysis,” J. Heat Transfer, 134(3), pp. 031004–1–031004–15. 10.1115/1.4005144
Wu, X. Z., Yan, J. J., Li, W. J., Pan, D. D., and Liu, G. Y., 2010, “Experimental Investigation of Over-Expanded Supersonic Steam Jet Submerged in Quiescent Water,” Exp. Thermal Fluid Sci., 34(1), pp. 10–19. 10.1016/j.expthermflusci.2009.08.006
Dahikar, S. K., Sathe, M. J., and Joshi, J. B., 2010, “Investigation of Flow and Temperature Patterns in Direct Contact Condensation Using PIV, PLIF and CFD,” Chem. Eng. Sci., 65(16), pp. 4606–4620. 10.1016/j.ces.2010.05.004
Wu, X. Z., Yan, J. J., Li, W. J., Pan, D. D., and Liu, G. Y., 2010, “Experimental Study on a Steam-Driven Turbulent Jet in Subcooled Water,” Nucl. Eng. Des., 240(10), pp. 3259–3266. 10.1016/j.nucengdes.2010.06.007
Kim, H. Y., Bae, Y. Y., Song, C. H., Park, J. K., and Choi, S. M., 2001, “Experimental Study on Stable Steam Condensation in a Quenching Tank,” Int. J. Energy Res., 25(3), pp. 239–252. 10.1002/(ISSN)1099-114X
Wu, X. Z., Yan, J. J., Shao, S. F., Cao, Y., and Liu, J. P., 2007, “Experimental Study on the Condensation of Supersonic Steam Jet Submerged in Quiescent Subcooled Water: Steam Plume Shape and Heat Transfer,” Int. J. Multiphase Flow, 33(12), pp. 1296–1307. 10.1016/j.ijmultiphaseflow.2007.06.004
Gulawani, S. S., Joshi, J. B., Shah, M. S., RamaPrasad, C. S., and Shukla, D. S., 2006, “CFD Analysis of Flow Pattern and Heat Transfer in Direct Contact Steam Condensation,” Chem. Eng. Sci., 61(16), pp. 5204–5220. 10.1016/j.ces.2006.03.032
Kerney, P. J., Faeth, G. M., and Olson, D. R., 1972, “Penetration Characteristics of a Submerged Steam Jet,” AIChE J., 18(3), pp. 548–553. 10.1002/(ISSN)1547-5905
Weimer, J. C., Faeth, G. M., and Olson, D. R., 1973, “Penetration of Vapor Jets Submerged in Subcooled Liquids,” AIChE J., 19(3), pp. 552–558. 10.1002/(ISSN)1547-5905
Chun, M. H., Kim, Y. S., and Park, J. W., 1996, “An Investigation of Direct Condensation of Steam Jet in Subcooled Water,” Int. Commun. Heat Mass Transfer, 23(7), pp. 947–958. 10.1016/0735-1933(96)00077-2
Chen, L. D., and Faeth, G. M., 1982, “Condensation of Submerged Vapor Jets in Subcooled Liquids,” J Heat Transfer, 104(4), pp. 774–780. 10.1115/1.3245199
Gulawani, S. S., Deshpande, S. S., Joshi, J. B., Shah, M. S., Prasad, C. S. R., and Shukla, D. S., 2007, “Submerged Gas Jet Into a Liquid Bath: A Review,” Ind. Eng. Chem. Res., 46(10), pp. 3188–3218. 10.1021/ie0608511
Taylor, G. I., 1945, “Dynamics of a Mass of Hot Gas Rising in Air,” Los Alamos National Laboratory, Tech. Rep. LA-236.
Morton, B. R., Taylor, G., and Turner, J. S., 1956, “Turbulent Gravitational Convection From Maintained and Instantaneous Sources,” Proc. Roy. Soc. London A. Math. Phys. Sci., 234(1196), pp. 1–23. 10.1098/rspa.1956.0011
Ricou, F. P., and Spalding, D. B., 1961, “Measurements of Entrainment by Axisymmetrical Turbulent Jets,” J. Fluid Mech., 11(1), pp. 21–32. 10.1017/S0022112061000834
Fauske, H. K., and Grolmes, M. A., 1992, “Mitigation of Hazardous Emergency Release Source Terms Via Quench Tanks,” Plant/Oper. Prog., 11(2), pp. 121–125. 10.1002/(ISSN)1549-4632
Epstein, M., and Fauske, H., 2001, “Applications of the Turbulent Entrainment Assumption to Immiscible Gas-Liquid and Liquid–Liquid Systems,” Chem. Eng. Res. Des., 79(4), pp. 453–462. 10.1205/026387601750282382
Villermaux, E., 1998,“Mixing and Spray Formation in Coaxial Jets,” J. Propul. Power, 14(5), pp. 807–817. 10.2514/2.5344
Raynal, L., 1997, “Instabilité et entrainement à l’interface d’une couche de mélange liquide-gaz—Instability and Entrainment at the Interface of a Liquid-Gas Mixing Layer,” Ph.D. thesis, Université de Grenoble, Grenoble, France.
Weiland, C., and Vlachos, P. P., 2013, “Round Gas Jets Submerged in Water,” Int. J. Multiphase Flow, 48, pp. 46–57. 10.1016/j.ijmultiphaseflow.2012.08.002
Varga, C. M., Lasheras, J. C., and Hopfinger, E. J., 2003, “Initial Breakup of a Small-Diameter Liquid Jet by a High-Speed Gas Stream,” J. Fluid Mech., 497, pp. 405–434. 10.1017/S0022112003006724
Guildenbecher, D. R., López-Rivera, C., and Sojka, P. E., 2009, “Secondary Atomization,” Exp. Fluids, 46(3), pp. 371–402. 10.1007/s00348-008-0593-2
Wert, K. L., 1995, “A Rationally-Based Correlation of Mean Fragment Size for Drop Secondary Breakup,” Int. J. Multiphase Flow, 21(6), pp. 1063–1071. 10.1016/0301-9322(95)00036-W
Hsiang, L. P., and Faeth, G. M., 1992, “Near-Limit Drop Deformation and Secondary Breakup,” Int. J. Multiphase Flow, 18(5), pp. 635–652. 10.1016/0301-9322(92)90036-G
Ishii, M., and Kim, S., 2004, “Development of One-Group and Two-Group Interfacial Area Transport Equation,” Nucl. Sci. Eng., 146(3), pp. 257–273. [CrossRef]
Brucker, G. G., and Sparrow, E. M., 1977, “Direct Contact Condensation of Steam Bubbles in Water at High Pressure,” Int. J. Heat Mass Transfer, 20(4), pp. 371–381. 10.1016/0017-9310(77)90158-2
Weinberg, S., 1952, “Heat Transfer to Low Pressure Sprays of Water in a Steam Atmosphere,” Proc. Inst. Mech. Eng., London, 1(6), pp. 240–252.
Hughmark, G. A., 1967, “Mass and Heat Transfer From Rigid Spheres,” AIChE J., 13(6), pp. 1219–1221. 10.1002/(ISSN)1547-5905
Ishii, M., and Mishima, K., 1984, “Two-Fluid Model and Hydrodynamic Constitutive Relations,” Nucl. Eng. Des., 82(2–3), pp. 107–126. 10.1016/0029-5493(84)90207-3
Fehlberg, E., 1969, “Low-Order Classical Runge-Kutta Formulas With Stepsize Control and Their Application to Some Heat Transfer Problems,” National Aeronautics and Space Administration, Washington, DC, .
Gough, B., ed., 2009, GNU Scientific Library Reference Manual, 3rd revised ed., Network Theory Ltd., Bristol.
Loth, E., and Faeth, G. M., 1989, “Structure of Underexpanded Round Air Jets Submerged in Water,” Int. J. Multiphase Flow, 15(4), pp. 589–603. 10.1016/0301-9322(89)90055-4
Wagner, W., Cooper, J. R., Dittmann, A., Kijima, J., Kretzschmar, H.-J., Kruse, A., Mareš, R., Oguchi, K., Sato, H., Stöcker, I., Šifner, O., Takaishi, Y., Tanishita, I., Trübenbach, J., and Willkommen, T., 2000, “The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam,” J. Eng. Gas Turbine Power, 122(1), pp. 150–185. 10.1115/1.483186
Wu, X. Z., Yan, J. J., Li, W. J., Pan, D. D., and Chong, D. T., 2009, “Experimental Study on Sonic Steam Jet Condensation in Quiescent Subcooled Water,” Chem. Eng. Sci., 64(23), pp. 5002–5012. 10.1016/j.ces.2009.08.007
Heinze, D., Schulenberg, T., and Behnke, L., 2013, “Modeling of Steam Expansion in a Steam Injector by Means of the Classical Nucleation Theory,” Proceedings of the 15th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-15).


Grahic Jump Location
Fig. 1

Entrainment and atomization at a gas–liquid interface according to Varga et al. [26]. (1) Primary instability due to velocity shear, (2) secondary instability due to acceleration of wave crests, and (3) primary atomization

Grahic Jump Location
Fig. 2

The DCC flow model divides the two-phase jet into a dispersed droplet flow regime and a dispersed bubbly flow regime which are surrounded by the stagnant water

Grahic Jump Location
Fig. 4

Comparison of empirical correlations and of the present simulations results for the dimensionless penetration length Lcalc to experimental values Lexp. Experimental data from [7,10,11,39]

Grahic Jump Location
Fig. 5

Axial temperature profile: Experimental values [7] for different pool temperatures T∞ (dashed filled circles 20°C; dashed filled triangles 30°C; dashed filled squares 40°C; dashed filled diamonds 50°C) and respective simulation results for the mean temperature Tm in the two-phase region (thick solid lines) and the liquid temperature Tl (solid lines). The gas temperature Tg in the two-phase region is equal to the constant saturation temperature and is not shown

Grahic Jump Location
Fig. 6

Jet half radius r0.5 along the jet axis z for the condensation-induced liquid jet: Experimental values [9] for different pool temperatures T∞ (filled circles 20°C; filled triangles 50°C) and respective simulation results (solid lines)

Grahic Jump Location
Fig. 3

Dimensionless penetration length L for different pool temperatures T∞ and steam stagnation pressures p0: Comparison between experimental and calculated values. (a) Experimental data from Kim et al. [10] and (b) Experimental data from Wu et al. [11]



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In