Numerical Analysis of Laminar Reflux Condensation from Gas-Vapour Mixtures in Vertical Parallel Plate Channels

Authors: Foad Hassaninejadafarahani, Scott Ormiston

Abstract:

Reflux condensation occurs in vertical channels and tubes when there is an upward core flow of vapour (or gas-vapour mixture) and a downward flow of the liquid film. The understanding of this condensation configuration is crucial in the design of reflux condensers, distillation columns, and in loss-of-coolant safety analyses in nuclear power plant steam generators. The unique feature of this flow is the upward flow of the vapour-gas mixture (or pure vapour) that retards the liquid flow via shear at the liquid-mixture interface. The present model solves the full, elliptic governing equations in both the film and the gas-vapour core flow. The computational mesh is non-orthogonal and adapts dynamically the phase interface, thus produces a sharp and accurate interface. Shear forces and heat and mass transfer at the interface are accounted for fundamentally. This modeling is a big step ahead of current capabilities by removing the limitations of previous reflux condensation models which inherently cannot account for the detailed local balances of shear, mass, and heat transfer at the interface. Discretisation has been done based on finite volume method and co-located variable storage scheme. An in-house computer code was developed to implement the numerical solution scheme. Detailed results are presented for laminar reflux condensation from steam-air mixtures flowing in vertical parallel plate channels. The results include velocity and gas mass fraction profiles, as well as axial variations of film thickness.

Keywords: Reflux Condensation, Heat Transfer, Channel, Laminar Flow

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100843

References:

[1] J. Palen and Z. Yang, “Reflux condensation flooding prediction: Review of current status,” Chemical Engineering Research and Design, vol. 79, no. A4, pp. 463–469, May 2001.
[2] Y. Moon, H. Park, Y. Bang, U. N. R. C. O. of Nuclear Regulatory Research, H. Kisurwon, H. Y ˘ onoguso, and H. Kisurw ˘ on, ˘ Assessment of RELAP5/MOD3. 2 for Reflux Condensation Experiment. Office of Nuclear Regulatory Research, US Nuclear Regulatory Commission, 2000.
[3] Y. Utanohara and M. Murase, “Numerical analysis of steam-air behavior in a pressurizer during reflux cooling,” Nucl. Eng. Des., vol. 240, no. 12, pp. 3930–3941, Dec. 2010.
[4] S. Chen, J. Reed, and C. Tien, “Reflux condensation in a two-phase closed thermosyphon,” International Journal of Heat and Mass Transfer, vol. 27, no. 9, pp. 1587 – 1594, 1984. (Online). Available: http://www.sciencedirect.com/science/article/pii/0017931084902710
[5] R. Seban and J. Hodgson, “Laminar film condensation in a tube with upward vapor flow,” International Journal of Heat and Mass Transfer, vol. 25, no. 9, pp. 1291 – 1300, 1982. (Online). Available: http://www.sciencedirect.com/science/article/pii/0017931082901235
[6] R. Girard and J. S. Chang, “Reflux condensation phenomena in single vertical tubes,” Int. J. Heat Mass Trans., vol. 35, no. 9, pp. 2203–2218, 1992.
[7] G. Chou and J. Chen, “Heat transfer characteristics of reflux condensation phenomena in a single vertical tube,” Nucl. Sci. Eng., vol. 127, no. 2, pp. 220–229, Oct. 1997.
[8] ——, “A general modeling for heat transfer during reflux condensation inside vertical tubes surrounded by isothermal fluid,” International Journal of Heat and Mass Transfer, vol. 42, no. 12, pp. 2299–2311, June 1999.
[9] Y. Pan, “Condensation characteristics inside a vertical tube considering the presence of mass transfer, vapor velocity and interfacial shear,” International Journal of Heat and Mass Transfer, vol. 44, no. 23, pp. 4475 – 4482, 2001. (Online). Available: http://www.sciencedirect.com/science/article/pii/S0017931001000874
[10] S. Fiedler and H. Auracher, “Experimental and theoretical investigation of reflux condensation in an inclinded small diameter tube,” Int. J. Heat Mass Trans., vol. 47, pp. 4031–4034, 2004.
[11] Y. Liao, S. Guentay, D. Suckow, and A. Dehbi, “Reflux condensation of flowing vapor and non-condensable gases counter-current to laminar liquid film in a vertical tube,” Nucl. Eng. Des., vol. 239, no. 11, pp. 2409–2416, Nov. 2009.
[12] V. K. Liao, Y., “A generalized diffusion layer model for condensation of vapor with noncondensable gases,” ASME Journal of Heat Transfer 129, 988-994, 2007.
[13] F. Hassaninejadfarahani, M. Guyot, and S. Ormiston, “Numerical analysis of mixed-convection laminar film condensation from high air mass fraction steamair mixtures in vertical tubes,” International Journal of Heat and Mass Transfer, vol. 78, pp. 170 – 180, 2014. (Online). Available: http://www.sciencedirect.com/science/article/pii/S0017931014005195
[14] Y. Q. Wang, L. A. Penner, and S. J. Ormiston, “Analysis of laminar forced convection of air for crossflow in banks of staggered tubes,” Numerical Heat Transfer, Part A (Applications), vol. 38, no. 8, pp. 819–845, 2000.
[15] S. V. Patankar, Numerical Heat Transfer and Fluid Flow. Washington: Hemisphere, 1980.
[16] C. M. Rhie and W. L. Chow, “Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation,” AIAA J., vol. 21, no. 11, pp. 1525–1532, 1983.
[17] B. Yu, Y. Kawaguchi, W. Tao, and H. Ozoe, “Checkerboard pressure predictions due to the underrelaxation factor and time step size for a nonstaggered grid with momentum interpolation method,” vol. 41, no. 1, pp. 85–94, 2002.
[18] S. Vakilipour and S. Ormiston, “A coupled pressure-based co-located finite-volume solution method for natural-convection flows,” Numerical Heat Transfer, Part B (Fundamentals), vol. 61, pp. 91–115, 2012.
[19] F. Hassaninejadfarahani and S. Ormiston, “Fully coupled elliptic numerical model for film condensation from vapour-gas mixtures in vertical parallel plate channels,” in Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, vol. 8A, Montreal, Canada, 2014.
[20] S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, K. Rupp, B. F. Smith, and H. Zhang, “PETSc users manual,” Argonne National Laboratory, Tech. Rep. ANL-95/11 - Revision 3.5, 2014. (Online). Available: http://www.mcs.anl.gov/petsc