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4.8. Observations and Recommendations

Based on the previous discussion, the following conclusions can be drawn:

  1. The Homogeneous-Equilibrium Model (HEM) underpredicts the critical flow rates for short pipes and near liquid saturation or subcooled upstream conditions.
  2. The equilibrium slip models of Fauske, Moody and others, although successful for long tubes, underpredict the critical flow rates for short pipes. This is particularly true if the upstream condition is subcooled or near saturation.
  3. Effects of thermal nonequilibrium must be taken into account for short pipes. However, it is not clear whether the pipe length, L, or the pipe length-to-diameter ratio, L/D, or both are important in determining the effects of thermal nonequilibrium.
  4. More mechanistic models do exist for critical flow that can account for the nonequilibrium effects of velocity differences and temperature differences between the phases; but require iterative or numerical solution.
  5. At present, there is no general model or correlation for critical flow which is valid for a broad range of pipe lengths, pipe diameters, and upstream conditions including subcooled liquid. The more sophisticated the model used for a more precise design, the more prudent it is to consider some data benchmarking under similar conditions.

References

  1. J. Keenan, Thermodynamics, J. Wiley and Sons, Inc., New York (1941).
  2. E. Obert, R. Gaggioli, Thermodynamics, McGraw Hill, New York (1960).
  3. A.H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1, Chap. 4, Ronald Press, New York (1953).
  4. R.E. Henry, H.K. Fauske, "The Two-Phase Critical Flow of One-Component Mixtures in Nozzles, Orifices, and Short Tubes," Jnl. Heat Transfer, p 179 (May 1971).
  5. D.J. Maneely, "A Study of the Expansion Process of Low Quality Steam Through a deLaval Nozzle," LICRL-6/30, Univ of CA (1962).
  6. K.F. Neusen, "Optimizing the Flow Parameters for the Expansion of Low Quality Steam," UCRL-6152, University of CA (1962).
  7. M.E. Deich et al., "Investigation of Flow of Wet Steam in deLaval Nozzles," High Temperature, V7, p 294 (1966).
  8. H.K. Fauske "Contribution to the Theory of Two-Phase One-Component Critical Flow," ANL-6633, Argonne Nat Lab (1961).
  9. H.K. Fauske, "The Discharge of Saturated Water Through Tubes," Chem Engr Prog Symp Ser, V61, p 210 (1965).
  10. F.J. Moody, "Maximum Flow Rate of a Single Component Two-Phase Mixture," Jnl Heat Transfer, Tran ASME Series C, V87, No 1, p 134 (Feb 1965).
  11. M.M. Bolstad, R.C. Jordan, "Theory and Use of the Capillary Tube Expansion Device," Jnl. of ASRE, Vol 6, p 518 (1948).
  12. H.K. Fauske, "Two Phase Critical Flow with Application to Liquid-Metal Systems (Mercury, Cesium, Rubidium, Potassium, Sodium, and Lithium, ANL 6779 (October 1963).
  13. R.V. Smith, "Choking Two-Phase Flow Literature Summary and Idealized Design Solutions for Hydrogen, Nitrogen, Oxygen and Refrigerants 12 and 11," NBS Tech. Note 179, Supt. of Documents, Washington, D.C., U.S. Government Printing Office (1967).
  14. R.E. Henry, M.A. Grolmes, H.K. Fauske, "Pressure-Pulse Propagation in Two-Phase One and Two-Component Mixtures," ANL 7792 (March 1971).
  15. F.R. Zaloudek, "The Low Pressure Critical Discharge of Steam-Water Mixtures from Pipes," Report HW-68934, Rev. General Electric Co. (1961).
  16. R.E. Henry, "A Study of One and Two-Component Two-Phase Critical Flows at Low Qualities," ANL 7430 (March 1968).
  17. P. Griffith, "MIT Critical Two-Phase Notes," Cambridge, MA (1976).
  18. P. Saha, "A Review of Two-Phase Steam-Water Critical Flow Models with Emphasis on Thermal Non-Equilibrium," NUREQ/CR-0417, Brookhaven Nat Lab (Sept 1978).
  19. R.R. Schultz, et al., "Marvihen Critical Flow Data: A Summary of Results and Code Assessment Applications," Nuclear Safety, V25, No 6 (Dec 1984).
  20. J.A. Boure, et al., "Highlights of Two-Phase Critical Flow," Int'l Jnl Multiphase Flow, V3 pp 1-22 (1978).
  21. M.N. Hutcherson, Numerical Evaluation of the Henry-Fauske Critical Flow Model, MDC-N9654-100, McDonnell Douglas Co, (July 1980).
  22. V.K. Ransom, et al., RELAP5/MOD2 Code Manual, NUREG/CR-5273, EGG-2555 (1987).
  23. M. Reocreux, "Contribution a l'etude des debits critiques en ecculement disphasique eau-vapeur," doctoral thesis, L'Univ. Scientifique et Medicale de Grenoble (1974) . Also: Contribution to the Study of Critical Flow Rates in Two-Phase Water Vapor Flow," NUREG-Tr-0002 (1977).
  24. M. Giot and A. Fritte, "Modeling in Critical Flow," Proc. of the NATO Advanced Research Workshop on the Advances in Two-Phase Flow and Heat Transfer, Spitzingsee, FRG, 31 Aug.-3 Sept. (1982). M. Giot and D. Meunier "Methodes de Determination du Debit Critique en Ecoulements Monophasiques et Diphasiques a un Consituant," Energie Primaire, 4, No. 102, 23 (1968).
  25. M. Reocreux, "Experimental Study of Steam-Water Choked Flow," in Transient Two-Phase Flow - Proceedings of the CSNI Specialists Meeting, August 1976, Atomic Energy of Canada, 2, 637-6669. (1977)
  26. J. Boure, A.A. Fritte, M. Giot and M.L. Rocreux, "Highlights of Two-Phase Critical Flow: On the Links Between Maximum Flow Rates, Sonic Velocities, Propagation and Transfer Phenomena in Single and Two-Phase Flows," Int. J. Multiphase Flow, 3, 1-22.
  27. C.W. Hirt and N.c. Romero, "Application of a Drift-Flux Model to Flashing in Straights Pipes," 1st CSNI Spec. Meet. on Transient Two-Phase Flow, Toronto, (1976).
  28. D. Durack and B. Wendroff, "Relaxation and Choked Two-Phase Flow," 2nd CSNI Spec. Meeting on Transient Two-Phase Flow, Paris, France, (1978).
  29. G. Yadigaroglu and M. Andreani, "Two-Fluid Modeling of Thermal-Hydraulic Phenomena for Best-Estimate LWR Safety Analysis," pp. 980-996 in NURETH-4, Proceedings Fourth Int. Topical Meeting on Nuclear Reactor Thermal-Hydraulics, Karlsruhe, 10-13 Oct. 1989, U. Mueller, K. Rehme and K. Rust (editors), G. Braun, Karlsruhe.
  30. A. Forge, R. Pochard, A. Porracchia, J. Miro, H.G. Sonnenburg, F. Steinhoss and V. Teschendorff, Comparison of Thermal-Hydraulic Safety Codes for PWR Systems, Graham and Trotman eds, (1988).


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