THERMAL SCIENCE

International Scientific Journal

ANALYTICAL AND SEMI-ANALYTICAL MODELS OF CONDUCTION CONTROLLED REWETTING: A STATE OF THE ART REVIEW

ABSTRACT
The phenomenon of rewetting finds application in several fields of industrial and scientific applications including the loss of coolant accidents (LOCA) in nuclear reactors. In order to analyze the phenomena of rewetting, usually a conduction controlled approach or hydrodynamic approach was considered. Because of complexity, most of the studies adopt a conduction controlled approach to analyze the phenomena of rewetting. In view of this, various analytical and semi-analytical techniques have been used to solve the conduction equation. Investigations have mostly considered different geometries, various convective boundary conditions for both the dry and wet surface, effect of heat generation, variable properties, coupling between conduction and convection as well as other variations of the problem. A comprehensive review of the available analytical modelsis presented in this paper.
KEYWORDS
PAPER SUBMITTED: 2012-12-31
PAPER REVISED: 2013-08-20
PAPER ACCEPTED: 2013-09-06
PUBLISHED ONLINE: 2013-09-22
DOI REFERENCE: https://doi.org/10.2298/TSCI121231125S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Issue 5, PAGES [1479 - 1496]
REFERENCES
  1. Groeneveld, D. C., Snoek, C. W., A Comprehensive Examination Heat Transfer Correlations Suitable for Reactor Safety Analysis, in: Multiphase Science and Technology, 2, (Ed. G.F. Hewitt, J.M. Delhaye and N. Zuber), Hemisphere, Washington, USA, 1986, pp. 181-271
  2. Duffey, R. B., Porthouse, D. T. C., Experiments On the Cooling of High Temperature Surfaces by Water Jets and Drops, Report No. RD/B/N2386, Berkeley Nuclear Laboratories, USA, 1972
  3. Butterworth, G., Owen, R. G., The Quenching of Hot Surfaces by Top and Bottom Flooding- A Review, Report No. AERE-R 7992, AERE Harwell, Oxfordshire, England, 1975
  4. Sawan, M. E., Carbon, M. W., A Review of Spray Cooling and Bottom Flooding Works for LWR Cores, Nuclear Engineering and Design, 32 (1975), 2, pp. 191-207
  5. Elias, E., Yadigaroglu, G., TheReflooding Phase of LOCA in PWRs, Part II: Rewetting and Liquid Entrainment, Nuclear Safety, 19 (1978), 2, pp. 160-175
  6. Aksan, S. N., A Review of Large Break Loss-Of-Coolant Accident Slowdown Quench and Effect of External Thermocouples, The 3rd Int. Code Assessment and Application Program (ICAP) Specialist Meeting, Grenoble, France, 1988
  7. Carbajo, J. J., Seigel, A. D., Review and Comparison among the Different Models for Rewetting in LWRs, Nuclear Engineering and Design, 58 (1980), 1, pp. 33-44
  8. Olivery, E., Castiglia, F., Tabi, S., Vella, G., Predicting Quench Front Velocity in the Rewetting of Hot Surfaces, Encyclopedia of Fluid Mechanics, Gulf Publishing Company, Texas, USA, 1986 pp.1339-1355
  9. Olek, S., Analytical Models for Rewetting of Hot Surfaces, Technical Report No. CH 5303, Paul Scherrer Institute, Wurenhingen, Switzerland, 1989
  10. Satapathy, A. K., A Comprehensive Review of Conduction Controlled Rewetting: Theoretical Models and Analyses, Int. J. Nuclear Energy Science and Technology, 5 (2010), 2, pp. 171-188
  11. Semeria, R., Martinet, B., Calcification Spots On a Heating Wall: Temperature Distribution and Resorption, Proceedings, Institute of Mechanical Engineers, London, 180, 1965, pp.192-205
  12. Yamanouchi, A., Effect of Core Spray Cooling in Transient State after Loss of Coolant Accident, J. Nucl. Sci. Tech.,5(1968), 11, pp. 547-558
  13. Duffey, R. B., Porthouse, D.T.C., The Physics of Rewetting in Water Reactor Emergency Core Cooling, Nuclear Engineering and Design, 25 (1973), 3, pp.379-394
  14. Thompson, T. S., Rewetting of a Hot Surface, Proceedings, 5th International Heat Transfer Conference, Japan, 1974
  15. Piggot, B. D. G., Porthouse, D. T. C., A Correlation of Rewetting Data, Nuclear Engineering and Design, 32 (1975), 2, pp.171-181
  16. Tien, C. L., Yao, L. S., Analysis of conduction-controlled rewetting of a vertical surface, ASME J. Heat Transfer, 97(1975), 2, pp. 161-165
  17. Coney, M. W. E., Calculations on the Rewetting of Hot Surfaces, Nuclear Engineering and Design31(1974), 2, pp. 246-259
  18. Olek, S., On the Two Region Rewetting Model with a Step Change in the Heat Transfer Coefficient, Nuclear Engineering and Design, 108 (1988), 3, pp. 315-322
  19. Castiglia, F., Oliveri, E., Taibi, S., Vella, G., Procedure for Correlating Experimental and Theoretical Results in the Rewetting of Hot Surfaces, Heat and Technology, 5 (1987), pp.82-99
  20. Blair, J. M., An Analytical Solution to a Two-Dimensional Model of the Rewetting of a Hot Dry Rod, Nuclear Engineering and Design, 32(1975), 2, pp. 159-170
  21. Yeh, H. C., An Analysis of Rewetting of a Nuclear Fuel Rod in Water Reactor Emergency Core Cooling, Nuclear Engineering and Design, 34(1975), 3, pp. 317-322
  22. Caflisch, R. E., Keller, J. B., Quench Front Propagation, Nuclear Engineering and Design, 65 (1981), 1, pp. 97-102
  23. Levine, H., On a Mixed Boundary Value Problem of Diffusion Type, Applied Scientific Research, 39 (1982), 4, pp. 261-276
  24. Bera, R. K., Chakrabarti, A., Cooling of an Infinite Slab in a Two Fluid Medium, Journal ofAustralian Mathematical Society, 33 (1992), 4, pp. 474-485
  25. Thomas, R. M., Methods for Calculating the Conduction Controlled Rewetting of Cladded Rod, Nuclear Engineering and Design, 110(1988), 1, pp.1-16
  26. Olek, S., Solution to a Fuel and Cladding Rewetting Model, Int. Comm. Heat and Mass Transfer,16 (1989), 1, pp. 143-158
  27. Sahu, S. K., Das, P. K., Bhattacharyya, S., A Comprehensive Analysis of Conduction-Controlled Rewetting by the Heat Balance Integral Method, Int. J. Heat Mass Transfer, 49 (2006), 25-26, pp. 4978-4986
  28. Sahu, S. K., Das, P. K., Bhattacharyya, S., How Good is Goodman's Heat Balance Integral Method for Solving the Rewetting of Hot Surfaces, Thermal Science, 13 (2009), 2, pp. 97-112
  29. Dwyer, H. A., Kee, R. J., Sanders, B. R., Adaptive Methods for Problems in Fluid Mechanics and Heat Transfer, AIAA Journal, 18 (1980), 10, pp.1205-1212
  30. Zhu, J. Z., Zienkiewicz, O. C., Adaptivity and Mess Generation, International Journal for Numerical Methods in Engineering, 32 (1991), 4, pp. 783-810
  31. Miller, K., Miller, R. N., Moving Finite Elements, SIAM Journal of Numerical Analysis,18 (1981), 6, pp. 1019-1030
  32. Nakamura, S., Marching Grid Generation Using Parabolic Partial Differential Equations, In: Numerical Grid Generation (Ed. J.F. Thompson), New York, 1982, pp. 775
  33. Thompson, T. S., An Analysis of the Wet-Side Heat Transfer Coefficient During Rewetting of a Hot Dry Patch, Nuclear Engineering and Design, 22(1972), 2, pp. 212-224
  34. Elias, E., Yadigaroglu, G., A General One Dimensional-Model for Conduction-Controlled Rewetting of a Surface, Nuclear Engineering and Design, 42 (1977), 2, pp. 185-194
  35. Anderson, J.G.M., Hensen, P., Two-Dimensional Heat Conduction in Rewetting Phenomena, Report No. NORHAV-D-6, AEC Research Establishment, Riso, Denmark, 1974
  36. Thompson, T. S., On the Process of Rewetting of Hot Surface by a Falling Liquid Film, Nuclear Engineering and Design, 31 (1974), 2, pp. 234-245
  37. Pearson, D. K., Piggot, B. D. G., Duffey, R. B., The Effect of Thermal Diffusion from Fuel Pallets on Rewetting of Over Heated Water Reactor Pins, Nuclear Engineering and Design, 41 (1977), 2, pp. 165-173
  38. Gurcak, A.W., Spencer, A. C., Porsching, T. A., Implicit Isotherm Migration: A Numerical Method for the Two Dimensional Quench Front Problem, Nuclear Engineering and Design, 61 (1980), 1, pp. 25-31
  39. Yu, S. K.W., Farmer, P. R., Coney, M. W. E., Methods and Correlations for the Prediction of Quenching Rates on Hot Surface, Int. J. Multiphase Flow, 3 (1977), 5, pp. 415-443
  40. Shires, G. L., Pickering, A. R., Blacker, P. T., Film Cooling of Vertical Fuel Rods, Report No. AEEW-R343, United Kingdom Atomic Energy Authority, UK, 1964, pp. 22
  41. Hsu, C. H., Chieng, C. H., Hua, T., Two-Dimensional Analysis of Conduction Controlled Rewetting with Internal Heat Generation, Proceedings, 4th International Conference on Numerical Methods in Engineering, Montreal, Canada, 1983
  42. Salcuden, M., Bui, T. M., Heat Transfer during Rewetting of Hot Horizontal Channels, Nuclear Engineering and Design, 108(1988), 2, pp.323-330
  43. Sun, K. H., Dix, G. E., Tien, C. L., Effect of Precursory Cooling on Falling-Film Rewetting, ASME J. Heat Transfer, 97(1974), 3, pp. 360-365
  44. Simopoulos, S. E., The Effect of Precursory Cooling on the Rewetting Rate, Atomkernenergie-Kerntechnik, 49 (1986), 1-2, pp. 37-42
  45. Dua, S. S., Tien, C. L., Two Dimensional Analysis of Conduction-Controlled Rewetting with Precursory Cooling, ASME J. Heat Transfer,98(1976), 3, pp. 407- 413
  46. Olek, S., The Effect of Precursory Cooling on Rewetting of Slab, Nuclear Engineering and Design, 108 (1988), 3, pp. 323-330
  47. Olek, S., Wiener-Hopf Technique Solution to a Rewetting Model with Precursory Cooling, Nuclear Science and Engineering, 105 (1990), 2, pp. 271-277
  48. Edwards, A. R., Mather, D. J., Some UK Studies Related to the Loss of CoolantAccident, Proceedings, Topical Meeting on Water Reactor Safety, Utah, USA, 1973, pp. 720-737
  49. Sawan, M., Temraz, H., A Three-Region Semi-Analytical Rewetting Model, Nuclear Engineering and Design, 64(1981), 3, pp. 319-327
  50. Olek, S., Rewetting of a Solid Cylinder with Precursory Cooling, Applied Scientific Research, 46 (1989), 4, pp. 347-364
  51. Sahu, S. K., Das, P. K., Bhattacharyya, S., Rewetting Analysis of Hot Vertical Surfaces with Precursory Cooling by the Heat Balance Integral Method, ASME J. Heat Transfer, 30 (2008), 3, pp. 024504
  52. Peng, X. F., Peterson, G. P., Analysis of Rewetting for Surface Tension Induced Flow, ASME J. Heat Transfer, 114 (1992), 3, pp. 703-707
  53. Yao, L. S., Rewetting of a Vertical Surface with Internal Heat Generation, AIChE Symposium Series: Solar and Nuclear Heat Transfer, 73 (1976), 164, pp. 46-50
  54. Sawan, M., Zaki, G., Temraz, H., Analysis of Rewetting of Hot Cladding Surfaces with Heat Generation, Arab Journal of Nuclear Science and Applications, 11 (1978), 2, pp. 237-259
  55. Duffey, R. B., Hughes, E. D., Dry Out Stability and Inception at Low Flow Rates, Int. J. Heat Mass Transfer, 34 (1991), 2, pp. 473-481
  56. Chan, S. H., Zhang, W., Rewetting Theory and the Dryout Heat Flux of Smooth and Grooved Plates with Uniform Heating, ASME J. Heat Transfer, 116 (1994), 1, pp. 173-179
  57. Rosenthal, D., The Theory of Moving Sources of Heat and its Application to Metal Treatments, Transactions of the ASME, 68 (1946), 11, pp. 849-866
  58. Carslaw, H. S., Jaeger, J. C., Conduction of Heat in Solids, 2nd edition, Oxford University Press, London, 1959, pp. 87-88
  59. Platt, J. A., An Analytical Investigation of Transient Effects on Rewetting of Heated Thin Plates, Report No. NASA-TM-106120, ASME Winter Annual Meeting, New Orleans, USA, 1993, pp. 145-153
  60. Peterson, G. P., Lu, X. J., Peng, X. F., Wang, B. X., Analytical and Experimental Investigation of Rewetting of Circular Channels with Internal V Grooves, Int. J. Heat Mass Transfer, 35 (1992), 11, pp. 3085-3094
  61. Stores, G., Fricker, D., Issacci, F., Cotton, I., Heat Flux Induced Dry Out and Rewetting Thin Films, Proceedings, 9th International Heat Transfer Conference, Jerusalem, Israel, 1990, pp. 359-464
  62. Satapathy, A. K., Sahoo, R. K., Rewetting of an Infinite Slab with Uniform Heating Under Quasi-Steady Conditions, ASME J. Heat Transfer, 124(2002), 5, pp. 875-880
  63. Satapathy, A. K., Sahoo, R. K., Rewetting of an Infinite Tube with a Uniform Heating, Heat and Mass Transfer, 38 (2002), 7-8, pp. 589-595
  64. Satapathy, A. K., Kar, P. K., Rewetting of an Infinite Slab with Boundary Heat Flux, Numerical Heat Transfer, Part A,37(2000), 1, pp. 87-99
  65. Sahu, S. K., Das, P. K., Bhattacharyya, S., Rewetting Analysis of Hot Surfaces with Internal Heat Source by the Internal Heat Balance Integral Method, Heat and Mass Transfer, 44(2008), 10, pp. 1247-1256
  66. Sun, K. H., Dix, G. E., Tien, C. L., Cooling of a Very Hot Vertical Surface by Falling Liquid Film, ASME J. Heat Transfer, 96(1974), 2, pp. 126-131
  67. Ishii, M., Study on Emergency Core Cooling, J. British Nuclear Energy Society, 14 (1975), pp. 237-242
  68. Sawan, M., Zaki, G., Temraz, H., A Three-Regions Rewetting Model with Heat Generation and Sub-Cooling, Atomkernenergie, 34 (1979), 1, pp. 199-204
  69. Bonakdar, H., McAssey, Jr. E. V., A Method for Determining Rewetting Velocity Under Generalized Boiling Conditions, Nuclear Engineering and Design, 66(1981), 1, pp. 7-12
  70. Bera, R. K., Chakrabarti, A., The Sputtering Temperature of a Cooling Cylindrical Rod Without and with an Insulated Core in a Two-Fluid Medium, Journal of Australian Mathematical Society, Series B, 38 (1996), 1, pp. 87-100
  71. Sahu, S. K., Das, P. K., Bhattacharyya, S., A Three-Region Conduction-Controlled Rewetting Analysis by the Heat Balance Integral Method, International Journal of Thermal Sciences,48 (2009), 11, pp. 2100-2107
  72. Olek, S., Zvirin, Y., The Effect of Temperature Dependent Properties on the Rewetting Velocity, Int. J. Multiphase Flow, 11(1985), 4, pp. 577-581
  73. Olek, S., Zvirin, Y., Elias, E., Rewetting of Hot Surfaces by Falling Liquid Films as a Conjugate Heat Transfer Problem, Int. J. Multiphase Flow, 14(1988), 1, pp. 13-33
  74. Peng, X. F., Peterson, G. P, Wang, B. X., The Effect of Plate Temperature on the Onset of Wetting, Int. J. Heat Transfer, 35 (1992), 3, pp. 1605-1614
  75. Dorfman, A., Transient Heat Transfer Between a Semi Infinite Hot Plate and a Flowing Cooling Liquid Film, ASME J. Heat Transfer, 126(2004), 2, pp. 149-154
  76. Horvay, G., Temperature Distribution in a Slab Moving from a Chamber at one Temperature to a Chamber at another Temperature, ASME J. Heat Transfer, 83 (1961), 4, pp. 391-402
  77. Yao, L. S., Tien, C. L., Berger, S. A., Thermal Analysis of a Fast Moving Slab in Two Adjacent Temperature Chambers, ASME J. Heat transfer, 98 (1976), 2, pp. 326-329
  78. Dua, S. S., Tien, C. L., A Generalized Two-Parameter Relationship for Conduction Controlled Rewetting of Hot Vertical Surface, Int. J. Heat Mass Transfer,20 (1977), 2, pp. 174-176
  79. Olivery, E., Castiglia, F., Tabi, S., Vella, G., A Correlation for Quench Front Velocity in the Rewetting of a Rod by a Falling Film, Int. J. Heat Mass Transfer,25 (1982),10, pp. 1589-1593
  80. Castiglia, F., Oliveri, E., Taibi, S., Vella, G., A Correlation for Quench Front Velocity in the Rewetting of a Rod by a Falling Film, Int. J. Heat and Technology,7 (1989), pp. 21-28
  81. Castiglia, F., Oliveri E., Taibi S., Vella G., On the Precursory Cooling in the Rewetting Phenomena, Proceedings, International Conference on Multiphase Flows, Japan, 1991, pp. 271-274
  82. Davidy, A., Elias, E., Olek, S., Quenching of Hot Oxidizing Surfaces, Nuclear Engineering and Design, 204(2001), 1-3, pp. 361-368

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