Abstract
Molten fuel–coolant interactions in postulated severe accident scenario of nuclear reactors lead to the formation of a porous debris bed. Substantial heat generation takes place within such debris beds as a result of radioactive decay, and this needs to be continuously removed in order to maintain the temperature of the debris material within acceptable limits. This is achieved by boiling heat transfer using cooling water. Any failure in this regard can lead to re-melting of the material in an extreme situation and lead to further catastrophic consequences. In this context, it becomes imperative to have an assessment of the limit beyond which the debris cannot be maintained in a coolable condition. This limit is typically identified by the occurrence of dryout, i.e. water vapour accumulation within the debris bed. This chapter attempts to highlight the underlying mechanism and the pertinent factors contributing to dryout occurrence in typical debris beds. Various experimental studies and numerical modelling carried out in this regard are thoroughly reviewed. Augmentation of the dryout limit using available techniques is discussed in detail. A numerical model that has been developed for analysing multiphase flow and the associated heat and mass transfer in such porous debris beds are also presented in this chapter along with some salient results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- a i :
-
Interfacial area density, m−1
- c p :
-
Specific heat capacity, J/kg.K
- D p :
-
Particle diameter, m
- F :
-
Solid–fluid drag force, kg.m−2.s−2
- g :
-
Acceleration due to gravity, m/s2
- h :
-
Enthalpy, J/kg
- K :
-
Permeability, m2
- K r :
-
Relative permeability
- m :
-
Mass transfer rate, kg.s−1
- p :
-
Pressure, Pa
- q :
-
Volumetric heat transfer rate, W.m−3
- R :
-
Interfacial momentum exchange coefficient, kg.m−3.s−1
- T :
-
Temperature, K
- V :
-
Velocity, m.s−1
- α :
-
Volume fraction
- ɛ f :
-
Porosity
- η :
-
Passability, m
- η r :
-
Relative passability
- λ :
-
Thermal conductivity, W.m−1.K−1
- μ :
-
Viscosity, kg.m−1.s−1
- ρ :
-
Density, kg.m−3
- ψ :
-
Sphericity
- f :
-
Fluid phase
- i :
-
Liquid–vapour interface
- j :
-
Primary phase index
- k :
-
Dispersed phase index
- l :
-
Liquid phase
- LC :
-
Liquid continuous regime
- s :
-
Solid phase
- sat :
-
Saturation value
- v :
-
Vapour phase
- VC :
-
Vapour continuous regime
- ′′′:
-
Volumetric quantities
References
ANSYS Inc. (2012a) ANSYS FLUENT theory guide
ANSYS Inc. (2012b) ANSYS FLUENT UDF manual
Atkhen K, Berthoud G (2006) SILFIDE experiment: Coolability in a volumetrically heated debris bed. Nucl Eng Des 236:2126–2134
Bachrata A (2012) Modeling of core flooding in a highly degraded reactor. Ph.D. thesis, University of Toulouse, France
Bang KH, Kim JM (2010) Enhancement of dryout heat flux in a debris bed by forced coolant flow from below. Nucl Eng Tech 42(3):297–304
Baytaş AC (2003) Thermal non-equilibrium natural convection in a square enclosure filled with a heat-generating solid phase, non-darcy porous medium. Int J Energy Res 27:975–988
Beckermann C, Ramadhyani S, Viskanta R (1987) Natural convection flow and heat transfer between a fluid layer and a porous layer inside a rectangular enclosure. J Heat Transf 109:363–370
Berthoud G (2006) Models and validation of particulate debris coolability with the code MC3D-REPO. Nucl Eng Des 236:2135–2143
Bromley LA (1950) Heat transfer in stable film boiling. Chem Eng Prog 46:221–227
Bürger M, Buck M, Schmidt W, Widmann W (2006) Validation and application of the WABE code: investigations of constitutive laws and 2D effects on debris coolability. Nucl Eng Des 236:2164–2188
Cha JH, Chung MK (1986) Forced flow dryout heat flux in heat generating debris bed. J Korean Nuclear Soc 18(4):273–280
Chakravarty A, Datta P, Ghosh K, Sen S, Mukhopadhyay A (2016) Numerical analysis of a heat-generating, truncated conical porous bed in a fluid-filled enclosure. Energy 106:646–661
Chakravarty A, Datta P, Ghosh K, Sen S, Mukhopadhyay A (2017) Thermal non-equilibrium heat transfer and entropy generation due to natural convection in an enclosure with a truncated conical, heat-generating porous bed. Transp Porous Med 116:353–377
Chakravarty A, Datta P, Ghosh K, Sen S, Mukhopadhyay A (2018) Mixed convective heat transfer in an enclosure containing a heat-generating porous bed under the influence of bottom injection. Int J Heat Mass Transf 117:645–657
Fichot F, Duval F, Trégourès N, Béchaud C, Quintard M (2006) The impact of thermal non-equilibrium and large-scale 2D/3D effects on debris bed reflooding and coolability. Nucl Eng Des 236:2144–2163
Hidaka M, Ujita H (2001) Verification for flow analysis capability in the model of three-dimensional natural convection with simultaneous spreading, melting and solidification for the debris coolability analysis module in the severe accident analysis code ‘SAMPSON’. J Nucl Sci Technol 38(9):745–756
Hu K, Theofanous TG (1991) On the measurement of dryout in volumetrically heated coarse particle beds. Int J Multiph Flow 17:519–532
Huang Z, Ma W (2018) Validation and application of the MEWA code to analysis of debris bed coolability. Nucl Eng Des 327:22–37
Huhtiniemi I, Magallon D (2001) Insights into steam explosions with corium melts in KROTOS. Nucl Eng Des 204:391–400
Karbojian A, Ma WM, Kudinov P, Dinh T (2009) A scoping study of debris bed formation in the DEFOR test facility. Nucl Eng Des 239:1653–1659
Li L, Kong L, Zou X, Wang H (2015) Pressure drops of single/two-phase flows through porous beds with multi-sizes spheres and sands particles. Ann Nucl Energy 85:290–295
Li L, Zou X, Wang H, Zhang S, Wang K (2018) Investigations on two-phase flow resistances and its model modifications in a packed bed. Int J Multiphase Flow 101:24–34
Lin S, Cheng S, Jiang G, Pan Z, Lin H, Wang S, Wang l, Zhang X, Wang B (2017) A two-dimensional experimental investigation on debris bed formation behaviour. Prog Nucl En 96:118–132
Lindholm I, Holmström S, Miettinen J, Lestinen V, Hyvärinen J, Pankakoski P, Sjövall H (2006) Dryout heat flux experiments with deep heterogeneous particle bed. Nucl Eng Des 236:2060–2074
Lipinski RJ (1984) A coolability model for post-accident nuclear reactor debris. Nucl Technol 65:53–66
Ma WM, Dinh TN (2010) The effects of debris bed’s prototypical characteristics on corium coolability in a LWR severe accident. Nucl Eng Des 240:598–608
Magallon D (2006) Characteristics of corium debris bed generated in large-scale fuel-coolant interaction experiments. Nucl Eng Des 236:1998–2009
Mahapatra PS, Datta P, Chakravarty A, Ghosh K, Manna NK, Mukhopadhyay A, Sen S (2018) Molten drop to coolant heat transfer during premixing of fuel coolant interaction. In: Basu S, Agarwal A, Mukhopadhyay A, Patel C (eds) Applications paradigms of droplet and spray transport: paradigms and applications. Springer, Singapore, pp 201–235
Manickam L, Kudinov P, Ma W, Bechta S, Grishchenko D (2016) On the influence of water subcooling and melt jet parameters on debris formation. Nucl Eng Des 309:265–276
Miscevic M, Rahli O, Tadrist L, Topin F (2006) Experiments on flows, boiling and heat transfer in porous media: Emphasis on bottom injection. Nucl Eng Des 236:2084–2103
Miyazaki K, Murai K, Ohama T, Yamaoka N, Inoue S (1986) Pressure dependence of the particle bed dryout heat flux. Nucl Eng Des 95:271–273
Nayak AK, Sehgal BR, Stepanyan AV (2006) An experimental study on quenching of a radially stratified heated porous bed. Nucl Eng Des 236:2189–2198
Rahman S (2013) Coolability of corium debris under severe accident conditions in light water reactors. Ph.D. thesis, Institute of Nuclear Technology and Energy Systems (IKE), University of Stuttgart, Germany
Ranz WE, Marshall WM (1952) Evaporation from drops. Chem Eng Prog 48:141–146
Rashid M, Kulenovic R, Laurien E, Nayak AK (2011) Experimental results on the coolability of a debris bed with multidimensional cooling effects. Nucl Eng Des 241:4537–4543
Rashid M, Kulenovic R, Laurien E (2012) Experimental results on the coolability of a debris bed with down comer configurations. Nucl Eng Des 249:104–110
Raverdy B, Meignen R, Piar L, Picchi S, Janin T (2017) Capabilities of MC3D to investigate the coolability of corium debris beds. Nucl Eng Des 319:48–60
Reed AW (1982) The effect of channeling on the dryout of heated particulate beds immersed in a liquid pool. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, USA
Reed AW, Bergernon ED, Boldt KR, Schmidt TR (1986) Coolability of UO2 debris beds in pressurized water pools: DCC-1 and DCC-2 experiment results. Nucl Eng Des 97(1):81–88
Rhosenow W (1952) A method of correlating heat transfer data for surface boiling of liquids. Trans. ASME 74:969–976
Schäfer P, Groll M, Kulenovic R (2006) Basic investigations on debris cooling. Nucl Eng Des 236:2104–2116
Schiller L, Naumann Z (1935) A drag coefficient correlation. Z Ver Deutsch Ing 77:318–320
Schmidt W (2007) Interfacial drag of two-phase flow in porous media. Int J Multiph Flow 33:638–657
Schrock VE, Wang CH, Revankar S, Wei LH, Lee SY (1986) Flooding in particle beds and its role in dryout heat flux prediction. In: Proceedings of the sixth meeting on debris coolability, Los Angeles, California, EPRI NP-4455, Palo Alto, California
Schulenberg T, Müller U (1987) An improved model for two-phase flow through beds of coarse particles. Int J Multiphase Flow 13:87–97
Singh N, Kulkarni PP, Nayak AK (2015) Experimental investigation on melt coolability under bottom flooding with and without decay heat simulation. Nucl Eng Des 285:48–57
Song JH, Hong SW, Kim JH, Chang YJ, Shin YS, Min BT, Kim HD (2003) Insights from the recent steam explosion experiments in TROI. J Nucl Sci Technol 40(10):783–795
Squarer D, Pieczynski AT, Hochreiter LE (1982) Effect of debris bed pressure, particle size and distribution on degraded nuclear reactor core coolability. Nucl Sci Eng 80(1):2–13
Taherzadeh M, Saidi MS (2015) Modeling of two-phase flow in porous media with heat generation. Int J Multiph Flow 69:115–127
Takasuo E (2015) Coolability of porous core debris beds: Effects of bed geometry and multi-dimensional flooding. PhD Thesis, VTT Technical Research Centre of Finland
Takasuo E (2016) An experimental study of the coolability of debris beds with geometry variations. Ann Nucl Energy 92:251–261
Takasuo E, Holmström S, Kinnunen T, Pankakoski P, Hosio E, Lindholm I (2011) The effect of lateral flooding on the coolability of irregular core debris beds. Nucl Eng Des 241:1196–1205
Takasuo E, Holmström S, Kinnunen T, Pankakoski P (2012) The COOLOCE experiments investigating the dryout power in debris beds of heap-like and cylindrical geometries. Nucl Eng Des 250:687–700
Thakre S, Li L, Ma WM (2014) An experimental study on coolability of a particulate bed with radial stratification or triangular shape. Nucl Eng Des 276:54–63
Theofanous TG, Saito M (1981) An assessment of class 9 (core-melt) accidents for PWR dry-containment systems. Nucl Eng Des 66:301–332
Tung VX, Dhir VK (1987) Quenching of debris bed having variable permeability in axial and radial directions. Nucl Eng Des 99:275–284
Tung VX, Dhir VK (1988) A hydrodynamic model for two-phase flow through porous media. Int J Multiph Flow 14:47–65
Wang CH, Dhir VK (1988) An experimental investigation of multidimensional quenching of a simulated core debris bed. Nucl Eng Des 110:61–72
Widmann W, Bürger M, Lohnert G, Alsmeyer H, Tromm W (2006) Experimental and theoretical investigations on the COMET concept for ex-vessel core melt retention. Nucl Eng Des 236:2304–2327
Acknowledgements
The authors are grateful to AREVA SA for providing fellowship to the first author.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Chakravarty, A., Datta, P., Ghosh, K., Sen, S., Mukhopadhyay, A. (2019). Coolability of Heat-Generating Porous Debris Beds in Severe Accident Situations. In: Saha, K., Kumar Agarwal, A., Ghosh, K., Som, S. (eds) Two-Phase Flow for Automotive and Power Generation Sectors. Energy, Environment, and Sustainability. Springer, Singapore. https://doi.org/10.1007/978-981-13-3256-2_12
Download citation
DOI: https://doi.org/10.1007/978-981-13-3256-2_12
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-3255-5
Online ISBN: 978-981-13-3256-2
eBook Packages: EngineeringEngineering (R0)