li THERMAL HYDRAULICS OF CORE/CONCRETE INTERACTION by

THERMAL HYDRAULICS OF CORE/CONCRETE INTERACTION IN SEVERE LWR ACCIDENTS by L.S. Kao and M.S. Kazimi li A i5l MITNE-276 Department of Nuclear Engineering Massachusetts Institute of Technology June 1987 THERMAL HYDRAULICS OF CORE/CONCRETE INTERACTION IN SEVERE LWR ACCIDENTS by L.S. Kao and M.S. Kazimi Work Supported by Electric Power Research Institute Project Manager: Dr. B.R. Sehgal THERMAL HYDRAULICS OF CORE/CONCRETE INTERACTION IN SEVERE LWR ACCIDENTS ABSTRACT Several physical processes, including melt freezing, liquid/liquid interfacial heat transfer, layer mixing, and droplet entrainment, involved in the analysis of the core/concrete interaction were investigated by scoping simulant experiments. Water and cyclohexane were used to form a multi-layer pool in a test unit designed with cooling capability and air injection through a porous plate. In the freezing tests with gas velocities in the range of 5 to 126 mm/s, a stable solidified layer was formed across the bubble agitated horizontal liquid/solid interface, while no boundary crust was found at either the top surface or liquid/liquid interface. The interfacial heat transfer between the water and cyclohexane layers was measured under different air injection rates. The experimental data showed good agreement with both the modified Szekely model and the Lee and Kazimi model. In the layer mixing tests, it was found that the water and cyclohexane with density ratio of 0.78 were entirely mixed under a modest superficial gas velocity of 50 mm/s. The amount of liquid droplet entrainment measured in the simulant experiments agreed qualitatively with the Kataoka and Ishii model. The heat transfer from the corium to concrete will affect the cooling rate of the corium and the amount of gas generated by concrete decomposition, which will, in turn, affect the pressurization rate of the containment building and the degree to which fission products could be released from the melt. A semiempirical correlation was developed to describe the heat transfer at the horizontal core/concrete interface. The model assumes periodic contact between corium and concrete at low gas evolution rates, and separation by a stable gas film at high gas generation rates. The proposed model has been incorporated into an existing computer code, CORCON/MOD2, for integral analysis of the corium/concrete interactions. Good agreement was found when using this model to analyze the German BETA experiments involving several hundred kg oxidic and metallic melt with sustained internal heating by induction. The proposed model is capable of producing erosion results of the BETA experiments with a mean error of 5% and a standard deviation of 27%. Less accuracy was found in the calculation of transient, one-dimensional experiment results obtained at the Sandia National Laboratory. The impact of the downward heat. transfer model on the calculations of concrete erosion, gas generation, and ex-vessel aerosol release was studied by using COR- CON/MIT (revised version of CORCON/MOD2) and VANESA. It was found that with high initial melt temperatures, the fission product release calculated by the periodic contact model was three to five times higher than the original gas film model used in the CORCON code. At low initial melt temperatures, with the ii formation of an initial bottom crust, the various heat transfer models did not lead to significant differences in the fission product release. Sensitivity studies involving variations in several parameters, such as initial melt temperature, concrete properties, amount of unoxidized zirconium, amount of melt, decay heat, and layering potential of melt constituents, were also performed to identify the important sources of uncertainties in calculation of the ex-vessel aerosol release. The initial debris temperature was found to be the most significant parameter in the calculation. The release fraction of the non-volatile fission products such as lanthanum was the most sensitive result of the parameter variations. iii ACKNOWLEDGMENTS This report is based on the thesis submitted by the first author to M.I.T. in fulfillment of the requirements for the degree of Doctor of Philosophy in Nuclear Engineering. The authors would like to thank Professor J. Meyer for the time he devoted to comment on this work. Dr. B.R. Sehgal of EPRI is especially appreciated for the continuous guidance he provided. This work would not have been possible without the financial support of EPRI. The first author would also like to extend special acknowledgment to his wife, Ann-Tinn Shen, for the support and encouragement she provided. iv TABLE OF CONTENTS Page ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Iv . . .. .. . .... ACKNOWLEDGMENTS .. . .. ....... .......... . .. V .......... TABLE OF CONTENTS . . . .. . . . . .. . . . .. .. . ... ix . . .. .. ..... . . . ......... LIST OF FIGURES .... .......... xviii .. ........ LIST OF TABLES ...... ..................... Chapter 1 INTRODUCTION AND BACKGROUND 1.1 Introduction ........................... 1.1.1 The Molten Core/Concrete Interaction 1.1.1.1 Severe Accident Sequence..... 1.1.1.2 Physical Phenomena of MCCI 1.1.1.3 Consequences of MCCI ....... 1.1.2 Scope of This Work ................. 1.2 Background ........................... 1.2.1 G eneral ........................... 1.2.2 Melt/Concrete Interaction Experiments 1.2.2.1 Simulant Experiments ....... 1.2.2.2 Real Material Experiments 1.2.3 Analytical Modeling of MCCI 1 2 2 4 5 6 6 8 8 .. . .... ....... 1.2.4 Ex-Vessel Source Term Assessment ... 1.2.4.1 Integrated Approach ......... 1.2.4.2 Estimates of Uncertainties 1.3 Structure of This Work Chapter 2 ... ................. 10 .... 13 .... .... .... .... 22 24 28 29 SIMULANT EXPERIMENTS 2.1 Objective ...................... 2.2 Introduction .................... 2.2.1 Freezing Phenomena ........ 2.2.2 Interfacial Heat Transfer ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... .... .............. 2.2.3 Layer Mixing 2.2.4 Droplet Entrainment ........ 2.3 Experiment Descriptions .......... 2.3.1 General Features ............ 2.3.2 Apparatus .................. 2.3.3 Simulant Materials .......... 2.3.4 Test Procedures ............ 2.4 Experimental Results ............ 2.4.1 Freezing Phenomena ........ v 31 31 31 32 37 42 45 45 45 49 49 52 52 TABLE OF CONTENTS (Continued) Page 2.4.2 Interfacial Heat Transfer 2.4.3 Layer M ixing 2.4.4 Droplet Entrainment 2.5 Summary and Conclusions Chapter 3 ..................... 56 61 63 63 ............................... ......................... ......................... DOWNWARD HEAT TRANSFER MODEL FOR THE MELT/CONCRETE INTERACTION 68 71 71 76 82 85 85 . 86 . 88 . 88 . 90 . 92 3.3.2 Transition Criteria of the Film Collapse Model .... . 95 3.3.3 Post-Freezing Heat Transfer Model .............. . 97 ............ 3.3.4 Sum m ary .................................... . 97 . . . . . . . . .. . . 3.4 Downward Heat Flux Calculation .................... . 97 3.4.1 Cases Studied ............................................ 3.4.1.1 Molten Core Configuration in Concrete Cavity .......... .104 .105 .................... 3.4.1.2 Concrete Type of Reactor Cavity .105 3.4.1.3 Solidus Temperature of Molten Core .................. .106 3.4.2 Results and Discussions .................................... .106 3.4.2.1 Downward Heat Transfer Model .................... .110 3.4.2.2 M olten M aterial .................................... .117 3.4.2.3 Concrete Type ..................................... .119 .............. 3.4.2.4 Solidus Temperature of Molten Material . . .. .. . . . . . . .. . . . . . . . . . . .. . . . . . . . . .. . . . . . . . . . . . . . . . . .124 3.5 Summary 3.1 Introduction ...................................... 3.2 Review of the Downward Heat Transfer Models ........ 3.2.1 The Gas Film Model .......................... 3.2.2 The Periodic Contact Model .................... 3.2.3 The Film Collapse Model ...................... 3.3 Model Development and Implementation in CORCON .. 3.3.1 Revised Periodic Contact Model ................ 3.3.3.1 Basic Definition ........................ 3.3.1.2 Transient Heat Conduction .............. 3.3.1.3 Bubble Dynamics ...................... 3.3.1.4 Interface Temperature .................. Chapter 4 . . . . . . HEAT TRANSFER MODEL VALIDATION BY COMPARISON TO INTEGRAL EXPERIMENTS 4.1 Introduction .................................................... 4.2 Review of Real Material Experiments .............................. vi 125 126 TABLE OF CONTENTS (Continued) Page 4.2-1 BETA Experim ents .......................................... 4.2.1.1 Descriptions of BETA Facility .......................... 4.2.1.2 Experimental Results and Discussions .................. 4.2.2 Sandia Experim ents ........................................ 4.2.2.1 Descriptions of Sandia Experiments .................... 4.2.2.2 Results and Conclusions .............................. 4.2.3 Summary ................................................ 4.3 Experiment Analysis and Model Validation .......................... 4.3.1 Experiments Analyzed and Input Parameters Used .............. 4.3.2 Results and Discussions ...................................... 4.3.2.1 BETA Experiments .................................. 4.3.2.2 Sandia Experim ents .................................. 4.3.3 Model Validation ........................................... 4.4 C onclusions .................................................... Chapter 5 126 126 130 137 137 142 145 145 145 150 150 179 187 194 SENSITIVITY STUDY OF THE EX-VESSEL SOURCE TERM 5.1 Objective .................................................... 195 5.2 Introduction .................................................... 196 5.2.1 Characteristics of Ex-Vessel Source Term ..................... 196 5.2.2 Background .............................................. 197 5.3 Formulation of This Study ....................................... 200 5.3.1 Analysis Methods and Computer Codes ...................... 200 5.3.2 Input Param eters .......................................... 201 5.3.2.1 Specifications of the Base Case ........................ 201 5.3.2.2 Cases Analyzed ...................................... 204 5.4 Results and Discussions .......................................... 204 5.4.1 Impact of the Downward Heat Transfer Models .......... ..... 207 5.4.2 Effect of Concrete Decomposition Temperature ........... .. 221 5.4.3 Effect of Concrete Type ................................... 226 5.4.4 Effect of Zirconium M etal .................................... 231 5.4.5 Effect of Initial Debris Temperature ......................... .243 5.4.6 Effect of Amount of M elts .................................... 262 5.4.7 Effect of Ferrous Oxide ...................................... 262 5.4.8 Effect of Decay Heat ........................................ 269 5.4.9 Effect of Layer Configuration ................................ 281 5.4.10 Effect of CORCON/MOD2 Version 2.01 ...................... 288 5.4.11 Revised Periodic Contact Model ............................. 288 5.4.12 Sum m ary ................................................ 303 5.5 Conclusions ............. ................................... 311 Vii TABLE OF CONTENTS (Continued) Page Chapter 6 SUMMARY AND CONCLUSIONS 6.1 Summary of This Work ............................. 6.1.1 Experimental Observations ..................... 6.1.2 Development and Validation of Heat Transfer Models 6.1.3 Impact of Heat Transfer Models ................. 6.1.4 Sensitivity Study on Ex-Vessel Aerosol Release ..... ............ ............. ........... ............ ............ REFEREN CES ....................................... ............. VIll . 313 313 . 315 . 318 . 319 321 LIST OF FIGURES Page Figure 17 .. .............. 1.1 Schematic Diagram of CORCON System (Ref.[C3]) 1.2 BM I-2104 Codes Suite (Ref.[S2]) 1.3 Source Term Code Package (Ref.[S2]) 2.1 Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Predicted by Different Models .................... 38 Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Based on Different Temperature Differences ........ 39 2.2 2.3 2.4 26 .............................. 27 .......................... Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Based on Different Bubble Diameters .............. .40 Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Based on Different Layer Configurations ............ .41 46 .... 2.5 Schematic Diagram of the Simulant Experimental Apparatus 2.6 Illustration of the Temperature Measurement Locations 2.7 Water Pool Temperature Histories . 55 2.8 Interfacial Heat Transfer between Water and Cyclohexane Layers . . 60 2.9 Water Droplet Entrainment from the Bubbling Pool 3.1 Illustration of the Downward Heat Transfer of the Core/Concrete ................................................ Interaction .48 .......... ............................ 66 ............ 70 .72 ...................... 3.2 Analytical Picture of the Gas Film Model 3.3 Analytical Picture of the Periodic Contact Model ................ 3.4 Downward Ablation Distance of BETA Test VO.2 . . .... ...... . . 83 3.5 Analytical Picture of the Revised Periodic Contact Model ........ . 87 3.6 Downward Ablation Distances of Early BETA Tests 3.7 Descriptive Downward Heat Flux of the Film Collapse Model 3.8 Comparison between the Predicted and Measured Downward ..................... Erosion Distances of BETA Test V0.2. 3.9 .79 .......... Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test VO.3 .......................... ix . . .94 99 .... .. 100 101 LIST OF FIGURES (Continued) Page Figure 3.10 3.11 3.12 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.2 .......................... 102 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.3 .......................... 103 Downward Heat Fluxes of the Various Models for Core Oxide Interacting with Limestone/Common Sand Concrete 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 ............ 109 Downward Heat Fluxes of the Various Models for Core Oxide Interacting with Limestone Concrete .......................... 111 Downward Heat Fluxes of the Various Models for Core Oxide Interacting with Basaltic Concrete ............................ 112 Downward Heat Fluxes of the Various Models for Core Oxide Interacting with KfK Concrete ................................ 113 Downward Heat Fluxes of the Gas Film Model for Various Melts Interacting with Limestone/Common Sand Concrete ............ 114 Downward Heat Fluxes of the Periodic Contact Model for Various ...... Melts Interacting with Limestone/Common Sand Concrete 115 Downward Heat Fluxes of the Revised Periodic Contact Model for Various Melts Interacting with Limestone/CS Concrete .......... 116 Downward Heat Fluxes of the Gas Film Model for Steel Melt Interacting with Various Concretes ............................ 120 Downward Heat Fluxes of the Periodic Contact Model for Steel Melt Interacting with Various Concretes ........................ 121 Downward Heat Fluxes of the Revised Periodic Contact Model for Steel Melt Interacting with Various Concretes .................. 122 Downward Heat Fluxes of the Revised Periodic Contact Model for Core Oxide Interacting with Various Concretes .............. 123 ............ 127 4.1 Schematic Diagram of BETA Experiment (Ref.[A5]) 4.2 Dimensions of Concrete Cavity of BETA Experiment (Ref.[A5]) 4.3 Measured Concrete Erosion Distances of BETA Test V1.8 ........ 132 4.4 Measured Concrete Erosion Distances of BETA Test V2.3 ........ 133 4.5 SWISS Experimental Apparatus (Ref.[G12]) x .................... 128 139 LIST OF FIGURES (Continued) Page Figure 4.6 TIURC-ISS Experiment Facility (Ref.[G4]) .................... 141 4.7 Comparison of the TURC-1SS Test Data and the Predictions of the VANESA Code (Ref.[P13]) ................................ 144 4.8 Power Input History of BETA Test V1.3 ...................... 148 4.9 Power Input History of BETA Test V2.3 ...................... 149 4.10 Power Input History of Sandia SWISS-1 Test 4.11 Comparison between the Predicted and Measured Erosion Distances of BETA Test V1.5 ................................ 154 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.6 .......................... 155 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.7 .......................... 156 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.8 .......................... 157 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.9 .......................... 158 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V2.1 ........................ 159 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V2.3 .......................... 160 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V3.3 .......................... 161 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test VO.2 ........................ 162 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V 1.3 ........................ 163 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.5 ..................... 164 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V 1.6 ........................ 165 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V 1.7 ........................ 166 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 xi .................. 152 LIST OF FIGURES (Continued) Figure 4.24 4.25 4.26 4.27 4.28 Pag Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.8 ........................ 167 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.9 ........................ 168 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V2.3 ........................ 169 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V3.3 ........................ 170 Gas Generation Rates of BETA Test V1.3 Calculated by the Film Collapse M odel 4.29 4.30 4.31 4.32 ........................................ Gas Generation Rates of BETA Test V1.9 Calculated by the Film Collapse M odel ........................................ 173 Gas Generation Rates of BETA Test V2.3 Calculated by the Film Collapse M odel ........................................ 174 Gas Generation Rates of BETA Test V3.3 Calculated by the Film Collapse M odel ........................................ 175 Comparison between the Predicted and Measured Downward Erosion Distances of SW ISS-1 Test 4.33 172 ............................ 180 Comparison between the Predicted and Measured Downward Erosion Distances of SWISS-2 Test ............................ 4.34 Comparison between the Predicted and Measured Downward Erosion Distances of TURC-1T Test 4.35 181 .......................... 182 Comparison between the Predicted and Measured Downward Erosion Distances of TURC-1SS Test .......................... 4.36 Comparison between the Predicted and Measured Downward Erosion Distances of TURC-2 Test 4.37 ............................ 4.39 4.40 184 Comparison between the Predicted and Measured Melt Temperature Histories of SWISS-1 Test 4.38 183 ........................ 186 Downward Erosion Distances of BETA Tests (Prediction versus Experiment) ......................................... .189 Least Square Fits of the Various Heat Transfer Models on the Predictions of the Downward Erosion of BETA Tests ............ 191 Relative Downward Erosion Distances of BETA Tests 192 xii ............ LIST OF FIGURES (Continued) Page Figure 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 Concrete Ablation Distances Predicted by Different Heat Transfer Models ........................................... 209 Melt Temperature Histories Predicted by Different Heat Transfer Models ........................................... 210 Gas Generation Rates Predicted by Different Heat Transfer Models ........................................... 212 Aerosol Generation Rates Predicted by Different Heat Transfer Models ........................................... 213 Accumulated Aerosol Releases Predicted by Different Heat Transfer Models ........................................... 215 Lanthanum Release Rates Predicted by Different Heat Transfer Models ........................................... 216 Lanthanum Release Fractions Predicted by Different Heat Transfer Models ........................................... 217 Tellurium Release Fractions Predicted by Different Heat Transfer Models ........................................... 218 Antimony Release Fractions Predicted by Different Heat Transfer Models ........................................... 219 Strontium Release Fractions Predicted by Different Heat Transfer M odels ...... ...................................... 220 Downward Ablation Distances for Different Concrete ............................... Decomposition Temperatures 222 Melt Temperature Histories for Different Concrete ................................ Decomposition Temperatures 223 Gas Generation Rates for Different Concrete ............................... Decomposition Temperatures 224 Aerosol Generation Rates for Different Concrete ................................ Decomposition Temperatures 225 Accumulated Aerosol Releases for Different Concrete ................................ Decomposition Temperatures 227 Lanthanum Release Fractions for Different Concrete ................................ Decomposition Temperatures 228 Downward Ablation Distances for Different Types of Concrete XHi' .... 229 LIST OF FIGURES (Continued) Figure Page 5.18 Melt Temperature Histories for Different Types of Concrete 5.19 Gas Generation Rates for Different Types of Concrete 5.20 Aerosol Generation Rates for Different Types of Concrete 5.21 Accumulated Aerosol Releases for Different Types of Concrete 5.22 Tellurium Release Fractions for Different Types of Concrete 5.23 Downward Ablation Distances for Different Amounts of Zirconium ................................................. ...... .......... 230 .. ........ 232 233 .... 234 ...... 235 237 5.24 Melt Temperature Histories for Different Amounts of Zirconium 5.25 Gas Generation Rates for Different Amounts of Zirconium 5.26 Aerosol Generation Rates for Different Amounts of Zirconium 5.27 Accumulated Aerosol Releases for Different Amounts of Zirconium ................................................... 241 Lanthanum Release Fractions for Different Amounts of Zirconium .................................................. 242 5.29 Tellurium Release Fractions for Different Amounts of Zirconium 244 5.30 Downward Ablation Distances Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ................ 246 5.28 5.31 5.32 5.33 5.34 5.35 5.36 5.37 .. ........ 238 239 .... 240 Downward Ablation Distances Predicted by the Gas Film Model with Different Initial Debris Temperatures ................ 247 Melt Temperature Histories Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ................ 248 Melt Temperature Histories Predicted by the Gas Film Model with Different Initial Debris Temperatures ................ 249 Gas Generation Rates Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ................ 251 Gas Generation Rates Predicted by the Gas Film Model with Different Initial Debris Temperatures ................ 252 Aerosol Generation Rates Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ................ 253 Aerosol Generation Rates Predicted by the Gas Film Model with Different Initial Debris Temperatures ................ xiv 254 LIST OF FIGURES (Continued) Page Figure 5.38 5.39 5.40 5.41 5.42 5.43 5.44 Accumulated Aerosol Releases Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ................ 255 Accumulated Aerosol Releases Predicted by the Gas Film Model with Different Initial Debris Temperatures ................ 256 Fission Products Release Rates Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ........ 257 Lanthanum Release Fractions Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ................ 258 Lanthanum Release Fractions Predicted by the Gas Film Model with Different Initial Debris Temperatures ................ 259 Tellurium Release Fractions Predicted by the Periodic Contact Model with Different Initial Debris Temperatures ................ 260 Tellurium Release Fractions Predicted by the Gas Film Model with Different Initial Debris Temperatures ................ 261 Downward Ablation Distances for Different Amounts of Melt 5.46 Melt Temperature Histories for Different Amounts of Melt ........ 5.47 Gas Generation Rates for Different Amounts of Melt 5.48 Aerosol Generation Rates for Different Amounts of Melt . 5.49 Accumulated Aerosol Releases for Different Amounts of Melt 5.50 Lanthanum Release Fractions for Different Amounts of Melt 5.51 Downward Ablation Distances Predicted by the Periodic Contact ........................ Model with Different Amounts of FeO 5.52 .... 266 .... 267 ...... 268 .. .271 ........................ ........................ ........................ 272 273 274 Melt Temperature Histories of the High Initial Debris Temperature Cases with Different Amounts of Decay Heat 5.56 265 Lanthanum Release Fractions Predicted by the Gas Film Model with Different Amounts of FeO 5.55 .. ............ Lanthanum Release Fractions Predicted by the Periodic Contact Model with Different Amounts of FeO 5.54 264 Accumulated Aerosol Releases Predicted by the Periodic Contact Model with Different Amounts of FeO 5.53 263 .... 5.45 ................... 276 Accumulated Aerosol Releases of the High Initial Debris Temperature Cases with Different Amounts of Decay Heat xv .................. 277 LIST OF FIGURES (Continued) Page Figure 5.57 5.58 5.59 Accumulated Aerosol Releases of the Low Initial Debris Temperature .................. Cases with Different Amounts of Decay Heat 278 Lanthanum Release Fractions of the High Initial Debris Temperature .................. Cases with Different Amounts of Decay Heat 279 Lanthanum Release Fractions of the Low Initial Debris Temperature .................. Cases with Different Amounts of Decay Heat 280 . . 282 5.60 Downward Ablation Distances for Different Layer Configurations 5.61 Melt Temperature Histories for Different Layer Configurations 5.62 Aerosol Generation Rates for Different Layer Configurations 5.63 Accumulated Aerosol Releases for Different Layer Configurations 286 5.64 Lanthanum Release Fractions for Different Layer Configurations 287 5.65 .................. ........................ 5.70 5.71 5.72 5.73 290 291 292 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Accumulated Aerosol Release .................. 293 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Lanthanum Release Fraction .................. 294 Effect of the Corrected Version of CORCON/MOD2 on the .................... Prediction of the Radial Ablation Distance 295 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Released Gas ................................ 296 Effect of the Revised Periodic Contact Model on the Prediction of the Downward Ablation Distance .................. 5.74 289 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Aerosol Generation Rate ...................... 5.69 285 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Gas Generation Rate 5.68 ...... Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Melt Temperature Histories 5.67 283 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Downward Ablation Distance .................. 5.66 .... 297 Effect of the Revised Periodic Contact Model on the Prediction of the Melt Temperature Histories xvi .................. 298 LIST OF FIGURES (Continued) Page Figure 5.75 5.76 5.77 5.78 Effect of the Revised Periodic Contact Model on the ........................ Prediction of the Gas Generation Rate 299 Effect of the Revised Periodic Contact Model on the Prediction of the Aerosol Generation Rate ...................... 300 Effect of the Revised Periodic Contact Model on the Prediction of the Accumulated Aerosol Release .................. 301 Effect of the Revised Periodic Contact Model on the Prediction of the Lanthanum Release Fraction .................. 302 xvii LIST OF TABLES Table Page 1.I Analytical Models of Corium/Concrete Interactions .............. 14 1.2 Elements and Vapor Species Considered in the VANESA Model 20 1.3 Output Data of the VANESA Model 23 2.1 Corium M aterials Properties 2.2 Simulant M aterials Properties 2.3 Freezing Phenomena Test 2.4 Interfacial Heat Transfer Test 2.5 Layer M ixing Test 2.6 Counts per Minute of Different Particle Sizes 2.7 Filter Collection Test 3.1 Downward Heat Transfer Calculated by the Gas Film Model ...... 77 3.2 Test Matrix of the Early BETA Experiments 93 3.3 Empirical Constants of the Film Collapse Model 3.4 Compositions and Physical Properties of Various Melts 3.5 Compositions and Physical Properties of Concretes 3.6 Typical Values of the Parameters Used in the Periodic Contact M od el .......................... . .................................. 36 50 ................................ .................................... . 54 59 ................................ .......................................... 62 .................. ........................................ .................. ................ .......... .............. .................................................... ... 64 . 65 98 107 108 118 4.1 Test Matrix of the BETA Experiments ........................ 131 4.2 Test Matrix of the SWISS Experiments ........................ 140 4.3 Test Matrix of the TURC Experiments ........................ 143 4.4 Test Conditions of the BETA Experiments 4.5 Melt Compositions of the BETA Experiments 4.6 Test Conditions of the Sandia Experiments 4.7 Input Parameters Used in CORCON/MIT for Experiment .................................................. A n aly sis Xvii .................... .................. .................... 146 147 151 153 LIST OF TABLES (Continued) Page Table ........ .188 4.8 AxiaTConcrete Erosion Rates of the BETA Experiments 4.9 Statistics for the Various Heat Transfer Models in the ............................ Calculations of the BETA Results 193 ...................... 202 5.1 Parameters Used in the Base Case Study 5.2 Melt Inventory of the Base Case (Ml) at the Start of MCCI 5.3 Phenomena and Parameters Range Used in the CORCON/MIT- VANESA Sensitivity Study 5.4 ...... 203 205 .................................. Compositions of Various Melts Used in the CORCON/MIT-VANESA Sensitivity Study ............................................ 206 5.5 Phenomena and Timing of Events of the Base Case .............. 208 5.6 Timing of Events of the Cases with Different Initial Melt Temperatures and Different Amounts of FeO .................... 5.7 Integral Results of the Base Case at 3 Hours after the Start of M C C I 5.8 Radial and Axial Concrete Erosion Distances Relative to PCM1 5.11 305 306 307 Accumulated Releases of Decomposition Gases Relative to GFM1 .................. 308 Fission Products and Total Aerosol Releases Relative to PCM1 Base Case at 3 Hours after the Start of MCCI 5.13 .................. Accumulated Releases of Decomposition Gases Relative to PCM1 Base Case at 3 Hours after the Start of MCCI .................. Base Case at 3 Hours after the Start of MCCI 5.12 .................. Radial and Axial Concrete Erosion Distances Relative to GFM1 Base Case at 3 Hours after the Start of MCCI 5.10 304 .................................................. Base Case at 3 Hours after the Start of MCCI 5.9 270 .................. Fission Products and Total Aerosol Releases Relative to GFM1 Base Case at 3 Hours after the Start of MCCI .................. xix 309 310 CHAPTER 1 INTRODUCTION AND BACKGROUND 1.1 Introduction In the current design of nuclear power plants, reactor containment systems must withstand a set of design basis accidents, for example, the large loss-ofcoolant accident (LOCA), without the release of excessive amounts of radioactive material. The March 28, 1979, accident at Three Mile Island (TMI) has prompted new initiatives regarding nuclear safety. This accident, which involved a degraded core, reached conditions more severe than those of design basis accidents. Since then, concern about the potential for accidents beyond the design basis, namely, core meltdown accidents, has correspondingly increased. Before the TMI accident, the Reactor Safety Study (RSS or WASH-1400) [N1], published by the U.S. Nuclear Regulatory Commission (NRC) in 1975, had indicated that the core meltdown accidents were the dominant contributors to the risk. This provided motivation for further investigation of physical phenomena that may influence the consequences of postulated core meltdown accident sequences. The Nuclear Regulatory Commission (NRC) issued, on October 2, 1980, an "advance notice of long-term rulemaking to consider to what extent. if any, nuclear power plant should be designed to deal effectively with degraded core and core melt accidents" [N2). This advance notice of rulemaking proposed to address the-objectives and content of a degraded core regulation, the related design and operational improvements, and their costs and benefits. NRC subsequently issued a proposed Commission Policy Statement N3,N4] which would implement the Advance Notice of Rulemaking with severe accident regulatory determination on specific standard plant designs and regulatory decisions on classes of existing plants. The Commission decision. which could have certain economic impact. on the indtistry, will slowly evolve diring the next several years. 1 1.1.1 The Molten Core/Concrete Interaction 1.1.1.1 Severe Accident Sequence In the event of a LWR degraded core accident with complete failure of normal and emergency coolant flow, the decay heat would cause fuel rods to heat up to templ~eratures above the design limit. If the cooling failure persisted for extended time periods, the combination of decay heat and the exothermic zirconium/water reaction would cause melting of the reactor core. This could lead to slumping of the molten core material (corium) down into the vessel lower plenum. Mechanical and thermal loads imposed on the reactor vessel by the corium could lead to vessel failure and deposition of these materials into the concrete reactor cavity. C'orium could then attack the concrete of the cavity floor, releasing gas and vapor (CO2 and H 2 0) and ablating the solid concrete, a phenomenon known as Molten Core/C'oncrete Interaction (MCCI). 1.1.1.2 Physical Phenomena of MCCI The MCCI is a long term endothermic erosion of concrete by high temperature corium, and results in decomposition and melting of the concrete with production of very large quantities of carbon dioxide and steam. Radiodecay power and chemical reaction heat are the sources which sustain long term core-concrete interactions. While the sensible heat content of the corium pool will be lost by heat transfer either to the containment atmosphere and containment structure directly or to the concrete. Both the heat transfer and gas release into the containment atmosphere would pressurize and threaten the integrity of the containment building. During the concrete decomposition, weight loss in the concrete consist of three distinct events P11: loss of evaporable water (30 to 250 'C). loss of chemicallyconstituted water (400 to 550 C), and loss of carbon dioxide (550 to 800 C). Loss of evaporable water is due to vaporization of molecular water from species such as Tobermorite. Ettringite. and 3CaO - 25i0 2 - 3H 2 0. The weight loss assigned to chemically-constituted water is caused mainly by dehydration of Ca(OH)2. The decarboxylation weight loss in basaltic concrete is due to thermal decomposition of CaCO3 formed in the cementituous phase during concrete fabrication. Decarboxylation weight loss in calcareous concrete is, of course, principally the result of thermal decomposition of the aggregate. The corium melt contains both oxidic (U0 2, ZrO2 , FeO, and fission product oxides) and metallic (Fe, Cr, Ni, Zr, and metallic fission products) materials, which may differ in density from each other. The experimental evidence shows that the various oxides in the corium are highly miscible, as are the metallic species, but that the two groups are mutually immiscible [P1]. Buoyancy forces may be sufficient to separate the molten debris into two layers. However, the layer formation may be destroyed by the large turbulence produced by the gases and concrete constituents entering the pool from the bottom interface with concrete. A homogeneously mixed pool could be formed if the gas generation rate is high and the density difference between the oxidic and metallic materials is small. The concrete decomposition gases, initally CO2 and H 2 0, may percolate through the pool unless they can escape at the pool periphery, e.g. the gases generated from the sideward erosion. The gases which pass through the pool may encounter the metallic elements and be reduced as the metal is oxidized. These chemical reactions will change the composition of the pool, add energy to the pool and generate flammable gases H 2 and CO. The composition of the pool is also changed by the addition of slag (molten concrete oxide) to the oxidic phase of coriui. The slag will dilute the oxidic layer, decrease its power density and reduce the freezing point. Thermal properties of the melt mixtures will also be changed. The presence of the gases in the pool will elevate the pool surface and increase the layer thickness, therefore changing the geometry of the corium pool. The bubbling of gases through the pool tends to enhance the heat transfer between 3 layers. The heat transfer process between corium and concrete is also complicated by this gas percolation. Furthermore, the gases, the fission products and other materials in the melt form various chemical compounds, which may be vaporized and carried away with the flowing gases. These vaporized materials, after emerging from the corium pool, will form an aerosol source as they condense in the containment atmosphere. In addition to the vapor source the flowing gases may entrain some melt material, which could contain fission products. The releases of radionuclides and production of aerosols from core/concrete interactions into the containment atmosphere are identified as ex-vessel source terms. As time progresses, the pool grows, its surface area increases and decay heat decreases. Therefore, the pool temperature will decrease and eventually the possibility of freezing arises. In general, concrete melts between 1250 and 1775 K, while corium melts between 1800 and 2700 K (depending upon compositions). These data imply that even solidified core debris could melt the concrete. After the pool solidification, the attack on the concrete shifts from the molten pool to partially solidified debris. The relatively slow attack on concrete by solidified or partially solidified debris may persist for a few days. 1.1.1.3 Consequences of MCCI The accident sequences developed by the Reactor Safety Study indicated that the interaction of molten core materials with concrete was important because it affects two primary modes of release of radioactive materials from the containment building. First, the overpressurization release occurs when the containment pressure is increased to containment failure pressure by the added heat and water vapor during blowdown phase and MCCI period. This release mode can be directly affected by the gas release and heat flow from the core/concrete interaction. Also, if the concentrations of the combustible gases (H 2 and CO) generated trom core concrete interaction are high enough inside the containment atmosphere, de- I flagration and detonation of these gases may occur and lead to containment failure by a pressure spike. Second, the molten core materials interacting with the concrete base erode the concrete which can lead to fission product release to the soil. The detailed phenomena of the core,/concrete interaction determine if and how fast these release modes can occur. The core/concrete interaction also affects the characteristics (such as the nagnitude, the content, the physical and chemical properties) of the radioactive release source term. In addition, the timing of the ex-vessel aerosol release, relative to that of the fission product aerosol release from the primary system, and to that of the containment failure, is largely determined by the physical phenomena of the core/concrete interaction. All of these parameters are extremely important in the estimation of the severe accident source term. Recently. results from the Containment Loads Working Group [S1], Containment Performance Working Group [N5], the NRC Accident Source Term Reassess- ment Program [G1.K1,S2,D2], IDCOR program (I1], and other studies [G2,L1] have demonstrated that the core/concrete interactions present the greatest threat to the containment integrity. Most importantly. it becomes clear that refractory fission products (such as Te, Sr, Ba, La and Ce) released during the core/ concrete interaction, dominate the environmental source terms if containment fails S21. [D2.K2, Especially in some of the accident. scenarios for the BWR design, the importance of the ex-vessel releases stems from the fact that they take place into a failed drywell and are thus available for release to the environment without passing throughThe suppresion pool. 1.1.2 Scope of This Work This work will focus on thermal hydraulics of the core, concrete interaction. Some physical processes of the MCCI which are difficult to interpret from real material experimeit will be investigated by siimulant experimnents in this study. Tie experimental apparattus used is desigied with gas agitation aid coldiig capabilities of both a single-layer and a multi-layer simulant liquid pool to obtain an understanding of the fundamental processes of the MCCI, such as (1) freezing phenomena of a corium pool; (2) mixing phenomena of two immiscible layers; (3) liquid/liquid interfacial heat transfer; and (4) liquid droplet entrainment due to gas sparging. Major contributions of this work are development and validation of computational models describing the heat transfer across the horizontal corium/concrete interface. The proposed heat transfer model will be developed based on transient heat conduction theory and bubble dynamics. and it will be incorporated into an existing computer code for integral analysis of the MCCI. Validation of various downward heat transfer models will be performed by comparison of the calculated downward concrete erosion to results of real material experiments. A study of the uncertainty caused by the downward heat transfer modeling in the calculation of the ex-vessel source term will be made. Impacts of other parameters on the calculation of the ex-vessel release will be examined as well. 1.2 Background 1.2.1 General The Reactor Safety Study provided estimates of the radioactive source term that might result from a severe reactor accident. At that time, detailed knowledge of the phenomena that might occur in the severe accident was not available. The analyses were based, therefore, on simple bounding models, and the estimates given in the RSS were intended to be conservative. The Reactor Safety Study assumed that the mechanism for concrete erosion by the core melt was rapid spallation (i.e. mechanical disruption) of the first half meter depth of concrete in about 20 minutes, followed by concrete decomposition at a rate of 0.04 mm /s. This assumed mechanism resulted in rapid concrete erosion and ignored t he physical fact that the core mielt cools aid would eventually begin to 6 solidify; therefore this could be considered an upper bound on the rate of erosion. For the reference reactors in WASH-1400. concrete basemat melt-through was predicted to occur in about 18 hours. Because of this rapid concrete erosion rate, the rate of gas generation was also high and the containment was predicted to fail by overpressure well within the first day of the accident. This early containment failure time may have caused an overestimate of the health consequences of the accident because of the large airborne radioactive inventory early in the accident and the lack of time for population evacuation. Since then, considerable progress in developing both a scientific basis and computational ability have been achieved. Simulant experiments as well as large scale real material experiments have been conducted in recent years providing useful data, which can lead to better understanding of the phenomena that might take place in a severe reactor accident. Analytical models for core-concrete interactions have been developed to calculate erosion rate, melt temperatures, gas evolution and other parameters. The chemical reactions that occur in the debris and the related aerosol production can also be calculated. Based on the new developments, calculation of the volatile radioactive material that could be released to the environment is substantially smaller than those reported in the RSS [A1,A2). This finding resulted from better understanding of containment integrity, natural retention potential of reactor systems and chemistry of cesium iodine (CsI). However, one mechanism that might, for some sequences. increase the radionuclide releases above those calculated in the Reactor Safety Study is the release of nonvolatile radionuclides in the core-concrete interaction. The magnitude of the contribution from the nonvolatile radioniclide which could be available for long-term release is still open to question. primarily because of the modeling unmcertainty of the MCCL. While the fundamental concepts of current models have been generally accepted, heat transfer modeling is not fully developed and validation of chemical effects is inconplete. The understanding of core/concrete interaction is far from complete, and calculations are also known to depend strongly on the details of core melt progression for which many uncertainties still exist. It is important to spend more efforts on both experimental and analytical research to improve our knowledge of the physics and chemistry in this crucial area. 1.2.2 Melt/Concrete Interaction Experiments The interaction between molten corium and concrete consists of many physical and chemical processes, such as heat and mass transfer. gas genention, melting of concrete, oxidization of metal, and aerosol release. To understand these processes, small scale simulant material tests as well as large scale real material experiments have been conducted. These experimental programs have provided valuable qualitative and quantitative information, enhancing the understanding of core/concrete interactions. 1.2.2.1 Simulant Experiments Due to the extremely high temperature involved in the melt/concrete interaction experiments, the physical details of the interaction processes are difficult to interpret. Various simulant experiments have been conducted to investigate separate physical phenomena that might occur in the core/concrete interaction. Among those simulant experiments, a conceptually simple experiment of gas agitated ablation can be realized by using dry ice as the eroding (sublimating) material due to heat transfer from an overlying pool of water or other low temperature liquids. Indeed, such experiments were conducted by Dhir et a]. [Di1 and Alsmeyer et a]. [A3]. Such experiments address only the non-radiative heat transfer phenomena without accounting for mass transfer effects resulting from the inclusion of the molten concrete slag. Based on observations from these experiments, a gas film was expected to be formed at the -olid-liqiid interface, which would control the downward rate of energ' transfer. However, in an experiment by Felde et a). F1 usiig gas injection thiroighi a porus plate ito a volunetricallv heated liquid pool, no continuous gas film was identified at modest superficial gas velocities-(- 10 mm/s). A simulant experiment using adipic acid (T, 151 *C) to simulate corium and azelaic acid, sodium bicarbonate plus polyethylene glycol mixture to simulate substrate concrete was performed by Plys [P2. This experiment preserved most of the major phenomena of melt/concrete interaction. On decomposition, gas was generated and the remainder of the melt substrate became miscible with the pool material. The decay heat of the corium was simulated by an immersed heater. In this experiment, the measured pool temperatures indicated rapid initial cooling, followed by slow heatup, and then renewed attack. An early aggressive phase of the interaction showed limited effects of crusting. After crust buildup, erosion was severely reduced due to the increase in heat transfer resistance. Pool heatup was observed at this phase. Finally, the interface temperature rose, the crust broke up, and a quasi-steady attack was established. With regard to the heat transfer rate after pool solidification, an experiment was conducted by Ahmed and Dhir [A4] in which a solid copper block embedded with electric heaters penetrated an underlying dry ice slab. It was concluded that the heat transfer coefficient depends on the temperature difference between the solid and substrate. An experiment was performed at M.I.T. [L21 to study the phenomena of crust stability. In this experiment, air was injected through a porous plate into a single-layer water pooland heat was removed from the bottom of the pool by a condensing unit. The superficial gas velocity achieved in the experiment ranged between 6.5 and 130 mm/s. No gas film was observed and a stable ice crust was always formed across the liquid/solid interface under bubble agitation condition. The thickness of the ice crust increased gradually. Gas bubbles penetrated the ice crust through several locations. Air bubbles trapped in the crust layer were observed as well. 9 Recently, an experiment conducted at the University of Wisconsin [G3] was intended to investigate the effect of gas injection on liquid-liquid entrainment in an isothermal system. In this scoping experiment, air was injected into a layered pool of two immiscible liquids of different densities. Different refrigerants. oil, mercury, and water were used in various comiblinations to scope out the effects of density ratio, surface tension, and viscosity on the onset of entrainment. The experiments performed to date covered a range of density ratios of 1.5 to 15. At the lower end of this density ratio for water and RI 13, the entrainment threshold was observed to be at a superficial gas velocity of 20-30 mm/s. At the higher end of this density ratio for water and mercury, the entrainment threshold was reached at a velocity of 150-200 mm/s. Simulant experiments have the advantage that they are relatively easy to perform to allow detailed observations of the basic processes. However, questions may be raised about their direct applicability to a real case situation, in view of the potential for unforeseen scaling effects. In addition, radiative heat transfer, which is the dominant heat transfer mechanism in a real case, was neglected in the sinuilant experiments. 1.2.2.2 Real Material Experiments Many experimental programs using molten core material and various concretes have been performed to study the phenomena and provide data bases for corium/ concrete interactions. Thefirst real material experiment was reported by Baker et al. (BI . consisted of a small scale apparatus with resistive heating to melt 1 kg of It 02 . A penetration rate of 0.003--0.03 mm/s was measured and some spallation of concrete was observed. In a number of large scale experiments conducted by Perinic et al. P3) no large spallat ion was noted and an erosion rate of about 0. 17 mm a was measured when the iron-alumina therniite melts dropped into concrete cricibles. Vigorous gas stirring by decomposed coicrete gases was observed. 10 Peehs et al. [P4] at Kraftwerk Union conducted a number of small scale experiments in which molten steel was deposited into a concrete crucible. The experiments have been both transient and steady state. The experiments were mainly scoping experiments in which concrete erosion was observed. Concrete thermophysical properties and enthalpy of decomposition were also measured. Separate-effect experiments were conducted at Sandia National Laboratory [C1,M1,P1] to investigate the response of concrete exposed to a high heat flux. In these experiments, cylindrical concrete samples were exposed to nominal heat fluxes of 280 to 2800 kW/m 2 provided by a plasma jet or radiant sources. At each experiment, after a brief initial transient period (30~60 seconds), erosion took place at a constant rate. Tests at various applied heat fluxes showed that the rate of erosion was approximately linear to the heat flux actually deposited in the concrete. A large variety of scoping experiments, both small scale and large scale, were performed at Sandia by Powers et al. [M2,P5,S3]. These experiments were transient tests without internal sustained heating of melts. Various melts were generated either by thermite reaction or inside an induction furnace, and poured on a basaltic or calcareous concrete crucible. The erosion rate was traced by the response of thermocouples embedded in the concrete crucibles. In these experiments, the interaction was marked by vigorous evolution of gases. Chemical analysis showed the composition of the gases to be predominantly a mixture of C0, C'02, H 2 , and H20. The decomposition products (slag) were largely immiscible with steel melt. Density driven stratification of the melt into slag and metal phases occurred quickly and was not greatly disrupted by the gas evolution process. The erosion rates in the radial and axial directions were approximately the same and were proportional to the absolute temperature of the melt. Several experiments [P6,S4] have been also made at Sandia to provide internal heating within the melt to simulate the decay heat generation of corium. It was I1 found that the erosion was dominantly downward and radial erosion of the concrete cavity was fairly insignificant. There are limited available quantitative results for these tests. An experimental program, sponsored by EPRI, has been undertaken at Argonne National Laboratory [S5] to study corium/concrete interactions, with particular emphasis on measurements of the magnitude and chemical species present in the aerosol releases. In addition, other aspects of the interaction to be examined include the downward heat transfer and concrete ablation rates, mixing of corium melt, and gas release rate. Experiments have been performed inside rectangular corium containments with base dimensions measuring 100 mm square for small-scale tests and 200 mm square for intermediate-scale tests. Two types of the corium containments have been constructed for different tests. One had a water-cooled brass base with gas sparge tubes in which hydrogen and carbon monoxide were injected into the corium to represent the concrete decomposition gases. This containment was designed for the gas sparge test. Another was used for a corium/concrete interaction test in which a concrete block with 305 mm thickness was placed within the containment as a concrete basemat. Both containments consisted of water-cooled brass sidewalls where heat losses through these walls were determined by measuring the water flow rate and temperature rise. Various core melt mixtures (5 - 27 kg) consisting of UO 2 , ZrO2 , Zr, Fe, Cr, Ni, CaO, SiO2 , and fission product mockup were melted by direct electrical heating inside the corium containment. The direct heating technique has been successfully used in generating an internal heating rate of 1 kW/kg and achieving melt temperatures of 2000 0C. Downward erosion was measured by the response of embedded thermocouples. An aerosol and gas sampling system was used to collect aerosol samples. In the corium-concrete interaction tests, downward erosion rate of about 0.02 mm/s of concrete was measured. Some quantitative results of tl)e released aerosol and gas composition were reported. A new facility is being developed to preform 12 larger scale (300 kg corium inventory inside 50 cm square concrete base cavity), integral tests for addressing issues important to the modeling of the MCCI. Recently. two major programs designed to investigate the integral behavior of the MCCI were conducted at the Sandia Large Melt Facility and the German BETA Facility. The Sandia experiments included molten corium/concrete [G4,G51, melt/concrete with overlying water [B2], and hot solid/concrete interactions [C2]. The BETA experiments [A5,A6,A7] were performed at various temperature levels using sustained induction heating of the metallic melt to reach a quasi-steady state condition. Concrete erosion rates, melt temperatures, aerosol production, and evolved decomposition gases were measured during the tests. Detailed descriptions and results of these tests will be discussed in Chapter 4. 1.2.3 Analytical Modeling of MCCI The analytical studies of the MCCI include three general areas: (1) The proportion of core-melt heat transferred downward or sideward into the concrete causing erosion versus upward into the containment or an overlying water layer; (2) The rate of condensible and noncondensible gas generation due to the concrete erosion; (3) Characterization of the aerosol source term and transport during the MCCI. Various models have been developed to calculate the concrete erosion, decomposition gas generation, upward heat flux, aerosol production, and other parameters (see Table 1.1). Among those analytical models, the one to describe the heat transfer across t he horizontal corium/concrete interface has the most direct impact on the calculations of the important parameters specified above. Two fundamental assumptions about the existence of a stable gas filn at the horizontal corium/concrete interface laid the foundation for development of different downward heat transfer models. Some of the downward heat transfer models have been extensively used in the analysis of MCCI. i3 Table 1.1 Analytical Models of Corium/Concrete Interactions Reference Subject Heat Transfer across Dhir [D1]; Alsmeyer [A3]; Corium/Concrete Interface Felde [F1]; Benjamin [B3]; Blottner [B4]; Murfin [M3]; Muir et al. [M4]; Henry [H1]; Ahmed and Dhir [A4]; Lee and Kazimi [L3,L4]; Muir and Benjamin [M5]; Reimann and Murfin [R1]; Kutateladze and Malenkov [K3] Heat Transfer across Szekely [S6]; Grief [G6]; Liquid/Liquid Interface Konsetov [K4]; Werle [Wi]; Blottner [B4]; Greene [G7]; Muir et al. [M4]; Lee and Kazimi [L4]; Reimann and Murfin [Ri] Heat Transfer across R.Cole,Jr. [C3,C4]; Solid Crust Plys [P2]; Henry [H1] Heat Transfer to R.Cole,Jr. et al. [C3]; Henry [Hi]; Overlying Water Pool Ginsberg and Greene [G8] Aerosol Generation Powers et al. [P7]; Ginsberg [G9]; Plys et al. (P8,PIO,P11]; Butland et al. [B51; Clough et al. [C5] Layer Mixing Gonzalez and Corradini [G3] 14 Since the physical processes involved in the core/concrete interactions are quite complex and interrelated, computer codes have been developed to analyze the integral behavior of the MCCI. They are INTER [M3], CORCON [C3,M4], DECOMP [H1], WECHSL [R11 and VANESA [P7]. The first such program, INTER, was developed by W.B. Murfin at Sandia in 1977. This model was developed based on very limited experimental data and many untested assumptions. INTER was incorporated into the MARCH [W2] code as a qualitative tool for sensitivity analysis. A more detailed modeling effort was undertaken and produced the CORCON series of codes, which replaced INTER in the calculation of the core/concrete interaction. DECOMP was developed for the IDCOR (Industrial Degraded Core Rulemaking) [I1]. WECHSL was developed at KfK, West Germany, and is in many respects similar to CORCON. VANESA was developed at Sandia to calculate aerosol generation during the MCCI. Among these codes, CORCON and VANESA have the most advanced modeling capability and will be described in detail here. (i) CORCON The code predicts the behavior of the core melt-concrete interaction, including heat transfer, concrete ablation, cavity shape change, melt temperature history, and gas generation. The first version, CORCON/MOD1, was released in 1981. An improved model called CORCON/MOD2 based on insights from additional experimental data became available in 1984. The major changes are the inclusion of models for solidification of the melt and for its interactions with coolant water. The CORCON/MOD2 code is now widely used in the ex-vessel source term calculations. CORCON is a stand-alone computer code which models most of the physical and chemical processes which may occur during the thermal interaction between molten core debris and concrete. The concrete is assumed to have a cavity initially of one of several axisymmetric geometries. A mixture of molten oxidic and metallic 15 melts is deposited into the cavity, consisting primarily of molten fuel, U0 2 and oxidized iron and zirconium for the oxide phases, and steel and zirconium for the metallic phases. These oxides and metals, being immiscible. are assumed to separate into distinct layers with no mixing between oxides and metals. The pool structure is assumed to consist of up to six layers with their spatial orientation determined by their respective densities (see Fig. 1.1). Several of the layers, i.e.. oxide-metal mixture layers are not currently modeled in the code although present in the numerical solution scheme, and as such are assumed to have zero mass. In a typical calculation, the oxidic layer is calculated to be more dense initially than the metallic layer. Later, when molten concrete slag dilutes the heavy oxide layer, the oxidic layer becomes lighter than the metal layer and rises to the top. Energy transfer in the system is modeled by empirical and analytical correlations from the literature based upon available empirical data wherever possible. The heat transfer modes that are modeled include heat transfer across the melt/concrete interfaces, between layers in the pool, and from the pool surface to the surrounding atmosphere and structures. The gas film model [A3,D1] is employed to describe heat transfer across the melt /'concrete interface. It assumes the existence of a stabilized gas film on the pool bottom and a flowing gas film along steeper portions of the sides of the pool. The gas film is assumed to be composed of concrete decomposition gases. Without-water coolant layer, upward heat transfer to the containment atmosphere is described by a combination of radiative and convective processes. With coolant layer, boiling heat transfer is also included to describe the upward heat loss of the molten pool. The model in CORCON/MOD2 includes the full boiling curve, based on standard pool boiling correlations. No correction is made for the effects of gas injection at the melt/coolant interface. 16 SURROUNDINGS MELT ATMOSPHERE (REACTING GAS MIXTURE) COOLANT/ CONCRETE INTERFACE REGION J L- VENT TO IF CONTAINMENT SCOOLANT LAYER UGHT OXIC LAYER METALLIC LAYER CONCRETE HEAVY OXDIC LAYER (PRINCIPALLY UO2 ) MELT/CONCRETE INTERFACE REGION Figure 1.1 CONCRETE Schematic Diagram of CORCON System (Ref.'C3) 17 The solidification model in the CORCON/MOD2 assumes that a crust forms on any surface whose temperature falls below the solidification temperature. The mechanical stability of the crust is not considered. It is believed that other regimes may exist, and that both the mechanical strength of a crust and the loads imposed on it by concrete decomposition gases are important in determining the true behavior in any given case. Heat transfer across the crust is modeled as heat conduction. At the solid core/concrete interface, existence of a stable gas film is assumed and the heat transfer is again described by the gas film model. Mass transfer between layers and the surroundings is assuned to be instantaneous between time steps of the calculation. Light concrete oxides entering the pool in the oxidic layer remain there and reduce the average density of the oxidic layer. Those entering the metallic layer rise through the layer to form a light oxide layer above. Oxidized metallic components also leave the metallic layer to join the light oxide layer. Eventually, when concrete slag has diluted the heavy oxide layer such that its density is less than that of the metallic layer, the layers flip and the heavy oxide and light oxide layers, being soluble combine to form one. Concrete decomposition is treated as a one-dimensional, quasi-steady state ablation process, dependent on the local heat transfer rates at several hundred integration points around the periphery of the melt/concrete interface. Based on the assumption that the concrete erosion is a quasi-steady process, all the sensil;ie heat, reaction heat and latent heat of the concrete are lumped together to form an effective decomposition enthalpy. The concrete ablation rate is then determined by the energy balance at the decomposition interface. Two phase hydrodynamics is accounted for by a bubbly/churn-turbulent flow drift flux model based upon the gas flow rates resulting from the concrete decomposition rate. The void fraction of each layer is calculated to determine pool swell and layer geometry. Comparisons have been made between calculations of CORCON/MOD2 and results of the Sandia and KfK BETA experimental programs. Despite good agreement with some tests (B6,K51, the gas film model is not adequate for describing the downward heat transfer of the core/concrete interaction for most of the tests "K6". (ii) VANESA VANESA is a mechanistic description of the aerosol generation and fission product release during core debris interaction with concrete. The model predicts the mass, composition, and mean particle size of radioactive and non-radioactive materials liberated as vapors or particles during the interaction. Thus, mass release by vaporization and mechanical processes are included. A substantial portion of the VANESA model is devoted to the analysis of vaporization. It contains a library of thermodynamic properties (free energies from which vapor pressures are calculated) for about 125 chemical species (mostly elements, oxides and hydroxides) that might be formed by fission products and other melt constituents. The gas phase chemical species recognized by the model are shown in Table 1.2. This model considers not only the detailed thermochemistry of vaporization but also the kinetic factors which might. prevent the vaporization process from reaching the equilibrium limit defined by the thermochemistry. Equilibrium partial pressures of the melt constituents are first calculated to be driving forces for vaporization of these constituents into gas bubbles. Secondly, inhibition of vaporization due to kinetic factors is considered to be caused by: (1) available surface area, (2) mass transport in the condensed phase, (3) surface vaporization rates, and (4) transport of vapors within the bubble. The behavior of gas bubbles. such as bubble shape, trajectory, rise velocity and bubble size. must be counted in a vaporization kinetics model. Standard equationii for these calculations. 19( taken from the literature are used Table 1.2 Elements and Vapor Species Considered in the VANESA Model Element Hydrogen Oxygen Carbon Iron Chromium Nickel Molybdenum Ruthenium Tin Antimony Tellurium Silver Manganese Calcium Aluminum Sodium Potassium Silicon Uranium Zirconium Barium Strontium Cesium Lanthanum Cerium Niobium Iodine Vapor Species H, H2, OH, H2 0 0, 02, OH, H20, CO, CO 2 CO, CO 2 Fe, FeO, FeOH, Fe(OH)2 Cr, CrO, Cr0 2 , Cr03 , H 2 CrO4 Ni, NiO, NiOH, Ni(OH)2 Mo, MoO, MoO 2 , MoO 3 , H 2 MoO4 , (MoO 3 )2 , (MoO 3 )3 Ru, RuO, RuO 2 , RuO 3 , RuO4 Sn, SnO, SnOH, Sn(OH)2 , SnTe Sb, SbOH, Sb(OH)2 , Sb 2 , Sb 4 , SbTe Te, TcO, TeO 2 , Te 2 0 2 , H 2 TeO 4 , Te 2 H 2 Te, SnTe, SbTe, AgTe Ag, AgOH, Ag(OH) 2 , AgTe Mn, MnOH, Mn(OH) 2 Ca, CaO, CaOH, Ca(OH)2 Al, AIO, AlOH, Al 2 0, A10 2 , Al 2 02 Al(OH) 2 , AIO(OH) Na, Na 2 , NaOH, (NaOH)2 , NaO, NaH K, K2, KOH, (KOH)2 , KO, KH Si, SiO, SiO2 , SiOH, Si(OH)2 , Si(OH)4 U, UO, U0 2 , U0 3 , H 2 UO4 Zr, ZrO, ZrO2 , ZrOH, Zr(OH)2 Ba, BaO, BaOH, Ba(OH)2 Sr, SrO, SrOH, Sr(OH)2 Cs, Cs 2 , CsOH, Cs 2 (OH) 2 , CS 2 O CsO, CsI La, LaO, LaOH, La(OH)2 Ce, CeO, CeOH, Ce(OH)2 Nb, NbO, NbO 2 , NbOH, Nb(OH) 2 Cs!, HI, 12, 1 20 The VANESA model also accounts for aerosol production by mechanical processes. Mechanical aerosols have the bulk composition of the melt from which they are formed rather than being enriched in volatile species as are aerosols formed by vaporization. Within the context of the VANESA model only the uppermost portion of the core debris (oxidic layer) participates in the mechanical aerosol production process. The contribution of mechanical action is relatively small compared to the vaporization process, however, the amount of mechanically generated aerosol is not negligible. Especially, later in the course of core/concrete interactions, mechanical process may be the dominant source of aerosols. The layer configuration assumed in the VANESA model is rather simple, a stratified configuration with the oxidic layer on top of the metallic layer. The actual density of each layer and the possibility of mixing are not considered in the determination of the layer configuration. Fission products and other melt constituents (steel, zircaloy, and concrete) are apportioned initially to the metallic and oxidic layers based on prior experimental observations and calculations. In case of an overlying water pool, the VANESA code will account, for aerosol scrubbing by gravitational settling, random diffusion, and inertial impaction. A decontamination factor for each particle size is calculated to give the mass within the size range that emerges from the water pool. The key input requirements of VANESA are: " chemical composition of the core debris including fission product inventories at the start of core/concrete interaction: " chemical composition of the concrete; " temperature histories of the melt during the core/Iconcrete interaction; " the rate at which molten concrete is incorporated into the melt; * gas (C'02 and H 2 0) generation rates by melt attack on tihe concrete: and " the geometric top surface area of the molten pool during core/concrete interact ion. 21 The first of these input quantities is obtained from the results of accident analyses with the MARCH and CORSOR [K7] models. The second of the input quantities is obtained from specifications of the reactor plant under analysis. The remaining input data are obtained from the CORCON code. A detailed listing of the specific output quantities from the VANESA model is provided in Table 1.3. The most important of these output quantities for subsequent use in the analysis of a severe accident source term are: " aerosol mass generation rate; " chemical composition of the aerosolized mass in terms of fission products, concrete constituents, and strurctural materials; e particle size of the aerosol; " material density of the aerosol; " gas flux during core/concrete interaction; and " chemical composition of released gases. These quantities specify the ex-vessel source term for calculations of containment response with the NAUA [B7] or CONTAIN [B81 code. At this time, few experimental data exist for overall validation of the VANESA code. Additional validation is being carried out as more data becomes available. Uncertainties certainly exist (e.g., the assumptions of a layered melt, of unity activity coefficients, of initial chemical form, and continued gas permeability below the solidus temperature) in the calculation of aerosol release. 1.2.4 Ex-Vessel Source Term Assessment A source term is defined as the quantity, timing, and characteristics of the release of radioactive materials to the environment following a postulated severe reactor accident. Source term assessment is employed for a variety of regulatory applications [S2], including plant siting evaluation, emergency planning, evaluation of engineering safety features such as containment isolation and containment spray 99 Table 1.3 Output Data of the VANESA Model 1. Aerosol Properties * Density of aerosol material (g/cm3 ) " Mean aerosol particle size (ym) " Aerosol generation rate (g/s) " Aerosol concentration at STP (9/m 3 ) " Aerosol concentration in cavity (g/m 3 ) 2. Aerosol Composition " Fission products (mass percent CsI, Cs 2 0, Te, Ru, Sb, Mo, SrO, BaO, CeO2 , La 2 0 3 , Nb 2 Os) " Concrete constituents (mass percent Na 2 0, K 2 0, Al 2 03, SiO 2 , CaO, FeO, Cr 2 03) * Fuel and structural materials (mass percent Fe, Ni, Cr, Mn, Sn, Ag, ZrO2 , U0 2 ) 3. Melt Composition " Change caused by aerosol formation " Change caused by metal oxidation " Change caused by concrete melting 4. Released Gas Characteristics " Composition (volume percent CO, CO 2 , H 2 , H20, " Gas flow rate (moles/s) " Superficial velocity (m/s) 23 02, OH, 0, H) additives, qualification of safety-related electrical equipment for performance under accident conditions, environmental impact statements, post-accident monitoring requirements, and criteria for re-entry of a plant after an accident. Furthermore. an understanding and quantitative assessment of source terms is necessary for conducting probabilistic risk assessments, which are becoming a significant part of the regulatory decision process. The core/concrete interactions could persist for many days, and the ex-vessel fission products and aerosols released from core/concrete interactions into the containment atmosphere, denoted as the ex-vessel source term, could be crucial to the total aerosol concentration in the containment. The resulting higher aerosol concentration in containment could lead to increases in agglomeration rates which could produce a significant reduction in source terms. In the cases where containment failure is substantially delayed, the fission products escaping from the core/concrete interaction might become the principal source of radioactivity transported to the environment. The less volatile fission product species would be the principal concern in this event, since the more volatile species would have escaped from the fuel and be largely removed from the containment atmosphere by condensing on surfaces or agglomerating and settling earlier in the sequence. The overall effect of the core/concrete interaction on source terms depends on the relative quantities of materials and the timing of the peak release rate. These parameters, in turn, are strong functions of the modeling of the core/concrete interaction process, the specifics of the accident sequence, and the plant parameters. 1.2.4.1~Integrated Approach A 1981 review of source term technical bases, NUREG-0772 [N6), pointed out the need for an integrated approach to source term assessment and an improved data base. To initiate this reassessment, the NRC funded a source term study at Battelle Columbus Laboratories reported in BMI-2104 [G1]. This study was the first integrated assessment of source terms, involving a number of computer 21 codes based on the recent severe accident reseaech results. These codes were then coupled to form the BMI-2104 code suite (see Fig. 1.2) that provided the appropriate feedback involved in realistic accident sequences. Subsequently, the NRC made improvements to the BMI-2104 suite of codes as a result of extensive reviews. The revised set of codes is referred to as the NRC's Source Term Code Package (see Fig. 1.3) [G10]. Also, anticipating further research advances, NRC is developing a new, fully integrated, code package called MELCOR. The industry has also made substantial effort to provide integrated source term assessment by developing its own integrated code package called MAAP (a proprietary code) [F2]. MAAP simulates an accident transient, and specifically accounts for system events which occur during the transient including operator interventions, until a permanently coolable state is achieved or until the containment has failed and depressurized. MAAP includes models for the important phenomena which might occur during accident sequences leading to degraded cores. The code is highly modularized so that it can incorporate alternate physical models as they are developed and so that it can be adapted for different reactor plant configurations. When the effort of BMI-2104 was initiated, there was an expectation among many in the nuclear community that a correct treatment of the physical and chemical behavior of fission product release and transport would show a reduction of several orders of magnitude in calculated source terms compared with the Reactor Safety Study. The American Nuclear Society concluded in the technical summary of its report [Al], under the heading "Major Findings" that current knowledge is sufficient "to warrant the reduction of calculated source terms from estimates in WASH-1400 by more than an order of magnitude to several orders of magnitude, except for noble gases". However, the results presented in NUREG-0956 based on the analyses of the Source Term Code Package do not substantiate such generalization for certain severe accident sequences. For some sequences, it was 25 Fission Product Transport Thermal Hydraulic ORIGEN MARCH -Behavor--7 Fission Product Inventory in Fuel Overall I I Behavior of Reactor Coolant System, Molten Core, and Containment CORSOR I Retained Release in Fuel fromFe TRAPMELT MERGE 3 Reactor Coolant System m mm Transport and Reactor Coolant System Retention Release from Core-Concrete Melt I Detailed Temperature, Pressure, and Flow in <* H ConcN Detaild CoreConcrete Temperature and Interactions ~1 I I I I I I I I I I I I -J 1 I NAUA, SPARC, ICEDF Containment Transport and Retention Release of fission products to the environment: Source Term Figure 1.2 BMI-2104 Codes Suite (Ref.(S21) 26 Release of Fission Products to the Environment: Source Term Figure 1.3 Source Term Code Package (Ref.['S21) 27 found that the calculated release fractions of refractory, nonvolatile fission products (such as Sr, Ba, La and Ce), which are critically depend upon the modeling of the core/concrete interactions, are even higher than those of the Reactor Safety Study. 1.2.4.2 Estimates of Uncertainties Analytical models for corium/concrete interactions have been developed to calculate erosion rate, debris temperatures, gas evolution, aerosol production, fission product release, and other parameters. However, it is recognized [A2] that uncertainties inherent in the modeling efforts are still large. The calculation of the release of refractory fission products critically depends the modeling of the core/concrete interaction. A considerable effort is being made by several groups in the US and abroad to estimate the uncertainty of the results that come from various calculational methods. A study aimed on estimation of the uncertainty of radiological source term, referred to as Quantitative Uncertainty Estimation for the Source Term (QUEST) [L1], has been performed at Sandia National Laboratories. In this study, several computer codes were incorporated to model the whole possible sequences during the course of a severe reactor accident. It was pointed out that the uncertainty can develop in two ways. First, because the models of a particular stage of the accident are not accurate, uncertainty in the calculations can be introduced. Second, uncertainty in the previous stage of the accident will be propagated through the present stage, and can be either amplified or attenuated during the propagation througirthe series of codes. The QUEST study provided the first attempt to evaluate the changes in the calculated source terms resulting from reasonable changes in the input parameters and the models. Only three seqiences were evaluated. Based on this study, however, it can be concluded for those sequences that if the mode and timing of containment failure is considered to be fixed. the release fractions would likely 2S show a span of two decades because of input and model changes. An important development in the QUEST study was a method of scanning the entire calculation to determine the important parameters for a particular output of interest. Based on this method, future studies can focus on the estimation of the uncertainty factors important to the purpose at hand. Recently, a program called QUASAR (Quantification and Uncertainty Analysis of Source Terms for Severe Accidents in LWRs) was initiated at Brookhaven National Laboratory [P9). The QUASAR study is, in a way, an extension of the earlier QUEST study. Several important improvements are being incorporated in QUASAR. The major improvement is related to data interpretation; QUASAR will provide probability distribution functions for the ranges of parameter (input) variations, and will determine a probability distribution for source term values (output). QUEST used ranges of input parameter variations that were considered reasonable, and provided high and low source term estimates based on a judgmental selection of compatible input values. Several industry efforts to analyze uncertainties and sensitivities in their results have recently been reported [F3,F4). These efforts identified major factors and parameters controlling uncertainties, but they did not result in quantified ranges of source term values. 1.3 Structure of This Work Simulant experiments using water and cyclohexane were conducted to simulate several physical phenomena related to the core/concrete interaction. In these experiments, water and/or cyclohexane were poured into a test cell to form a single- or a multi-layer liquid pool. The test cell was constructed with porous plates where air was injected through the bottom of the pool. Heat content of the pool was removed by a condensing unit. Various phenomena of the gas agitated pool were observed. Results of these experiments are presented in Chapter 2. 29 In Chapter 3, a downward heat transfer model was formulated from transient heat conduction theory and bubble dynamics to describe the heat transfer across the horizontal corium/concrete interface. The proposed model is a revision of the Lee and Kazini approach [L4] which assumes that no gas film exists at the bottom interface. Based on the early BETA experimental observations, a combined gas film-periodic contact model was also developed involving hydrodynamic stability limits of the gas film to determine the actual mode of the downward heat transfer. In addition, a simple model was developed to calculate the heat transfer between a solid pool and concrete. These proposed models were incorporated into CORCON/MOD2 to form a new version CORCON/MIT for integral analysis of the MCCI. A review of existing models and their differences in the calculation of the downward heat flux is also presented. In Chapter 4, several large scale real material experiments were reviewed. Analyses of these experiments using CORCON/MIT were performed. Validation of various downward heat transfer models by comparisons of their calculations with experimental results was made. Since significant differences among various models of the downward heat transfer were found, a sensitivity study was made to investigate the impact of the downward heat transfer model on the ex-vessel aerosol release. CORCON/MIT and VANESA codes were used in this study. Uncertainties of the calculated aerosol release caused by other parameters were studied as well. The results and discussions are presented in Chapter 5. Finally, conclusions are drawn in Chapter 6, and some recomendations for future wortare made. 30 CHAPTER 2 SIMULANT EXPERIMENTS 2.1 Objective Several physical processes, such as melt freezing, liquid/liquid interfacial heat transfer, layer mixing, and droplet entrainment due to gas sparging, are involved in the analysis of the core-concrete interaction. Since these processes are hard to observe in a real material experiment, simulant experiments are designed with gas agitation and cooling capabilities of both a single-layer and a multi-layer liquid pool to investigate such phenomena in qualitative and quantitative ways. 2.2 Introduction 2.2.1 Freezing Phenomena During early stages of the MCCI, the corium pool can be fully molten and result in a vigorous thermal attack on the concrete. Since the MCCI is an endothermic reaction, and internal heating by fission products decreases as time progresses, the temperature of the corium will fall below its solidification point and freezing begins after some period of interaction. Initially, before freezing, the dominant heat transfer process within the pool is convection. After solidification begins, the heat transfer mode at the pool boundaries has to be determined by the freezing characteristics of the corium pool. There are two possible situations for melt freezing. First, a thin crust may form on the boundaries separating the molten material and its surroundings. Second, solid crystals may precipitate out of solution creating a two phase solid-liquid slurry pool. These two models of freezing lead to different heat transfer modeling of the core/concrete interaction. If a slurry pool forms, it is expected that the heat transfer rates across the pool boundaries is governed by the convective process before the pool is fully solidified. On the other hand, if the solid exists as a stable 31 growing crust surrounding the molten pool, then the crust provides an additional thermal resistance between the interior of the pool and its boundaries, and the heat transfer rate is limited by a conductively controlled process which is far less effective than the convective process. In CORCON/MOD2, a crust freezing model was developed assuming that a stable growing crust forms on any surface (such as the corium/concrete, metallic layer/oxidic layer, and corium/water interfaces) whose temperature falls below the solidification temperature. This model also assumes that the mechanical strength of the crust is enough to hold it coherent in spite of the loads imposed by the concrete decomposition gases. However, there is no experimental evidence to substantiate these assumptions. In this study, a simulant experiment will be conducted to investigate the freezing phenomena of molten materials under the gas agitation condition. 2.2.2 Interfacial Heat Transfer In MCCI, the immiscible metallic and oxidic phases will be separated into two layers due to the density difference, provided that the layer mixing due to gas agitation is limited. The temperature responses of the metallic and oxidic materials depend not only on the amount of heat generated (decay heat in the oxidic layer and chemical reaction heat in the metallic layer) but also the heat transfer rates along various heat transfer paths. The interfacial heat transfer between these two immiscible layers is characterized by natural convection agitated by transverse gas flow. As the interfacial heat transfer increases, the heat transferred downward into the concrete from the initially heavy oxidic layer is reduced and the upward heat flux into the overlying metallic layer is increased. Therefore, the amount of decomposed concrete, the melt temperatures, and the gas generation rate are all affected to some extent by the magnitude of the interfacial heat transfer. Actually, it has been found by a sensitivity study [G7] that the interfacial heat transfer is an important factor in predicting the melt behavior of MCCI. 32 Several correlations have been proposed to calculate the interfacial heat transfer (see Table 1.1). The one used in CORCON/MOD1 was developed by Konsetov [K4] and later modified by Blottner [B4], which is expressed in terms of heat transfer coefficients for the upper, U, and lower, L, layers as: hL,U - k (Pr ) 1/3 (2.1) 0.00274A.42]1/3 where ATia,,ye, is the temperature difference between the layer bulk and its interface boundary, and a is the void fraction. Applying the definition of the heat transfer coefficient to each layer separately and then together yields the following expression for the liquid/liquid interface temperature, Tint: (2.2) hLTL + hUTU hL + hU where TL and TU are the lower and upper layer temperatures, respectively. The overall interface heat transfer coefficient, hj, can be expressed as: hy = hUhL hLT+ hL ATBulk where q'j is the heat flux across the liquid/liquid interface, and the temperature difference ATBik is equal to (TU7 - TL). The modified Konsetov correlation has taken into account the effect of natural convection in terms of A Ti yer, and also the effect of superficial gas velocity in terms of the void fraction a. The void fraction a is obtained by [M4]: a = , u 1.53 gA (2.4) where tit is the terminal velocity of the rising bubble, and the Laplace constant A is defined as: -g0.5 A g(e-P)(2.5) 33 The constants appearing in the modified Konsetov correlation were obtained by fitting limited experimental data (only one data point) of a slag-metal system [S6]. It was found later that this correlation significantly underestimates the oil/water experimental data of Werle [W1], by as much as two orders of magnitude. Based on the assumption of transient heat conduction between the arrival of consecutive bubbles, Szekely [S6] derived an interfacial heat transfer coefficient for bubble stirred interface of two immiscible liquid layers. It was given in the following form: hU,L = 2 (2.6) (pkc) where t, is the time interval between the arrival of consecutive bubbles, and Szekely suggested that te can be calaulated as: A Ab No te = A (2.7) where A = total cross section area of interface Ab = surface area swept by single bubble No = number of bubbles produced per unit time The Szekely's model was later modified by Blottner [B4] based on the derivation of t, as: t, AVb AbNoV (2.8) 0.445- Vb Abig j( where V is bubble volume and rb is equivalent bubble radius. Combining equations (2.6) and (2.8), gives: NuUL = 1.69 (Re - Pr)0 '5 (2.9) where NUU,L = k L; 'bh Re =34 p - Pr = k (2.10) The modified Szekely model was then incorporated in the WECHSL code for interfacial heat transfer calculation. In CORCON/MOD2, an empirical correlation developed by Greene [C3] is Greene modified the Szekely correlation based on his own experimental used. data (oil/water and water/mercury) as: 0 8 0 NuU,L = 5.05 Re .5Pr - (2.11 In this correlation, the interfacial heat transfer increases with the increasing of the liquid viscosity. Lee and Kazimi of te, [L4] have considered a different approach in the derivation and the contribution from the carried liquid along with the rising bubble. They proposed an interfacial heat transfer correlation based on the Szekely model as: 0 5 5 Nuv,L = 8.84 (J *)1' (Re- Pr) (2.12) where the dimensionless superficial gas velocity J* was defined as: jg J*L59(2.13) = P -r(0.25 L . and PL is the density of the lower liquid layer. The correlation constant was obtained by fitting the water/mercury [G7] and oil/Wood's metal [W1] data with an assumption of constant bubble radius of 1 mm. This model increases the dependency of the interfacial heat transfer on the superficial gas velocity from the power of 0.5 (equation 2.9) to the power of 1.0 (equation 2.12). All these correlations have )een applied to a real case (metal-over-oxide liquid pair) based on the physical properties of the coriumn materials (Table 2.1) and assumed values of bubble radius and ATBulk. 35 It is found that there are order Table 2.1 Corium Materials Properties Oxidic Layer Metallic Layer p (kg/m 3 ) 7000 5750 c, (J/kg K) 600 740 k (W/m K) 3.3 40.0 (1/K) 1.0x10- 4 0.6 x 10-4 y. (pPa - s) 4000 4000 a (N/m) 0.45 1.5 Tsol (K) 2673 1673 # 36 of magnitude differences among the interfacial heat transfer coefficients predicted by the various models (see Fig. 2.1). The effects of the parameters (rb, \TBaLk, and layer configuration) on the prediction of the 'interfacial heat transfer are also shown from Figs. 2.2 through 2.4. In this experimental study, the interfacial heat transfer between two immiscible simulant liquid materials under different gas velocities will be measured, and compared with these analytical models. 2.2.3 Layer Mixing In the BETA experiments [A6], it was observed that as the input power increased, the amount of the metallic materials entrained into the oxidic layer increased significantly due to the increased gas generation rate. This entrainment was recognized by the observation of a sharp decrease in the input power because of the induction method of heating used in the BETA test. This observation supported the assumption that there may be times during the core/concrete interaction when the gas sparging rate is high enough to lead to mixing of the two immiscible layers, oxidic and metallic materials. At other times, when the gas generation rates are reduced, the two layers will separate. This physical phenomenon has not been properly modeled in the integral analysis codes, and it may affect the core/concrete interaction. First, the heat transfer rate between the melt and concrete could be affected not only because the physical properties of the reaction materials will be altered but also the freezing phenomena of the mixed layer could be changed. Second, the vaporization rate and chemical composition of the melt may be changed due to the change of the oxygen potential and zirconium oxidation rate. A sensitivity study [B5] has indicated that the degree of mixing of the pool is important in determining the magnitudes of fission product release during core/concrete interaction. However, the mixing criterion of the gas flow limit is not well-developed and very difficult to be identified in a real material experiment. A study group at the University of Wisconsin [G3] is now conducting simulant 37 6 LJ 10 z 105 E0 z 'N 2 10 1[_ 00 10-4 SUPERFICIAL GAS VELOCITY [m/s] Figure 2.1 Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Predicted by Different Models 38 MODIFIED KONSETOV CORRELATION z 1. E-a z I= 10 2 L 10-4 100 SUPERFICIAL GAS VELOCITY [m/s] Figure 2.2 Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Based on Different Temperature Differences 39 108 - - I I I 1 1 11111 1 111111 Modified Szekely (rb=0. 001 I m) Greene (rb=0.001 m) Lee & Kazimi (rb=0.001 r m) Modified Szekely (rb=0.01 m) Greene (r '=0.01 m) Lee & Ka zimi (rb= 0.01 m E" Q I 1 1 1 1 111i 106 raw C2 z r ................ 44 wei 10 2 101 I I 1 I II i 1 I I 1 1 1 11 10 -4 I I 1 1 1 1 11 I I I I II 10-1 100 SUPERFICIAL GAS VELOCITY [m/s] Figure 2.3 Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Based on Different Bubble Diameters 40 LEE & KAZIMI CORRELATION 107 Bottom Layer: Oxide Bottom Layer: Metal - -. 10 6 E--- z 105 4 z E-- E- 103- 2 Si 10- 1I iii 10-4 lmol 10-3 i ii i ml 10-2 I iiiii ii 10-1 100 SUPERFICIAL GAS VELOCITY [m/s] Figure 2.4 Interfacial Heat Transfer Coefficient of the Metallic/Oxidic Corium Pool Based on Different Layer Configurations 41 experiments, involving various combinations of liquid pairs (refrigerants, oil, mercury, and water) to scope out the effects of density ratio, surface tension, and viscosity on the layer mixing. In this study, the intermixing phenomena of an immiscible liquid pair will be examined with and without the influence of the freezing process. 2.2.4 Droplet Entrainment An aerosol can be generated from a pool of molten corium due to mechanical breakup of the liquid melt by the flowing gases. The mechanical aerosol generation process can occur in two ways - bursting of bubbles at the melt surface and melt splashing at a liquid/gas interface. At low gas velocities (bubbly flow), the liquid droplets are expected to generate from the bursting of individual bubbles as they break through the liquid surface. If the gas generation rate is high enough to achieve a churn-turbulent flow regime, the gas velocities would be sufficiently high to entrain droplets of liquid (caused by liquid filament and sheet instabilities at the liquid/gas interface) within the bulk of the two phase medium. The entrainment of liquid by sparging gases has been reviewed by Kataoka and Ishii [K9] and by Ginsberg [G9]. Kataoka and Ishii suggested that gas flow through liquids in the churnturbulent regime can cause noticeable entrainment when: jg ;> 0.325 [got(Pl 2 Pg)] 0 .25 (2.14) They also found that correlations of the amount of material entrained had to be categorized in terms of distance from the liquid surface. Their analysis revealed three regions of entrainment in the axial direction from a pool surface. In the near surface region, entrainment is independent of height and gas velocity. In a momentum controlled region, the amount of entrainment decreases with increasing height from the free surface and increases with increasing gas velocity. In the deposition controlled (far field) region, the entrainment increases with increasing 42 gas velocity and decreases with increasing height due to deposition of droplets. The boundaries between the regions are also dependent on the gas velocity. Kataoka and Ishii developed single correlations for the entrainments present in the near surface and far field regions, however, they found that the correlations for the momentum controlled region had to be categorized in terms of the magnitude of the gas velocity, defined as low gas flux, intermediate gas flux, and high gas flux flow regimes. Several dimensionless parameters have been used by Kataoka and Ishii in the development of entrainment correlations; defined as follows: E Gas Velocity: J* = . 5g 0.25 a9(pl - pg 9) Height: H* 2 H = 05 [g(pt - pg) Gas Viscosity: Ni = 0.5 t [pgO D* = Vessel Diameter: [ D ]0.5 g(pt - E* Entrainment: where jg pg) Pg.g is the superficial gas velocity, H is the height above the pool surface, and DH is the equivalent diameter of the pool. The boundaries and entrainment correletions were then given by: (i) Near Surface Region This region is limited to the viscinity of the pool surface given by: 0 < H* 0-5 (D*)04 2 ( < 1038J*N; 9 _ H~ )03 (2.15) A~P In this region, the entrainment is given as: E* = 4.84 x 10- 3 ) ( pg 43 (2.16) (ii) Momentum Controlled Region This region is limited to the intermediate height range given by: lo.42( 1038JNo45(D* 3 P )- < H* < 1970N, .3(D* )o.42 o-2 (2.17) This region is subdivided into three regimes, depending on the gas velocity: Low Gas Flux Regime ( ) < 6.39 x 10-4 (2.18) with E= 2.213N 5 (D* )1 25 0.3 ( ) (2.19) Intermediate Gas Flux Regime ( ) 6.39 x 10~4 withH with 5.7 x 10-4N-5(D* )-o.42(g o)0 E* =54 7 E 0 N " D )H g x A.1 1N7(D)1(P 5.417 x (2.20) )31 2.1 (2.21) Jg High Gas Flux Regime (i ) > 5.7 x 10-4 N 5(D*) 0.42 0. (2.22) with )7~20 E*c (2.23) (iii) Far Field Region This region is above the height given by: H* > 1970N,.33(D* )o.42(g o. 2 3 (2.24) In this region, the entrainment when considering the deposition is given by: J* ) 3 exp[-0.205H/DH] E* = 7.13 x 10-4N,.5 (2.25) Pg Without the deposition effect, the entrainment in the far field region is given by: E 1.99 x 10- 3 N 44 5 Ag ( Pg )(J)3 (2.26) For most reactor accident analyses, the correlation suggested by Kataoka and Ishii in the far field region, without considering the deposition effect, is the most proper model for mechanical aerosol generation from core melt into the containment atmosphere. In this experiment, however, an attempt is made to develop a procedure which can be employed to characterize the liquid droplets entrainment in the momentum controlled region under low gas flux conditions. 2.3 Experiment Description 2.3.1 General Features The apparatus was designed by M. Lee [L2] to simulate two fundamental physical processes of the corium/concrete interaction, namely, gas evolution at the pool boundary and freezing of the pool material. However, the physical processes of internal heat generation of the corium and melting of the concrete are not included in this experiment. The experiment apparatus consisted of four major parts: a test cell, a cooling unit, an air supply system, and measurement instruments. A schematic diagram of the experimental apparatus is shown in Fig. 2.5, and a detailed description of the apparatus can be seen in Ref. [L2]. 2.3.2 Apparatus (i) Test Cell The test cell is a rectangular pool bounded from the bottom and two sides by bronze porous plates. The front and back walls of the test cell are made of transparent plexiglass plates from which the behavior of the pool can be observed. The dimensions of the test unit are 225.5 mm by 244.5 mm in cross section and 250 mm in depth. Simulation of gas evolution from the pool boundary is accomplished by injecting air through the porous plate into the liquid pool. The cooling capability of the test cell is provided by a freon 12 refrigeration cycle. An evaporator is placed behind each porouis plate for removal of the heat content of the pool. 45 TEST CELL F B COOLING UNIT E A AIR SUPPLY UNIT I ~~~;&, Figure 2.5 rgauge Schematic Diagram of the Simulant Experimental Apparatus (ii) Cooling Unit The major part of the cooling unit is a Tecumseh AH7514AC condensing unit with a maximum capacity of 16800 BTU/hr (4.9 kW). The cooling unit contains three independent cooling loops which are controlled by refregeration shut off valves to activate the heat extraction in the sideward or downward directions. A back pressure regulator was installed between the suction and discharge lines of the freon compressor to control the operating pressure and temperature of the condensing unit. (iii) Air Supply Sysytem The injected air is supplied by the air compressor of the laboratory building. The volumetric air flow rate is measured by a Fisher & Porter 10A3557 series (tube size 12.7 mm) rotameter. The maximum air flow reading of the rotameter is 6.43 SCFM (3.03 £/s). A pressure gauge was installed at the upstream of the rotameter to measure the air system pressure. Accounting for a pressure correction factor and the flow area, the maximum superficial gas velocity achieved in this experiment was 126 mm/s. (iv) Temperature Measurement All temperatures are measured with Type E thermocouples. A KAYE ramp processor and scanner system are used to record the temperature data at every prespecified time interval. The positions of the temperature measurements are shown in Fig. 2.6. (v) Entrainment Measurement An optical particle counter is used to investigate the size distribution of the entrained liquid droplets generated from the bubbling pool. A millipore membrane (0.2 pm pore size FG filter) contained within a filter holder is looped together with a conventional carbon-vane pump (with flow capacity of 2 e/s) to collect the liquid droplets. During the collection procedure, the liquid droplets above the pool surface together with air flow are driven into the filter holder by the pump, 47 AIR INLET Figure 2.6 Illustration of the Temperature Measurement Locations 48 and deposited on the millipore membrane. A microbalance with accuracy to 1 pg is used to find the weight difference of the millipore membrane before and after the collection procedure. 2.3.3 Simulant Materials The simulant materials selected for the experimental study were water (H 2 0), cyclohexane (C6 H 2 ), and air. Physical properties of these simulant materials are listed in Table 2.2. There are advantages for using the water and cyclohexane as simulant materials because they are transparent, nontoxic, noncorrosive, inexpensive, chemically inert, easy to handle, and immiscible. In addition, the density ratio of water and cyclohexane (0.78) is very close to the density ratio of the metallic and oxidic materials (0.82) at early stages of the MCCI. This preserves an important factor in the simulation of the intermixing phenomena of the MCCI. In the simulation of the freezing phenomena, the solidification temperature of the cyclohexane is higher, therefore, the upper cyclohexane layer will be frozen earlier than the lower water layer during the cooling down process. This is similar to the situation at later stages of the MCCI, in which freezing of the upper layer (oxidic material) occurs earlier than that of the lower layer (metallic material). With this feature, the freezing phenomena of the cyclohexane can be used to indicate whether the oxidic material in the MCCI will be frozen in the form of a slurry or a crusting layer. 2.3.4 Test Procedures Various experiments were conducted in this study to investigate different physical phenomena, divided into the following categories: " FP Test: Freezing Phenomena " HT Test: Interfacial Heat Transfer " LM Test: Layer Mixing " DE Test: Droplet Entrainment Detailed description of these tests will be given in what follows. 49 Table 2.2 Simulant Materials Properties Water Cyclohexane Air p (kg/m 3 ) 1000 778 1.28 c, (J/kg K) 4180 1770 1000 k (W/m K) 0.55 0.10 0.025 / (1/K) p (pPa- s) a (N/m) Tso 0 (K) 4 1.8x10- 2.0x10-4 1000 960 0.0728 0.0253 273 279.6 50 18 (i) FP Tests These tests were performed to observe the freezing phenomena of a bubble agitated liquid pool. Both single-layer (water dr cyclohexane) and two-layer (cyclohexane-over-water) pools were tested under different gas velocities to identify the existence and stabilities of the boundary crusts. During the experiment, the air flow rate was kept constant, and the pool temperature was continuously monitored. Heat content of the liquid pool was removed in the downward direction only. Sideward cooling was not activated in these tests. The experiment was started with liquids at room temperature, and ended at the time when significant solidification occurred. The freezing phenomena of the liquid pool were visually observed. (ii) HT Tests In this test series, fixed amounts of water (3.0 kg) and cyclohexane (1.56 kg) were poured together into the test unit. The highest gas flow rate employed in this test was based on the limitation of keeping the water and cyclohexane layers well-separated without significant mixing. Heat subtraction was activated in the downward direction. The liquid layers temperatures as well as the surrounding (above the pool) temperature were recorded every two minutes. Each experiment was tested for more than 30 minutes before the cyclohexane started freezing. (iii) LM Tests The mixing phenomena were examined in the tests with different gas injection rates. The water was colored congo red in order to assist the visual identification of the mixing phenomena. The tests were performed with and without cooling the pool to scope out the effect of solidification on the layer mixing process. (iv) DE Tests These tests were conducted to investigate the characteristics of the liquid particles generated from an aqueous solution pool under bubble agitation conditions. Two types of experiments were performed: (1) optical particle counter experiments 51 for droplet size measurement; and (2) filter collection experiments for quantifying the amount of liquid entrainment. In the optical counter experiments, two tests were performed, one with a pure water pool for background test, another with 1% by weight aqueous solution of potassium sulfate (K 2 SO4 ). Both tests were conducted at a gas velocity of jg = 8.0 mm/s. Under this condition, the entrained liquid droplets accompanied with the flowing air were sucked into the optical particle counter. A dryer using silica gel was set up on the collection loop in front of the counter to ensure that only solid K 2 SO 4 particles passed through, and the numbers of particles of different sizes in the flowing gas stream were counted by the counter. In the filter collection experiment, several tests with the aqueous solution pool were performed to quantify the droplet entrainment subjected to different gas injection rates. During the experiment, the bubble-induced liquid droplets suspended in the air stream were forced by the carbon-vane pump into the filter holder which was located at certain positions above the pool surface. After several tens of minutes, the filter was carefully removed and placed into an oven to dry the water. Residual aerosol particles (K 2 SO4 ) remained on the filter. The amount of collected potassium sulfate was weighed by a microbalance. The total amount of liquid entrainment could then be calculated from the known weight fraction of potassium sulfate in the solution pool. 2.4 Experimental Results 2.4.1 Freezing Phenomena During the initial, transient stages of the core/concrete interaction, the debris may be relatively hot and gas generation rates can be quite high. Superficial gas velocities over 1 m/s have been observed in a real material experiment [P12]. However, as the melt cools down, the gas velocities can be reduced to 100 mm/s during the freezing stages. In this experiment, a superficial gas velocity of up to 52 126 mm/s was used to investigate the freezing phenomena of the simulant materials. A list of the freezing experiments is shown in Table 2.3. Observed phenomena are described as follows. (i) Single Water Layer In the water experiments, two different phenomena were observed at the moment of freezing. One is defined as bulk freezing (FP-1,2,3 tests), in which pieces of ice appear and float around in the middle of the pool accompanied with a thin layer of ice crust across the bottom liquid/solid interface simultaneously. Significant supercooling (liquid below solidification temperature before freezing actually starts) was found in this type of freezing. Upon freezing, the pool bulk temperature jumped up to the solidification temperature of water. Another phenomenon is defined as layer freezing (FP-4,5,6 tests), in which only a bottom ice crust was formed upon freezing, and slight supercooling was observed. The bulk temperature histories of the water pool are shown in Fig. 2.7. In any event, the bottom ice crust was always stable and the thickness of the crust increased gradually. No top crust at the water/atmosphere interface was observed during these tests. Even though some of the bubble generation sites were completely blocked by the bottom crust, the permeation of the gas through the ice crust was always observed. The porous nature of the ice crust layer could easily be seen by post-test examination. Air bubbles trapped in the crust layer were observed as well. (ii) Single Cyclohexane Layer In the cyclohexane experiments, the pool was always frozen in the same fashion of the bulk freezing of the water pool. However, in the test of low gas velocity (FP-7,8 tests), a stable growing crust was formed at the the top surface at a later time than the formation of the bottom crust. In the test with higher gas velocity (FP-9,10,11 tests), no top crust was observed even though the bottom crust was still stably formed. 53 Table 2.3 Freezing Phenomena Tests Water Cyclohexane ig Test (kg) (kg) (mm/s) FP-1 1.00 6.3 FP-2 1.00 13.1 FP-3 1.00 83.3 FP-4 1.00 9.2 FP-5 4.00 51.7 FP-6 2.00 FP-7 - 1.56 6.3 FP-8 - 1.56 13.1 FP-9 - 2.34 45.0 FP-10 - 1.56 66.3 FP-11 - 1.56 126.0 - 126.0 FP-12 2.00 1.56 6.3 FP-13 2.00 1.56 13.1 FP-14 2.00 2.34 20.1 FP-15 2.00 1.56 40.0 FP-16 3.00 2.34 51.7 FP-17 3.00 2.34 104.1 54 15 o -A FP-5 Test (Layer Freezing) 10 0- - 5I 0 I I I I 20 40 60 80 TIME [min] Figure 2.7 Water Pool Temperature Histories 'A,4 100 120 (iii) Water/Cyclohexane Layers In the low gas flow tests (FP-12,13,14 tests), in which the two liquids stayed separate into distinct layers, small pieces of solidified cyclohexane appeared in the upper layer at the moment when the pool temperature reached the melting point of the cyclohexane. After a while, the cyclohexane layer was frozen as a single piece floating atop the water layer. During this time period, no cyclohexane crust was actually formed on any of its boundaries. As the cooling process progressed, a stable ice crust was eventually formed at the bottom interface. In the high gas flow rate tests (FP-15,16,17 tests), in which these two liquids were mixed into one homogenous layer, cyclohexane was frozen as small pieces in the homogenized layer at the beginning. After a while, bigger pieces of the solidified cyclohexane appeared attached to the sidewall of the test unit. Some of the peripheral areas of the bottom plate were covered by the solidified cyclohexane. When the pool temperature dropped further, a pure ice crust was formed at the center region of the bottom plate. No other boundary crust was observed during this test. The important observation of the water/cyclohexane test is that the cyclohexane was always frozen in the slurry form without any formation of a boundary crust. 2.4.2 Interfacial Heat Transfer The interfacial heat transfer can be analyzed according to a macroscopic energy balance of the cyclohexane layer. Heat flow into and out of the cyclohexane layer are calculated from measured temperatures and some estimations, given as follows: Qdown [McP dT] + QP + Q.ide - Qar (2.27) where Qdown is the heat extraction rate in the downward direction through the water/cyclohexane interface. M and c, are the mass and heat capacity of the 56 cyclohexane, respectively. and Qzd, are the heat addition rates from the Q2, pool upper surface and side walls, respectively. Qai, is the heat reduction rate due to cool air injection. These heat flow rates are calculated as: Qup = hup(Tatm Qside = haide(Tv Qair Tu)At, (2.28) Tu)A, (2.29) - (ThCp)air(TU - TL) (2.30) and the overall interfacial heat transfer coefficient is calculated by: h = dow Atu(TU - TL) (2.31) where Tatm = upper surrounding temperature Tw = sidewall surface temperature Tu = upper layer (cyclohexane) temperature TL = lower layer (water) temperature Atu = cross section area of the test unit A, = sidewall contact area mair = mass flow rate of the injected air (cp)air = heat capacity of air Based on the natural convection over a plate with gas injection, the heat transfer coefficient hu, can be estimated as [M4]: hu, = 10.0 W/m 2 K Without gas injection on the sidewall, a relatively small sideward heat transfer coefficient was assumed as: hsIde 1.0 W/m 57 2 K In the experiments, the sideward heat transfer area A, upward heat transfer area At, is comparable to the but the temperature drop in the sideward direction ((T. - TLJ) < 1.0 K) is far less than that in the up vard direction ((Ttrn - TT) ~_ 10.0 K). Therefore, the sideward heat addition rate, Qside, can be neglected in the energy balance calculation. In equation (2.30), it is assumed that the injected air is thermally equilibriated with each layer. A major error in the experimental data reduction can be caused by the uncertainty of the measured temperature difference (TU - TL). The accuracy of the temperature measurement is ±0.05 K while the temperature difference measured at the high gas flux test can reach as low as 0.1 K. However, the results of the experiments shown in Table 2.4 are calculated from the measured temperatures averaged over a time interval of 20 minutes (one measurement every two minutes). Comparisons of the various interfacial heat transfer models to the cyclohexanewater experiment data are shown in Fig. 2.8. It is seen that both the modified Szekely and Lee and Kazimi models agree reasonably well with the experimental data. The Greene's model overpredicts and the modified Konsetov correlation underestimates the experimental data. At low gas velocity (Jg < 10 mm/s), the experimental data disperse over a wider range and seem to deviate from the trend of the experimental data obtained at higher gas fluxes. This is caused by the non-uniform pattern of the rising bubbles observed in the low gas flux test. Unfortunately, most of the bubbles were generated at the peripheral region of the pool when the injected gas rate was low. At the center region of the pool, where the thermocouples were located to measure the layers temperatures, the bubble-induced internal circulation was quite limited because of low bubble frequency. Therefore, the non-uniform bubble pattern will result in a higher thermal gradient, i.e. a higher temperature difference (TLT - TL), which gives a lower interfacial heat transfer coefficient than one can expect from a pool with uniform bubble distribution. Table 2.4 Interfacial Heat Transfer Tests jg -MC UJj Q, Qair Qdown (Tu - TL) h (W) (W) (W) (K) (W/m 2 K) 5.5 0.31 10.4 0.733 258 4.97 5.5 0.27 10.2 0.626 296 6.67 6.25 5.5 0.22 11.5 0.459 455 HT-4 7.30 5.10 5.5 0.18 10.4 0.343 551 HT-5 7.93 5.10 5.5 0.10 10.5 0.177 1078 HT-6 9.19 6.89 5.5 0.42 12.0 0.636 341 HT-7 9.19 6.38 5.5 0.12 11.8 0.182 1174 HT-8 9.19 6.25 5.5 0.09 11.7 0.131 1611 HT-9 9.19 7.52 5.5 0.10 12.9 0.152 1548 HT-10 9.84 6.89 5.5 0.22 12.2 0.318 694 HT-11 11.2 8.54 5.5 0.31 13.7 0.394 632 HT-12 11.8 6.63 5.5 0.11 12.0 0.136 1598 HT-13 12.4 7.78 5.5 0.27 13.0 0.303 780 HT-14 12.4 10.2 5.5 0.35 15.4 0.394 707 HT-i5 12.4 7.65 5.5 0.11 13.0 0.126 1873 HT-16 12.4 11.0 5.5 0.18 16.3 0.202 1463 HT-17 13.8 9.31 5.5 0.12 14.7 0.121 2198 HT-18 14.4 9.56 5.5 0.23 14.8 0.229 1173 HT-19 15.7 9.44 5.5 0.21 14.7 0.192 1393 HT-20 17.2 11.6 5.5 0.22 16.9 0.182 1686 HT-21 17.2 8.80 5.5 0.24 14.1 0.192 1330 HT-22 19.5 11.3 5.5 0.19 16.6 0.139 2174 HT-23 19.5 8.54 5.5 0.14 13.9 0.101 2497 HT-24 21.0 7.14 5.5 0.20 12.4 0.136 1655 HT-25 21.0 11.4 5.5 0.22 16.6 0.146 2060 HT-26 21.8 8.16 5.5 0.16 13.5 0.106 2309 HT-27 22.5 10.8 5.5 0.23 16.1 0.146 1995 HT-28 25.0 12.9 5.5 0.24 18.1 0.136 2413 HT-29 27.4 16.9 5.5 0.26 22.2 0.132 3050 HT-30 27.4 14.8 5.5 0.20 20.1 0.101 3605 Test (mm/s) (W) HT-1 6.04 5.24 HT-2 6.04 HT-3 59 %% 105 Modified Szekely - -- E- Z-- . Greene Lee & Kazimi Modified Konsetov ~ Experiment -- 10 C z 10 3 0 5 10 15 20 SUPERFICIAL GAS VELOCITY 2z Figure 2.8 25 (mm/s] Interfacial Heat Transfer between Water and Cyclohexane Layers 30 2.4.3 Layer Mixing The layer mixing tests are listed in Table 2.5. In these tests, four different liquid patterns were observed in both LM-1 and LM-2 tests with different gas injection rates: (1) At j < 15 nm/s, the two liquid materials stay separate. Small amounts of water drops were entrained into the upper cyclohexane layer when the gas bubbles penetrated through the layer interface. The entrained water droplets then fell back into the water layer due to their higher density. Basically, a clear water/cyclohexane interface was observed at this low gas velocity, and both layers were in the regime of bubbly flow. (2) As J, ranged from 15 to 30 mm/s, the rate of water droplet entrainment was high enough to create a mixing layer sandwiched between the water and cyclohexane layers. The thickness of the mixing layer increased with increasing superficial gas velocity. (3) As jg reached 30 to 50 mm/s, the pool exhibited a two-layer pattern: a well-mixed layer (in churn flow regime) formed on top of a pure water layer (in bubbly flow regime) while distinguished cyclohexane layer no longer existed. (4) At jg > 50 mm/s, the two liquids were violently agitated and mixed into one homogenous layer. A churn flow pattern was observed in this gas velocity range. Based on the correlation (equation 2.14) proposed by Kataoka and Ishii to characterize the transition between the bubbly flow and churn-turbulent flow, the critical superficial gas velocities of the water-air and cyclohexane-air systems are 53.0 and 43.0 mm/s, respectively. The flow regimes observed in the experiment are in good agreement with these predictions. The observed mixing phenomena discussed above seem to indicate that the two immiscible layers are entirely mixed when the superficial gas velocity is higher than the critical velocities of both layers. In the cooling tests (LM-3,4,5,6 tests), it was found that the mixing patterns were not affected by the solidification of the pool materials. Since no boundary crust was formed at the liquid/liquid interface, the extent of layer mixing was not disturbed by the freezing phenomena. 61 Table 2.5 Layer Mixing Tests Water Cyclohexane jg Test (kg) (kg) (mm/s) Cooling LM-1 2.0 1.56 6.0-126.0 No LM-2 2.0 2.34 6.0-126.0 No LM-3 2.0 1.56 6.0 Yes LM-4 2.0 1.56 21.0 Yes LM-5 2.0 1.56 45.0 Yes LM-6 2.0 1.56 65.0 Yes 62 2.4.4 Droplet Entrainment The numbers of the K 2 SO4 particles with different particle sizes in the gas stream were counted by the optical particle counter. Each size particle was counted ten times with the counting period of two minutes. Averaged values (counts/min) of different particle sizes are shown in Table 2.6. It is seen that the detected solid K 2 SO 4 particles had a median size of 0.5 pmp and a maximum size of 5.0 pm. The particle size of the entrained liquid droplet can be calculated by: -11/3 DH 20 1 _ .f where f 20 PK 2 SO - PH 4 DK2SO 4 (2.32) J is the weight fraction of K 2 SO4 in the aqueous solution, and D is the diameter of particle. Therefore, the median and maximum sizes of the water droplets entrained by the bubbly flow (j9 = 8.0 mm/s) were about 2.0 and 20.0 pm,, respectively. The amounts of collected potassium sulfate in the filter collection tests are listed in Table 2.7. The dimensionless parameters of these tests are also shown in this table. Comparison of the data with the Kataoka and Ishii correlation is presented in Fig. 2.9. It is seen that the differences between the experimental data and-the prediction of entrainment are within a factor of four. 2.5 Summary and Conclusions The freezing phenomena experiments conducted in this study are of scoping nature. It was observed that a bottom crust could be formed across the bubble agitated horizontal liquid/solid interface, with gas velocities up to 126 mm/s. This observation confirms a freezing model assumption used in the current MCCI integral analysis codes. However, the liquid/liquid interface crust also assumed in the analysis codes was not formed in the simulant experiments. The stability of a top crust is also called into question by the observations of this experiment. Therefore, the freezing of the oxidic layer involved in the MCCI could be in the slurry form rather than a crusting boundarv. In addition, 63 the supercooling plhenonenon Table 2.6 Counts per Minute of Different Particle Sizes Particle Size (pim) Test DE-Al 0.3-0.5 0.5-0.7 0.7-1.0 1.0-3.0 3.0-5.0 5.0-7.0 7.0- 504703 109942 27455 9169 371 16 6 479706 73422 12357 3230 125 13 7 24997 36520 15098 5939 246 3 -1 (Aqueous Solution) DE-A2 (Pure Water) Difference 64 Table 2.7 Filter Collection Tests H Collected Water J*/H* E* 9.38 x 10-6 Test (mm/s) (mm) (mg/s) DE-B1 16.4 180 0.0108 5.44 x10-5 DE-B2 16.4 180 0.0102 5.44 x 10- 5 8.80x 10 DE-B3 19.1 180 0.0517 6.34 x 10- 5 3.84x10-5 DE-B4 32.9 180 0.177 1.09 10- 4 7.62x 10~ 5 DE-B5 46.9 180 0.248 1.56x 10- 4 7.51x 10-5 DE-B6 70.1 180 0.492 2.33x10- 4 9.96x10-5 DE-B7 82.6 320 0.0908 1.54x 10- 4 1.57 x 10-5 65 x 6 bA bi 10-5_ 10 6 10-5 I 10-4 I 11 1 J9*/H* Figure 2.9 Water Droplet Entrainment from the Bubbling Pool 66 observed in the experiments contradicts the assumption used in predicting the timing of freezing. The interfacial heat transfer between the water and cyclohexane layers was measured under various superficial gas velocities. Comparisons of the data with the existing models were made. The modified Szekely model used in the WECHSL code agrees well with the experimental data. While the Greene model incorporated in the CORCON/MOD2 seems to overpredict the experimental results. In the mixing test, it is found that two immiscible liquids with density ratio of 0.78 were entirely homogenized under a modest superficial gas velocity of 50 mm/s. The transition patterns of the mixing phenomena with different gas velocities were observed as well. Liquid droplets entrained by the flowing gas were quantified by the experiment. The median and maximum-sizes of the water droplets entrained by a gas flow of j 9 = 8.0 mm/s were found to be 2.0 and 20.0 pm, respectively. The amount of entrainment was found in good agreement with the prediction by the Kataoka and Ishii model. 67 CHAPTER 3 DOWNWARD HEAT TRANSFER MODEL FOR THE MELT/CONCRETE INTERACTION 3.1 Introduction The behavior of a pool of molten core materials in a concrete cavity is governed by a simple energy balance. The decay heat and chemical reaction heat generated in the pool may be lost through its top surface to the containment atmosphere and containment structure or to the surrounding concrete. The partition of energy between concrete and the top surface is determined by the various thermal resistances from the pool of molten core materials to the surroundings. Heat transfer phenomena involved include: radiative heat loss from hot corium boundaries, convective heat transfer within the internally heated pool, heat transfer between immiscible liquid layers with bubble agitation, heat transfer at eroding interfaces with gas injection and conductive heat transfer through solidified crust. All these heat transfer processes will, in fact, affect the corium temperature in a coupled fashion. Among various phenomenological heat transfer models, the one having the most direct impact on the core-concrete interactions process is that describing the heat transfer across the melt/concrete interface. The extent of concrete ablation, the melt temperature response, the amount of decomposition gas release and therefore the amounts of chemical heat and aerosol releases, all directly depend on the amount of heat that can be transferred across the melt/concrete interface. The downward heat transfer is driven by the temperature difference between the molten core materials and the concrete. Vigorous agitation of the melt by concrete decomposition gases is expected to enhance the convective heat transfer 68 process. Besides the decomposition gases, melting concrete (slag) generated beneath the corium pool will be buoyed up due to its relatively low density, and will also affect the downward heat transfer. As the pool cools down, formation of a bottom crust provides an additional thermal resistance to the downward heat flow path. This conductive thermal resistance will limit the amount of heat loss to concrete. For some accident scenarios, the core debris may initially be solid or partially solid. If the degree of solidification is such that internally generated heat cannot be removed, the debris temperature will rise and the core materials will melt until the convective heat transfer is sufficient to allow a thermal balance to be achieved. Both analytical and experimental efforts have been reported on the heat transfer between the molten core and the concrete. M. Plys [P2] and M. Lee [L2] presented excellent reviews of these efforts. In this chapter, only a brief review of the previous downward heat transfer work will be presented. In Fig. 3.1, schematic diagrams of the melt/concrete heat transfer in the downward direction are shown. The principal components involved in the process are: molten core materials, an underlying concrete, a solidified bottom crust if present, and an interface region which comprises the decomposed concrete materials. The various analytical models that have been proposed to predict the downward heat transfer rate can be divided into two types: a film boiling-like model and a nucleate boiling-like model. The major difference between these models concerning the interface region is based on the observations of different simulant experiments. The objectives of this study are to develop downward heat transfer models for various stages of the interaction, and to incorporate them into CORCON/MOD2 so as to analyze the integral behavior of the melt/concrete. The new version of CORCON/MOD2 with additional downward heat transfer models will be referred to as CORCON/MIT. Important factors affecting the calculation of the downward 69 0 0 0 O0 MOLTEN POOL 0 O0 Figure 3.1 0 1*1j 0 0 0 0 O0 0 0 O0 0 0 0 0~ 0 0 0 Illustration of the Downward Heat Transfer of the Core/Concrete Interaction 70 heat flux will be discussed and presented in the following sections. Validation of various models based on real material experimental data will be presented in the next chapter. 3.2 Review of the Downward Heat Transfer Models 3.2.1 The Gas Film Model Prototypic melt/concrete interaction tests and concrete decomposition experiments showed that large amounts of gases are produced as the concrete dehydrates and decomposes while it is exposed to a thermal attack [P1,P5]. Separate effects experiments using simulant materials for the molten pool and decomposing concrete have been performed by placing a horizontal slab of dry ice beneath a pool of warm water or benzene. These simulant experiments indicated the existence of a gas film at the pool/solid interface [D1,A3]. In view of these observations, an assumption was made that the melt/concrete interface consists of a gas film comprised of concrete decomposition gases during a MCCI. Based on this assumption, a gas film model was developed and used in the CORCON and WECHSL codes to describe the heat transfer between the molten core and concrete. As shown in Fig. 3.2(a), interfacial heat transfer across the gas film is composed of radiative (q/ad) and convective (q' ,) processes. The radiative flux across the interface is given by the relation: qrad = FCTB(Tj - T6) where Oc (3.1) is the Stefan-Boltzmann constant and T, and TD are the core melt surface and ablating concrete wall temperatures, respectively. The radiation form factor, F, for two infinite parallel plates is defined as: F- (3.2) 1 1 ep 6c where e and c, are the emissivities of the molten pool and concrete, respectively. 71 1 00 '~ o. 0 U 0 0 0 0 0 0 0 0 0 0 0 MOLTEN POOL 0 0 0 S0 oAL o CRUST -mk 0 -1 6AS FILM CONCRETE (a) (b) Figure 3.2 Analytical Picture of the Gas Film Model ,i* 0 0 0 0 o 0 0 0 0 0 000 1lilllilllllIIIIIIIIIIIli'illilllll11111lIIIIIIIIII 0 The convective heat flux across the gas film is given by: (3.3) q"onv = heonv(T1 - TD) where the interface heat transfer coefficient, hconv, is described using Taylor instability models for a horizontal surface developed by Dhir et al. [D1], or Alsmeyer et al. [A3]. The dimensionless convective heat transfer coefficient for this gas film model is given by: NUB = CoRe-" 3 (3.4) where NuB= ;L_-1/ = pcnL;Re k9 y, gp9(pt - pg) and the Laplace constant A is defined as: A [g L ]1 2 (3.5) g( pt - p, ) where j, is the superficial gas velocity, and subscripts f and g refer to liquid pool materials and gas film properties, respectively. The constant Co in equation (3.4) is 0.326 and 0.256 for the Alsmeyer and Dhir models, respectively. The downward heat flux is then given by the combination of the radiative and convective heat fluxes as: =q#d to~0 (3.6) However, there are still two unknowns which cannot be determined explicitly in the calculation of the downward heat flux. One is the superficial gas velocity j, another is the interface temperature TI. The superficial gas generation velocity in the melt/concrete interaction is defined by: qI# j= d** P 9 HDecomp 73 (3.7) where x is the weight fraction of the gas content in concrete and HDecomp is the decomposition enthalpy of concrete. The jg cannot be determined before the downward heat flux is known, while the downward heat flux can be calculated only if the j 9 is given. An iteration is needed to calculate both the downward heat flux and superficial gas velocity. As for the interface temperature TI, it can be found by applying continuity of heat flow at the core-melt surface. Heat transfer from pool bulk to its periphery is equal to that transfer across the gas film (see Fig. 3.2(a)), i.e. don qFrad + nv it = "oot (3.8) where the pool internal heat transfer is given by: "o= h, 00I(Tp - TI) (3.9) and Tp is the pool bulk temperature. Models describing the heat transfer coefficient hpoo, were developed using available data and correlations from simulant experiments [B4]. The one used in the CORCON/MOD1 code is a modified Konsetov correlation [K4] which combines the effects of natural and gas driven convection. It is given by: hpool = k (Pr+) 1/3 [0.0003,3aT + 0.4a 2] 1/3 (3.10) where the unsubscripted variables are liquid pool properties and AT is the temperature difference between the pool bulk and its periphery (Tp - TI). The gas volume fraction a is given by: a= B 1 - B' B = 74 __ g 1.53 g (3.11) (.1 where jg is the superficial velocity of the gas entering the pool and A is the Laplace constant defined in equation (3.7). Since the release of CORCON/MOD1, Ginsberg and Greene [G8] have compared simulant data for horizontal liquid/liquid interface subjected to a gas flux with the predictions of several models and concluded that the Konsetov forms of CORCON/MOD1 seriously underpredicted the data. In fact, for very thin layers, CORCON/MOD1 would sometimes predict convective heat transfer rates smaller Therefore, in the CORCON/MOD2, an than would occur by conduction [C3]. empirical correlation developed by Greene, accompanied with a conduction limit, was used to predict the pool internal heat transfer. The Greene's correlation is given by: hp = 5.05 rb Reo' 5 Pr"'8 (3.12) where the Reynold number is defined as : Re = pajrb (3.13) and rb is the effective radius (based on volume) of the bubbles in the pool. This model is similar to a so-called surface renewal model developed by Szekely [S6]. Szekely's model was derived from the idea that heat is transferred by transient conduction with bubbles periodically disrupting the developing thermal gradients. This model was adopted in the WECHSL code, and is given by: hpoo = 1.69- rb (Re - Pr)0 '5 (3.14) Based on the pool side heat transfer correlation, coupled with the heat transfer coefficient across the gas film, the interface temperature T 1 can be calculated implicitly. During the post-freezing stage, a bottom boundary crust or an entirely solid layer sitting on a blanket of gas film is again assumed in the CORCON model. For a liquid pool with a solid crust, as shown in Fig. 3.2(b), heat transfer in the liquid region is governed by convection (natural or bubble-enhanced) with conduction as a limit. In the solid region, heat transfer is governed by conduction. Heat transfer across the gas film is again described by a combination of the convective and radiative processes. A simplified procedure has been employed in the CORCON/MOD2 to construct a steady-state solution to the heat transfer equations in a right circular cylinder whose average temperature, boundary temperature, crust and layer thicknesses, and volume all match those of the actual layer. Detailed descriptions of the post-freezing model used in the CORCON/MOD2 can be found in Ref. [C4]. In the gas film model, the effect of the slag has been neglected. Heat transfer across the interface region depends only on the thermal properties of the released gases. For the pre-freezing stage, the gas film provides a major thermal resistance in the downward heat transfer. Typical values of the downward heat fiux based on the gas film model for different melt temperatures are shown in Table 3.1. It can be seen that when the melt temperature is high, the radiative process dominates the downward heat transfer. At lower temperatures, the fraction of the convective part will increase. 3.2.2 The Periodic Contact Model In an experiment by Felde et al. [Fl] using gas injection through a porous plate into a volumetrically heated liquid pool, no continuous gas film was identified at modest superficial gas Velocities, 0.0 ~ 20.0 mm/s. In an experiment at M.I.T. [L2], air was injected through a porous plate into a water or cyclohexane pool, and heat was removed from the bottom of the pool by a condensing unit. The superficial gas velocity of the experiment ranged between 0.0 and 130.0 mm/s. No gas film was observed at the liquid/solid interface. Based on these observations, it is believed that a stable gas film will exist only if the superficial gas velocity exceeds a certain limit, and one could not expect to have a stable gas film under 76 Table 3.1 Downward Heat Transfer Calculated by the Gas Film Model Metallic Pool/Limestone Concrete: (TD = 1750 K) {, Tp T1 heon, (K) (K) (W/m 2 K) hpoi (W/m 2 K) 2950 2941 2.878 x 102 2.566 x 105 3.428 x 105 1.936 x 106 2.279 x 106 2750 2742 3.175 x 102 2.225 x 105 3.151 x 105 1.396 x 106 1.711 x 106 2450 2444 3.765 x 102 1.744 x 105 2.613 x 105 7.781 x 105 1.039 x 106 2050 2046 5.223 x 102 1.098 x 105 1.548 x 105 2.413 x 105 3.961 x 105 1850 7.408 x 102 6.648 x 104 7.252 x 104 6.749 x 104 1848 q" (W/m 2 ) q'r'ad (W/m own 2 ) (W/m 2 ) 1.390 x 105 Oxidic Pool/Limestone Concrete: (TD = 1750 K) Tp TI hconv hpooi qq','aod (K) (K) (W/m 2 K) (W/m 2 K) (W/m 2 ) 2950 2939 3.844 x 102 2.093 x 105 4.569 x 105 1.929 x 106 2.386 x 106 2750 2740 4.231 x 102 1.896 x 10 5 4.191 x 105 1.391 x 106 1.810 x 106 2450 2442 4.993 x 102 1.468 x 105 3.457 x 105 7.752 x 105 1.121 x 106 *2050 1855 9.405 x 102 - 9.843 x 104 7.256 x 104 1.710 x 105 1753 2.510 x 103 - 7.296 x 103 3 1.848 x 103 9.144 x 10 *1850 * Entirely solidified pool. 77 (W/m 2 ) (W/m 2 ) certain MCCI conditions. The gas injection into the pool can be viewed as being analogous to the Based on this analogy and experimental nucleate boiling of a saturated pool. data, Felde et al. developed purely empirical correlations for the downward and sideward heat transfer. The one for the downward heat transfer is of the following form: kg h = 5.69- ptj 3 0 A (gyt (3.15) The direct application of this model to the analysis of melt/concrete interaction is questionable. The correlation was obtained by empirical curve fitting based on the data of an experiment without having the eroding phenomena - a major physical process of MCCI. Nevertheless, their work suggested that a nucleate boiling-like process may occur at the horizontal melt/concrete interface. A periodic contact model developed at M.I.T. [L3,L4] was proposed to govern the heat transfer process when a gas film cannot be sustained at the interface. The periodic contact model considers the heat transfer mechanism as a transient heat conduction process between the hot pool and the relatively cold concrete surface. As the decomposed gas and molten slag rise up and away from the surface due to the buoyancy force, the interface will be stirred and some hot liquid will be periodically (based on the bubble departure frequency) brought into contact with concrete surface. This model includes the slag effect by treating the decomposed material as a two phase rising fluid which is contained in the interface region. Thermal properties of this rising fluid are calculated from the volume-averaged or weight-averaged values of the slag and decomposed gases. The physical picture at the melt/concrete interface during a completed bubbling cycle assumed by the periodic contact model is shown in Fig. 3.3. As indicated in the figure, the downward heat flux across the pool/rising fluid interface is represented by q". It can be expected that the downward heat flux is characterized 78 0 0 O0 molten pool 0 O 0 0 Oo o n 0I I Figure 3.3 Analytical Picture of the Periodic Contact Model 79 by a transient behavior during the growth of the rising fluid in each bubbling cycle. In the periodic contact model, a time-averaged downward heat flux q' was defined as: q' = hPc(Tp - (3.16) TD) The dimensionless downward heat transfer coefficient of the h-c is given by: [ ,f c(Te Nuf = Coo TD) HDecomnp f( p TD (3.17) where: Nuf = hpcA/kf; A= 1/2(3.18) - pp) g(p yo = - TP - TI; Of .TP - TD_ = (3.19) /pkc and the effective decomposition enthalpy, HeCmp is defined as: Hbecomp = HDecomp + cf - (TI2TD) Subscripts p, f (3.20) and s used in these equations refer to liquid pool materials, rising fluid and solid concrete, respectively. In equation (3.19), the T, represents the average temperature of the pool/rising fluid interface during each bubbling cycle, and it is given by: TP TP I [Tp-T Of(321 Op +Of TD 1 1(3.21) which leads to: Yo= I+ O (3.22) Thermal properties of the rising fluid are defined by: Pf =Pgas - C + pslag (II - a) 80 (3.23) + kslag k 1 = kgasCf = Cgas - + Cslag (3.24) (-a) (1 - x) (3.25) where X is the weight fraction of gas content in concrete, and the void fraction a of the two phase rising fluid is defined by: = 1-x~ 1+ X (3.26) 1 pga., -S Pslag with slip ratio S= (PL''g)1/3 Pgas (3.27) During early development of the periodic contact model, without having real material experimental data, the constants appearing in equation (3.17) have been determined by a least square curve fitting of the simulant experiment data of Dhir et aL.. This procedure leads to Co = 767 n = 1.53 m = 0.32 (3.28) As mentioned in Ref. [L3], a correction factor (k,/k,) was applied in equation (3.17) without theoretical justification to fit both the Water/Dry Ice and Benzene/Dry Ice experimental data. This could be a questionable term, since in the dry ice experiments only one material (dry ice) was used as an eroded substrate. It is therefore impossible to obtain the proper dependence of the downward heat transfer coefficient on the thermal conductivity of the eroded material (k,) based on the dry ice experimental data. On the other hand, it seems unreasonable that the downward heat transfer coefficient based on a conduction mechanism be inversely proportional to the thermal conductivity of the substrate. Most important 81 of all, it is unpersuasive that the periodic contact model is obtained by fitting the data of those experiments which have observed phenomena in contradiction to the assumption that has been made in the model development. When data of the first four BETA experiments became available, the constant Co was reduced by a factor of 0.6 in order to best fit into the observed downward concrete penetration distances [L4]. The constants n and m were kept the same as those in equation (3.28). The periodic contact model has been incorporated into the CORCON/MOD1 to analyze the integral behavior of the melt/concrete interaction. It is found that there are significant differences between the gas film and the periodic contact models in the predictions of the concrete ablation, gas generation and melt temperature response [K5,L4]. The periodic contact model was developed based on the assumption of direct periodic contact of the liquid melt with the concrete surface. While the debris cools down, direct contact will be prohibited by the formation of a bottom crust. Therefore, the applicability of the periodic contact model is limited to the early stages of the MCCI. 3.2.3 The Film Collapse Model Both the gas film and the periodic contact models are conceptualized based on presumable physical phenomena which cannot be directly observed in the real material experiments. The actual heat transfer mode may depend on the melt temperature and is not well understood. In the BETA experiments (VO.2 and V1.2), in the case of high initial melt temperature (2473 K), the downward erosion rate was initially somewhat limited, and a significant increased erosion rate was observed after a period of time (see Fig. 3.4). Based on this observation, a socalled film collapse model was proposed [K5]. It assumes that the downward heat transfer may follow a combination of the gas film and periodic contact models. If 82 BETA EXPERIMENT VO.2 500 I I I i 400 /1(0 - 300 0 o200 100 0 0 500 1000 1500 2000 2500 TIME [s] Figure 3.4 Downward Ablation Distance of BETA Test VO.2 3000 the melt initial temperature is high enough, a stable film may exist, and the heat flux presumably follows the gas film model until a minimum stable film limit is reached. When the film collapses, the heat transfer mode undergoes a transition to the periodic contact model. If the melt initial temperature is too low to generate a stable film, the heat transfer will be governed by the periodic contact model all the time until the solidus temperature is reached. The transition criteria of a stable gas film used in the film collapse model are based on hydrodynamic considerations. The film establishment criterion was related to the Kutateladze's flooding limit which is given by [K3]: with (3.29) o/pg A (jg)ilm = K, { 30.0 M 2 / 3 K 6.3 M 2 / 3 Ar "/6 Ar > 104 Ar < 104 M 2 =pggA/P Ar = g A 3 1v A = [o-/g(p1 2 pg)]0.5 - where P is the system pressure and subscripts e and g refer to liquid and gas, respectively. The film collapse limit was related to Berenson's minimum gas flux to stabilize the film, and is given as [B9]; (jg)min = - 0.25 0.09 [o!(Pe Pg) . ( pt + pg ) _ (3.30) For the case of melt/concrete interaction, those limits differ by two orders of magnitude. In the early development of the film collapse model, multiplication factors (Ai and MB) were applied to both limits in order to get the best fit of the early BETA experimental data. 84 For a given initial melt temperature, the superficial gas velocity calculated by the periodic contact model is to be compared to the Kutateladze's limit to determine the existence of an initial stable gas film. If the following relation (3g)c ;> MK* (ig) ilm (3.31) is true, then the downward heat transfer would be calculated by the gas film model. Otherwise, the periodic contact model is used. The superficial gas velocity (j,), appearing in equation (3.31) is calculated by: (ig) = P9 H Decomp -gx (3.32) For an initially stable gas film, film collapse is assumed when the superficial gas velocity of the gas film model falls below a certain limit: (jg)p _<MB - (j,)m (3.33) as the melt cools down. If the relation (3.33) is true, then the downward heat transfer process switches from the gas film model to the periodic contact model. When the film collapse model was first implemented into the CORCON/ MOD1 to analyze the early BETA experiment, the value of MB was found to be 6.0, while the multiplier MK had to be varied among different experiments (0.85 for VO.3 and 0.5 for VO.2 and V1.2) in order to obtain a predicted stable gas film at the beginning whenever experimental data showed such a trend. 3.3 Model Development and Implementation in CORCON 3.3.1 Revised Periodic Contact Model When more data became available from the BETA facility, it was found that, in general, the periodic contact model somewhat overestimates the downward-penetration distance of the concrete [K6,K10]. A revised periodic contact model based 85 on theoretical considerations is developed to overcome a deficiency found in its original derivation and improve its accuracy. 3.3.1.1 Basic Definition In the revised periodic contact model, the downward heat transfer coefficient is redefined as: hPc = """n) c (3.34) (Tp - TD) Variables appearing in this equation are indicated in Fig. 3.5(a). Compared to the original definition in equation (3.16), it can be seen that the downward heat flux across the pool/rising fluid interface, qg, is replaced by the one across the rising fluid/concrete interface, (q'jow),,, in equation (3.34). The downward heat transfer coefficient ho, as shown in Fig. 3.5(a), is then defined as: (3.35) g - ho = (Tp- T1 ) The relation between q" and (q"o 1 ),, can be found by accounting for the energy needed to heat up the rising fluid layer above the decomposition temperature: = qg - (j)M,,pc where the average superficial rising fluid velocity (jf)A - jf TD) (3.36) is given by: "" = p fAvg HDecomp (3.37) Substituting equation (3.37) into (3.36), one can get: (qqdown) pc _n. o [HDecomp H*Decomp (3.38) where: H*ecomp HDecomp + Cf (TI-TD) (3.39) The effective decomposition enthalpy Heccomp is obtained by assuming a parabolic temperature profile, instead of a linear profile, exists in the rising fluid layer. 86 0 0 0 0 o0 0 0 molten pool 0 0 0 0 o 0 oU o0 0 0 0 crust 0o rising fluid concrete (a) (b) Figure 3.5 Analytical Picture of the Revised Periodic Contact Model NA W" Combining equations (3.34), (3.35) and (3.38) and defining a new parameter r as follows: (3.40) r = HDecomp Hecomp gives: - -P hP = ho IT (3.41) r - TD 3.3.1.2 Transient Heat Conduction Based on transient heat conduction, the amount of heat transfer out of the pool (through the pool/rising fluid interface) per unit area within a certain time period td can be obtained as: q 2p c (3.42) aPt(Tp-$I) where a, is the thermal diffusivity of the pool material and td is the bubble departure time. Therefore, the averaged downward heat flux qg as defined can be written as: q to q' = - (3.43) Combination of equations (3.35), (3.42) and (3.43) leads to: ho = C1 . 3 (3.44) where C1 is a constant and , = V/(pkc),. 3.3.1.3 Bubble Dynamics As discussed in Ref. [L3], the bubble departure time can be obtained by the integration of bubble growth rate and rising fluid generation rate, which gives: td o( ^ d L2If 88 (3.45) The bubble departure radius Rd was derived based on the balance of surface tension and buoyancy force as: [r 1/2 Rd oc = (3.46) A g(p, - p5 )] where A is the Laplace constant defined in equation (3.18). The length L is the dimension of a square area influenced by single bubble, and it was assumed to be proportional to the Taylor wavelength as: [~ L oc [ g(pp 11/2 ) (3.47) -A Substituting equations (3.46) and (3.47) into (3.45) and combining the result with equation (3.44), leads to: ho = C 2 3, ( Oj A (3.48) "f)"Ag where C 2 is a constant. Based on equations (3.37) (3.38) and (3.40), the superficial rising fluid velocity can be rewritten as: (if )Avgpf H&comp = ho(Tp - T 1 ) (3.49) or (if )Avg = (3.50) ho(Tp - T)r pf HDecomp Substituting equation (3.50) into (3.48), after some manipulations, the heat transfer coefficient ho can be cast into the following form: ho = Co(k, A p cT pf 89 - HDecomp r I (3.51) Substituting this expression into equation (3.41), gives: h)1 [CTP A Of Tp - TD .. - TD) Decomp 1 2 (3.52) This equation can then be rearranged into a dimensionless form: e Nuf = CyO (3.53) TD) Decomp_ where Nuf = hpcA/kf; yo O [T-TI Tp -TD Of 1 3.3.1.4 Interface Temperature As shown in equation (3.21), the average interface temperature Ti is obtained by assuming direct contact between semi-infinite slabs of the pool material and rising fluid. If one assumes that the pool material is instead brought into contact with the solid concrete, the rising fluid property of should be replaced by the concrete property /, in equation (3.21) to obtain the interface temperature, i.e. [Tp -Tr 1 J TP - TDI ITP-TD _ ___ 13p 13(3.54) + 0.s However, due to the phase change of the eroded concrete in a periodic cycle, neither equation (3.21) nor equation (3.54) gives proper representation of the average interface termperature. Nevertheless, these two equations impose an upper and lower bounds on the interface temperature. Therefore, one can employ a weighting factor F for estimation of the interface temperature as: T- TDK TI TP1.s where 0.0 < F F( p (1.0 - F)( 13) +Of ) + Op + < 1.0. 90 (3.55) In the original model, the F factor in effect was 1.0, which gives an upper bound estimation of the interface temperature. For the new model, the F factor is taken as: F = 1.0 - r (3.56) where r is defined in equation (3.40). The weighting factor F is selected based on the following argument. As the pool temperature drops, the interface temperature T1 will approach TD, and little concrete will be decomposed. Under this condition, the weighting factor F will approach zero. Therefore, the interface temperature Tr will be determined as if the pool material is in contact with the solid concrete. At higher pool temperature, more concrete will be decomposed. The increased value of F leads to an increasing effect of the rising fluid on the determination of the interface temperature. This leads to: Tj = (1.0 - F) 3Tp +l,3TD + pTp + 3 fTD 3 + F p+ f(3.57) An iteration is needed to determine Ti and r in equations (3.57) and (3.40), respectively. The final form of the downward heat transfer coefficient of the revised periodic contact model can be written as: Nu = Co 2 cf (Tp -TD)] (3.58) + (3.59) with 7 (- r Equation (3.58) has been incorporated into the CORCON/MIT, and the only unknown constant Co will be determined by curve fitting of the early BETA experimental data. The thermal conductivity ratio appearing in the original model 91 has been dropped and the constant n is kept at the theoretical value of 1.0 in the revised model. 3.3.2 Transition Criteria of the Film Collapse Model The first four sets of the BETA experiment were performed by February 1984. The downward concrete penetration distances obtained from these tests have been used as basis to determine the constants and multipliers appearing in the film collapse and revised film collapse (combination of the revised periodic contact and gas film models) models. The experimental conditions as well as the measured initial (over the first hundred seconds) downward penetration rates of the BETA tests are summarized in Table 3.2. The measured downward penetration distances of those tests are shown in Fig. 3.6. It is interesting to see that the initial downward penetration rate of test VO.3 is quite different than those of tests VO.2 and V1.2 even though all three tests have the same initial melt temperature. The V1.3 test has a lower initial melt temperature, but double the initial penetration rate than those of VO.2 and V1.2 tests. Based on these observations, the assumption of the film collapse model has been made. The transition criteria have to be determined by distinguishing the differences among these tests. In both the original and the revised periodic contact model, it can be seen that the downward heat flux is barely affected by the density of the released gas. However, examination of the existence of an initial stable gas film requires the magnitude of the superficial gas velocity which is directly related to the released gas density as shown in equation (3.32). In CORCON, the released gas density at the bottom interface is calculated based on the ideal gas law: Pg = Pin * nRTint (3.60) where R is the gas constant and Pint and Tint are the bottom interface pressure 92 Table 3.2 Test Matrix of the Early BETA Experiments Melt Composition Initial Melt Oxidic Temperature Test Metallic (K) (kg) Planned Power (kW) 200 400 Average tErosion Rate Power (kW) (mm/s) 370 0.25 VO.2 Fe(300) 2473 VO.3 Fe(300) A1 2 0 3 (150) 2473 1700 1180 1.0 V1.2 Fe(200) A12 0 3 (150) 2473 Pulse 380 0.30 2173 1000 780 0.60 Fe(246) A12 0 3 (105) V1.3 Cr( 30) SiO2 ( 45) Ni( 24) t Average over the first one hundred seconds. 93 BETA EXPERIMENT VO.2 TEST VO.3 TEST 4 V1.2 TEST -A V1.3 TEST 400 U z 300 o200 -L 100 * A *A 0 -AL 0 0 A A 100 0 300 200 400 500 TIME [s) Figure 3.6 Downward Ablation Distances of Early BETA Tests t 600 and temperature, respectively. Unfortunately, the original CORCON initializes the interface pressure as atmospheric pressure without taking the pool weight into account at the first time step. A modificatiort has been made in the COR- CON/MIT by having: Pt = Patm + ppgH where Pat, is the environment pressure and H is the pool height. (3.61) Given the high density of the core melt, the pressure difference is significant in determining whether an initial gas film exists. A smaller pool mass will result in a lower interface pressure and released gas density, thus leading to a higher superficial gas velocity, which tends to stabilize the initial gas film. Comparing the BETA VO.2, V1.2 and VO.3 experiments, all tests start with the same temperature, but with different total masses. With the pressure modification in the CORCON/MIT, it can be predicted, with a unique multiplier MK, that VO.2 and V1.2 would start with a stable gas film and VO.3 would start with a periodic contact mode. 3.3.3 Post-Freezing Heat Transfer Model The gas film is destabilized at a sufficiently low superficial gas velocity condition, which may occur earlier than the crust formation. The applicability of the periodic contact model as discussed in the previous section is limited to the early stages of the MCCI before any freezing occurs. Therefore, neither the gas film nor the periodic contact model can be used to describe the downward heat transfer during the post-freezing stages of MCCL. In order to complete the downward heat transfer model in the CORCON/MIT, a post-freezing model was developed. Basically, this model assumes that thermal resistance between the pool boundary and the concrete surface, i.e. resistance across the rising fluid, is continuous on the basis of the superficial gas velocity that can be achieved after the formation of a crust. In Fig. 3.5(a), it is seen that the condition of a freezing crust initiation is: T where T 01 T30 1 (3.62) . is the solidus temperature of the molten pool materials. Imposing this in equation (3.57), the following equation can condition and replacing Tp by T be obtained: T T 0 = [1 - F) + fF + ,+Op F + 0 o,+p 1- F - ( OP 9 + TD (3.63) )f and a downward heat transfer coefficient h* based on the periodic contact model at the condition of Tp = T; can then be calculated by equation (3.58). Once the pool bulk temperature and its corresponding downward heat transfer coefficient at the initiation freezing are obtained, the heat transfer coefficient across the rising fluid can subsequently be defined as: , h*rf = h*c(T -TD) (Tsol - TD) (3.64) With this definition, the heat transfer coefficient, hrf, for the post-freezing stage as shown in Fig. 3.5(b), is obtained by: hrf = h*,- (9 39 .. h*c(T C= -D )0.5 (3.65) where -(X PgHDecomp and the superficial gas velocity jg for the post-freezing stage is defined by: 11 S.(3.67) PgHDecomp 96 (3.66) with the downward heat flux across the rising fluid/concrete interface given as: q'oln = hrf(TI - TD). (3.68) The implementation of the post-freezing model in the CORCON/MIT is quite similiar to the original gas film model. Only the heat transfer across the gas film (the combination of radiative and convective processes) has been replaced by the heat transfer across the rising fluid described above. The pool internal heat transfer coefficient hP,.I (see Fig. 3.5(b)) is determined by Greene's model, and heat transfer across the solidified crust is described by heat conduction. 3.3.4 Summary After several preliminary integral analyses of the BETA experiments using CORCON/MIT, the constants and multipliers used in both the original and revised film collapse models were obtained by the best fitting to the experimental data and are summarized in Table 3.3. Typical boiling curve of the film collapse model, at both pre-freezing and post-freezing stages, with those specified transition limits can be seen in Fig. 3.7. The downward concrete ablation distances of the BETA experiments predicted by the Film Collapse (FC), Revised Film Collapse (RFC) and Gas Film (GF) heat transfer models compared to the experimental data are shown in Figs. 3.8 through 3.11. 3.4 Downward Heat Flux Calculation 3.4.1 Cases Studied Besides the downward heat transfer model, there are several parameters in the MCCI which could affect the prediction on the magnitude of the downward heat transfer. An analysis of the impact on the downward heat flux of some of the parameters will be studied here. Some of the uncertain parameters are outlined first. 97 Table 3.3 Empirical Constants of the Film Collapse Model Original FC Model Revised FC Model CO 460.0 2.8 n 1.528 1.0 m 0.32 0.0 MK 0.65 0.40 MB 6.0 6.0 98 10 Kf K Concrete: T =1570 K Melt Material: &eel Metal 9 r 108 LJ 106 0 105 0 800 400 Figure 3.7 1200 1600 TD[K] Descriptive Downward Heat Flux of the Film Collapse Model 99 BETA EXPERIMENT VO.2 500 r z 400 300 200 z 100 0 v 0 500 1000 1500 2000 2500 TIME [s] Figure 3.8 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test VO.2 I~ N~ BETA EXPERIMENT VO.3 500- 400 z 300- z 0 ~0 o200 z 100 0 0 100 200 300 400 500 TIME [s] Figure 3.9 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test VO.3 *~N~ BETA EXPERIMENT V1.2 500r, 400- z 300 z 0 200 LQ 100 0 0 300 600 900 1200 1500 1800 2100 TIME [s] Figuire 3.10 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.2 Now& BETA EXPERIMENT V1.3 500 r z 400 300 0 CO) 0 0 200 100 Q 0 0 100 200 300 400 500 600 TIME [s] Figure 3.11 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.3 3.4.1.1 Molten Core Configuration in Concrete Cavity The amount of heat that can be transferred downward during the MCCI depends on the temperature and properties of the'melt directly in contact with the horizontal concrete surface. The molten materials involved in the MCCI can be classified into oxidic and metallic materials. The oxidic materials primarily consist of uranium dioxide and zirconium dioxide. The constituents of the metallic phase are structural materials, such as steel and zirconium. These oxidic and metallic materials are immiscible, and the differences in the physical properties can be large. In the CORCON code, these two immiscible melts are assumed to be stratified into layers in the reactor cavity. Physical orientation of the core debris conceived in CORCON depends on the layers' densities. At the start of core debris attack on concrete, the oxidic phase is heavier and is assumed to form a bottom layer of the molten pool. The less dense metallic material forms a layer above this dense oxide. As concrete ablation progresses, the decomposed concrete oxide, miscible with the molten core oxide, will be incorporated into the oxidic layer thus reducing the bulk density of this layer. On the other hand, the density of the metallic phase may increase due to the inclusion of melted reinforcing steel and exclusion of zirconium and chromium which are oxidized by the evolved gases. At some point in time, the upper and lower pools of this debris configuration may flip due to the density changes so that the oxidic layer will float atop the metallic phase. A second hypothesis states that uranium metal may be present in the metallic phase due to the reducing reaction of uranium dioxide with zirconium metal before core meltdown. In this case, the density of the metallic phase may become heavier than that of the oxidic phase at the start of the MCCI. This gives a debris configuration, as depicted in the VANESA model, with the metallic layer at the bottom all the time. However, the stratified layers configuration may in fact be destroyed by the evolved gas if the superficial gas velocity is high enough. Gases sparging through the melt will entrain and mix the oxidic and metallic phases into an approximately l04 homogeneous mixture. This phenomenon could happen during the early stage of the MCCI when the melt temperature is high. Actual configuration of the core debris in the reactor cavity is not certain. These possible assumptions could affect the prediction of the ex-vessel aerosols release in two ways. One is the downward heat transfer rate, another is the vaporization potential of the melt. In this study, the downward heat fluxes from different melts contacting the concrete will be analyzed. 3.4.1.2 Concrete Type of Reactor Cavity All concretes used in construction have the same types of cement. What is variable in the concrete is its aggregate composition and its free-water content. When concrete is specified in the Final Safety Analysis Report for a plant, there is no such data as the decomposition temperature, decomposition enthalpy, the amount of water and the amount of carbon dioxide evolved upon heating the concrete. However, these characteristics of the concrete are of crucial importance to the analysis of MCCI. There are three concretes, namely, Limestone/Common Sand, Limestone and Basaltic, which have been widely adopted by severe accident analysts as representative of reactor concretes. These concrete compositions are available as user-selected default compositions in the CORCON code. In addition to these concretes, a German silicate concrete, so called KfK concrete, was analyzed in this study. 3.4.1.3 Solidus Temperature of Molten Core In order to determine whether the concrete attack is by a molten or solid material, well-known solidus temperatures of molten materials are needed. The solidus temperature of any melt depends on its composition. Available phase diagrams are quite restricted to simple systems. However, the melt composition 105 that may develop in the MCCI is extremely complicated, therefore, precise prediction of the solidus temperature can be difficult or impossible. In the CORCON/MOD2, simple procedures for estimating the liquidus and solidus temperatures of various melts have been developed. A sensitivity study with various melt compositions will be analyzed to recognize the possible effect on the downward heat transfer estimation. 3.4.2 Results and Discussions The downward heat fluxes resulting from different conditions of the melt in the melt/concrete interactions were calculated by using CORCON/MIT. The melts chosen for this study are listed in Table 3.4. Melt properties shown in this table are those calculated by the CORCON code. Since the melt compositions will change after the start of interactions, one-step calculations with different initial melt temperatures were followed. Various concretes used as counterpart of the interactions are listed in Table 3.5. The selection of melts and concretes has been made to cover a range of materials that may result from various accident scenarios. Physical properties, such as thermal conductivities of the melts and gas content of the concretes, vary significantly among these selections. 3.4.2.1 Downward Heat Transfer Model The calculated downward heat fluxes, based on the Gas Film (GF) model, the Periodic Contact (PC) model and the Revised Periodic Contact (RPC) model, are presented as follows. In Fig. 3.12, the downward heat flux versus A T, (the difference between pool bulk temperature and concrete decomposed temperature) are plotted for the case of a core oxide overlying Limestone/Common Sand concrete. The solidus point of the core oxide is shown in this figure. It is seen that there is about an order-ofmagnitude difference between the PC model and GF model predictions when the nielt temperature is above its solidus point. The RPC model gives about 50% 106 Table 3.4 Compositions and Physical Properties of Various Melts Steel Steel+Zr Core Core+Concrete Metal Metal Oxide Oxide Fe 76.0 55.5 - Cr 18.0 13.5 - Ni 8.0 6.0 - 25.0 - Melt Composition(wt%): Zr - - 80.0 76.6 Zr0 2 - - 11.0 10.5 FeO - - 9.0 8.6 CaO - - - 2.0 SiO 2 - - - 2.0 - - - 0.2 U0 2 A1 2 0 3 Melt Properties: 6767 6428 8206 7371 C, (J/kg K) 798 694 567 598 K (W/m K) 49.8 45.6 2.58 2.91 16400 14260 3465 3580 y (pPa- s) 3300 3000 6600 5200 a (N/m) 1.78 1.73 0.50 0.50 T901 (K) 1748 1748 2118 1941 Tiz, (K) 1758 1758 2744 2665 3 p (kg/m j3 (J/m 2 ) so 'K) 107 Table 3.5 Compositions and Physical Properties of Concretes Limestone/C.S. Limestone Basaltic KfK 35.8 0.48 31.3 0.08 1.22 1.44 3.60 21.2 2.70 2.00 3.60 5.67 45.4 0.08 0.68 1.20 1.60 35.7 3.94 2.00 54.8 6.16 8.82 1.80 5.39 6.26 8.32 1.50 3.86 2.00 76.6 p (kg/m 3 ) C, (J/kg K) K (W/m K) 2340 903 1.17 2340 979 1.17 0 sK) 0 (J/m 2so HDecomp (MJ/kg) TDecomP (K) TSo 0 id. (K) 1572 2.500 1500 1420 1637 3.476 1750 1690 2340 913 1.59 1843 1.745 1450 1350 2300 910 1.59 1824 2.000 1573 1350 (K) 1670 '1875 1650 1650 p (kg/m 3 ) C, (J/kg K) K (W/m K) 2666 1132 1.3 3245 1087 1.3 2456 1191 1.3 2346 1225 1.3 13.1 1596 0.203 65.1 7.08 1854 0.200 51.2 38.0 1319 0.214 103.6 32.5 1373 0.212 97.3 Compositions(wt%): SiO2 MgO CaO Na 2 0 K20 Fe 2 0 A1 2 0 CO 3 3 2 H20 Evap H20 Chem - 9.22 - 5.32 2.92 4.22 1.77 Concrete: TLiquidus Slag: Rising Fluid: p (kg/m 3 ) C, (J/kg K) K (W/m K) 0 (J/m 2 s 0 -'K) 108 Sand: Limestone/Common Melt Material: Core Oxide TD= 1500 K 108 r_ 0 400 800 - AT, Figure 3.12 1200 1600 TD [K] Downward Heat Fluxes of the Various Models for Core Oxide Interacting with Limestone/Common Sand Concrete 109 higher downward heat flux than the PC model in this case. The differences among various downward heat transfer models with different types of concretes can be seen in Figs. 3.13, 3.14 and 3.15. It is noteworthy that the RPC model results in three times higher downward heat flux than the PC model in the case of Limestone concrete. For silicate concrete (Basaltic and KfK), the downward heat flux predicted by the RPC model is lower than the PC model by a very small value. As predicted by all models, the downward heat fluxes drop dramatically near the solidus temperature. The downward heat transfer is governed by conduction through the crust, rather than a more effective convective controlled process. Additional thermal resistance across the solidified melt reduces the amount of heat that can be transferred downward. Therefore, the calculated downward heat fluxes for the post-freezing stage are rarely affected by different heat transfer models which are used to predict the relatively small themal resistance at the pool/concrete interface. As shown in these figures, the downward heat fluxes calculated by various models are almost equal at low debris temperatures. 3.4.2.2 Molten Material The downward heat fluxes calculated for various melts interacting with Limestone/Common Sand concrete by the GF, PC and RPC models are shown in Figs. 3.16, 3.17 and 3.18, respectively. At high melt temperature conditions, it is interesting to note that the differences in the downward heat fluxes among these melts are small even though the physical properties of the melts are widely different. Above the solidus points, the PC model predicts that the downward heat flux of the metallic material is about 20% higher than the oxidic material. On the contrary, the RPC model results in 30% higher downward heat flux with the oxidic material. The differences predicted by the GF model are negligible. There are reasonable explanations of these small differences for all models. In the GF model, the downward heat transfer is predominately controlled by the gas film. 110 Lirnestone: TD= 1750 K Melt Material: Core Oxide 108 E-1 106 LJ 0 400 AT Figure 3.13 800 =Tp - 1200 1600 TD[K] Downward Heat Fluxes of the Various Models for Core Oxide Interacting with Limestone Concrete 111 10 9 Basaltic: TD=1 4 5 0 K Melt Material: Core Oxide 1- 1- 1 1 108 Lj X "U> 106 0 400 800 1200 1600 = Tp - TD [K] Figure 3.14 Downward Heat Fluxes of the Various Models for Core Oxide Interacting with Basaltic Concrete 112 Kf K Concrete: T= 1 5 7 0 K Core Oxide 9 Melt Material: r-n C\1 106 Ae. 5 0 Q 104 0 400 800 - Figure 3.15 1200 1600 TD [K] Downward Heat Fluxes of the Various Models for Core Oxide Interacting with KfK Concrete 113 GAS FILM MODEL Limestone/Common Sand; TD=1 50 0 K 108 E-- 106 LJ 0 400 800 1600 - TD [K) ATp Figure 3.16 1200 Downward Heat Fluxes of the Gas Film Model for Various Melts Interacting with Limestone/Common Sand Concrete 114 PERIODIC CONTACT MODEL Limestone/ Common Sand: TD=1 10 9 E- 500 K 106 10 5 0 400 800 - Figure 3.17 1200 1600 TD [K] Downward Heat Fluxes of the Periodic Contact Model for Various Melts Interacting with Limestone/Common Sand Concrete 115 REVISED PERIODIC CONTACT MODEL Limestone/Common Sand: TD= 1500 K 108 E-L 106 105 0 400 800 - ATp Figure 3.18 1200 1600 TD [K] Downward Heat Fluxes of the Revised Periodic Contact Model for Various Melts Interacting with Limestone/CS Concrete 116 Physical properties of the melt play only a minor role. The downward heat flux obtained from the PC model increases with the thermal conductivity of the melt as well as the periodic contact frequency. The periodic contact frequency is directly reverse proportional to the Laplace constant A. Typical values of several parameters used in the periodic contact model associated with the thermal properties of molten pool materials are shown in Table 3.6. Melt consisting of metallic material has higher themal conductivity but lower frequency of periodic contact compared with the oxidic melt. In the PC model, the dependence of the downward heat transfer coefficient on the pool properties has been weakened by the approximate estimation of the interface temperature (notice the small variation of the first column in Table 3.6), and then it has been strengthened by including the thermal conductivity ratio. Combination of these effects results in a higher downward heat flux of the metallic pool with the PC model. For the RPC model, with the combination of those parameters in the first, second and fourth columns of Table 3.6 (see equations (3.58) and (3.59)), the calculated downward heat flux of an oxidic pool is higher than that of a metallic one. The thermal conductivity of the melt can be, however, an important factor in determining the downward heat flux at low melt temperature condition. Below the solidus temperatures of the melts, the calculated downward heat fluxes of the metallic material, shown in Figs. 3.16 through 3.18, are about 6 to 10 times higher than the oxidic material. 3.4.2.3 Concrete Type At a melt temperature above the solidus point the downward heat flux will be determined by the temperature of the heat sink, i.e. the temperature of the decomposed concrete surface. The higher the decomposition temperature the lower is the heat flux that can be transferred downward. With the lowest decomposition temperature of the Basaltic concrete, as shown in Table 3.5, the calculated downward heat flux is the highest among the various concretes. Limestone concrete 117 Table 3.6 Typical Values of the Parameters Used in the Periodic Contact Model 1/(1+ k) ()/( + ) k,/k. A (mm) Oxidic Pool: Limestone/Common Sand 0.982 16.6 2.21 2.50 Limestone 0.985 21.7 2.21 2.49 Basaltic 0.971 11.6 1.62 2.50 KfK 0.973 12.3 1.62 2.50 Limestone/Common Sand 0.996 22.0 42.6 5.19 Limestone 0.997 29.1 42.6 5.18 Basaltic 0.994 16.0 31.3 5.20 KfK 0.994 18.6 31.3 5.19 Metallic Pool: 118 with the highest decomposition temperature gives the lowest heat flux. Both the GF and PC models predicted the same trend for these concretes, but the differences among these concretes calculated by the PC model are larger than the GF model, see Figs. 3.19 and 3.20. However, in the RPC model, the effect of ATp is no longer a dominant factor when the melt temperature is relatively high. The dependence of -yo shown in equation (3.59) on the thermal properties of the concrete and its decomposed materials (rising fluid) can be seen in Table 3.6. Among various concretes, the Limestone concrete has the largest -yo value, therefore, the RPC model gives Limestone concrete the highest heat flux at high melt temperature condition, see Fig. 3.21. 3.4.2.4 Solidus Temperature of Molten Material In figures 3.16 to 3.21, it can also be seen that the solidus temperature is an important boundary in the prediction of the downward heat fluxes. The solidification model in the CORCON/MOD2 assumes that a crust forms on any surface whose temperature falls below the solidus temperature of the molten material. In CORCON/MOD2, the simple procedures used for estimating the liquidus and solidus temperatures of various melts give two questionable results. First, the solidus temperature of a metallic material is determined by a simple fit to the Fe - Cr - Ni ternary phase diagram without considering the effect of the presence of other metals, such as zirconium. This leads to an equal solidus temperature for the steel and the steel+Zr melts in this study. The second interrogative result can be seen in Fig. 3.22. The solidus temperature of the core oxide, specified in the Table 3.4, is affected by the concrete assumed in the interactions. The differences of the calculated solidus temperature can be as large as 200 K between the cases of Limestone/Common Sand and Basaltic concretes. Intuitively, there is no reason for the solidus temperature of the melt to depend on the concrete. This curious result is caused by the iron oxide in the oxidic material since CORCON treats all oxides other than fuel-oxides as decomposed concrete oxides. The solidus and liquidus temperatures of the oxidic melt are then determined by those of fuel119 GAS FILM MODEL 1 9 Melt Material: LI0 Steel Metal I II I- TONE /COMMON LIMES TONE -. -BASAL TIC 108 SAND KfK gji 04 i6 106 r -7 - - - 105 I 1500 I 1800 I I II I I 2100 2400 I I II 2700 3000 TPool [K] Figure 3.19 Downward Heat Fluxes of the Gas Film Model for Steel Melt Interacting with Various Concretes 120 PERIODIC CONTACT MODEL 10 9 Melt Material; I I Steel Metal I I I I I I I 108 E-n 106 X0 1030 1500 1800 2100 2400 2700 3000 TPool [K] Figure 3.20 Downward Heat Fluxes of the Periodic Contact Model for Steel Melt Interacting with Various Concretes 121 REVISED PERIODIC CONTACT MODEL 10 9 Melt Material: LI I Steel Metal I I I I 2100 2400 I I I Z 108 Emi 106 0-- 103L_ 1500 1800 2700 3000 TPool [K] Figure 3.21 Downward Heat Fluxes of the Revised Periodic Contact Model for Steel Melt Interacting with Various Concretes 122 REVISED PERIODIC CONTACT MODEL 10 9 Melt Material: Core Oxide 10 8 E--1 10 6 1500 1800 2100 2400 2700 3000 TPool [K] Figure 3.22 1 Downward Heat Fluxes of the Revised Periodic Contact Model for Core Oxide Interacting with Various Concretes 123 oxides and those of concrete weighted by the molar fractions of the non-fuel and fuel-oxides in the melt. However, the iron oxide, an element that very likely participates in the oxidic melt before the start of MCCI, has nothing to do with the concrete properties. The way that CORCON calculates the solidus temperature may lead to a fallacious prediction of formation of a bottom crust at the initiation of the MCCI. This could have a significant impact on the prediction of ex-vessel aerosols behavior if the initial melt temperature is close to the calculated solidus point. 3.5 Summary 1. A revised periodic contact model has been developed based on more complete theoretical consideration than earlier derivations. Under certain conditions, there are considerable differences between the downward heat fluxes predicted by the revised and original periodic contact models. 2. When the debris temperature is above its solidus point, the downward heat flux predicted by the PC model is about an order-of-magnitude higher than the GF model. 3. With a bottom crust or an entirely solid layer, the downward heat fluxes predicted by all models are about equal. 4. There is an order-of-magnitude reduction in the downward heat flux when the melt temperature drops across its solidus point. A more precise estimation of the solidus temperature of melt is warranted. 5. At high debris temperature, the downward heat flux is not affected significantly by the composition of the melt which may contact the horizontal concrete surface. When the debris has a low temperature, allowing formation of a bottom crust, a metallic pool with higher thermal conductivity has ten times higher downward heat transfer than an oxidic one. 6. For a given condition of the molten pool materials, the differences in the calculated downward heat fluxes for different concretes can be large. 124 CHAPTER 4 VALIDATION OF HEAT TRANSFER MODEL BY COMPARISONS TO INTEGRAL EXPERIMENTS 4.1 Introduction To describe the heat transfer processes involved in the melt/concrete interaction, computer codes (such as CORCON and WECHSL) have been developed during recent years, based mainly on small scale separate effect simulant material experiments or on transient tests with prototypic materials. To gain a wider data base for validation of the existing models, integral experiments considered to be reliable extrapolation of real reactor situations were later undertaken. The BETA program at Kernforschungszentrum Karlsruhe (KfK), West Germany is a key experimental program for core melt/concrete interactions. This program carried out successful experiments between early 1984 and early 1986. Data with regard to the concrete ablation, gas generation and aerosol releases were obtained. Phenomena important to the modeling of MCCI were observed as well. At Sandia National Laboratory, an experimental program to investigate melt/concrete interaction was initiated in July 1975. Various experiments using real materials have been performed to identify characteristics of the melt/concrete interaction. Some conclusive statements have been reached based on the observations of the experiments, however, much of the data which can be used to corroborate theoretical work remains unpublished. These real material experiments will be reviewed in the following sections, and the measured downward concrete ablation distances will be used to validate various downward heat transfer models developed for the melt/concrete interaction. 125 4.2 Review of Real Material Experiments 4.2.1 BETA Experiments 4.2.1.1 Descriptions of BETA Facility The BETA facility is a large scale high power inductive heating experiment to allow sustained heating of a simulated core melt in a concrete crucible. A schematic diagram of the BETA facility is shown in Fig. 4.1. To fulfill the requirements of code verification with various needs of model development, different interaction regimes were studied by a sequence of experiments at various temperatures and power levels. The controlled quasi-steady conditions of the power level were selected to result. in a heat flux to the concrete of the same magnitude expected in reactor accidents. The inner diameter of the cylindrical concrete crucible which contains hot melt is 380 mm. This dimension was selected to allow mutually undisturbed downward and sideward melt propagations. This diameter also guarantees that the gas release at the bottom and the stabilization of a top crust are not affected by the vertical wall. The effects of the crucible diameter were examined in the V4 test with a 600 mm crucible diameter. The detailed concrete crucible diagram is shown in Fig. 4.2. The dots in the figure are the locations of embedded thermocouples. The propagation of the melt front was inferred from the time of failure of the thermocouple in the concrete. The experiment concrete in the BETA tests was a silicate concrete of the type commonly used in German reactors. This concrete is called here the KfK concrete. Additionally, in the V3 test series, three crucibles of high carbonate content have been used, farbricated from limestone material imported from USA. The materials were Limestone concrete for V3.2 test, and Limestone/Common Sand concrete for V3.1 and V3.3 tests. The compositions and the physical properties of the various concretes can be found in Table 3.4. 126 MOLTEN POOL PERIPHERY SYSTEMS fThM~cUPIAs lpflssm m 1 2 3 CONCRETE CRUCIBLE INDUCTION COIL OFFGAS SYSTEM Figure 4.1 4 5 THERMITE REACTION TANK CONTAINER FOR MEASUREMENT PROBES Schematic Diagram of BETA Experiment (Ref.[A5]) 127 IwoI - om -O 00 ILII Figure 4.2 Dimensions of Concrete Cavity of BETA Experiment (Ref.[A5]) 128 High power inductive heating of the melt - one of the main characteristics of the BETA facility with up to 1900 kW net input power - can be induced in the metallic layer. This high power capability allows observation of various physical and chemical processes during an extended period of time under quasi-steady conditions. Up to 350 kg metallic and 150 kg oxidic melt could be generated outside the crucible by a thermite reaction and then poured into the concrete crucible. The initial melt temperature was close to 2000 0C or higher, as determined by the composition of thermite without having direct measurement. The simulated melt was initially composed of a steel melt with Fe, Cr, and Ni, and in most of the tests, oxidic melt of Al 2 03 and Si0 2 . CaO was added to some of the oxidic melts to lower the viscosity and solidification temperature of the oxide. The melt did not contain simulants for the radioactive fission products. Dip-in material sampling and temperature measurement instruments for melt analysis were available above the crucible. The temperature of the melt was measured at predefined time intervals by W - Re thermocouples which were dipped simultaneously into the metallic and oxidic phases. Also, the lances of dip-in temperature of the melt were measured continuously by a ratio pyrometer installed on top of the crucible. The hood and offgas pipe collected all gaseous products generated during melt/concrete interaction for physical and chemical analysis. Two methods were used independently for determination of the composition of the gas phase: On-line measurements were realized by means of a quadrupole mass spectrometer (MS). Off-line investigations of the gas phase by application of grab samples, filled during the experiment and analyzed by gas chromatograph (GC) later on. Aerosol concentration in the offgas line was analyzed by an on-line scattering device (laser photometer) and by probe analysis. 129 Throughout the experiments, the behavior of the melt surface was observed by a TV camera which provided valuable information on gas flow through the melt, surface crust formation and aerosol production. After each experiment, the crucible was sectioned and the post-test cavity shape observed. 4.2.1.2 Experimental Results and Discussions A listing of BETA experiments is shown in Table 4.1. There were 19 tests divided into the following categories: " VO-series : Test of facility " Vi-series : High power tests " V2-series : Low power tests " V3-series : U.S. concretes tests e V4-series : Large cavity test The results of these tests will be reviewed and discussed in what follows. (i) Concrete Erosion For melts with high power input and small influence of crusts at the melt/ concrete interface, propagation of the melt was predominantly downward. Typical downward and sideward melt front propagations are given in Fig. 4.3. It shows a nearly constant and very high downward erosion rate of 1.0 mm/s in V1.8 test. Sideward erosion was much slower and ended after some 100 seconds. The dominant downward erosion indicated a very effective heat transfer mechanism at the bottom of the crucible, which was different from the sideward heat transfer mechanism. Experiments with low power input showed the role of the solidification process. Sideward and downward propagations were found to be more balanced due to the heat resistance of the metal crust at the bottom of the crucible. Fig. 4.4 shows the erosion rates for V2.3 test, with the downward erosion rate of some 0.1 mm/s being a factor of 10 less than that of V1.8 test. 130 Table 4.1 Test Matrix of the BETA Experiments Test Melt Planned Power (kW) VO.1 Iron 0 VO.2 Iron 400 VO.3 Iron+Oxide 1700 V1.1 Iron Pulsed Pour Failed V1.2 Iron+Oxide Pulsed Lorentz-Forces V1.3 Steel+Oxide 1000 V1.4 Steel 0 V1.5 Steel 450 V1.6 Steel+Oxide 1000 V1.7 Steel+Oxide 1700 V1.8 Steel+Oxide 1900 V1.9 Steel+Oxide 200-400 V2.1 Steel+Oxide 120-150 V2.2 Steel+Oxide 50-90 CaO Added V2.3 Steel+Oxide 240 CaO Added V3.1 Steel+Oxide 1700-2500 Remarks Transient II No Dispersion (CaO) CaO Added Limestone/Common Sand Heating from 0-66 seconds V3.2 Steel+Oxide 40- > 1000 V3.3 Steel+Oxide 400-600 Limestone/Common Sand V4.1 Steel+Oxide 300-1000 600 mm Diameter Limestone 300 kg Oxide with Cao 550 kg Steel 131 BETA EXPERIMENT V1.8 500 I II IIIII * AXIAL o RADIAL 400 A - z 300 7,- z 0 OWN 200 100 0 100 0 200 300 400 TIME [s] Figure 4.3 I ON Measured Concrete Erosion Distances of BETA Test V1.8 500 BETA EXPERIMENT V2.3 500 * AXI AL LJ 40 RADIAL L-j400 -- z 3000 8200 100 - 0 0 1000 2000 3000 4000 TIME [s] Figure 4.4 Measured Concrete Erosion Distances of BETA Test V2.3 5000 In the test with Limestone/Common Sand concrete, the dominating downward erosion was also observed. However, in comparison with KfK concrete, the sideward penetration was more pronounced. (ii) Melt Temperature Fast initial cooling of the melt was always observed in the BETA tests. With- out considering the possible uncertainty of the high temperature measurement, the melt cooled down from its high initial temperature (as high as 2573 K) to its solidus point (around 1870 K) typically in less than few hundred seconds, even with the power input per unit volume to the melt being an order of magnitude higher than decay power. This fast cooling is believed to be caused by the considerable downward heat transfer. The long-term temperatures of the melts were close to the freezing temperature of the metal. (iii) Release Gas Composition Gas analysis showed the major releases from melt/concrete interaction were H2 , H 2 0, CO and CO2 with a small amount of CH 4 . With silicate concrete, H2 and H 2 0 were the dominating gases, while in the limestone concrete test, CO and CO 2 were the main components. Thermodynamic calculations based on the minimization of Gibbs free energy were performed. It was found that at the beginning of the experiments, released gases were in equilibrium (correspondence temperature 1200 K). for both kinds of concrete. This is valid After the initial phase of the experiments the gas composition deviated from equilibrium. (iv) Aerosol Release The aerosol release in the BETA experiments with KfK concrete was characterized by a short dense aerosol peak during, and some seconds after, pouring of the melt, with the main components being iron and small amounts of chromium, 134 silicate, and other species from the decomposed concrete. Due to the small size of the aerosols, the aerosol releases were judged to be formed by evaporation and condensation of volatile species, while sparging was a negligible aerosol generation process. A typical rate of 0.1 g aerosol per mole gas during the heating period, with a reduction of an order-of-magnitude after shutting the power off, was measured in the high power tests. In V2.3 test with low power input, the aerosol concentration reduced from a short initial peak to 0.01 g per mole gas throughout the experiment. For V3.2, the Limestone concrete test, the release of aerosols was considerably more intense than in all other experiments. The aerosols were mainly CaO crystals with a typical 1 micron size. During the heating period, however, the aerosol photometer gave no data because of the very high aerosol concentration. The minimum concentration in that period was estimated to be 1.2 g per mole gas. The Limestone/Common Sand concrete showed considerably less aerosol generation rates but of the same constitution as Limestone concrete. The aerosol generation rate of Limeston/Common Sand concrete was comparable to that of KfK concrete experiments, even for the high power heating phase. The aerosols production in the limestone concrete test was attributed to the process of lime burning. The calcium oxide forming at the decomposing concrete surface can be easily powdered and transferred as solid particles into the gas stream. For Limestone/Common Sand concrete, the presence of a relatively large amount of SiO2 reduced this process by the formation of low melting SiO2 CaO mixtures. Therefore, the aerosol generation of the Limestone/Common Sand concrete was not as intense as the Limestone concrete. (v) Boundary Crust Formation The video observation of the melt surface during test V2.3 showed that, some minutes after pouring, a thin unstable surface crust formed at the top of the oxidic melt. This crust, however, did not influence the gas release. With additional melting and admixture of silica, the crusts disappeared and the melt became less 135 viscous. Throughout the experiment, the heat transfer in the oxide was controlled by the percolating gas. The steel melt, underlying the oxide, was at solidification temperature and had probably formed a crust at. the concrete interface. The bottom crust gave a reasonable explanation of the relativly low downward erosion rate in test V2.3. (vi) Layer Mixing Some of the experiments of the high power test series showed the occurence of dispersion of the metal into the oxidic melt. The process of dispersion was driven by the high gas flux evolving from the concrete, and resulted in fine metal droplets distributed all over the oxidic melt. In BETA, dispersion was detected by the loss of heating efficiency as the dispersed metal did not couple to the induction heater. The low density difference between the metallic and oxidic species and the high viscosity of the oxide facilitated dispersion. In test V1.8, the addition of CaO to the oxidic melt avoided the occurence of dispersion even for very high gas release by a reduction of the oxidic viscosity. Under similar experimental conditions but with higher viscosity, test V1.7 ended with the metallic melt completely dispersed. In all low power experiments, the metallic and oxidic melts remained segregated, as the gas flow was low. (vii) Melt Splashing In the V3.1 test, due to the extremely vigorous gas release and agitation of the melt, a considerable amount of the melt was splashed to the upper crucible wall and formed a metallic layer. This metal layer cylinder increased the coupling efficiency of the induction coil. The net power in the melt increased to 2500 kW, the highest rate ever obtained in BETA, and caused failure of the power control system by running out of range at 66 seconds. Various attempts to reactivate the induction system were not successful and freezing of the melt occurred very rapidly. 136 (viii) Spallation As limestone concrete interacts with a high temperature melt, the aggregates are reduced by the lime burning process to CaO which has virtually no mechanical strength. The concrete with a certain amount of CaO may break by the pressure generated inside the concrete. In V3.2 test, some thermocouples failure by mechanical breakup were detected. In V3.3 test, spalled material from the upper crucible was observed to drop into the melt. The removal of the CaO by spallation may reduce the effective decomposition temperature of the concrete, and result in a higher concrete erosion rate. 4.2.2 Sandia Experiments The most intensive experimental study in the USA on the melt/concrete interaction was initiated about a decade ago at Sandia National Laboratory. Various experiments [C1,M2,P1,P5,P6,P12,S3,S4] have been performed by using real materials or prototypic materials at different scales to investigate the phenomena of the melt/concrete interaction. Unfortunately, the details and the results of most of these experiments have not been systematically published. Only few quantitative results are available at this time. Recently, results of two of the programs, SWISS and TURC, were brought into attention since the results of these experiments were adopted for validation of the models developed at Sandia. Since then, more information about these experiments has been released [B2,G4,G5,G12]. These two experimental programs will be discussed and analyzed in the following sections. 4.2.2.1 Descriptions of Sandia Experiments (i) Sustained Melt-Concrete Interaction with Overlying Water (SWISS) The objective of the SWISS program was to study the interaction between molten debris, concrete and an overlying water pool. Principal observations included concrete erosion, crust formation, heat transfer, gas generation, aerosol transport and overlying water effect. 37 A schematic view of the experimental apparatus is shown in Fig. 4.5. A crucible designed with magnesia oxide (MgO) sidewall and Limestone/Common Sand concrete bottom was utilized in order to limit .melt/concrete heat transfer to the axial direction only. Radial heat losses from the melt were determined from the response of thermocouples embedded in the MgO walls. Water coolant was injected on top of melt at planned times during the experiments. About 45 kg of molten stainless steel generated by induction heating in a melt generator was poured into the crucible. Power input to the melt by an induction coil surrounding outside the MgO wall was sustained at approximately 100 kW level. Release gas was guided into an instrumented flow tube on top of the crucible to measure the flow rate and aerosol mass generation rate. In the SWISS program, a series of experiments was planned (see Table 4.2), however, only the first two experiments (SWISS-1 and 2) were documented. The major difference of these two experiments was the water quench time. The water flow was activated late (~35 minutes after melt pouring) in the SWISS-1 test. While in SWISS-2 test, the water was introduced in less than 2 minutes. Both experiments were extended for a period of 40 minutes. These two experiments provided valuable information about the effects of overlying water. (ii) Transient Urania Concrete Experiments (TURC) The TURC facility was designed to identify melt/concrete interaction and quantify the physical source term. This experiment could be of great interest to reactor accident analysis since it contains several unique features: " Well characterized experimental measurement of the released aerosols. " Fuel-oxide (U0 2 /Zr02) melt/concrete interaction. " The melt was doped with fission product mockup (such as Te, La, Ce and Ba). A schematic diagram of the TURC facility is shown in Fig. 4.6. The crucible was once again configured with MgO sidewall to ensure the melt attack on the 138 SWISS EXPERIMENTAL APPARATUS TOP HAT INSTRUMENTED FLOW TUBE AERSOLS GAS SAMPLING FLOW RATE CHAMBER MELT PENETRATOR CYLINDER MELT GENERATOR (MgO) ZIRCONIA INSULATION 25.4 INDUCTION COIL STAINLESS STEEL 46 kg WATER INLET CRUCIBLE (MgO) - WATER EXIT WATER POOL Figure 4.5 SWISS Experimental Apparatus (Ref.[G 12]) 139 r .,:2 Table 4.2 Test Matrix of the SWISS Experiments Test Crucible SWISS-1 LCSt Purpose Melt Water Quench Temperature Late - 2000 K Base Line Data Thick Crust Quench SWISS-2 LCS Early - 2000 K Melt/Water Interaction Thin Crust Quench SWISS-3 MgO Early - Melt/Water Interaction For Small jg: Heat Transfer Fission Product Transport t Limestone/Common Sand concrete 140 TURC ISS EXPERIMENT FACILITY I Figure 4.6 TURC-1SS Experiment Facility (Ref.[G4]) 141 concrete was one-dimensional. The radius of the MgO cylinder was 0.208 m enclosing a Limestone/Common Sand concrete block at bottom. Several tests involved transient interaction of about 150 kg metallic or oxidic melt with the concrete. see Table 4.3. In TURC, a great deal of work has concentrated on the aerosol/fission product source term measurement by using filter samplers, impactors, cyclone and photometer. The mass source rate, distribution and the composition of the release aerosol quantified by the analysis of aerosol sampling of TURC test can be a valuable data base and well suited for VANESA model validation. 4.2.2.2 Results and Conclusions Some of the more significant reported observations in the Sandia experiments are summarized below: (i) SWISS Tests " Concrete erosion rate: - 0.08 mm/s. " The effect of overlying water on concrete erosion rate was negligible. " Significant, reduction by a factor of 10 to 20 of the aerosol mass generation rate after water was added. * Neither steam explosion nor apparant fragmentation was observed. " Reduction of aerosol release due to the formation of top crust was detected. (ii) TURC Tests " The concrete erosion rates of TURC-1SS and TURC-1T were 0.4 and 0.1 mm/s, respectively. While in the oxidic melt test, TURC-2, the formation of stable crust reduced the concrete erosion rate to 0.008 mm/s. " Combustible gases at thermal equilibrium were detected in both metallic and oxidic melt tests. " Aerosol generation rates measured in TURC-1SS test as well as the VANESA predictions are shown in Fig. 4.7. 14-2 Table 4.3 Test Matrix of the TURC Experiments Test Melt Mass (kg) Melt Composition Melt Temperature (K) TURC-1T 150 Fe - Al 2 03 (Thermite) 2700 TURC-1SS 147 S.S. 304 2350 TURC-2 144 LTO 2 , ZrO2 2820 TURC-3 200 U0 2 , ZrO2 , Zr 143 2670 10 0.1 - TURC-188 MEASUREMENT$ 0-01 PREDICTIONS BASED ON OE-0' VANESA EXPERIMENTAL TEMPERATURES. GAS FLOWS. AND EROSION 2 1 3 TIME (Minutes) Figure 4.7 Comparisons of the TURC-lSS Test Data and the Predictions of the VANESA Code (Ref. [P13]) 144 4.2.3 Summary The experimental programs have succeeded in enhancing the understanding of melt/concrete interaction and the resulting consequences, important in reactor severe accident analysis. A qualitative understanding of the melt/concrete interaction has been obtained, and quantitative data have been obtained for many specific phenomena. It is likely that the most significant phenomena that might be present in a core meltdown accident have already been identified in these programs. 4.3 Experiment Analysis and Model Validation As discussed in the previous chapter, the downward heat fluxes calculated by the various heat transfer models are different by an order-of-magnitude. It is important that the accuracy of these analytical models be justified based upon the real material experimental data. In the real material experiments, the physical phenomena at the pool bottom interface cannot be directly observed. However, the downward concrete erosion rate directly related to the magnitude of the downward heat flux can be measured to validate the precision of the analytical model. Integral analyses based on CORCON/MIT using different downward heat transfer models have been done to predict the downward erosion of the BETA and Sandia experiments. The erosion distances measured at the end of BETA tests are used to quantify the standard deviations of the various heat transfer models. 4.3.1 Experiments Analyzed and Input Parameters Used Twelve BETA tests were analyzed with different downward heat transfer models. The experimental conditions and melt compositions of these tests used in the CORCON/MIT calculation are listed in Tables 4.4 and 4.5, respectively. The experiment duration was determined by the maximum of the concrete erosion distance to be allowed. When the melt front reached a certain range, the power was turned off and the experiment was terminated before meltthrough of the concrete crucible. Typical power input histories are shown in Figs. 4.8 and 4.9. 145 Table 4.4 Test Conditions of the BETA Experiments Melt Mass Initial Melt Temperature tExperiment Duration tAverage Power Total Energy (kg) (K) (s) (kW) (MJ) VO.2 300 2473 2500 370 930 VO.3 450 2473 462 1180 540 V1.2 350 2473 2075 380 780 V1.3 450 2173 510 780 400 V1.5 300 2273 1300 330 430 V1.6 350 2273 742 710 530 V1.7 380 2373 375 1010 380 V1.8 490 2073 386 1600 620 V1.9 410 2173 2420 260 630 V2.1 450 2273 4620 140 640 V2.3 400 2173 4480 190 860 V3.3 350 2573 2930 350 1020 Test t Determined by the last data point of the axial erosion distance. Average power input over the experiment duration. 146 Table 4.5 Melt Compositions of the BETA Experiments A12 0 3 (kg) - - 150 - - 200 - - 150 - - V1.3 246 30 24 105 45 - V1.5 246 30 24 - - - V1.6 246 30 24 45 5 - V1.7 246 30 24 72 8 - V1.8 315 17.5 17.5 91 - 39 V1.9 315 17.5 17.5 42 - 18 V2.1 270 - 30 105 45 - V2.3 270 15 15 70 10 20 V3.3 246 30 24 50 - - Fe (kg) VO.2 300 VO.3 300 V1.2 Cr (kg) 147 SiO 2 (kg) CaO (kg) Ni (kg) Test BETA EXPERIMENT V1.3 1500 1000 z oc 500 0 L 0 500 1000 1500 TIME [s] Figure 4.8 Power Input History of BETA Test V1.3 I~m~ 2000 BETA EXPERIMENT V2.3 800 700 600 500 z 400 300 200 100 0 0 1000 2000 3000 4000 TIME [s] Figure 4.9 Power Input History of BETA Test V2.3 'I L f 5000 For Sandia experiments, the conditions of the analyzed tests are shown in Table 4.6. The one-dimensional erosion mode was treated in the CORCON/MIT by cutting off the sideward heat transfer. The sideward heat loss to the MgO wall was compensated for by reduction of the actual power input to the code calculation. The actual power input and the one for code calculation of the SWISS-1 test are shown in Fig. 4.10. To initiate the CORCON calculation, parameter values other than the specifications of the experiment are required to specify the boundary conditions and emissivities of various components. The values commonly used for these parameters are listed in Table 4.7. 4.3.2 Results and Discussions 4.3.2.1 BETA Experiments The experimental results and analytical predictions of the concrete erosion of early BETA tests have been shown in the previous chapter, while those of the other BETA tests are shown in Figs. 4.11 through 4.18. In general, the GF model significantly underestimates the downward erosion, and the FC model overpredicts some of the BETA tests, especially in the low power tests. As one can see the RFC model gives the best agreement to the experimental data. The precisions of these heat transfer models will be quantified in the following section. The melt temperature responses of some of the BETA tests are shown in Figs. 4.19 through 4.27. As indicated, most of the experiments showed a rapid initial melt temperature drop for both metallic and oxidic layers. In the calculated results, the FC model gives the highest rate of the initial melt temperature drop among various models. However, the melt temperature is still greatly overpredicted by the FC model both at the initial transient period and at the steadystate. This may be caused by an error in the melt temperature measurement. As indicated in these figures, most of the measured metallic temperatures drop below the solidus temperature of the metallic layer, and some of them are even lower 150 Table 4.6 Test Conditions of the Sandia Experiments SWISS-1 SWISS-2 TURC-1T TURC-ISS TURC-2 Melt (kg) Fe 33.3 32.3 Ni 8.1 7.9 Ni 3.6 108.8 - - 26.5 - 3.5 - 11.8 - - - - - Zr0 2 - - - - A12 0 - - U0 2 120.0 100.8 43.2 Total 45.0 43.7 30.0 150.0 Initial Melt Temperature (K) 2000 2000 2700 2350 2820 Concrete Crucible Radius (m) 0.108 0.108 0.208 0.208 0.208 Water Quench Late Early No No No Power Input (kW) - 0 0 0 Concrete LCSt LCS LCS LCS LCS Erosion Mode 1-D 1-D 1-D 1-D 1-D 40 40 30 30 15 2400 2400 735 120 600 3 Heat Loss to MgO Wall (kW) Duration (s) t 90 100 - Limestone/Common Sand concrete 151 - - 147.0 144.0 SNADIA SWISS- I EXPERIMENT 150 I -1--Epe - I I Dt Data -Experiment ......... Code Calculation -/ 100 / - --- . J I Lz... I. 50 I: I: Q1 I: 0 -50 I I 0 I I 20 10 I I 30 TIME [min] Figure 4.10 11"WWOMP Power Input History of Sandia SWISS-1 Test It A*t4 I - 40 Table 4.7 Input Parameters Used in CORCON/MIT for Experiment Analysis Initial Concrete Temperature 300 K Initial Coolant Temperature SWISS Tests 300 K Surrounding Pressure 1.0 atm (Constant) Surrounding Temperature Beginning 300 K End 500 ~ 800 K Emissivity Concrete Melt Surrounding 0.6 0.8 0.8 153 BETA EXPERIMENT V1.5 500 i 0 r, 400 - I I I I EXPERIMENT AXIAL EXPERIMENT RADIAL FC MODEL AXIAL FC MODEL RADIAL RFC MODEL AXIAL RFC MODEL RADIAL GF MODEL AXIAL GF MODEL RADIAL 300 S 200 -- 100 --- O 0 & 0 --- I -I 300 -_- 900 600 1200 1500 TIME [s] Figure 4.11 Comparison between the Predicted and Measured Erosion Distances of BETA Test V1.5 ft BETA EXPERIMENT V1.6 500 r 400 z 300 0 0 CI) 200 100 0 0 100 200 400 300 500 600 700 800 TIME [s] Figure 4.12 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.6 14 At BETA EXPERIMENT V1.7 500 400 z E-- 300 Do z 0 p- z 200 100 0 0 100 200 300 400 TIME [s] Figure 4.13 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.7 Rp MONlftItO*h# BETA EXPERIMENT V1.8 500 r - S-- EXPERIMENT FC MODEL RFC MODEL 400 ....... GF MODEL z 300- - z o200 100 0 0 100 200 300 400 TIME [s] Figure 4.14 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.8 BETA EXPERIMENT V1.9 500 r z 400 300 0 200 00 z 100 0 0 500 1000 1500 2000 2500 TIME [s] Figure 4.15 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V1.9 ROM -vow -PWOW - BETA EXPERIMENT V2.1 500 400 z U)1 300 z 0 Now 200 100 OL 0 1000 2000 3000 4000 5000 TIME [s] Figure 4.16 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V2.1 It.A BETA EXPERIMENT V2.3 500 400 z 300 z0 WE" 200 0 z 100 0 k 0 1000 2000 3000 4000 5000 TIME [s] Figure 4.17 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V2.3 BETA EXPERIMENT V3.3 500 r z 400 300 0 - 200 z 100 0k 0 500 1500 1000 2000 2500 3000 TIME [s] Figure 4.18 Comparison between the Predicted and Measured Downward Erosion Distances of BETA Test V3.3 ..lost BETA EXPERIMENT VO.2 2800 II ' I j I I ' ' I v I EXPERIMENT r-w - 2600 -- -FC - - --- MODEL RC MODEL GF MODEL 2400 2200 2000 I, -. E- 1800 - 1600 Solidu. . Temper ture .- 4 Concrete Decomposition Temperature 1400 0 100 200 300 400 500 600 TIME [s] Figure 4.19 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test VO.2 losIt BETA EXPERIMENT V1.3 2600 * I, -- 2400 - -.-.-. EXPERIMENT FC MODEL RFC MODEL GF MODEL 2200 Emu 2000 CA3 Q 1800 - Soliusu 1600 - Concrete Decomposition Temperature Temperature 1400 0 400 200 600 800 TIME [s] Figure 4.20 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.3 'I Iat BETA EXPERIMENT V1.5 2600 r-, 2400 - -eEXPERIMENT FC MODEL - RFC MODEL -- GF MODEL 2200 E- 2000 \ S1800 -~.* __ 1600 Solidus .. Temperature Concrete Decomposition Temperature 1400 12001000 F 0 t 600 1200 1800 2400 3000 3600 TIME [s] Figure 4.21 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.5 BETA EXPERIMENT V1.6 2600 EXPERIMENT -FC MODEL - 2400 - - -.--. RFC MODEL GF MODEL 2200 m 2000 E- 1800 Solidus Temperature 1600 Concrete o -- C)' Decompoition Temperature 1400 0) 400 200 600 800 TIME [s] Figure 4.22 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.6 1. 10 a BETA EXPERIMENT V1.7 2800 EXPERIMENT - 2600 -- -FC - - MODEL RFC MODEL -.---- GF MODEL 2400 -- - 2200 2000 1800S1600 Solidus Temperature -Concrete Decomposition Temperature 100 200 1400 0 300 400 500 TIME [s] Figure 4.23 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.7 BETA EXPERIMENT V1.8 2600 EXPERIMENT * - - FC MODEL - 2400 - -. RFC MODEL GF MODEL - S 2200 --.--. 02000E--- 1800 i Solidus Temperature - 1600 - Concrete DecompoSition Temperature 14001 0 100 200 300 400 500 TIME [s] Figure 4.24 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.8 - BETA EXPERIMENT V1.9 2600 EXPERIMENT FC MODEL 2400 - RFC MODEL ---.--- GF MODEL -'Q A 2200 - 2000 Solidus 1800 1600 Temperature - Concrete Decomposition Temperature 1400 0 500 1000 1500 2000 2500 TIME [s] Figure 4.25 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V1.9 losta - - .WIKl" BETA EXPERIMENT V2.3 2600 -F ~' 2400 -- I EXPERIMENT FC MODEL - RFC MODEL ..... GF MODEL 2200 Q> 2000 1800 Temperature -Solidus 1600 Concrete Decomposition Temperature 1400 II 0 400 ' I I I 800 1200 1600 2000 TIME [s] Figure 4.26 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V2.3 dw BETA EXPERIMENT V3.3 3000 , 1 , -OEXPERIMENT FC MODEL 2800 - - RFC MODEL 2600 ....... GF MODEL 2400 2200 o 2000 S1800 Solidus Temperature 1600 -- 16Concrete Decomposition Temperature 14001200 0 100 200 300 400 500 600 TIME [s] Figure 4.27 Comparison between the Predicted and Measured Metallic Layer Temperatures of BETA Test V3.3 than the concrete decomposition temperature. It is believed that when the thermocouples dipped into the melt, a rapid formation of melt crust surrounding the thermocouple resulted in a melt temperature rea:ding which is lower than the actual melt temperature. Another possible reason for the initial cooling of the melt which was not reproduced in the calculation could be splashing of the melt on the wall when it was poured into the cavity. This can effectively cool down the melt, but is not considered by the computer model. Of course, it may be also caused by underestimation of the sideward and upward heat losses in the code calculation. The amounts of the released gases predicted by the FC model are shown from Figs. 4.28 through 4.31 for several typical tests. It shows that CO and CO 2 are the major components of the released gas with the KfK concrete, while H2 and H 2 0 are dominant releases in the Limestone/Common Sand concrete test. This prediction agrees qualitatively with the experimental observation. (i) BETA V1.5 Test r In the analysis of test V1.5, both the FC and RFC models overpredict the axial erosion at early times and then converge to experimental results later on. The radial erosion is slightly underestimated by these models. In the GF model application, the axial erosion is underpredicted especially at the end of the experiment. The experimental results showed that the interaction started with a stable gas film and then collapsed at about 400 seconds later. However, this initial stable gas film cannot be predicted by the film collapse models based on the criterion obtained from the data fitting of the first four BETA tests. This disagreement may be caused by the uncertainty of the initial melt temperature of V1.5. The GF model gives roughly equal downward and sideward erosion. The FC and RFC models predict a dominant downward erosion which agrees with the 171 BETA EXPERIMENT V1.3 101 100 0 s 10-1 z 10-3 L 0 500 1000 1500 2000 TIME [s] Figure 4.28 Gas Generation Rates of BETA Test V1.3 Calculated by the Film Collapse Model BETA EXPERIMENT V1.9 101 0 w> 100 LJ F" zI 0 10-1 -1 P 10-2 0 500 1000 1500 2000 2500 TIME [s] Figure 4.29 Gas Generation Rates of BETA Test V1.9 Calculated by the Film Collapse Model BETA EXPERIMENT V2.3 101 0 0 100 L-j z 10 -1 -1 z 10-2 0n 0 1000 3000 2000 4000 5000 6000 TIME [s) Figure 4.30 Gas Generation Rates of BETA Test V2.3 Calculated by the Film Collapse Model *I~pit BETA EXPERIMENT V3.3 101 mCV2 U, 4) 0 S 100 L~J z 1 -1 0 z 102 0 (I) 0 1000 2000 3000 4000 TIME [s] Figure 4.31 Gas Generation Rates of BETA Test V3.3 Calculated by the Film Collapse Model experimental observation. This is also true for the analyses of the other BETA experiments. (ii) BETA V1.6 Test The power input of test V1.6 was initially sustained at 1000 kW. After 300 seconds, the power was reduced to below 500 kW until the end of the experiment. Before the power reduction, the calculated erosion distances based on the RFC model are in fairly good agreement with the experimental data, while the FC model overpredicts and GF model underestimates the concrete erosion. After the power reduction, the experimental data showed a significant reduction in the axial erosion rate (from 0.6 mm/s to 0.12 mm/s) which can not be reproduced with any of the heat transfer models. This could be caused by overestimation of the melt temperatures. In Fig. 4.22, the calculated temperature histories show an enhanced cooling at 300 second, but still not enough to follow the measured cooling rate of the melt. (iii) BETA V1.7 Test With an initial melt temperature of 2373 K in test V1.7, the interaction predicted by the film collapse models starts with a periodic contact mode. The FC model significantly overpredicts while the RFC model moderately overestimates the downward erosion distance. Nevertheless, the experimental data do not show the existence of an initial stable gas film . The measured erosion rates, during both the initial transient period and at steady-state, are higher than the predictions of the GF model by a factor of two to three. In test V1.7, a power reduction from more than 1500 kW to 200 kW occurred at 250 seconds. However, the experimental data showed a smooth decrease in the downward erosion rate after the power reduction. This is quite different from the V1.6 observation. 176 (iv) BETA V1.8 Test The measured axial erosion rate of test V1.8 was 1.0 mm/s, which is the highest erosion rate ever measured in real material experiments. All the heat transfer models used in the analysis cannot predict such a high erosion rate. The best prediction is calculated by the FC model (no initial gas film) which gives a downward erosion rate of 0.8 mm/s. The RFC and GF models further underpredict the erosion distance with erosion rates of 0.6 and 0.2 mm/s, respectively. Comparison between the tests results of V1.7 and V1.8 shows that V1.8 has twice the erosion rate while its initial melt tempeature is 300 K lower than that of V1.7. The reason for the extremely high erosion rate in test V1.8 may be its high power input. However, in the code prediction, the axial erosion is affected mildly by the power input. The calculated melt temperatures shown in Fig. 4.24 remain constant or even rise slightly for the first 300 seconds, while the experimental data showed a rapid initial cooling rate despite the high power input. Both the axial erosion and melt temperature data of test V1.8 suggest that there is an extremely effective downward heat transfer between the melt and concrete, and this heat transfer is higher than the prediction of any of the models. The FC model overestimates the downward erosion of most other experiments, but still falls short in the prediction of the concrete erosion of test V1.8. (v) BETA V1.9 Test Test Vi.9 was a good experiment in terms of the duration and the power input density. This test was sustained for 2400 seconds with initial melt temperature of 2173 K. The average power density induced in the melt was 0.65 kW per kg melt mass which is comparable with the decay power in a real reactor accident situation. 177 As predicted by the film collapsed models, the interaction starts with the periodic contact mode. The agreement between the experimental data and the results of the RFC model, both in the axial erosion and melt temperature, is excellent, while the calculated results based on the FC model are less accurate. The GF model, as usual, underpredicts the axial erosion significantly. (vi) BETA V2.1 and V2.3 Tests The erosion data of the low power test showed that a fast erosion of 0.4 mm/s occurred during the first one hundred seconds. After the initial periods, the erosion rate was reduced by an order-of-magnitude to 0.03 mm/s for about 2000 seconds, and then started increasing to 0.08 mm/s and remained approximately the same until the end of the experiment at 4500 seconds. One possible scenario is that the steel melt formed a crust at these low power levels soon after contacting the cold concrete. After a while, the crust would begin to remelt and the concrete ablation rate would increase. However, the measured temperatures showed no trend of remelting. The possibility of an initial stable gas film is ruled out due to the relatively low initial melt temperature (about 300 K lower than required for stabilization of a gas film). If an initial gas film was stabilized, it would have been collapsed at earlier time, before 2000 seconds, due to the low power input. Compared to the experimental data, the RFC model significantly overpredicts the downward erosion at the initial periods, and then converges to experimental results later on. This is due to the delay of the solidification. In the RFC model application, the calculation starts with a periodic contact mode and predicts the formation of a bottom crust at 300 seconds later without remelting throughout the experiment. The axial erosion rates predicted by the RFC model before and after the melt solidification are 0.4 and 0.08 mm/s, respectively. The FC model predicts the same trend with a little higher erosion rate than the RFC model. The 178 GF model shows the best agreement with the low power test data. It follows the slow erosion at the initial periods, but can not match the increase of the measured erosion rate at later times. (vii) BETA V3.3 Test A nonuniform concrete erosion pattern was observed in test V3.3. As shown in Fig. 4.18, certain erosion levels have more than one data point, and these correspond to the failure times of thermocouples located at the same vertical but different horizontal positions. In this test, an initially stable gas film collapsed at 570 seconds, as also predicted by the RFC and FC models. The axial erosion is underestimated for the initial periods before the gas film collapsed. After the film collapse, the calculated erosion distances increase and follow the trend of experimental data. At the end of the experiment, the RFC and FC models slightly underestimate the total axial erosion distance. Unlike the other analyses, the RFC model predicts a higher downward erosion than the FC model in the Limestone/Common Sand concrete test. It is interesting to note that the RPC model, as discussed in the previous chapter, predicts a lower heat flux with the KfK concrete but a higher heat flux with the Limestone/Common Sand concrete than the PC model. Based on the experimental observation, it can be seen that the revised model is more adequate in predicting the cases with different concretes. 4.3.2.2 Sandia Experiments The downward concrete erosion distances of the Sandia experiments are shown from Figs. 4.32 through 4.36. In general, the RFC and GF models are better than the FC model in the predictions of the downward erosion distances of the Sandia experiments. For sustained heating experiments (SWISS), the RFC model is able to produce a fairly good agreement in the axial erosion distance. While in the transient tet 179 SANDIA SWISS- I EXPERIMENT 500 400 z C,) 300 z0 200 O-A z 100 0 0 L 0 500 1000 1500 2000 2500 TIME [s] Figure 4.32 Comparison between the Predicted and Measured Downward Erosion Distances of SWISS-1 Test SANDIA SWISS-2 EXPERIMENT 500 400 z 300 z 0 U) I A 200 100 0 0 500 1000 1500 2000 2500 TIME [s] Figure 4.33 Comparison between the Predicted and Measured Downward Erosion Distances of SWISS-2 Test SANDIA TURC-IT EXPERIMENT 120 r,1 7 100 14 80 z U) 0 60 40 z 20 0 0 200 400 600 800 1000 TIME [s] Figure 4.34 Comparison between the Predicted and Measured Downward Erosion Distances of TURC-1T Test lost SANDIA TURC-1SS EXPERIMENT 50 r 40 z 30 C) 20 z 0 10 9z OL 0 40 60 80 100 120 TIME [s] Figure 4.35 Comparison between the Predicted and Measured Downward Erosion Distances of TURC-1SS Test SANDIA TURC-2 EXPERIMENT 10 8 z 6 z0 Ul) 00 0 4 2 0 0 100 300 200 400 500 600 TIME [s] Figure 4.36 Comparison between the Predicted and Measured Downward Erosion Distances of TURC-2 Test lost (TURC) analyses, the RFC model cannot predict the axial erosion very well in most cases. (i) Sandia SWISS Tests The temperature histories of test SWISS-1 are shown in Fig. 4.37. The experimental data shown in this figure from different publications [G11,G12] are inconsistent. It is important to notice that the initial melt temperature indicated by Ref. [G11] and [G12] was 1925 K and 2000 K, respectively. This initial temperature difference is considered to be small and within the uncertainty range. However, it has significant effect in determining the stabilization of an initial gas film. With the initial melt temperature of 1925 K, both the FC and RFC models will predict a periodic contact mode for SWISS tests. In the code calculations, the initial melt temperatures of the SWISS tests (both SWISS-1 and SWISS-2) were specified as 2000 K. At this initial temperature, the RFC model predicts an initial stable gas film while the FC model predicts a periodic contact mode. The reasons for these different predictions of the initial gas film between the FC and RFC models are: (1) the downward heat flux at the initial conditions of the SWISS test predicted by the PC model is lower than the RPC model; (2) the multiplier of the Kutateladze's limit used in the FC model is higher than that in the RFC model. In the RFC model calculations, the gas film stabilized initially is sustained throughout the whole period of experiment without collapsing. Therefore, the calculated axial erosion distances of the RFC model are exactly the same as those of the GF model, and are in fairly good agreement to the experimental data. However, the melt temperatures are significantly overpredicted by both the RFC and GF models (see Fig. 4.37). In the FC model calculations, the axial erosion distances of SWISS tests are overpredicted by a factor of two compared to the experimental results, even though the calculated melt temperatures are close to the experimental data. 185 SNADIA SWISS-1 EXPERIMENT 2400 2300 2200 'Un 2100 2000 r 1900 1800 1700 1600 1500 0 5 10 15 20 25 30 35 40 TIME [min] Figure 4.37 Comparison between the Predicted and Measured Melt Temperature Histories of SWISS-1 Test 186 (ii) Sandia TURC Tests Since both the FC and RFC models predict a stable gas film throughout the whole period of tests TURC-1T and TURC-1SS, the calculated erosion distances by various models are exactly the same. The predicted erosion distances of test TURC-1T agree closely with the experimental data. While in the TURC-1SS analysis, the predicted erosion distances are significantly lower than the experimental data by a factor of three. The highly irregular erosion data of TURC-1SS indicate that the interaction may have started with a gas film and switched to the periodic contact mode 20 seconds later. The failure of the predictions may be caused by the uncertainties of the initial melt temperature and the heat losses to the MgO sidewall. TURC-2 test is the only real material experiment with oxidic melt. The solidus temperature of the oxidic melt calculated by CORCON is 2825 K, and the reported initial melt temperature was 2820 K. Therefore, in the code calculations the melt/concrete interaction is governed by a solidified pool. As discussed in the pervious chapter, the downward heat fluxes of the post-freezing stage predicted by the various models are about the same, therefore, the calculated erosion distances of the TURC-2 test with different models are almost equal. These predicted erosion distances are higher than the experimental data by a factor of two. It seems that the downward heat transfer of a solidified pool is overestimated by the post-freezing models. However, before more data corresponding to the postfreezing regime become available, a firm conclusion is hard to be made. 4.3.3 Model Validation The average downward erosion rates of the BETA tests, both the experimental and calculational results, are summarized in Table 4.8. The total erosion distances predicted by the various heat transfer models versus the measured distances are shown in Fig. 4.38. 187 Table 4.8 Axial Concrete Erosion Ratest of the BETA Experiments t Test Experiment Data GF Model PC Model FC Model RPC Model RFC Model VO.2 0.160 0.106 0.233 0.185 0.223 0.196 VO.3 0.866 0.186 0.800 0.800 0.624 0.624 V1.2 0.241 0.0911 0.234 0.181 0.219 0.180 V1.3 0.500 0.151 0.551 0.551 0.450 0.450 V1.5 0.231 0.114 0.280 0.280 0.266 0.266 V1.6 0.337 0.159 0.580 0.580 0.486 0.486 V1.7 0.533 0.197 0.907 0.907 0.706 0.706 V1.8 1.036 0.184 0.815 0.815 0.622 0.622 V1.9 0.145 0.0786 0.165 0.165 0.153 0.153 V2.1 0.0649 0.0502 0.0902 0.0902 0.0868 0.0868 V2.3 0.0893 0.0678 0.108 0.108 0.105 0.105 V3.3 0.136 0.0626 0.229 0.109 0.215 0.118 Average erosion rate in units of mm/s over the experiment duration. 188 DOWNWARD EROSION DISTANCE 700 600 500 -'400 z0 ip Z 300 200 100 0 0 100 200 300 400 500 600 700 EXPERIMENT [mm] Figure 4.38 Downward Erosion Distances of BETA Tests (Prediction versus Experiment) 189 In order to examine the trend of erosion with respect to the power input and the initial melt temperature, a decomposable concrete volume, VDC, is defined and plotted against the axial erosion distance for .each BETA test in Fig. 4.39. The decomposable concrete volume is defined by: VDC = QTotal PconcHDecomp (4.1) where QTotal is total available energy and given by: QTotal = Qinput where Qinput + [(mcp)metal + (mcp)ozide] ATi (4.2) is the total energy input shown in Table 4.4, and ATi is the temperature difference between the initial melt temperature and a reference temperature. Since the melt temperatures approached the metallic solidus point at the end of the BETA tests, the reference temperature in the calculation of the sensible heat is selected to be the metallic solidus temperature (1760 K). The heat capacities of the metallic and oxidic materials are 790 and 1780 J/kg K, respectively. Based on this definition, the decomposable concrete volume appears to be a proper combined index of the power input and the initial melt temperature. In Fig. 4.39, it can be seen that the axial erosion increases with the increase of the power input and the initial melt temperature. Least square fits of the predictions of various models are also shown in the figure. Both the FC and RFC models show good agreement, within the data spread. Individual erosion distances of the predictions relative to the experimental data are shown in Fig. 4.40. By using the definitions specified in Table 4.9, standard deviations in the predicted downward erosion are calculated for various heat transfer models. As indicated in the table, the GF model shows a significant discrepancy with the experimental data. It can also be seen that the revised periodic contact model is better than the original one. Among various downward heat transfer models, the 190 0.6 I I I I I I I I I I I EXPERIMENTAL DATA GF MODEL FC MODEL RFC MODEL 0.5 0. 4 z Cn) z0 0.3 r 0.2 0.1 0.0L 0.10 I I I I I I I 0.15 I I I 0.20 I I I I 0.25 DECOMPOSABLE CONCRETE VOLUME [m3] Figure 4.39 Least Square Fits of the Various Heat Transfer Models on the Predictions of the Downward Erosion of BETA Tests 191 -I 2.0 z 1.8 E- 1.6 1 .4 C-) cn 1.2 1.0 Q 0 z 0.8 0.6 cn 0.4 0 .2 0.0I0.10 0.15 0.20 0.25 DECOMPOSABLE CONCRETE VOLUME [M 3 ] Figure 4.40 Relative Downward Erosion Distances of BETA Tests 192 Table 4.9 Statistics for the Various Heat Transfer Models in the Calculations of the BETA Results GF Model PC Model FC Model RPC Model RFC Model 0.564 0.409 0.349 0.319 0.266 -0.533 0.275 0.158 0.133 0.046 Standard Deviation (6ca)i - (6ep)i]2 \n ( 6 ep)i Mean Relative Error 1 n [( 6 cal)i - (bezp)i n (bep)i 193 RFC model is the best in the prediction of the downward concrete erosion of the real material experiment. 4.4 Conclusions 1. The gas film model, developed earlier and commonly used in severe accident analysis, significantly underestimates the downward heat transfer in many experiments. 2. The film collapse model is more adequate than either of the gas film or the periodic contact model alone. 3. The revised film collapse model is better than the original one in predictions of both BETA and Sandia experiments. 4. The revised film collapse model is capable of producing erosion results of the BETA experiments with a mean error of 5% and a standard deviation of 27%. Less accuracy is found in the predictions of transient, one-dimensional experiments performed at Sandia National Laboratory. 5. Based on the revised and original film collapse models, the increase in axial erosion with power input and initial melt temperature is predicted, within the data spread. 6. The results of certain low power tests (BETA V2.1 and V2.3 in particular) do not fit the pattern set by the other experiments. A reexamination of data uncertainty is warranted. 7. The initial rapid cooling of the melt observed in BETA tests cannot be successfully predicted. Further investigations of the initial heat losses in the sideward and upward directions are necessary. Models for the splashing and layer mixing phenomena may be needed to explain the initial melt temperature behavior. 194 CHAPTER 5 SENSITIVITY STUDY OF THE EX-VESSEL SOURCE TERM 5.1 Objective The interaction of molten core with the concrete cavity of a reactor containment is an important phase in a severe reactor accident. Major concerns in the safety assessment include: the possibility of a basemat meltthrough; containment over-pressurization due to the generation of noncondensible gases; and most importantly the release of the fission products from the corium pool if containment fails. During the molten core/concrete interaction, radioactive fission products as well as nonradioactive materials can be released as aerosols from the molten pool into the containment atmosphere by either evaporation or mechanical processes. This ex-vessel source of aerosols has a direct impact on the estimation of the radiological consequence of a severe reactor accident. The magnitude, physcial and chemical characteristics, and timing of the ex-vessel aerosol release, determined largely by the heat transfer between the molten core and the concrete, are important factors affecting the potential amount of radioactive fission product that could be released from the containment building if it fails. The primary purpose of this chapter is to identify the impact of the downward heat transfer model on the concrete erosion, gas generation and ex-vessel aerosol release in analysis of a real reactor case. A parametric study on the significant variables, such as (1)initial melt temperature; (2)concrete properties; (3)amount of unoxidized zirconium; (4)amount of melt; (5)decay heat; and (6)layering potential of melt constituents, is performed to identify the important source of uncertainties in calculation of the ex-vessel aerosol release. 195 5.2 Introduction 5.2.1 Characteristics of Ex-Vessel Source Term Exposure of concrete to the high temperature melt will result in the decomposition of concrete and release of steam and noncondensible gases. As the steam and noncondensible gases bubble through the molten debris, they react chemically with the melt constituents, and also provide a tremendous free surface within the pool to enhance the vaporization process of the high vapor pressure constituents of the melt. The vaporized materials, both radioactive and nonradioactive, after emerging from the molten debris into the containment atmosphere, can be condensed as aerosol particles due to the relatively low temperature of the containment atmosphere. This is the evaporation process of forming the ex-vessel aerosols. Once gas bubbles reach the molten pool surface, some amount of surface melt can be injected into the containment atmosphere as aerosol-sized droplets due to bubble burst. This is a mechanical process of producing ex-vessel aerosols. Aerosol production during MCCI is not as intense but lasts far longer than aerosol production during in-vessel phases of an accident. Aerosols produced during MCCI are predicted to consist primarily of nonradioactive material, from control rods, structures, and concrete. These nonradioactive aerosols are important in the prediction of radionuclide aerosol behavior in the containment. The aerosols evolved from the corium pool will mix with the radioactive aerosols released earlier during the in-vessel phase of an accident, and then enhance the agglomeration and sedimentation in the containment atmosphere. The amount of radioactive aerosols suspended at the time of containment failure is the source that could be released from the containment to the public. In order to properly assess the radiological consequence of a severe reactor accident, it is necessary to understand the phenomena governing the physical and chemical processes involved which could lead to the release of ex-vessel aerosols. 196 5.2.2 Background Early research on severe accidents has pointed out the need to integrate the analysis of complex severe accident phenomena'to obtain realistic estimates of source terms. While recent studies have permitted advances in the analysis of source terms, the improved understanding has also allowed a more clear identification of the major uncertainties. In the QUEST study [L1), uncertainties were grouped into two categories: code input uncertainties and code phenomena uncertainties. Code input uncertainties were investigated by allowing certain important user-input parameters to vary over a reasonable range. Phenomena uncertainties were examined by varying values for the important phenomena described in the code. Since there were numerous parameters involved in the BMI-2104 code set, it was impossible to have all parameters analyzed in detail. A scheme was employed to determine which parameters warranted inclusion in the study. This scheme addresses the codes in the BMI-2104 suite in reverse order starting with NAUA. A sensitivity study of NAUA was performed first by varying one input parameter by output from another code or directly by the user - whether provided at a time about a base case. If a parameter had a strong influence on the interested output, for example the suspended aerosol mass as calculated by NAUA, it was identified as an important parameter. Once an input parameter of a downstream code provided by the output of a upstream code was identified to be important, sensitivity study of the upstream code was performed in the same fashion to determine the effect of each input parameter on that specific output. In this manner, the entire suite of codes was examined to determine a list of the most important parameters for further quantitative evaluation. In the BMI-2104 code suite, CORCON/MOD1 and VANESA were used to predict the behavior of ex-vessel aerosol during the MCCI. The estimates obtained from the VANESA model are sensitive to the features of the plant and accident 197 in question. The VANESA calculations are quite dependent on initial conditions specified as input to the model. These initial conditions are typically obtained from models such as MARCH and CORSOR. The calculations are also somewhat sensitive to the boundary conditions, such as the melt temperatures, gas generation rates which depend on the modeling of corium/concrete interactions and the nature of concrete assumed present in the plant. More specifically, the aerosol releases calculated by the VANESA model increase exponentially with increasing temperature of the melt, and vary approximately linearly with gas generation rate and concentration of volatile species in the melt. Therefore, anything that could cause an increase in the melt temperature, the gas generation rate or the concentration of volatile species in the melt would increase the ex-vessel aerosol release. For example, the increase of the heat transfer into the concrete will increase the concrete ablation and gas generation rate, thus it will increase the aerosol release. On the other hand, the melt temperature and the concentration of volatile species will be depressed due to the increased heat transfer, therefore, the aerosol generation will be reduced. The total effect of such parameters needs to be examined by integral analyses. The input parameters examined by the QUEST study were rank-ordered in terms of decreasing effect on the ex-vessel source term as follows [L1]: o Amount of core involved in the MCCI o Amount of zirconium in the melt e Amount of steel in the melt o Initial debris temperature e Reactor pressure vessel failure time * Concrete type . Water content of the concrete * Free energies of gas species . Cavity floor area As mentioned in QUEST, the results of the sensitivity study and the above rank 196 ordering apply only to calculations involving single-parameter variation around the TMLB' accident at the Surry plant and ought not be generalized. Since the updated version CORCON/MOD2 was not available at the time of the QUEST study, CORCON/MOD1 was used. Unfortunately, it should be noted that while the initial melt temperature specified in the QUEST for most of the cases is far below the solidus temperature of the melt, the CORCON/MOD1 is applicable only to the high temperature phase of the MCCI when the melt is hot enough to be entirely liquid to erode the concrete at a relatively rapid rate. There are reasons, as discussed in the QUEST report, to believe that the CORCON/MOD1 code does not, in fact, calculate reliable melt temperatures. In some cases, such as the high zirconium content and low steel mass cases, the melt experiences a dramatic temperature excursion during the MCCI. Melt temperatures can reach completely unjustifiable levels - in excess of 3200 K during this excursion. Therefore, the effects of those parameters on the ex-vessel source term could not be reliably ascertained in QUEST. Furthermore, the completeness of the list of important parameters in QUEST needs to be examined. Because only limited cases have been analyzed, it is likely that some other parameters which could be important were not identified. For instance, the importance of the amount of FeO or the solidus temperature of the oxidic melt related to the user-input uncertainties could be underestimated due to improper post-freezing modeling in CORCON/MOD1. Also, the effects of various parameters on the source term based on different initial melt temperatures still remain questionable. With respect to the code phenomena uncertainties, the effect of the downward heat transfer model has never been studied. As identified in the previous chapter, the gas film model adopted in the original CORCON code is not adequate in describing the downward heat transfer of the melt/concrete interaction. Both the periodic contact and film collapse models are better than the gas film model in 199 calculation of the experimentally observed concrete erosion and melt temperatures. The downward heat flux effect on the calculation of the ex-vessel source term based on the CORCON/MIT is described in this study. 5.3 Formulation of This Study 5.3.1 Analysis Methods and Computer Codes The methods used to identify the uncertainties in the calculation of ex-vessel aerosol resulting from various components are similar to the QUEST study, in which calculations were performed by varying one input parameter at a time about a base case. Instead of the CORCON/MOD1 used in the QUEST study, the revised version CORCON/MIT was used in this study to predict the behavior of the corium/ concrete interaction. The VANESA code was used to calculate aerosol generation and the releases of radionuclides based on the time dependent melt temperatures, gas flow rates, concrete erosion mass and aerosol release area from the CORCON/MIT output. To avoid possible typo-error during data transfer, VANESA has been coupled with CORCON/MIT in a simple way. In the simplified linkage, necessary data calculated by the CORCON/MIT are stored temporarily during execution and then transferred to VANESA at the end of the CORCON/MIT calculation. No attempt has been made to couple the calculations of these two codes step by step. The releases of radionuclides and non-radioactive materials calculated by the VANESA model do not feedback to the CORCON/MIT during each time step to update the amount of melt and the decay heat level in the concrete cavity. However, the amounts of the released materials during the MCCI are relatively small compared to the total inventory in the concrete cavity. The possible error due to the simplified procedure could be negligible. A more significant error from the simplified coupling belongs to the chemical reaction heat. Since the chemical reaction packages in the CORCON and VANESA are different, inconsistent calculations of thie 200 chemical reaction heat generation and zirconium depletion time would occur. In CORCON, the chemical reacton is calculated by thermodynamic analysis based on minimization of the Gibbs function of the system. In other words, the released gases and melt constituents are assumed to be in thermodynamic equilibrium and the chemical reaction in the system achieves a maximum rate. There can be, however, barriers that prevent or retard achieving the maximum reaction rate defined by the thermodynamic analysis. In VANESA, the extent of the chemical reaction is treated by kinetics theory which would reduce the reaction rate and decrease the zirconium depletion rate if the system deviates from thermodynamic equilibrium. However, there is no hard evidence at this moment to indicate a significant deviation from equilibrium during the corium/concrete interaction. Because of the elevated temperature, the impact of the chemical reaction difference on the ex-vessel source term could be small. The first correction set for CORCON/MOD2 (version 2.00) was issued from the Sandia National Laboratory in July 1986. This correction set (version 2.01) eliminates many of the coding and modeling errors that have been identified since the release of the code. From calculations for the CORCON Sample Problem, the results of the versions 2.00 and 2.01 were not widely different. However, it is not inconceivable that a particular set of input might trigger differences between the two versions. In this study, major parts of analysis were done based on the version 2.00 before the revised version became available. In addition, the differences between the results of the PC and RPC models were analyzed in several cases based on the version 2.01. 5.3.2 Input Parameters 5.3.2.1 Specifications of the Base Case Parameters used as the base case in this study are shown in Table 5.1. The initial fission products inventory is the same as in the base case of QUEST, and is given in Table 5.2. The base case conditions that have been chosen in this 201 Table 5.1 Parameters Used in the Base Case Study 2600 K Initial Melt Temperature (T) Fraction of Unoxidized Zr in Melt 50.0% Coolant (H20) Above Corium 60 Mg Radius of Concrete Cavity 3.0 m Timing of MCCI after Shutdown 180 minutes 0 Limestone/Common Sand Type of Concrete Concrete Decomposition Temperature (TD) 1500 K Reactor Nominal Power 3000 MWt 58.8% Fraction of Core Meltdown Emissivity of Concrete Melt Surrounding 0.6 0.8 0.8 202 Table 5.2 Melt Inventory of the Base Case (MI) at the Start of MCCI Species Mass (kg) Uranium Oxide (U02) 60000 Zirconium Oxide (ZrO2 ) Ferrous Oxide (FeO) Iron (Fe) Chromium (Cr) Nickel (Ni) Zirconium (Zr) Cesium (Cs) Iodine (I) Tellurium (Te) Barium (Ba) Tin (Sn) Ruthenium (Ru) Molybdenum (Mo) Strontium (Sr) Rubdium (Rb) Yttrium (Y) Technetium (Tc) Rhodium (Rh) Palladium (Pd) Lanthanum (La) Cerium (Ce) Praseodymium (Pr) Neodymium (Nd) Samarium (Sm) Plutonium (Pu) Antimony (Sb) Niobium (Nb) Silver (Ag) 8400 3600 18700 2200 1100 6000 0.7 0.1 16.4 49.1 152.0 103.0 140.0 43.7 0.1 22.9 36.7 20.7 52.0 62.3 131.0 50.7 171.0 34.0 469.0 0.31 4.0 1460.0 203 study were similar to the conditions specified in the CSNI benchmark problem No. 1 [N7]. It has a relatively small amount of metallic melt and high initial melt temperature compared to the base case of the TMLB' sequence in the QUEST study. 5.3.2.2 Cases Analyzed In this study, analyses will primarily focus on the differences that might occur in the calculation of the ex-vessel aerosol release between the PC model and the GF model. Both the PC model and GF model were applied to all cases to study the maximum effects on the aerosol release due to the heat transfer models. The FC model, a combination of these two, was applied only in some cases to illustrate its relative tendency with respect to the PC and GF models. Limited cases have been analyzed based on the RPC model to show the differences compared to the PC model. The parameters studied and their application range used in the test are given in Table 5.3. Detailed melt compositions used in the cases can be found in Table 5.4. Each case has been named by a short-hand representation in the following sections. For instance, PCM1 Base Case is the one with the specifications of the base case and melt compositions of M1, and calculated by the periodic contact model. Another example, GFM4 T = 2320 K represents the case of M4 melt with initial temperature of 2320 K and calculated by the gas film model, while the other parameters are the same as the base case. 5.4 Results and Discussions Effects of uncertain input parameters on the ex-vessel aerosol release analyzed by the CORCON/MIT-VANESA codes will be discussed and compared to the QUEST results. Not only the calculated aerosol generation but also those factors affecting the calculation of the aerosol generation will be discussed. The results of the various cases presented in the followings include: concrete erosion, gas 204 Table 5.3 Phenomena and Parameters Range Used in the CORCON/MIT-VANESA Sensitivity Study Phenomena and Parameters Case Downward Heat Transfer Model Periodic Contact (PC & RPC) Film Collapse (FC & RFC) Gas Film (GF) Initial Melt Temperature (Ti) 2600 2400 2320 2000 1807 Melt Composition K K K K K Base Case (Mi) Enriched Core Oxide (M2) Enriched Metal Steel (M3) Enriched FeO (M4) Fraction of Unoxidized Zr in Melt 50 % 20% 0% Concrete Type Limestone/Common Sand Limestone Basaltic Concrete Decomposition Temperature (TD) 1500 K 1670 K 1420 K Initial Layer Configuration Metal - aver - Oxide Oxide - over - Metal Decay Heat CORCON ANS Standard 205 Table 5.4 Compositions of Various Melts Used in the CORCON/MIT-VANSEA Sensitivity Study M1 Case M2 Case M3 Case M4 Case (kg) (kg) (kg) (kg) 60000 90000 60000 60000 ZrO2 8400 12600 8400 8400 FeO 3600 3600 3600 6000 Fe 18700 18700 37400 18700 Cr 2200 2200 4400 2200 Ni 1100 1100 2200 1100 Zr 6000 9000 6000 6000 Oxidic Layer: U0 2 Metallic Layer: * Other materials are the same as in Table 5.2. 206 generation, melt temperatures, aerosol generation rate, fission products release fraction and accumulated release of the ex-vessel aerosol. It should be mentioned that, in the following presentations, the decontamination factor due to the scrubbing effect of the overlying coolant has been applied to the total aerosol (radioactive and non-radioactive) release. But this factor has not been applied to correct individual fission product release. 5.4.1 Impact of the Downward Heat Transfer Models Estimated melt behavior using different heat transfer models for the base case is described in Table 5.5. It is seen that significant differences in the predicted melt behavior can result from the various models. The downward heat transfer based on the PC model is higher than the GF model. Therefore, the axial erosion rate as well as the melt cooling down rate are larger based on the PC model (see Figs. 5.1 and 5.2). Results of the FC model before the film collapse, which is predicted at 860 seconds after the start of MCCI, are the same as those of the GF model. After the film collapse, the results of the FC model fall between those of the PC and GF models. It should be noted that the temperature trends of the oxidic and metallic layers are essentially identical. An initial sharp decrease of the melt temperature followed by a slow-varying quasi-steady temperature is calculated with all heat transfer models in the base case study. Both phases reach below 1800 K almost at the same time as shown in Fig. 5.2. The temperature difference between the oxidic and metallic layers at the quasi-steady state calculated by the GF model is about 50 K, and the temperature differences calculated by the PC and FC models are even smaller. While in the QUEST study, the temperature behavior of these two layers calculated by the CORCON-MOD1 models were quite different. The calculated oxidic temperature was sustained above 2100 K for several hours, while the metallic temperature dropped rapidly to its liquidus point (1790 K). 207 Table 5.5 Phenomena and Timing of Events of the Base Case GF Model PC Model FC Model Yes No Yes Zirconium depletion (min) 11 2 11 Layer flip (min) 12 2 12 Initial stable gas film Film collapse (min) 14 Formation of bottom oxidic crust before layer flip No No No Time of bottom metallic crust formation (min) 40 15 25 Time for oxidic temperature drops below 1720 K (min) 63 27 36 Coolant left after 3 hours interaction (kg) 1900 8400 3900 Oxidic solidus temperature after 3 hours interaction (K) 1657 1615 1642 208 800 700 600 500 z 400 z0 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.1 Concrete Ablation Distances Predicted by Different Heat Transfer Models 209 3000 2800 2600 I, 2400 2200 2000 1800 1600 1400 0 10 20 30 40 50 60 TIME [min] Figure 5.2 Melt Temperature Histories Predicted by Different Heat Transfer Models 210 The calculated gas generation rates are given in Fig. 5.3. It is shown that initially the gas generation rate calculated by the PC model is five times higher than the GF model. However, at the quasi-steady .state, the gas generation rate of the PC model is lower than the GF model because lower melt temperature is calculated by the former model. A sudden increase of the gas generation due to the coking effect after the depletion of zirconium can be seen in the GF and FC models. However, this sudden surge of the gas generation is compensated for by the sharp decrease of melt temperature calculated by the PC model, therefore, there is no peak in the gas generation rate in the PC model predictions. Increased gas generation rate due to film collapse calculated by the FC model also can be seen in Fig. 5.3. In Fig. 5.4, the aerosol generation rate calculated with the PC model is 1 kg/s initially, and it drops to below 10 g/s in 15 minutes of interaction due to significant decrease in the melt temperature. In the GF and FC applications, an initial aerosol generation rate of 200 g/s, 5 times less than that of the PC model, is calculated. However, in less than 10 minutes, the aerosol generation rates calculated by both the GF and FC models are higher than that of PC model. The coking effect of the increase in gas generation gives an increase in the aerosol generation rate at 11 minutes after the start of MCCL. With both GF and FC models, the aerosol generation rates drop below 10 g/s at 35 and 26 minutes, respectively. Using all heat transfer models, a dramatic decrease, about an order-ofmagnitude, in the areosol release rate is calculated at different times (27 minutes for PC model, 36 minutes for FC model and 63 minutes for GF model). The reason for this sharp decrease is that there exists a critical oxidic temperature (1720 K) in the VANESA model, above which the vaporization of calcium oxide is viable. For the base case analysis, the aerosol composition calculated by VANESA is dominated by the calcium oxide. As soon as the oxidic temperature drops below 1720 K, the vaporization process of calcium oxide and hence the areosol generation rate 211 C L-s zC r 106 z 0 U) 0 105 0 30 60 90 120 150 180 TIME [min] Figure 5.3 Gas Generation Rates Predicted by Different Heat Transfer Models 212 II Lj 102 z 101 0 C12 100 10-1 10-2L 0 30 90 60 120 150 180 TIME [min] Figure 5.4 Aerosol Generation Rates Predicted by Different Heat Transfer Models 213 is reduced significantly. The timing of this significant drop in the aerosol generation rates calculated by various models coincides with the time required for the oxidic temperature to reach below 1720 K as listed in Table 5.5. After this sharp decrease, the aerosol generation rates from the various models fall between 0.2 and 0.4 g/s. In the QUEST study, because of the relatively high oxidic temperature calculated by the CORCON-MOD1, the calculated aerosol generation rates in all cases remain above 1 g/s. In Fig. 5.5, it is shown that the total aerosol mass production is mildly affected by the different heat transfer models except in the first ten minutes. The accumulated aerosol release calculated by the PC model shows a rapid initial rise and reaches 180 kg in 15 minutes. After that, it almost stays constant for three hours of MCCI. As for the GF model calculation, the accumulated aerosol achieves 200 kg release at 40 minutes without further significant increase. Results of the FC model are about the same as the GF model. However, the radionuclide releases resulting from different heat transfer models have significant differences. As indicated in Fig. 5.6, the initial lanthanum release rate calculated by the PC model is five times that of the GF model. The accumulated release fractions of lanthanum are shown in Fig. 5.7. It is seen that the PC model gives three times higher total lanthanum release at 3 hours than the GF model. Differences of the lanthanum release between the calculations of the FC and GF models are negligible. The releases of other radionuclides are shown in Figs. 5.8, 5.9 and 5.10. All these figures show similar trends for the impact of the different heat transfer models. The rate of the radionuclide release from the vaporization process depends not only on the melt temperature but also the available free surface. At the initial temperature of the base case, the gas generation rate, and hence the available free surface calculated by the PC model is larger than the GF model. Therefore, higher radionuclides release rates are calculated by the PC model at the start of 214 300 250 C,) 200 C,) 150 100 50 0h 0 20 60 40 80 100 120 TIME [min] Figure 5.5 Accumulated Aerosol Releases Predicted by Different Heat Transfer Models 215 101 100 r, 10-1 10-2 10 -3 10~5_ z E-- 0-6 10-7 10-8 0 20 60 40 80 100 120 TIME [min] Figure 5.6 Lanthanum Release Rates Predicted by Different Heat Transfer Models 216 101 I -E- ---- 3 RELEASE FRACTION (La) LANTHANUM I I PCM1 BASE CASE GFM 1 BASE CASE FCMI BASE CASE 100 0 30 90 60 120 150 180 TIME [min] Figure 5.7 Lanthanum Release Fractions Predicted by Different Heat Transfer Models 217 TELLURIUM (Te) 10 2 1 1 1 RELEASE FRACTION 1 Ct) p z so 101 0 30 90 60 120 150 180 TIME [min] Figure 5.8 Tellurium Release Fractions Predicted by Different Heat Transfer Models 218 ANTIMONY (Sb) RELEASE FRACTION 100 z 0 10 -1 0 30 60 90 120 150 180 TIME [min] Figure 5.9 Antimony Release Fractions Predicted by Different Heat Transfer Models 219 STRONTIUM (Sr) RELEASE FRACTION 102 1 1 1 1 z 101 0 30 60 90 120 150 180 TIME [min] Figure 5.10 Strontium Release F~actions Predicted by Different Heat Transfer Models 220 MCCI. As predicted, the initial gas film assumed by the FC model collapses at a relatively low melt temperature condition, in other words, it collapses at the moment when the radionuclide release rate is reduced significantly. Therefore, the differences in the calculation of radionuclide release between the FC and GF models are negligible. Because the melt temperatures calculated by the PC model drop quickly at the start of MCCI, the radionuclides release rates are promptly reduced, and no major releases are calculated after the first time step (3 minutes internval) of the VANESA calculation. While in the GF model application, the time of the accumulating of radionuclides can extend as long as 30 minutes. 5.4.2 Effect of Concrete Decomposition Temperature The phase change of the concrete mixture is characterized by its solidus and liquidus temperatures. In CORCON, the concrete is always assumed to be decomposed and melted at a user specified temperature. The best choice of this decomposition temperature was suggested as the solidus temperature plus one third of the difference between the solidus and liquidus temperatures of the concrete [C3]; however, it may be affected by the gas pressure created below the decomposed concrete surface. In addition to the suggested value, the solidus and liquidus points of the Limestone/Common Sand concrete were chosen in this test to illustrate the effect of the decomposition temperature variation. The most direct effect of the decomposition temperature is the heat transfer between the melt and the concrete. The lower the decomposition temperature the higher is the downward heat flux and, therefore, the higher is the initial gas generation rate. Integral results of the axial ablation distances, the melt temperatures and the gas generation rates are shown in Fig. 5.11, 5.12 and 5.13, respectively. As noted, the quasi-steady oxidic temperature is also affected by the decomposition temperature. The time for the oxidic melt to reach below the critical temperature (1720 K), and hence the time of the significant decrease of the aerosol generation rate is delayed by an increased decomposition temperature (see Fig. 5.14). For the 221 800 700 600 z 5 0 0 CC, *400 z rI 300 S200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.11 Downward Ablation Distances for Different Concrete Decomposition Temperatures 222 3000 2800 2600 a:' 2400 2200 E- 2000 1800 1600 1400 [ 0 10 20 30 40 50 60 TIME [min] Figure 5.12 Melt Temperature Histories for Different Concrete Decomposition Temperatures 223 108 0 r A. z E 106 0 30 60 90 120 150 180 TIME [min] Figure 5.13 Gas Generation Rates for Different Concrete Decomposition Temperatures 224 105 104 0 101 CI) 100 10~1 10-2 0 30 60 90 120 150 180 TIME [min] Figure 5.14 Aerosol Generation Rates for Different Concrete Decomposition Temperatures 225 high decomposition temperature case, the areosol generation rates calculated by the GF model remain above 2 g/s for three hours of MCCI. The initial aerosol generation rate increasing with the decrease of the .decomposition temperature is calculated by the PC model, while in the GF model, the differences of the initial areosol release rate are small. In Fig. 5.15, it is shown that the total aerosol mass production is not affected by the variation of the decomposition temperature. A more significant effect can be found in the lanthanum release. Based on the PC model, the lanthanum release of the base case is a factor of two higher than the high decomposition temperature case, while the low decomposition temperature case has the same results as the base case (see Fig. 5.16). In the GF model, less significant effect is calculated for the decomposition temperature variation. In general, the effect of the decomposition temperature on the melt behavior calculated by the PC model is more significant than that of the GF model, since the rate of heat transfer in the PC model is more sensitive to the variation of (Tp - TD) than the GF model (see Fig. 3.7). 5.4.3 Effect of Concrete Type This test was done to illustrate the effect of using different concretes in the calculation of the ex-vessel aerosol release. Three generic concretes specified as default choices in the CORCON were used in this study. Physical properties of these concretes can be found in Table 3.4. Basaltic concrete has the lowest decomposition temperature and enthalpy which result in the highest axial ablation distance and melt cooling rate, as shown in Figs. 5.17 and 5.18. On the other hand, the Limestone concrete, with the highest decompositon temperature and enthalpy, has the lowest axial ablation distance and melt cooling rate. It is interesting to note that the quasi-steady oxidic temperatures for the Limestone concrete calculated by both heat transfer models remain above 1850 K while those of the other concretes drop below the critical temperature (1720 K). 226 300 1 -&--- PCM1 PCM1 PCM1 GFM1 GFM1 GFM1 -E- ---A-- 250 --- I I BASE CASE TD=1 4 2 0 K T=16 7 0 K BASE CASE TD=1 4 2 0 K TD=1 6 7 0 K 200 0r 0 150 E100 50 0 0 20 40 60 80 100 120 TIME [min] Figure 5.15 Accumulated Aerosol Releases for Different Concrete Decomposition Temperatures 227 LANTHANUM e I ---- E3-4---101 -U I RELEASE FRACTION (La) I II I I I ' I BASE CASE TD=1 4 2 0 K TI=1670 K BASE CASE TD=1420 K 67 O K GFM1 TD= PCM1 PCM1 PCM1 GFMI GFM1 00 z 00 0 30 60 90 120 150 180 TIME [min] Figure 5.16 Lanthanum Release Fractions for Different Concrete Decomposition Temperatures 228 900 800 700 600 z 500 z 400 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.17 Downward Ablation Distances for Different Types of Concrete 229 3000 I O ~s-8--- 2800 -A- --- PCMI PCM1 PCM1 GFM1 GFM1 GFM1 I I I I BASE CASE LIMESTONE BASALTIC BASE CASE LIMESTONE BASALTIC 2600 2400 m 2200 r 2000 0 1800 1600 1400 0 10 20 30 40 50 TIME [min] Figure 5.18 Melt Temperature Histories for Different Types of Concrete 230 60 Because of the high gas content of the Limestone concrete, the gas generation rate for this concrete is higher even though less concrete is being ablated (see Fig. 5.19). An important effect of the gas content of concrete is the depletion time of zirconium in the metallic phase. As calculated by the GF model, 6 tons of zirconium can be completely oxidized in 10 minutes for the Limestone/Common Sand and Limestone cases. While in the Basaltic concrete case, due to its relatively low gas content, it takes 2 hours to deplete the same amount of zirconium. In the GF model, the surges of the gas generation rates at the moment of zirconium depletion for various concretes can be seen in Fig. 5.19. The aerosol gerneation rates and the total releases are shown in Figs. 5.20 and 5.21, respectively. For the Limestone concrete, not only because of its higher gas content but also because of the higher quasi-steady oxidic temperature, the aerosol generation rates remain at relatively high values compared to the other concretes. Also, in general, the largest fission product release is calculated in the Limestone concrete case while the smallest release is calculated with the Basaltic concrete. In Fig. 5.22, the total tellurium releases for the three cases calculated by the GF model span a range of a factor of three. A smaller difference among these releases is resulted by the PC model. 5.4.4 Effect of Zirconium Metal To investigate the sensitivity of the calculations of the ex-vessel source term to the amount of metallic zirconium in the core debris initially, three cases with different amounts of zirconium metal were analyzed. Based on the M1 compositions listed in Table 6, these cases were specified by having 6 tons (50%), 2.4 tons (20%) and zero ton (0%) of unoxidized zirconium metal. The case with 6 tons zirconium metal was used as the base case. The most direct impact of the amount of zirconium metal is the temperature of the melt. The melt temperature can be affected by the heat of the chemical reaction of the zirconium metal with the gas evolved from the decomposed con231 108 C.) z0 r ar 106 z C-, Cl) 0 10 5 0 30 60 90 120 150 TIME [min] Figure 5.19 Gas Generation Rates for Different Types of Concrete 232 180 z 102 Er 101 Cf'2 100 10-1 10-2 L 0 30 60 90 120 150 180 TIME [min] Figure 5.20 Aerosol Generation Rates for Different Types of Concrete 233 400 1 1 --e-- 1 1 1- PCM1 BASE CASE -3-5- 350 ~-- -U- 1 - PCM1 LIMESTONE PCM1 BASALTIC GFM1 BASE CASE GFM1 LIMESTONE GFM1 BASALTIC 300 - 250C12 0 200 150 D 100 50 0 0 20 40 60 80 100 120 TIME [min] Figure 5.21 Accumulated Aerosol Releases for Different Types of Concrete 234 RELEASE FRACTION TELLURIUM (Te) 102 Cn2 z 0 101 0 30 60 90 120 150 180 TIME [min] Figure 5.22 Tellurium Release Fractions for Different Types of Concrete 235 crete. The more zirconium metal in the melt, the more chemical reaction heat is generated, thus, the more is the concrete ablation (see Fig. 5.23). The temperature histories of the oxidic melt with different amounts of zirconium are shown in Fig. 5.24. Up to about 30 minutes, the smaller the amount of zirconium, the lower is the temperature of the melt. After about 30 minutes, the oxidic temperatures reverse; the larger the initial amount of zirconium the lower the oxidic temperature. This inversion is caused by the enhanced concrete dilution of the melt. However, the temperature differences among these cases at late times are small. At early times, the temperature differences calculated by the GF model are larger than the PC model. In Fig. 5.25, it is shown that the gas generation rate calculated by the PC model is mildly affected by the amount of zirconium. In the GF model, it can be seen that the surge of the gas generation rate is affected by different amounts of zirconium. The larger the amount of zirconium, the later is the surge of the gas generation and the larger is the peak of the gas generation rate. After the gas generation surge, the effect of the amount of zirconium is weakened. The aerosol generation rates and the integral releases are shown in Figs. 5.26 and 5.27, respectively. It is seen that the larger the amount of zirconium, the more areosol release is calculated. At 3 hours, the accumulated aerosol release of the base case is higher than the 0% Zr case by a factor of 2 in the PC model and 2.4 in the GF model. As calculated by both the PC and GF models, the larger the amount of zirconium metal the greater is the fission product release. In Fig. 5.28, the base case release of lanthanum is orders-of-magnitude greater than the 0% Zr case despite similar melt temperatures and gas gerneration rates. The depressed release of the lanthanum in the 0% Zr case is caused by the high oxygen potential of gases evolved from the concrete. In the base case, reactions of H2 0 and CO2 from the concrete proceed far enough to depress the oxygen potential of the gas to the point 236 800 700 r, 600 z 500 let z 0 400 . 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.23 Downward Ablation Distances for Different Amounts of Zirconium 237 3000 2800 2600 2400 m 2200 E- 2000 1800 1600 1400 0 10 20 30 40 50 60 TIME [min] Figure 5.24 Melt Temperature Histories for Different Amounts of Zirconium 238 108 E- z 106 E- zU) r0r 0 30 90 60 120 150 180 TIME [min] Figure 5.25 Gas Generation Rates for Different Amounts of Zirconium 239 10 4 102 z r 0 101 100 10-1 10- 2 [ 0 30 90 60 120 150 180 TIME [min] Figure 5.26 Aerosol Generation Rates for Different Amounts of Zirconium 240 300 250 II Cn2 200 CI) r0r 150 100 EQ 50 0 0 20 40 60 80 100 120 TIME [min] Figure 5.27 Accumulated Aerosol Releases for Different Amounts of Zirconium 241 LANTHANUM PCM1I PCM1 PCM1 --4--GFM1 GFM 1 -AGFM1 ----& --- (La) RELEASE FRACTION BASE CASE 20% Zr 0% Zr BASE CASE 20% Zr 0% Zr S101 0 010 z z E--L 1 0-1 10-2 0 30 60 90 120 150 180 TIME [min] Figure 5.28 Lanthanum Release Fractions for Different Amounts of Zirconium 242 where LaO(g) is stable in the gas phase. The lanthanum release of the 20% Zr case falls between the other two cases. The orders-of-magnitude difference is also found in the barium and strontium releases for-different amounts of zirconium metal. It is important to note that the significant effect of the zirconium metal on the fission products release is based on the debris configuration assumed in the VANESA model, in which the oxidic layer stays on top of the metallic layer. The gas generation data calculated by the CORCON are the amounts of the gases - CO, C0 2 , H 2 and H 2 0 - emerging from the core melt. These data are accepted by the VANESA and then converted to the amounts of CO 2 and H20 liberated directly from the decomposed concrete. No matter at what location (either sidewall or basemat of the concrete cavity) the gases are released, VANESA assumes that all the released gases penetrate the metallic phase and react with the zirconium metal before entering the oxidic layer. In the meantime, the major forms of these fission products assumed in VANESA are BaO, SrO2 and La 2 0 3 . These fission product oxides in the oxidic layer can only react with the gas which is filtered by the bottom metallic layer. Therefore, the calculated fission product releases are affected significantly by the amount of zirconium in the metallic phase. However, this significant effect may disappear if the oxidic layer stays at the bottom initially or float atop the metallic layer after the zirconium depletion as depicted in the CORCON model. The tellurium release, as shown in Fig. 5.29, is mildly affected by the amount of zirconium metal. In the VANESA model, tellurium is assumed to be present as Te(l) in the metal phase. Since tellurium is, by itself, quite volatile, its release in the form of Te(g) is not affected by the oxygen potential differences in these cases. 5.4.5 Effect of Initial Debris Temperature The initial temperature of core debris in the reactor cavity will be determined by the temperature of the debris when it falls from the reactor vessel, i.e. it 243 I TELLURIUM (Te) RELEASE FRACTION 102 E-a z 101 0 30 90 60 150 180 TIME [min] Figure 5.29 Tellurium Release Fractions for Different Amounts of Zirconium 244 depends on the melt progression during the in-vessel phases of an accident. The possible range of the initial temperature of a molten core, as discussed in QUEST, is from 1807 K to 2600 K. In this study, five temperatures, 1807 K, 2000 K, 2320 K, 2400 K and 2600 K, were chosen to study the effect of the initial debris temperature. Among these initial temperatures, 2320 K is the solidus temperature of the oxidic melt used in the base case, and 1807 K is the liquidus temperature of the metallic phase. Initial melt temperatures higher than 2320 K are therefore categorized as high initial temperature while the others are referred to as low initial temperature. The axial ablation distances calculated by the PC and GF models are shown in Figs. 5.30 and 5.31, respectively. It is interesting to note that the axial ablation distances calculated by the GF model for all cases are almost equal at three hours. In the PC model, the axial ablation distances of the high initial temperature cases are higher than the low initial temperature cases. For the low initial temperature cases, the axial ablation distances appear as an S-curve. The initial ablation is limited by the formation of an oxidic crust at the bottom. Later, the ablation is accelerated because of the layer flip. When the layer flip occurs, the metallic layer with a temperature higher than its solidus point is brought down to the bottom. The conduction controlled downward heat transfer is then replaced by the more effective convective process, and the axial ablation rate is enhanced. The melt temperature response can be found in Figs. 5.32 and 5.33. For the Ti=1807 K and 2000 K cases, the debris temperature increases initially because the heat generated in the melt is more than the heat being dissipated. situation is reversed when the debris temperature reaches 2320 K. This In the PC model, the temperature drops at 50 minutes and 40 minutes after the initiation of the 1807 K and 2000 K cases, respectively. This temperature drop is caused 245 800 700 600 S500 z ~400 E0 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.30 Downward Ablation Distances Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 246 800 700 600 z 5 0 0 C,) E400 z 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.31 Downward Ablation Distances Predicted by the Gas Film Model with Different Initial Debris Temperatures 24 7 3000 2800 2600 2400 E" 2200 r 2000 1800 1600 1400 0 10 20 30 40 50 60 TIME [min] Figure 5.32 Melt Temperature Histories Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 248 3000 2800 2600 2400 2200 0 2000 1800 1600 1400 0 10 20 30 40 50 60 TIME [min] Figure 5.33 Melt Temperature Histories Predicted by the Gas Film Model with Different Initial Debris Temperatures 249 by the layer flip. For the 2320 K case, the layer flip occurs at an earlier time, 30 minutes after the initiation. In the GF model, the oxidic temperature responses are similar to those of the PC model for the low initial temperature cases. The gas generation rates are shown in Figs. 5.34 and 5.35 for the PC and GF models, respectively. Before 90 minutes, the differences of the gas generation rates between the low initial temperature and the high initial temperature cases are orders-of-magnitude. For the low initial temperature cases, again similar results are calculated by the PC and GF models, except sharper peaks of the gas generation rates are calculated by the PC model. These peaks are caused by the combination effects of the layer flip and coking phenomena. The aerosol generation rates and accumulated releases are given in Figs. 5.36 through 5.39. It is seen that the initial aerosol release rate is significantly affected by the initial debris temperature. After the first hour, the accumulated aerosol releases for various initial temperature cases differ only by small amounts. For the PC model, it is interesting to note that the accumulated aerosol releases of the low initial temperature cases can become higher than the high initial temperature cases after few hours interaction. The initial debris temperature has significant effect on the calculation of the fission product release. Some typical release rates resulted from different initial melt temperatures are shown in Fig. 5.40. As a result, the total lanthanum releases of the high initial temperature cases are higher than the low initial temperature cases by orders-of-magnitude, see Figs. 5.41 and 5.42. The tellurium releases for various cases are shown in Figs. 5.43 and 5.44. After the first hour, all cases with low initial temperatures result in the same fission products release. It is even more interesting that in the cases of low initial temperature, the fission product release is not affected by the different heat transfer models. 250 108 z 106 0n 0 30 60 90 120 150 180 TIME [min] Figure 5.34 Gas Generation Rates Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 251 I 108 L-1 z0 rI z 10 5 0 30 60 90 120 150 180 TIME [min] Figure 5.35 Gas Generation Rates Predicted by the Gas Film Model with Different Initial Debris Temperatures 252 E- z0 z 10 1 ra 0 10 0 10 -1 10- 2 L 0 30 60 90 120 150 180 TIME [min] Figure 5.36 Aerosol Generation Rates Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 253 E- z 102 0 z 101 100 10-1 1 0-2 I I 0 30 i 60 t 90 120 150 180 TIME [min] Figure 5.37 Aerosol Generation Rates Predicted by the Gas Film Model with Different Initial Debris Temperatures 254 300 250 r1 200 C C 150 1) 100 50 0 0 20 40 60 80 100 120 TIME [min] Figure 5.38 Accumulated Aerosol Releases Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 255 300 250 II C'2 200 U) 150 EU) 100 50 0 k 0 20 40 60 80 100 120 TIME [min] Figure 5.39 Accumulated Aerosol Releases Predicted by the Gas Film Model with Different Initial Debris Temperatures 256 101 100 10-1 10-2 Em 10-3 10 -4 0 105 M 10-6 Cf) 10~7 10 -8 0 20 40 60 80 100 120 TIME [min] Figure 5.40 Fission Products Release Rates Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 257 LANTHANUM RELEASE FRACTION (La) 102 101 0 100 10 -1 z* 10 -2 10 -3 0 30 60 90 120 150 180 TIME [min] Figure 5.41 Lanthanum Release Fractions Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 258 LANTHANUM (La) RELEASE FRACTION 102 101 U) 100 10 -1 Ez 10 -2 "a 10 -3 10 -4 10 -5 0 30 90 60 120 150 180 TIME [min] Figure 5.42 Lanthanum Release Fractions Predicted by the Gas Film Model with Different Initial Debris Temperatures 259 i TELLURIUM (Te) RELEASE FRACTION 102 101 z 100 me 10-1 10-2 0 30 60 90 120 150 180 TIME [min] Figure 5.43 Tellurium Release Fractions Predicted by the Periodic Contact Model with Different Initial Debris Temperatures 260 TELLURIUM (Te) RELEASE FRACTION 102 Q 101 z 100 0 10-1 10- 2 L 0 30 60 90 120 150 180 TIME [min] Figure 5.44 Tellurium Release Fractions Predicted by the Gas Film Model with Different Initial Debris Temperatures 261 5.4.6 Effect of Amount of Melts Besides the base case (Ml), an enriched core oxide case (M2), and an enriched metal steel case (M3), listed in Table 5.4, have been used to study the effect of the melt amount. The amount of zirconium metal in the enriched core oxide was increased correspondingly. The effect of the amount of melt on the concrete erosion, on the melt temperature and on the gas generation is shown in Figs. 5.45, 5.46 and 5.47, respectively. The oxidic temperature of the enriched core oxide case is the highest because of its increased zirconium. However, the differences of the oxidic temperatures among these cases are small. In Fig. 5.48, the aerosol generation rate is increased by increasing the oxidic material while it is only mildly affected by increasing the metallic material. The total aerosol release of the enriched core oxide case is higher than the base case by 60% and 40% for the GF and PC models, respectively (see Fig. 5.49). The lanthanum release as shown in Fig. 5.50 is not affected significantly by the amount of melts. 5.4.7 Effect of Ferrous Oxide Here, different amounts of FeO have been used to study its impact on the aerosol release. The enriched FeO case (M4), listed in Table 5.4, has been analyzed and compared to the M1 cases. It should be noted that the amounts of FeO are only small fractions of the oxidic layer in both cases. The most direct effect resulting from the variation of the amount of FeO is the solidus temperature of the oxidic melt. Increased FeO in the oxidic phase depresses the solidus temperature. Considering the possible effect caused by the formation of the initial bottom crust, three different initial debris temperatures (2000 K, 2320 K, and 2600 K) have been applied to the enriched FeO case. 262 900 800 700 600 z 500 z 400 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.45 Downward Ablation Distances for Different Amounts of Melt 263 3000 2800 2600 II LJ 2400 2200 2000 0 1800 1600 1400 0 10 30 20 40 50 60 TIME [min] Figure 5.46 Melt Temperature Histories for Different Amounts of Melt 264 10io1 GFM3 BASE CASE L1j 4107. z 10 6 z 105 10 4 0 I 30 I | 60 | | 90 120 150 TIME [min] Figure 5.47 Gas Generation Rates for Different Amounts of Melt 265 180 GFM3 BASE r--- CASE 03 z102 m 10 0 - 10~1 I 10-2I 0 30 60 90 120 150 TIME [min] Figure 5.48 Aerosol Generation Rates for Different Amounts of Melt 266 180 450 400 m LJ ci) U) 350 300 0 ci) 250 0 200 150 Q Q 100 50 0 0 20 40 60 80 100 120 TIME [min] Figure 5.49 Accumulated Aerosol Releases for Different Amounts of Melt 267 I LANTHANUM (La) RELEASE FRACTION 10 1 Cl) z zi W" 100 L 0 30 60 90 120 150 180 TIME [min] Figure 5.50 Lanthanum Release Fractions for Different Amounts of Melt 268 In Table 5.6, the timing of the important events calculated by CORCON is listed for both the M1 and M4 cases. It is seen that the zirconium depletion and layer flip are delayed by a significant period of time when the initial bottom oxidic crust is formed. When the initial temperature is 2600 K, there is no initial bottom crust in either the M1 or M4 case; at 2000 K, the initial bottom crust is formed in both cases; while at 2320 K, the initial bottom crust is formed only in the M1 case. This is because the oxidic solidus temperature of the M4 melt is lowered by the increased FeO. Therefore, the most significant effect of the amount of FeO on the behaviors of the corium/concrete interaction is found at the initial temperature of 2320 K (see Figs. 5.51 and 5.52). Similar trend is found in the calculation of the lanthanum release. As calculated by the PC model, the lanthanum release of the M4 case is about ten times higher than the M1 case when the initial temperature is 2320 K, see Fig. 5.53. While at the initial temperature of 2600 K, the M1 and M4 cases have exactly the same lanthanum release. A similar trend is found for the calculations using the GF model. The results of the lanthanum releases calculated by the GF model are shown in Fig. 5.54. It should be noted that the effect of the amount of FeO depends on the formation of the initial bottom crust, which in turn, depends on the prediction of the solidus temperature of the oxidic material. Therefore, if the initial debris temperature is close to its solidus point, it is important to know precisely the solidus point to determine the aerosol release. 5.4.8 Effect of Decay Heat The entire corium/concrete interaction process is driven by decay heat generated in the pool. Because of the loss of some of the more volatile fission products before the pool is formed, CORCON calculates the decay heat based on specified retention fraction of each element to account for partial loss of those volatile species. Apparently, this will result in a lower decay heat generation compared 269 Table 5.6 Timing of Events of the Cases with Different Initial Melt Temperatures and Different Amounts of FeO Zr Depleted Layer Flip Initial Bottom (min) (min) Crust PCM1 T = 2600 K 2.0 2.0 No PCM1 T = 2400 K 2.3 2.8 No PCM1 T = 2320 K 36.0 39.0 Yes PCM1 Ti = 2000 K 44.0 46.0 Yes PCM1 Ti = 1807 K 51.0 52.5 Yes PCM4 T =2600 K 2.1 1.8 No PCM4 Ti = 2320 K 2.7 3.1 No PCM4 T = 2000 K 25.3 26.5 Yes GFM1 T = 2600 K 10.7 12.3 No GFM1 T = 2400 K 11.0 14.0 No GFM1 T = 2320 K 34.0 40.0 Yes GFM1 T = 2000 K 46.0 51.0 Yes GFM1 T = 1807 K 55.5 60.5 Yes GFM4 T = 2600 K 10.3 11.3 No GFM4 T = 2320 K 10.5 12.0 No GFM4 T = 2000 K 33.0 37.5 Yes Case 270 r 800 700 600 500 z 400 r 0 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.51 Downward Ablation Distances Predicted by the Periodic Contact Model with Different Amounts of FeO 271 300 --- 250 Cl, Cl, '~U-- PCM4 T8=2320 K PCM4 T =2000 K 200 Cl, 50 r 00 -~100 S50 0 20 40 60 80 100 120 TIME [min] Figure 5.52 Accumulated Aerosol Releases Predicted by the Periodic Contact Model with Different Amounts of FeO 272 LANTHANUM (La) RELEASE FRACTION 101 100 10 -1 (*2 E- 10 -2 10 -3 10 -5 0 30 60 90 120 150 180 TIME [min] Figure 5.53 Lanthanum Release Fractions Predicted by the Periodic Contact Model with Different Amounts of FeO 273 I LANTHANUM (La) RELEASE FRACTION 102 101 C12 100 10-1 z A 10-2 0 0 30 60 90 120 150 180 TIME [min] Figure 5.54 Lanthanum Release Fractions Predicted by the Gas Film Model with Different Amounts of FeO 274 to the ANS standard decay curve. In the base case analysis, it is found that the decay powers calculated by CORCON are 11.4 and 9.86 MW at respectively 3 and 6 hours after scram. These values are about 50%.lower than those of the ANS standard. To study the effect of decay heat, two cases with initial melt temperature of 2600 K (HDHHT) and 1807 K (HDHLT) were analyzed by increasing the decay heat to the ANS standard level. In Fig. 5.55, the oxidic temperature of the increased decay heat case is seen to be higher than the base case initially. After a period of time, due to the concrete dilution of the melt, the situation is reversed. About two hours later, a slow increase in the oxidic temperature is calculated with increased decay power. In general, there is no significant effect on the melt temperature due to the 50% decay heat increase. The accumulated aerosol releases of the HDHHT and HDHLT cases are shown in Figs. 5.56 and 5.57, respectively. It is seen that the higher the decay heat, the more aerosols are released; however, the difference is small. For the low initial temperature, significant release of the ex-vessel aerosol in the case with increased decay heat occurs earlier (about 20 minutes) than the base case. The lanthanum release, as shown in Fig. 5.58, is not affected by the decay power variation in the high initial temperature case. While in the low initial temperature case, the initial heatup rate of the oxide material is increased with increasing decay heat. The difference in the lanthanum release can be as large as an order-of-magnitude due to the difference in the oxide temperature response for the first 30 minutes (see Fig. 5.59). After one hour, the lanthanum release of the increased decay heat case is about 50% higher than the base case. In general, the effect of the magnitude of the decay heat on the aerosol release is less in the PC model than in the GF model. Because in the PC model the pool temperature is primarily driven by the heat loss in the downward direction, the 275 3000 I I -E PCM1 PCM1 -A8- GFM1 GFM1 -k- - 2800 I i 1 I i1 i 1 BASE CASE HDHHT BASE CASE HDHHT 2600 2400 w 2200 2000 1800 1600 1400 I 0 I 10 I I 20 |I 30 | 40 50 60 TIME [min] Figure 5.55 Melt Temperature Histories of the High Initial Debris Temperature Cases with Different Amounts of Decay Heat 276 300 250 200 .W 150 E14 100 50 0 0 20 40 60 80 100 120 TIME [min] Figure 5.56 Accumulated Aerosol Releases of the High Initial Debris Temperature Cases with Different Amounts of Decay Heat 277 I 300 I -E- PCM1 T-=1807 K -A- GFM1 T-=1807 K GFM1 HDHLT I -4-- PCM1 HbHLT -A-- 250 C,) 200 C,) 0 150 r A. - 100 50 0 20 60 40 80 100 120 TIME [min] Figure 5.57 Accumulated Aerosol Releases of the Low Initial Debris Temperature Cases with Different Amounts of Decay Heat 278 LANTHANUM (La) RELEASE FRACTION I I I I PCM I BASE CASE -k- PCM 1 HDHHT -AT GFM1 BASE CASE GFM1 HDHHT 101 0 r z On A A 10 0 0 30 60 90 120 150 180 TIME [min] Figure 5.58 Lanthanum Release Fractions of the High Initial Debris Temperature Cases with Different Amounts of Decay Heat 279 LANTHANUM (La) RELEASE FRACTION 100 E PCM1 T.=1807 --- PCM1 HDHLT -A- GFM1 T=1807 -i--GFM1 HDH LT 10-1- 10-2 r Ar z 10-5 L 0 30 60 90 120 150 180 TIME [min] Figure 5.59 Lanthanum Release Fractions of the Low Initial Debris Temperature Cases with Different Amounts of Decay Heat 280 decay heat only contributes a relatively small fraction to the energy balance of the corium pool. 5.4.9 Effect of Layer Configuration As mentioned before, CORCON initially places the oxidic phase below the metallic phase due to the density difference. This configuration persists for a period of time before the density of the oxide is reduced by ablated concrete to a value less than that of the metallic material. WECHSL, where the reference density of U0 2 This is not the case with has been sufficiently reduced from the handbook value to yield an initial oxide-over-metal configuration. However, there are no direct measurements of the densities of the liquids involved. The relative densities of metal and oxide, and hence the layer ordering should be viewed as uncertain before conclusive results can be established. The most direct effect based on different layer configuration will be the potential of forming an initial bottom crust. The solidus temperature of the metallic phase is hundreds of degrees Kelvin lower than that of the oxidic phase. At certain melt temperature (between the solidus points of the metallic and oxidic materials), the bottom concrete attack could be relatively violent if the metallic material stays at the bottom. On the other hand, if the oxidic material settles below the metallic phase, the concrete attack could be quite restricted due to the formation of a bottom crust. In this test, the metallic phase is forced to be a bottom layer even though the oxide, based on the CORCON calculation, is more dense than the metal initially. Two cases with initial melt temperatures of 2600 K (MSBHT) and 2320 K (MSBLT) were analyzed by using the PC, GF and FC models. These cases will be compared with the base case (initial metal-over-oxide) to illustrate the possible effect resulting from different layer configurations. The effects on the axial ablation distance and the melt temperature are illustrated in Figs. 5.60 and 5.61, respectively. As discussed in the previous chapter, 281 800 1 700 ~* -7~-*- -e- PCM1 BASE CASE PCM1 MSBHT PCM1 Ti=2320 K PCM1 MSBLT '600 500 C14 400 z r 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.60 Downward Ablation Distances for Different Layer Configurations 282 3000 2800 2600 r-1 2400 2200 2000 1800 1600 1400 L 0 10 30 40 50 60 TIME [min] Figure 5.61 Melt Temperature Histories for Different Layer Configurations 283 the downward heat flux is not sensitive to the properties of the pool materials in the pre-freezing stages. It is seen that the axial ablation distance is mildly affected by the layer configuration when the initial melt -temperature is high enough to prevent any initial freezing in both the oxidic and metallic phases. In the case of T = 2320 K, the layer configuration has significant effects on the calculations of the concrete erosion and the melt temperature. The aerosol generation rate and total release are shown in Figs. 5.62 and 5.63, respectively. Compared to the base case (in Figs. 5.36 through 5.39), it is interesting to note that the aerosol release is not affected by the layer ordering if the initial melt temperature is above the solidus points of both phases. While at the low initial melt temperature (2320 K), there is an order-of-magnitude difference on the aerosol generation rate. For the fission product release, a significant effect is also found only in the low initial melt temperature case. The lanthanum release at three hours for the PCM1 MSBLT case as shown in Fig. 5.64 is about eight times higher than that of the PCM1 Ti = 2320 K case in Fig. 5.41. It is interesting to note the differences in the fission product releases based on different heat transfer models. The fission product release calculated by the FC model will be about the same as the GF model under one of the following two conditions. First, the initial melt temperature is high enough to stabilize an initial gas film. Second, the initial melt temperature is low enough to form an initial bottom crust. In the second condition, even the PC model gives about the same fission product release as the GF model. In the MSBLT case, neither an initial gas film nor an initial bottom crust is formed, the lanthanum release calculated by the FC model, exactly the same as that of the PC model, is about five times higher than the calculation of the GF model. In the MSBHT case, an initial gas film but no initial bottom crust is formed, the lanthanum release calculated by the FC model is about the same as that of the GF model, and it is three times less than the calculation of the PC model. 284 ha z 0 10 2 r z 0 101 100 10 -1 10 -2 0 30 60 90 120 150 180 TIME [min] Figure 5.62 Aerosol Generation Rates for Different Layer Configurations 285 300 -*- PCM1 MSBHT -A--- GFM1 MSBHT -e- PCM1 MSBLT GFM1 MSBLT FCMI MSBLT ---- 250 -9- FCM1 MSBHT Cl)A Ci) <200 Cl) 150 w r 100 50 0 0 20 40 60 80 100 120 TIME [min] Figure 5.63 Accumulated Aerosol Releases for Different Layer Configurations 286 LANTHANUM I -------E) -A-E- I PCMI GFM1 FCM1 PCM1 GFM1 FCM1 (La) RELEASE FRACTION I T MSBHT MSBHT MSBHT MSBLT MSBLT MSBLT 101 100 z ME 10-1 0 30 60 90 120 150 180 TIME [min] Figure 5.64 Lanthanum Release Fractions for Different Layer Configurations 287 5.4.10 Effect of CORCON/MOD2 Version 2.01 The only changes included in the version 2.01 concern the treatment of partially solidified layers. As a result significant differences between the version 2.00 and 2.01 results may only occur either early if the core debris is partially solidified, or later when the molten core material is beginning to solidify. Three cases, PCM1 Base Case, PCM1 0% Zr and PCM1 T, = 1807 K, have been analyzed with version 2.01 to ascertain the impact of the code correction on the calculated results. Comparsions between the version 2.00 and 2.01 results are shown in Figs. 5.65 through 5.70. As expected, significant differences of these output parameters associated with the code correction are found only in the PCM1 Tj = 1807 K case. However, some other parameters such as the radial ablation distance and released gas composition are affected significantly in all the three cases. As shown in Figs. 5.71 and 5.72, the radial ablation distance and the accumulated CO 2 release are reduced by a factor of two due to the code correction. These differences, however, do not have significant effects on the integral results of the ex-vessel source terms. 5.4.11 Revised Periodic Contact Model In the previous chapter, it was shown that the most significant difference in the calculation of the downward heat flux between the PC and RPC models is found in the case of the Limestone concrete, while the differences are relatively small in the Limestone/Common Sand and Basaltic concrete cases. In order to see the impact of the revised model on the ex-vessel source term calculation, several cases (the Base Case, Limestone and Ti = 1807 K) RPC model. have been analyzed by the In these cases, both the calculations of the RPC and PC models were performed using the version 2.01. The results of these calculations are shown in Figs. 5.73 through 5.78. As shown in these figures, although there are some effects associated with the modifi- 288 800 1 -e----A- 700 -*- -E- -- 1 1 PCM1 PCM1 PCM1 PCM1 PCM1 PCM1 BASE CASE V2.00 BASE CASE V2.01 0% Zr V2.00 0% Zr V2.01 Ti=1807 K V2.00 Tj=1807 K V2.01 6 00 500 z E-~400- 300 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.65 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Downward Ablation Distance 289 3000 2800 2600 2400 LJ 2200 E- 2000 1800 1600 1400 0 10 20 30 40 50 60 TIME [min] Figure 5.66 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Melt Temperature Histories 290 108 z 0 106 z 105 0 30 60 90 120 150 180 TIME [min] Figure 5.67 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Gas Generation Rate 291 10 5 E- z 102 r 101 E- 100 10-1 10-2 0 30 60 90 120 150 180 TIME [min] Figure 5.68 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Aerosol Generation Rate 292 300 250 C,) U) 200 0n 150 r 100 50 0 0 20 60 40 80 100 120 TIME [min] Figure 5.69 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Accumulated Aerosol Release 293 LANTHANUM (La) RELEASE FRACTION 102 101 100 10 -1 A. z 10-2 0 30 60 90 120 150 180 TIME [min] Figure 5.70 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Lanthanum Release Fraction 294 300 250 200 z z0 150 100 50 0 0 30 60 90 120 150 180 TIME [min] Figure 5.71 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Radial Ablation Distance 295 I 20 15 C 10 r Cf2 0e 5 0 0 30 60 90 120 150 180 TIME [min] Figure 5.72 Effect of the Corrected Version of CORCON/MOD2 on the Prediction of the Released Gas 296 800 700 r 600 LJ S 500 z E- 400 0) 300 0 200 100 0 0 30 60 90 120 150 180 TIME [min] Figure 5.73 Effect of the Revised Periodic Contact Model on the Prediction of the Downward Ablation Distance 297 3000 2800 2600 2400 E- II 2200 r ar Q 2000 1800 1600 1400 0 10 20 30 40 50 60 TIME [min] Figure 5.74 Effect of the Revised Periodic Contact Model on the Prediction of the Melt Temperature Histories 298 E- CE z0 106 z 10 4 0 30 60 90 120 150 180 TIME [min] Figure 5.75 Effect of the Revised Periodic Contact Model on the Prediction of the Gas Generation Rate 299 z r z 101 100 10-1 10- 2 0 30 60 90 120 150 180 TIME [min] Figure 5.76 Effect of the Revised Periodic Contact Model on the Prediction of the Aerosol Generation Rate 300 300 250 200 E-1 150 0 100 50 0 6 0 20 40 60 80 100 120 TIME [min] Figure 5.77 Effect of the Revised Periodic Contact Model on the Prediction of the Accumulated Aerosol Release 301 LANTHANUM --- (La ) RELEASE BSI I PCM I BASE CASE RPCM I BASE CASE PCM1 LUMESTONE RPCM 1 LIME STONE I I FRACTION I I I 101 C,) A z z "=I "a 100L 0 30 60 90fi 90 120 150 180 TIME [min] Figure 5.78 Effect of the Revised Periodic Contact Model on the Prediction of the Lanthanum Release Fraction 302 cation of the periodic contact model, the differences in the calculated aerosol and fission product releases between the RPC and PC models are in general small. In the Limestone concrete case, the RPC model predicts about 20% lower total aerosol release and 25% higher total lanthanum release than the PC model. 5.4.12 Summary Integral results of the PCM1 Base Case and GFM1 Base Case are shown in Table 5.7. While those of the other cases are summarized in Tables 5.8 through 5.13. The values shown in these tables are relative to those of the M1 base case stated in Table 5.7. The lanthanum release shows the largest variation while the total aerosol release has the smallest variation. The effect of the initial debris temperature on the fission products release is the most significant, followed by the amount of Zr present in the metallic phase. The differences in the fission product releases between the PC model and GF model are small when the melt is at a low temperature so that an initial bottom crust can be formed. At high initial debris temperature, the PC model results in higher fission product releases than the GF model. When an initial gas film or a bottom crust can be formed, the results of the FC model are close to the GF model. Otherwise, the FC model will follow exactly the PC model, and give higher fission product releases than the GF model. The difference in the calculation of the ex-vessel source term between the RPC and PC models is relatively small. The layering order, i.e. whether the metallic or oxidic layer is in contact with concrete, is unimportant if the initial melt temperature is high. However, at low initial temperature, if the metallic layer contacts the concrete, a higher rate of heat loss to concrete is possible, which leads to somewhat of an increased aerosol generation when using the PC model. The effects of layering on the predicted behavior by the GF model is very small. 303 Table 5.7 Integral Results of the Base Case at 3 Hours after the Start of MCCI GFM1 PCM1 Base Case Base Case CO 13.7 16.3 CO 2 2.25 3.19 H2 7.28 8.37 H20 1.36 2.19 Total 24.6 30.0 Axial 0.362 0.566 Radial 0.276 0.173 Sb 0.31 0.64 Te 37.7 63.9 Ba 19.8 25.0 Sr 35.4 50.3 La 2.08 6.36 Total Aerosol Release (kg) 207.8 184.4 Gas Release (104 moles) Concrete Erosion Distance (m) F.P. Release (% of Inventory) 304 Table 5.8 Radial and Axial Concrete Erosion Distances Relative to PCM1 Base Case at 3 Hours after the Start of MCCI Case Radial Erosion Axial Erosion PCM1 Base Case 1.0 1.0 PCM1 Limestone 0.70 0.79 PCM1 Basaltic 1.00 1.28 PCM1 TD = 1420 K 1.02 1.14 PCM1 TD = 1670 K 0.91 0.70 PCM1 20% Zr 0.89 0.87 PCM1 0% Zr 0.82 0.77 PCM1 Tj = 2400 K 0.92 0.88 PCM1 Ti = 2320 K 1.00 0.66 PCM1 T = 2000 K 0.94 0.67 PCM1 T = 1807 K 0.87 0.70 PCM2 Base Case 1.58 1.30 PCM3 Base Case 1.20 1.12 PCM4 Base Case 1.06 1.02 PCM4 T = 2320 K 0.96 0.87 PCM4 T = 2000 K 0.90 0.70 PCM1 HDHHT 1.45 1.07 PCM1 HDHLT 1.12 0.78 PCM1 MSBHT 0.98 0.98 PCM1 MSBLT 0.82 0.83 FCM1 MSBHT 1.20 0.89 FCM1 MSBLT 0.82 0.83 GFM1 Base Case 1.60 0.64 FCM1 Base Case 1.49 0.72 305 Table 5.9 Radial and Axial Concrete Erosion Distances Relative to GFM1 Base Case at 3 Hours after the Start of MCCI Case Radial Erosion Axial Erosion GFM1 Base Case 1.0 1.0 GFM1 Limestone 0.74 1.01 GFM1 Basaltic 0.95 1.42 GFM1 TD = 1420 K 1.13 1.12 GFM1 TD = 1670 K 0.94 0.80 GFM1 20% Zr 0.87 0.93 GFM1 0% Zr 0.78 0.88 GFM1 T = 2400 K 0.97 1.00 GFM1 T = 2320 K 0.71 0.97 GFM1 T = 2000 K 0.77 0.95 GFM1 T = 1807 K 0.86 0.94 GFM2 Base Case 1.56 1.24 GFM3 Base Case 1.23 0.98 GFM4 Base Case 1.08 0.98 GFM4 T = 2320 K 1.07 0.98 GFM4 T = 2000 K 0.89 0.92 GFM1 HDHHT 1.38 1.06 GFM1 HDHLT 1.07 1.00 GFM1 MSBHT 1.66 1.00 GFM1 MSBLT 0.76 1.00 306 Table 5.10 Accumulated Releases of Decomposition Gases Relative to PCM1 Base Case at 3 Hours after the Start of MCCI Case CO CO 2 H2 H20 Total PCM1 Base Case 1.0 1.0 1.0 1.0 1.0 PCM1 Limestone 1.37 1.16 0.98 1.07 1.22 0.092 0.068 1.74 0.95 0.61 PCM1 TD = 1420 K 1.12 1.09 1.11 1.16 1.12 PCM1 TD = 1670 K 0.77 0.53 0.80 0.43 0.73 PCM1 20% Zr 0.85 0.93 0.80 1.11 0.87 PCM1 0% Zr 0.74 0.88 0.65 1.18 0.76 PCM1 Ti = 2400 K 0.91 0.74 0.93 0.71 0.88 PCM1 T = 2320 K 0.77 0.31 0.81 0.25 0.70 PCM1 T = 2000 K 0.77 0.32 0.81 0.26 0.70 PCM1 T = 1807 K 0.77 0.34 0.82 0.27 0.70 PCM2 Base Case 1.34 1.96 1.34 1.83 1.45 PCM3 Base Case 1.17 1.16 1.19 1.06 1.17 PCM4 Base Case 1.01 1.11 1.01 1.10 1.03 PCM4 T = 2320 K 0.88 0.81 0.90 0.74 0.87 PCM4 T = 2000 K 0.77 0.39 0.82 0.32 0.71 PCM1 HDHHT 1.07 1.55 1.05 1.53 1.15 PCM1 HDHLT 0.84 0.67 0.87 0.59 0.81 PCM1 MSBHT 0.98 1.02 0.98 0.99 0.98 PCM1 MSBLT 0.83 0.69 0.86 0.60 0.81 FCM1 MSBHT 0.91 1.03 0.93 0.95 0.94 FCM1 MSBLT 0.83 0.69 0.86 0.60 0.81 GFM1 Base Case 0.84 0.71 0.87 0.62 0.82 FCM1 Base Case 0.90 0.73 0.92 0.69 0.87 PCM1 Basaltic 307 Table 5.11 Accumulated Releases of Decomposition Gases Relative to GFM1 Base Case at 3 Hours after the Start of MCCI Case CO C02 H2 H2 0 Total GFM1 Base Case 1.0 1.0 1.0 1.0 1.0 GFM1 Limestone 1.74 0.73 1.19 1.18 1.45 GFM1 Basaltic 0.092 0.075 1.69 1.18 0.62 GFM1 TD = 1420 K 1.09 1.27 1.08 1.34 1.12 GFM1 TD = 1670 K 0.82 0.68 0.83 0.62 0.80 GFM1 20% Zr 0.86 1.07 0.80 1.32 0.89 GFM1 0% Zr 0.77 1.09 0.67 1.60 0.81 GFM1 T = 2400 K 0.99 0.88 1.00 0.88 0.98 GFM1 T = 2320 K 0.94 0.54 0.96 0.52 0.89 GFM1 T = 2000 K 0.93 0.52 0.95 0.49 0.87 GFM1 T, = 1807 K 0.92 0.50 0.94 0.46 0.86 GFM2 Base Case 1.36 2.51 1.35 2.40 1.52 GFM3 Base Case 1.07 1.26 1.08 1.15 1.09 GFM4 Base Case 0.99 1.11 0.99 1.08 1.01 GFM4 Ti = 2320 K 0.80 1.15 0.78 1.19 0.85 GFM4 T = 2000 K 0.90 0.60 0.91 0.54 0.85 GFM1 HDHHT 1.06 1.79 1.04 1.78 1.16 GFM1 HDHLT 0.98 1.04 0.98 1.02 0.99 GFM1 MSBHT 0.89 1.47 0.90 1.32 0.97 GFM1 MSBLT 0.85 0.96 0.83 0.90 0.85 308 r Table 5.12 Fission Products and Total Aerosol Releases Relative to PCM1 Base Case at 3 Hours after the Start of MCCI Sb Te Ba Sr La Total Aerosol PCM1 Base Case PCM1 Limestone PCM1 Basaltic 1.0 1.18 0.55 1.0 1.15 0.61 1.0 1.08 0.71 1.0 1.0 1.0 1.04 0.74 0.86 0.62 1.40 0.74 PCM1 TD = 1420 K 1.14 1.09 0.99 0.99 1.00 0.91 PCM1 TD = 1670 K PCM1 20% Zr PCM1 0% Zr PCM1 T = 2400 K PCM1 T = 2320 K 0.70 0.79 1.09 1.11 0.99 0.95 0.92 0.30 0.047 0.87 0.31 0.0034 0.59 0.33 0.026 1.01 0.65 0.50 0.44 0.61 0.73 0.59 0.11 0.71 0.13 0.25 0.31 0.22 0.0049 1.04 PCM1 T = 2000 K PCM1 T, = 1807 K PCM2 Base Case PCM3 Base Case PCM4 Base Case 0.13 0.15 0.26 0.28 0.33 0.39 0.23 0.25 0.0034 0.0042 0.91 0.95 0.87 1.00 1.07 1.00 0.84 1.38 0.46 1.04 0.73 1.03 0.78 0.94 0.80 0.95 0.87 0.98 0.90 0.87- PCM4 T = 2320 K PCM4 T, = 2000 K PCM1 HDHHT PCM1 HDHLT PCM1 MSBHT 0.35 0.53 0.62 0.45 0.042 0.66 0.12 0.24 0.28 0.19 0.0015 0.82 1.03 0.17 1.02 0.32 1.00 0.46 1.00 0.28 1.01 0.0058 1.04 0.97 0.99 0.99 1.00 1.00 1.01 0.98 PCM1 MSBLT 0.29 0.45 0.60 0.037 FCM1 MSBHT 0.51 0.64 0.82 0.44 0.72 0.31 0.74 1.02 FCM1 MSBLT GFM1 Base Case 0.29 0.45 0.60 0.44 0.037 0.74 0.48 0.59 0.79 0.70 FCM1 Base Case 0.49 0.61 0.79 0.70 0.33 0.32 1.13 1.11 Case 309 Table 5.13 Fission Products and Total Aerosol Releases Relative to GFM1 Base Case at 3 Hours after the Start of MCCI Total Case Sb Te Ba Sr La Aerosol GFM1 Base Case 1.0 1.0 1.0 1.0 1.0 1.0 GFM1 Limestone 1.78 1.62 1.25 1.26 1.34 1.45 GFM1 Basaltic 0.57 0.59 0.65 0.69 0.71 0.79 GFM1 TD = 1420 K 1.04 1.04 1.01 1.02 1.08 1.02 GFM1 TD = 1670 K 0.90 0.91 0.96 0.94 0.83 1.07 GFM1 20% Zr 1.17 1.04 0.38 0.45 0.72 0.60 GFM1 0% Zr 1.31 1.06 0.029 0.0023 0.031 0.42 GFM1 T = 2400 K 0.59 0.75 0.76 0.62 0.11 0.92 GFM1 T = 2320 K 0.30 0.47 0.45 0.35 0.017 0.94 GFM1 T = 2000 K 0.31 0.49 0.50 0.36 0.013 0.92 GFM1 T, = 1807 K 0.33 0.51 0.55 0.38 0.015 0.91 GFM2 Base Case 1.16 1.25 1.17 1.13 1.16 1.62 GFM3 Base Case 0.41 0.68 0.81 0.84 0.99 1.03 GFM4 Base Case 1.04 1.02 1.05 0.96 1.01 1.01 GFM4 T = 2320 K 0.43 0.58 0.59 0.46 0.053 0.83 GFM4 T = 2000 K 0.29 0.45 0.43 0.31 0.0077 0.85 GFM1 HDHHT 1.04 1.05 1.02 1.02 1.02 1.07 GFM1 HDHLT 0.41 0.60 0.62 0.44 0.024 0.93 GFM1 MSBHT 0.84 0.87 0.90 0.91 0.88 1.02 GFM1 MSBLT 0.28 0.43 0.42 0.34 0.025 0.89 310 r a. 5.5 Conclusions Based on the results of the cases studied, the following conclusions are reached. These conclusions reflect single-parameter variation around the specified base case. 1. In the base case, the initial aerosol generation rate calculated by the PC model is five times higher than the GF model. In the low initial melt temperature cases, the initial aerosol generation rates calculated by these two models are close. 2. With the higher downward heat flux in the PC model, the melt temperature, the gas generation rate, and the aerosol release rate decrease faster than the GF model. 3. The fission product release calculated by the PC model is higher than the GF model. The difference was as large as three times in the base case. While in the oxide-over-metal configuration case, the release calculated by the PC model was five times higher than the GF model. 4. When an initial stable gas film or an initial bottom crust calculated by the FC model, the fission product release calculated by the FC model is about the same as that of the GF model. Otherwise, the FC model results in a higher (as much as five times) fission product release than the GF model. 5. The accumulated aerosol release (predominately non-radioactive materials) calculated by the PC model is higher than the GF model initially. After the transient stage, the GF model predicts a slightly higher aerosol release. 6. The difference in the calculation of the ex-vessel source term between the RPC and PC models is relatively small. 7. Based on the VANESA calculation, the amount of zirconium metal has significant effect on the fission products release. 8. The concrete decomposition temperature is important in determining the aerosol release rate during the quasi-steady state, because higher concrete decomposition temperature gives higher oxidic temperature which results in a higher aerosol release rate. 311 9. The aerosol release calculated with the Limestone concrete is higher than the Limestone/Common Sand concrete, which is higher than the Basaltic concrete. 10. Increasing the decay heat, the aerosol release is increased by a small amount in the case of high initial melt temperature. While for low initial melt temperatures, there is a striking effect due to the decay heat variation on the aerosol release in the initial period of time. 11. Significant effect of the layer ordering on the fission product release is found only when the initial melt temperature is between the solidus points of the metallic and oxidic materials. 12. The aerosol release is affected significantly by the formation of an initial bottom crust, therefore, the solidus temperature of the melt is important in determining the aerosol release. 13. In general, a relatively low aerosol generation rate is calculated by using the CORCON/MIT compared to the CORCON/MOD1. At quasi-steady state, except for the Limestone concrete case, the aerosol generation rates calculated by the CORCON/MIT drop below 1 g/s, while the CORCON/MOD1 used in QUEST gives about an order-of-magnitude higher aerosol generation rate. 14. At a high initial melt temperature, the transient behavior of the fission products release calculated by using the CORCON/MIT span a much shorter time than the CORCON/MOD1. The lanthanum release calculated by the PC model can be saturated in 3 minutes. 15. Among these studied cases, the calculations from the VANESA model of the ex-vessel source term can be rank-ordered in terms of decreasing sensitivity to the parameters as follows: (1)Initial melt temperature; (2)amount of zirconium in melt; (3)downward heat transfer model; (4)amount of steel in melt; (5)amount of core oxide involved; (6)amount of ferrous oxide in melt; (7)decay heat and (8)layer ordering. 312 CHAPTER6 SUMMARY AND CONCLUSIONS 6.1 Summary of This Work The radioactive aerosol formation and release in reactor severe accidents receive considerable attention in nuclear plant safety assessments as this is the most significant potential hazard to the public. Progress in the understanding of the aerosol phenomena has been made in recent years. Based on the new developments, the calculated amounts of volatile radioactive material that could be released to the environment is substantially smaller than was reported in the Reactor Safety Study. This finding resulted from better understanding of containment integrity, natural retention potential of reactor systems and chemistry of cesium iodine (CsI). However, one mechanism that might, for some sequences, increase the radionuclide releases above those calculated in the Reactor Safety Study is the release of nonvolatile radionuclides in the core-concrete interaction. The magnitude of the contribution from the nonvolatile radionuclides which could be available for long-term ex-vessel release is still open to question, primarily because of the modeling uncertainty of the MCCI. While the fundamental concepts of current models have been generally accepted, heat transfer modeling is not fully developed and validation is incomplete. In addition, calculations of the ex-vessel source term are also known to depend strongly on details of core melt progression for which many uncertainties still exist. All these have motivated this study focusing on modeling of the phenomena involved in thermal hydraulics of the core/concrete interactions. 6.1.1 Experimental Observations Simulant experiments were designed with air injection and cooling capabilities of both a single-layer and a multi-layer liquid pool to investigate several important physical processes of the core/concrete interaction, such as freezing, liquid/liquid 313 interfacial heat transfer, layer mixing, and droplet entrainment. Water and cyclohexane, which are immiscible, were used in the experiments to simulate the oxidic and metallic materials of the core/concrete interaction. The freezing phenomena experiments conducted in this study are of scoping nature. It was observed that a bottom crust could be formed across the bubble agitated horizontal liquid/solid interface, with gas velocities up to 126 mm/s. This observation validates the freezing model used in the current MCCI integral analysis codes. However, the liquid/liquid interface crust also assumed in the analysis codes did not form in the simulant experiments. The stability of a top crust is also called into question by the observations of this experiment. Therefore, if the oxidic materials form a top layer, the freezing of the oxidic layer involved in the MCCI could be in a slurry form rather than a crusting boundary. The heat transfer from the oxidic layer to either the metallic layer or the containment atmosphere at post-freezing stages will increase if there is no boundary crust. In addition, the supercooling phenomenon observed in the experiments is not usually accounted for in predicting the timing of freezing. Several correlations have been developed based on the surface renewal concepts to calculate the heat transfer rate between the bubble agitated immiscible oxidic and metallic layers. Significant differences of the interfacial heat transfer among these models' predictions were found. In the simulant experiment, the interfacial heat transfer between the water and cyclohexane layers was measured under various superficial gas velocities. Comparisons of the data with the existing models were made. The modified Szekely model used in the WECHSL code, and the model developed by Lee and Kazimi agree well with the experimental data. The Greene model incorporated in the CORCON/MOD2 seems to overpredict the experimental results, and the modified Konsetov model used in the CORCON/MOD1 underestimates the experimental data by an order-of-magnitude. 314 r In the layer mixing test, it was found that two immiscible liquids with density ratio of 0.78 were entirely homogenized under a modest superficial gas velocity of 50 mm/s. The transition patterns of the mixing phenomena with different gas velocities were observed as well. In the core/concrete interaction, the superficial gas velocity could reach as high as 1 m/s when the melt temperature is high, and the density ratio of the metallic and oxidic materials is about 0.8 initially when the oxidic layer consists of heavy core oxide only. From the observation of the simulant experiment, it is highly likely that the metallic and oxidic materials could be mixed into a single layer during some periods of the MCCI. Liquid droplets entrained by the flowing gas were quantified. The median and maximum sizes of the water droplets entrained by a gas flow of j, = 8.0 mm/s were found to be 2.0 and 20.0 pIm, respectively. The amount of entrainment was found in good agreement with the Kataoka and Ishii model. 6.1.2 Development and Validation of Heat Transfer Models The behavior of a pool of molten core materials in a concrete cavity is governed by an energy balance. The decay heat and chemical reaction heat generated in the pool may be lost through its top surface to the containment atmosphere or containment structure or to the surrounding concrete. The partition of energy between concrete and the top surface is determined by the various thermal resistances from the pool of molten core materials to the surroundings. Among various phenomenological heat transfer models, the one having the most direct impact on the core-concrete interactions process is that describing the heat transfer across the melt/concrete interface. The extent of concrete ablation, the melt temperature response, the amount of decomposition gas release and therefore the amounts of chemical heat and aerosol releases all directly depend on the amount of heat that can be transferred across the melt/concrete interface. In the first generation of MCCI integral analysis codes, a gas film model was used for the downward heat transfer. This model assumed that the downward heat 315 transfer of the corium pool is governed by a stable gas film across the horizontal corium/concrete interface. The stable gas film was inferred from water/dry ice simulant tests. However, in air injection simulant .experiments, no gas film was observed at the water/porous plate interface with superficial gas velocity up to 130 mm/s. A preliminary periodic contact model was proposed to govern the heat transfer process when a gas film cannot be sustained at the interface. This model considered the heat transfer mechanism as a transient heat conduction process of a periodic direct contact between the hot pool and the relatively cold concrete surface. In this study, a revised periodic contact model was developed based on more complete theoretical consideration to overcome a deficiency found in its original derivation. Both the gas film and periodic contact models are conceptualized based on assumed physical phenomena which cannot be directly observed in the real material experiments. The actual heat transfer mode may depend on the melt temperature and is not well understood. A film collapse model was proposed assuming that the downward heat transfer may follow a combination of the gas film and periodic contact models. If the melt initial temperature is high enough, a stable film may exist, and the heat flux presumably follows the gas film model until a minimum stable film limit is reached. When the film collapses, the heat transfer mode undergoes a transition to the periodic contact model. If the melt initial temperature is too low to generate a stable film, the heat transfer will be governed by the periodic contact model all the time until the solidus temperature is reached. The transition criteria of a stable gas film used in the film collapse model are based on hydrodynamic considerations. The film establishment criterion was related to the Kutateladze's flooding limit, and the film collapse limit was related to Berenson's minimum gas flux to stabilize the film. For the case of core/concrete interaction, those limits differ by two orders-of-magnitude. In the development of the film collapse model, multiplication factors were applied to both limits in order to get the best fit of the real material experimental data. 316 As the pool cools down, formation of a bottom crust provides an additional thermal resistance to the downward heat flow path. This conductive thermal resistance will limit the amount of heat loss to concrete and reduce the amount of gas gerneration. The gas film is destabilized at a sufficiently low superficial gas velocity condition, which may occur earlier than the crust formation. The applicability of the periodic contact model is limited to the early stages of the MCCI before any freezing occurs. Therefore, 'neither the gas film nor the periodic contact model can be used to describe the downward heat transfer during the post-freezing stages of MCCI. In this study, a post-freezing model was developed based on an assumption that thermal resistance between the pool boundary and the concrete surface, i.e. resistance across the rising fluid, is continuous on the basis of the superficial gas velocity that can be achieved after the formation of a solidified bottom crust. An integral analysis computer code CORCON/MIT was developed by incorporating the proposed downward heat transfer models into CORCON/MOD2 to analyze the integral behavior of the core/concrete interaction. Sensitivity study was performed to scope out the important parameters, such as the melt temperature and compositions, and the concrete types, in the calculations of the downward heat transfer. It was found that the downward heat flux of the core/concrete interaction predicted by the periodic contact model is about an order-of-magnitude higher than the gas film model if the corium temperature is higher than its solidus point. As predicted by all models, the downward heat fluxes drop dramatically when the melt temperature drops across its solidus point. The calculated downward heat fluxes for the post-freezing stage is rarely affected by different heat transfer models which are used to predict the relatively small thermal resistance at the melt/concrete interface compared to the dominant thermal resistance across the solidified melt. It was also found that the downward heat flux is not affected significantly by the compositions of the melt which may contact the horizontal concrete surface when the debris temperature is high. The possible implication 317 of this finding is that the downward heat transfer between the corium and concrete may not be affected significantly by the mixing of the metallic and oxidic materials. At low debris temperature, allowing formation of a bottom crust, a metallic pool with higher thermal conductivity has a higher downward heat transfer than an oxidic one. The differences in the calculated downward heat fluxes among different types of concrete can be large. The various models were validated by comparison to the German BETA experimental results. The BETA facility is a large scale (380 mm diameter concrete crucible contains up to 350 kg metallic and 150 kg oxidic melt) high power inductive heating (up to 1900 kW) experiment. The major finding of the BETA tests was that the dominant downward erosion indicates a very effective heat transfer mechanism at the bottom of the concrete crucible, which is different from the sideward heat transfer mechanism. The proposed downward heat transfer model is capable of producing the downward erosion results of the BETA experiments with a mean error of 5% (overestimation) and a standard deviation of 27%. Less accuracy is found by the other existing models in the calculation of the erosion data of the BETA tests. The gas film model, developed earlier and commonly used in severe accident analysis, significantly underestimates the downward heat transfer (with mean error of -53%, and standard deviation of 56%). The large scale, real material experiments (SWISS and TURC) conducted at the Sandia National Laboratory were also analyzed. It is found that the proposed model is able to produce a fairly good agreement in the axial erosion for sustained heating SWISS tests. While in the transient TURC tests, the proposed model cannot predict the axial erosion data very well in most cases. 6.1.3 Impact of Heat Transfer Models In view of the large differences among the downward heat fluxes predicted by the various models, a sensitivity study based on CORCON/MIT-VANESA calculation was performed to investigate the effect of the downward heat transfer 318 model on the concrete erosion, gas generation, melt temperature, and ex-vessel aerosol release in a real reactor case. It was found that the rate and history of the ex-vessel aerosol release is significantly affected by the downward heat transfer model used in the calculation. In the base case analyzed in this study, the initial aerosol generation rate predicted by the periodic contact model is five times higher than the gas film model because the initial downward heat flux and gas generation rate calculated by the periodic contact model are higher. However, the melt temperature, the gas generation rate, and the aerosol release rate decrease faster for the periodic contact model, therefore, the accumulated aerosol (including radionuclides and non-radioactive materials) release after three hours interaction calculated by the periodic contact model is not significantly different from the gas film model. Nevertheless, the accumulated fission products release (mostly released at elevated melt temperature) calculated by the periodic contact model was three times higher than the gas film model if the initial melt temperature is high. At low initial melt temperature, when a bottom crust is initially formed, the various heat transfer models do not lead to significant differences in the fission product release. The results of the film collapse model depend on the initial condition of the core/concrete interaction. If neither a bottom crust nor a gas film exists initially, the fission products release predicted by the film collapse model can be as much as five times higher than the gas film model. 6.1.4 Sensitivity Study on Ex-Vessel Aerosol Release A parametric study on significant variables, such as (1)initial melt temperature; (2)concrete properties; (3)amount of unoxidized zirconium; (4)amount of melt; (5)decay heat; and (6)layering potential of melt constituents, was performed to identify the important source of the uncertainties in calculation of the ex-vessel aerosol release. 319 It is found that the initial melt temperature is extremely important to the calculation of the ex-vessel aerosol release. In the cases studied, the total lanthanum release of the high initial melt temperature case can be an order-of-magnitude higher than the low initial melt temperature case. The amount of unoxidized zirconium in the melt has little effect on the melt temperature, however, it has significant effect on the calculation of the fission product release. The more unoxidized zirconium in the melt, the lower the oxygen potential of the reaction gases will be, which leads to a more stable vaporized fission product in the gas phase, and therefore a higher fission product release during core/concrete interaction. The concrete properties, such as concrete decomposition temperature and gas content, have certain effects in determining the ex-vessel release. The higher the concrete decomposition temperature is, the higher the oxidic temperature will be during the quasi-steady state, which will result in a higher aerosol release. Since the ex-vessel aerosol release increase with the increasing of the gas generation rate, the concrete with higher gas content will give higher aerosol release. 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