Air Ingress Benchmarking with Computational Fluid Dynamics Analysis Tieliang Zhai Professor Andrew Kadak Massachusetts Institute of Technology Nuclear Engineering Department 2nd I nt ernat ional Topical Meet ing on High Temperat ure React or Technology Beij ing, China Sept ember 22-24, 2004 Supported by the US Nuclear Regulatory Commission 1
Air Ingress Accident Objectives and Overall Strategy � Theoretical Study � Verification of Japan’s Experiments � Verification of NACOK experiments � Proposals for Real PBMR analysis � Future work and Conclusions � 2
Characteristics of the Accident 3 Stages: � � Depresurization � Pure Diffusion � Natural Convection Challenging: � � Natural convection � Multi-component Diffusion (air and graphite reactions) � Multiple Dynamic Chemical Reactions � Complicated geometry 3
Overall Strategy 1. Theoretical Study (Aided by HEATING-7) To understand the dominant physical processes qualitatively � 2. Verification of Japan’s Experiments (CFD) � Isothermal Experiment: Pure Diffusion � Thermal Experiment: Natural Convection � Multi-component: Chemical Reaction 3. Verification of Germany’s NACOK experiments (CFD) Natural Convection Experiment: Flow in Pebble Bed � Chemical Reaction Experiment: Chemical Reactions in Porous � Media 4. Model the real MPBR (CFD) 4
Theoretical Study � HEATING-7 and MathCad Code Air/COx out � The gas temperature is assumed Vary Choke to follow the temperature of the Flow solid structures � 5-minute time step � The reaction rate is proportional to the partial pressure of the oxygen � There is enough fresh air supply Bottom and the inlet air temperature is 20 Reflector ° C. Air In Figure 14: Open-Cylinder Model 5
Operative Equations Chemical Reaction: C + O 2 ---> CO 2 ( H = -393.51 KJ/mole) � R=K 1 *exp(-E 1 /T)(PO 2 /20900) � � When T<1273K: K 1 =0.2475, E 1 =5710; � When 1273K<T<2073K, K 1 =0.0156, E 1 =2260; = ρ − ρ Buoyancy: P ( ) gh � b c h Pressure drop in Pebble Bed [3] � − ε ρ 1 320 6 H ψ = + ∆ = ψ 2 p u Re Re ε 3 d 2 0 . 1 ( ) − ε − ε 1 1 6
Theoretical Study (Cont.) 0.10 1800 Core Hot-Point Temperature (C) 0.08 1600 Air Inlet Velocity (m/s) 0.06 1400 0.04 1200 0.02 1000 0.00 800 0 500 1000 1500 2000 2500 3000 0 100 200 300 400 the Average Temp. of the Gases (C) time(hr) 0.04 0.25 Mole Fraction of Oxygen in the Bottom Air Inlet Velocity (m/second) 0.036 0.2 0.032 0.15 Reflector 0.028 0.1 0.024 0.05 0.02 0 0 100 200 300 400 -5.25 -4.95 -4.65 -4.35 -4.05 -3.75 Time(hr) Z(m) 7 Figure 15: Results of the Open-Cylinder Model
Theoretical Study (Cont.) PBR_SIM Results with Chemical Reaction (By Hee Cheon No) Considering only exothermic C + O 2 reactions � Without chemical reaction - peak temperature 1560 C @ 80 hrs;With � chemical reaction - peak temperature 1617 C @ 92 hrs Most of the chemical reaction occurs in the lower reflector � As temperatures increase chemical reactions change; As a function of � height, chemical reactions change Surface diffusion of Oxygen is important in chemical reactions � 8
Theoretical Study (Cont.) Preliminary Conclusions for an open cylinder of pebbles: � Inlet air velocity will not exceed 0.08 m/s. � Viscosity increases with the increase of the temperature � Pressure loss in the pebble region increases rapidly with the increase of the velocity � The negative feedback: the Air inlet velocity is not always increase when the core is heated. � No meltdown for the core peak temperature is lower than 1650 C even with the conservative assumptions 9
Verification of JAERI’s Experiments � Solver used: FLUENT6.0 � GAMBIT for the mesh generation � Subroutines(UDF) for special problems 10
JAERI Experiments � Diffusion - Isothermal � Natural Circulation - Thermal � Thermal with graphite and air - Multi- component 11
Experimental Apparatus - Japanese C4 H4 C3 H3 C2 H2 Helium C1 H1 Valves 2 7 0 Nitrogen Figure 16: Apparatus for Isothermal and Figure 17: Structured mesh Non-Isothermal experiments 12
Isothermal Experiment � Pure Helium in top pipe, pure Nitrogen in the bottom tank � Only Diffusion Process and no Natural convection − + 7 1 . 75 10 [( ) / ] T M M M M = A B A B D − Σ + Σ A B 1 / 3 1 / 3 2 P ( ) A B � Taylor Expansion to convert diffusion coefficients into the following form: ≈ + + + + 1 2 3 4 D A A T A T A T A T − A B 0 1 2 3 4 13
Isothermal Experiment 0.80 0.60 Mole fraction 0.40 H-1 & C-1(Calculation) H-2 & C2 (Calculation) H-3 & C3 (Calculation) 0.20 H-4 & C4 (Calculation) H-1 & C-1(Experiment) H-2 & C2 (Experiment) H-3 & C3 (Experiment) H-4 & C4 (Experiment) 0.00 0 50 100 150 200 250 300 Time (min) Figure 18: Mole fraction of N 2 for the isothermal experiment 14
Thermal Experiment � Pure Helium in top pipe, pure Nitrogen in the bottom tank � N 2 Mole fractions are monitored in 8 points Hot leg heated � Diffusion Coefficients as a � function of temperature Figure 19: The contour of the temperature bound4ary condition 15
Additional Dynamic Force Analysis � Diffusion � Buoyancy � Pressure drop � Natural Circulation 16
CFD Initial Conditions and Assumptions � Subroutine to define the wall temperature distribution and the initial gas mole fraction � Structured Mesh � Grid Adaptation � Time step times: from 0.0001 second to 3 seconds 17
Thermal Experiment 1 1 H-1(FLUENT) H2(Experiment) C-1(FLUENT) C2(Experiment) H-1(Experiment) H-2(FLUENT) 0.8 C-1(Experiment) 0.8 C-2(FLUENT) Mole fraction of N2 0.6 Mole Fraction 0.6 0.4 0.4 0.2 0.2 0 0 0 50 100 150 200 0 50 100 150 200 Time (min) Time(min) Figure 20: Comparison of mole fraction of Figure 21: Comparison of mole fraction N 2 at Positions H-1 and C-1 of N 2 at Positions H-2 and C-2 18
Thermal Experiment (Cont.) 1 0.25 H4(Exp) C4(Exp) 0.20 0.8 H-4(Calc) Mole Fraction of N2 0.15 C-4(Calc) Velocity (m/second) 0.6 0.10 0.05 0.4 0.00 0 2 4 6 0.2 -0.05 -0.10 0 0 50 100 150 200 250 -0.15 Time(min) Time (Second) Figure 22: Comparison of mole fraction Figure 23: The vibration after the of N 2 at Positions H-1 and C-1 opening of the valves. 19
Thermal Experiment (Cont.) Helium Nitrogen Figure 24: Nitrogen Contour: Figure 25: Nitrogen Contour: T=0.00 min T=1.60 min 20
Thermal Experiment (Cont.) Figure 26: Nitrogen Contour: Figure 27: Nitrogen Contour: 21 T=75.50 min T=123.00 min
Thermal Experiment (Cont.) Figure 28: Nitrogen Contour: Figure 29: Nitrogen Contour: T=220.43 min T=222.55 min 22
Thermal Experiment (Cont.) Figure 30: Nitrogen Contour: Figure 31: Nitrogen Contour: 23 T=223.03 min T=223.20 min
Thermal Experiment (Cont.) Figure 32: Nitrogen Contour: Figure 33: Nitrogen Contour: T=223.28 min T=224.00 min 24
Multi-Component Experiment � Graphite Inserted 3 � Multiple gases: O 2 , CO, Heated Graphite CO 2 , N 2 , He, H 2 O 2 � Mole fraction at 3 points 4 are measured 1 � Much higher calculation Helium requirements � Diffusion Coefficients Air − + 7 1 . 75 10 T [( M M ) / M M ] = A B A B D − Σ + Σ A B 1 / 3 1 / 3 2 P ( ) A B Figure 34: Apparatus for multi- Component experiment of JAERI 25
Multi-Component Experiment(Cont.) Chemical Reactions � � 1 surface reaction: C + O2 = x CO + y CO2 (+ Heat) E = − n 0 r K exp( ) p − c o 0 o RT 2 � 2 volume Reactions: 2 CO + O2 = 2CO2 ( + Heat) 2 CO2 = 2 CO + O2 (- Heat) Figure 35: The temperature boundary conditions for the multi-component experiment 26
Multi-Component Experiment(Cont.) 0.21 O2(Experiment) O2(Calculation) 0.18 CO(Experiment) CO(Calculation) 0.15 CO2(Experiment) Mole Fraction CO2(Calculation) 0.12 0.09 0.06 0.03 0.00 0 20 40 60 80 100 120 140 Time(min) Figure 36: Mole Fraction at Point-1 (80% Diffusion Coff.) 27
Multi-Component Experiment(Cont.) 0.24 O2(Experiment) 0.20 O2(Calculation) CO(Experiment) CO(Calculation) 0.16 Mole Fraction CO2(Experiment) CO2(Calculation) 0.12 0.08 0.04 0.00 0 20 40 60 80 100 120 140 Time(min) Figure 37: Mole Fraction at Point-3 28
Multi-Component Experiment(Cont.) 0.25 O2(Experiment) O2(Calculation) 0.20 CO(Experiment) CO(Calculation) Mole Fraction 0.15 CO2(Experiment) CO2(Calculation) 0.10 0.05 0.00 0 20 40 60 80 100 120 140 Time (min) Figure 38: Mole Fraction at Point-4 29
NACOK Natural Convection Experiments no cont. 30 Figure 39: NACOK Experiment
NACOK Natural Convection Experiments � Square column on pebble side with pipe on cold leg � Actual Size (6 cm) Ceramic Pebbles in a 5x5 Array � Four Series of Tests � Hot and Cold Legs Maintained at Constant Wall Temperature � Cold Leg temperature at 200 °C, 400 °C , 600 °C and 800 °C . � The hot leg temperatures are higher than the cold leg by 50 °C, 100 °C, 150 °C etc., and the highest hot leg temperature is 1000 °C. � Output Measurements: Mass Flow Rate of Air � Steady State Calculation 31
Mesh Applied Figure 40: Meshes for the NACOK Experiment 32
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