Air Ingress Benchmarking with Computational Fluid Dynamics Analysis - - PowerPoint PPT Presentation

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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

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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

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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

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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)

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Theoretical Study

Vary Choke Flow

Bottom Reflector Air In Air/COx out

• HEATING-7 and MathCad Code
• The gas temperature is assumed

to follow the temperature of the solid structures 5-minute time step

• The reaction rate is proportional

to the partial pressure of the

• xygen
• There is enough fresh air supply

and the inlet air temperature is 20 °C.

Figure 14: Open-Cylinder Model

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Operative Equations

• Chemical Reaction: C + O2 ---> CO2 ( H = -393.51 KJ/mole)
• R=K1*exp(-E1/T)(PO2/20900)

When T<1273K: K1=0.2475, E1=5710; When 1273K<T<2073K, K1=0.0156, E1=2260;

• Buoyancy:
• Pressure drop in Pebble Bed [3]

gh P

h c b

) ( ρ ρ − =

2 3

2 1 u d H p ρ ε ε ψ − = ∆

1 .

) 1 Re ( 6 1 Re 320 ε ε ψ − + − =

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Theoretical Study (Cont.)

0.00 0.02 0.04 0.06 0.08 0.10 500 1000 1500 2000 2500 3000 the Average Temp. of the Gases (C) Air Inlet Velocity (m/s) 800 1000 1200 1400 1600 1800

100 200 300 400

time(hr) Core Hot-Point Temperature (C)

0.02 0.024 0.028 0.032 0.036 0.04 100 200 300 400 Time(hr) Air Inlet Velocity (m/second) 0.05 0.1 0.15 0.2 0.25

• 5.25
• 4.95
• 4.65
• 4.35
• 4.05
• 3.75

Z(m) Mole Fraction of Oxygen in the Bottom Reflector

Figure 15: Results of the Open-Cylinder Model

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Theoretical Study (Cont.)

PBR_SIM Results with Chemical Reaction (By Hee Cheon No)

• Considering only exothermic C + O2 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

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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

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Verification of JAERI’s Experiments

• Solver used: FLUENT6.0
• GAMBIT for the mesh generation
• Subroutines(UDF) for special problems

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JAERI Experiments

Diffusion - Isothermal Natural Circulation - Thermal Thermal with graphite and air - Multi-

component

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Experimental Apparatus - Japanese

C4 2 7

Nitrogen Helium Valves

C3 C1 C2 H4 H3 H2 H1

Figure 16: Apparatus for Isothermal and Non-Isothermal experiments Figure 17: Structured mesh

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Isothermal Experiment

Pure Helium in top pipe, pure Nitrogen in the bottom tank Only Diffusion Process and no Natural convection Taylor Expansion to convert diffusion coefficients into the following form:

2 3 / 1 3 / 1 75 . 1 7

) ( ] / ) [( 10

B A B A B A B A

P M M M M T D Σ + Σ + =

− −

4 4 3 3 2 2 1 1

T A T A T A T A A D

B A

+ + + + ≈

−

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Isothermal Experiment

0.00 0.20 0.40 0.60 0.80 50 100 150 200 250 300 Time (min) Mole fraction

H-1 & C-1(Calculation) H-2 & C2 (Calculation) H-3 & C3 (Calculation) H-4 & C4 (Calculation) H-1 & C-1(Experiment) H-2 & C2 (Experiment) H-3 & C3 (Experiment) H-4 & C4 (Experiment)

Figure 18: Mole fraction of N2 for the isothermal experiment

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Thermal Experiment

Figure 19: The contour of the temperature bound4ary condition

• Pure Helium in top pipe, pure

Nitrogen in the bottom tank

• N2 Mole fractions are monitored in

8 points

• Hot leg heated
• Diffusion Coefficients as a

function of temperature

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Additional Dynamic Force Analysis

Diffusion Buoyancy Pressure drop Natural Circulation

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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

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Thermal Experiment

0.2 0.4 0.6 0.8 1 50 100 150 200 Time (min) Mole fraction of N2

H-1(FLUENT) C-1(FLUENT) H-1(Experiment) C-1(Experiment)

Figure 20: Comparison of mole fraction of N2 at Positions H-1 and C-1

0.2 0.4 0.6 0.8 1 50 100 150 200 Time(min) Mole Fraction

H2(Experiment) C2(Experiment) H-2(FLUENT) C-2(FLUENT)

Figure 21: Comparison of mole fraction

• f N2 at Positions H-2 and C-2

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Thermal Experiment (Cont.)

0.2 0.4 0.6 0.8 1

50 100 150 200 250

Time(min) Mole Fraction of N2 H4(Exp) C4(Exp) H-4(Calc) C-4(Calc)

Figure 22: Comparison of mole fraction

• f N2 at Positions H-1 and C-1
• 0.15
• 0.10
• 0.05

0.00 0.05 0.10 0.15 0.20 0.25 2 4 6 Time (Second) Velocity (m/second)

Figure 23: The vibration after the

• pening of the valves.

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Nitrogen

Helium

Figure 24: Nitrogen Contour: T=0.00 min

Thermal Experiment (Cont.)

Figure 25: Nitrogen Contour: T=1.60 min

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Thermal Experiment (Cont.)

Figure 26: Nitrogen Contour: T=75.50 min Figure 27: Nitrogen Contour: T=123.00 min

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Thermal Experiment (Cont.)

Figure 28: Nitrogen Contour: T=220.43 min Figure 29: Nitrogen Contour: T=222.55 min

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Thermal Experiment (Cont.)

Figure 30: Nitrogen Contour: T=223.03 min Figure 31: Nitrogen Contour: T=223.20 min

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Thermal Experiment (Cont.)

Figure 32: Nitrogen Contour: T=223.28 min Figure 33: Nitrogen Contour: T=224.00 min

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Multi-Component Experiment

2 1 3 4

Heated Graphite Air Helium

• Graphite Inserted
• Multiple gases: O2, CO,

CO2, N2, He, H2O

• Mole fraction at 3 points

are measured

• Much higher calculation

requirements

• Diffusion Coefficients

2 3 / 1 3 / 1 75 . 1 7

) ( ] / ) [( 10

B A B A B A B A

P M M M M T D Σ + Σ + =

− −

Figure 34: Apparatus for multi- Component experiment of JAERI

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Multi-Component Experiment(Cont.)

• Chemical Reactions

1 surface reaction:

C + O2 = x CO + y CO2 (+ Heat)

2 volume Reactions:

2 CO + O2 = 2CO2 ( + Heat) 2 CO2 = 2 CO + O2 (- Heat)

n

• c

p RT E K r

2

) exp( − =

−

Figure 35: The temperature boundary conditions for the multi-component experiment

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Multi-Component Experiment(Cont.)

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 20 40 60 80 100 120 140 Time(min) Mole Fraction O2(Experiment) O2(Calculation) CO(Experiment) CO(Calculation) CO2(Experiment) CO2(Calculation) Figure 36: Mole Fraction at Point-1 (80% Diffusion Coff.)

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Multi-Component Experiment(Cont.)

Figure 37: Mole Fraction at Point-3

0.00 0.04 0.08 0.12 0.16 0.20 0.24 20 40 60 80 100 120 140 Time(min) Mole Fraction

O2(Experiment) O2(Calculation) CO(Experiment) CO(Calculation) CO2(Experiment) CO2(Calculation)

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Multi-Component Experiment(Cont.)

Figure 38: Mole Fraction at Point-4

0.00 0.05 0.10 0.15 0.20 0.25 20 40 60 80 100 120 140 Time (min) Mole Fraction O2(Experiment) O2(Calculation) CO(Experiment) CO(Calculation) CO2(Experiment) CO2(Calculation)

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NACOK Natural Convection Experiments no cont.

Figure 39: NACOK Experiment

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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

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Mesh Applied

Figure 40: Meshes for the NACOK Experiment

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Pressure Drop in Pebble Bed Using UDF

Porous media to model the pebble bed

1 .

)) 1 (Re/( 1 . ) 1 Re/( 205 ε ε − − − − = ∆p

Convert the pressure drop into: UDF to calculate the pressure drop Modifications made on the laminar pressure drop proposed by NACOK experiment Density, conductivity, specific heat, viscosity are defined using 12 points respectively.

9 . 1 1 . 9 . 5

* * * 3 . 10 * * 10 7 . 1

z z

u u P η ρ η − ∗ − = ∆

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Boundary Conditions

Figure 41: Temperature Profile for one experiment

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The Mass Flow Rates

Figure 42: Mass Flow Rates for the NACOK Experiment 0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 100 300 500 700 900 1100 Temperature of the Pebble Bed (C) Mass Flow Rate (kg/s)

T_R=200 DC(Exp.) T_R=400 DC(Exp.) T_R=600 DC(Exp.) T_R=800 DC(Exp.) T_R=200 DC(FLUENT) T_R=400 DC(FLUENT) T_R=600 DC(FLUENT) T_R=800 DC(FLUENT)

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Future Work

• Benchmark Chemical Corrosion Tests and other upcoming

NACOK Tests

• Develop PBMR model using FLUENT 6.1 to consider corrosion
• f graphite (loss of material in lower reflector)
• Integrate with systems analysis codes (RELAP-ATHENA)
• Conduct PBMR analysis showing slow corrosion - low inlet air

velocity and no burning.

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Future Work (Cont.)

Figure 43: The proposed models to study the chemical reactions in pebble bed

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Future Work (Cont.)

Figure 44: The models to study the chemical reactions in pebble bed

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The Detailed Model of PBMR

Figure 46: The geometry of the bottom reflector Figure 45: The detailed model for PBMR

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30 Degree Model

Figure 47: 3-D 30-degree Model

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Summary

• Hope is that there is a long diffusion stage and the air inlet velocity

after the natural circulation will be low enough not to support active burning but only slow corrosion.

• Need to expand the boundary conditions to assess the availability of

air - incorporate systems code.

• Need to develop mitigation strategies for ultimate cessation of air

ingress and reactor cool down post LOCA break spectrum.

• The surface reaction rate and the immediate products at the graphite

surface are important information for the air ingress accident study.

• The methodology developed in this work using FLUENT 6 appears to

be able to handle these challenges.

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THANK YOU!