1. FPTRAN: A Volatile Fission Product and Structural Material Transport Code for RELAP/SCDAPSIM EDUARDO HONAISER (Brazilian Navy Technological Center) SAMIM ANGHAIE (University of Florida)

2. OUTLINE Introduction Development of the Model – Numerical Treatment – Phenomena modeling Implementation into RELAP/SCDAPSIM/MOD3.2 Conclusions Development of a model to predict the transport of released fission products through the RCS, and to calculate the quantities each FP product deposited in the RCS and released to the containment OBJECTIVE

3. Fission Product Behavior Fission products initial inventory Fission Products Release Chemistry Fission Products Transport Containment Source Term

4. Fission Product Transport (Scope) Vapor phenomena – Adsorption – Condensation Onto structures Onto aerosol surfaces – Aerosol nucleation Aerosol Phenomena – Deposition – Agglomeration – Re-suspension

5. Characteristics of the Model Fixed speciation Phenomenological and convection model limited to piping system (upper plenum not considered) Decay heat of deposited FP not considered Mechanistic model for aerosol nucleation

6. Analytical Equations Analytical Equations Vapor species Aerosol Species

7. Transition Analytical-Numerical Use fractional step method to separate the convective term Discrete Ordinate Approach to treat Aerosol size Convert PDE into ODE Apply the Gear Method to solve the ODE system Hindmarsh (1993) package Change the integral terms into summation terns Define finite limits for particle size spectrum

8. Numerical Equations Bulk states (vapor+aerosol sections) Surface states (condensed, absorbed, and deposited) Total number of equations of the system: Sx(B+1+3N)

9. Vapor-Structural Surface Laminar flow (Re<2300) – Leifshitz model (1962) Turbulent flow Heat Transfer (empirical)Mass Transfer Nu=hd h /k=0.023Re 0.83 Pr 0.33 Sh=V d d h /D=0.023Re 0.83 Sc 0.33

10. Vapor-Aerosol Processes –Homogeneous nucleation –Heterogeneous nucleation

11. Nucleation Pattern Experimental evidence – PBF-SFD and Phebus-FP experiments Procedure – Calculate selectively nucleation rate for Ag and U – Select a model for homogeneous nucleation – Obtain the particle critical size, defining lower particle size as spectrum limit Critical radius for Ag-U particles : 850 K, S=20: O(10 -1  m) Experimental evidence: Winfrith Laboratories (1986): 0.5  0.9  m

12. Homogeneous Nucleation Models Analytical Models – Classical theory (Becker-Doring (1935) – Kinetic theory (Girshick et al (1990) Kinetic theory has better performance

13. Heterogeneous Nucleation Approach – Diffusion – Continuum region (Kn<<1) – Near Continuum region (Fuchs and Stuggin correction) rprp J- J+

14. Aerosol Processes Assumptions Aerosol spherical shape Empirical evidence – PBF-SFD and Phebus experiments Synergy – Mathematical Sticking coefficient Steady state Stokes Region (Re p <<1) Continuum region (Kn<<1)

15. Aerosol-Surface Gravitational Using the concept of mobility Upper limit of the spectrum: 50  m Laminar diffusion – Gormley and Kennedy (1954)

16. Early Models (theoretical) – Friedlander (1957), Davies (1966) and Beal (1968) Semi-empirical model (Sehmel-1970) Empirical Models – Liu (1974), Iam and Chung (1983), Chiang (1996) Aerosol-Surface (Turbulent) Chiang Correlation

17. Aerosol-Surface (Thermophoresis) Principle (Continuum) Brock Solution (1962) Springer (1970) Talbot (1980) Assessments – Dumaz (1994)

18. Other Models Bends depositionPui el al. (1989) ContractionsMuishondt (1996) Steam separators driersRAFT model AdsorptionEmpirical models from Sandia and Winfrith experiments Re-suspensionParozzi model (2000)

19. Aerosol-Aerosol (Agglomeration) Brownian agglomeration – Approach (continuum) – Target particle flux from other particles – Equation – Boundary conditions Continuum/near continuum region

20. Aerosol-Aerosol (Agglomeration) Differential gravitational – Simplified model – Realistic model Consider the fluid trajectories Approximations –Fuchs (1964) –Pruppacher and Klett (1978)

21. Turbulent agglomeration – Processes Diffusivity (small particles) Inertial (large particles) – Approaches Leifshitz (1962) –Solution of diffusion equation Saffman and Turner (1956) –Statistic approach for turbulence Aerosol-Aerosol (Agglomeration) ๑ ๑ ๑ ๑ ๑ ๑ ๑ ๑ ๑ ๑ ๑ ๑ Eddy Scale Length (100- 500  m)

22. Implementation RELAP5 TRCNL TRAN FPTRAN INPUTD FPREAD FPINIT Implementation in RELAP/SCDAPSIM/MOD 3.2

23. Verification Robustness of the math solver, positive masses Global mass error (OK) Sensitive studies Synergy Stability Studies Re-nodalization Number of Sections

24. Stability

25. Conclusions A FP transport model was developed, using a system of mass balance equations of first order Aerosol size was treated by a discrete ordinate approach, the convective term was treated using the fractional step method ODE system was solved using Hindmarsh package Phenomenological models: – Condensation onto structural surfaces – Condensation onto aerosol surfaces – Aerosol homogeneous nucleation – Aerosol deposition Gravitational settling, laminar diffusion, turbulent diffusion, thermophoresis – Aerosol Agglomeration Diffusive, turbulent, and due to gravitational difference – Additional models Aerosol Re-suspension, deposition onto singularities, vapor adsorption

26. Conclusions The model was implemented, and verified regarding: –Global mass balance –Stability For aerosol size discretization For spatial discretization PriorActivity 1. Develop a model for speciation, with a consistent thermo-chemical database 2. Implementation of upper plenum model 3. Review of release models in RELAP/SCDAPSIM/MOD3.2. Make it consistent with the developed speciation 4. Decay heat model review

27. Acknowledgments Dr. Chris Allison and Dick Wagner for their support and the use of RELAP/SCDAPSIM for this project