Modifications to the MELCOR code for application in fusion accident analyses

Transcription

1 Fusion Engineering and Design (2000) Modifications to the MELCOR code for application in fusion accident analyses B.J. Merrill, R.L. Moore, S.T. Polkinghorne, D.A. Petti * Fusion Safety Program, Idaho National Engineering and En ironmental Laboratory, PO Box 1625, Idaho Fall, ID 83415, USA Abstract For the past several years, the Fusion Safety Program at the Idaho National Engineering and Environmental Laboratory (INEEL) has modified the MELCOR code in order to assess safety issues associated with loss-of-cooling accidents (LOCAs) and loss-of-vacuum accidents (LOVAs) in the international thermonuclear experimental reactor (ITER) engineering design activity (EDA). MELCOR is a thermal hydraulics computer code developed by the Sandia National Laboratory for analyzing severe accidents in fission power plants. This paper describes these modifications and the role they played in LOVA and LOCA analyses performed for the non-site specific safety report (NSSR) for the ITER EDA. Published by Elsevier Science B.V. Keywords: MELCOR; International thermonuclear experimental reactor; Engineering design activity; Loss-of-cooling accidents; Loss-of-vacuum accidents 1. Introduction Fusion experiments, and eventually fusion power plants, will generate radioactive material in the form of activation products and tritium. A variety of energy sources exist in these facilities that can mobilize these radioactive materials during accidents such as loss-of-vacuum-accidents (LOVAs) or loss-of-cooling-accidents (LOCAs). The mobilized forms this radioactive material can take are, (1) dust containing tritium or activation products produced by plasma-facing-component (PFC) erosion during normal operation or disruptions; (2) aerosols from structure oxidation; (3) tritiated water produced by isotopic exchange of * Corresponding author. tritium from PFCs with spilt coolants; and (4) corrosion products. The extent to which these materials are confined during an accident will depend on whether or not the integrity of confinement barriers can be maintained during LOVAs and LOCAs. For the past several years, the Fusion Safety Program at the Idaho National Engineering and Environmental Laboratory (INEEL) has made modifications to the MELCOR code [1,2] to address these issues in support of the international thermonuclear experimental reactor (ITER) engineering design activity (EDA) [3 6]. MELCOR is a thermal hydraulics computer code developed for the United States Nuclear Regulatory Commission (USNRC) by the Sandia National Laboratory (SNL) for analyzing severe accidents in fission power plants. MELCOR /00/$ - see front matter Published by Elsevier Science B.V. PII: S (00)

2 556 B.J. Merrill et al. / Fusion Engineering and Design (2000) solves a set of conservation equations for the non-equilibrium flow of liquid and vapor water, and the transport of aerosols in both water phases, between computational volumes that collectively represent a system being modeled. As developed, the predictions of the MELCOR code depend heavily on empirical or semi-empirical correlations. Because of this, many code validation, code comparison, and peer review studies have been conducted for the MELCOR code [7 10]. The modifications made to MELCOR for fusion applications include, (1) oxidation of beryllium, carbon, or tungsten clad structures in steam environments; (2) condensation and freezing of air, water, or helium in cryogenic environments; (3) flow boiling heat transfer correlations; (4) air or helium as the working fluid; (5) turbulent and centrifugal aerosol deposition; and (6) enclosure radiant heat transfer. This paper describes these modifications and the role they played in LOVA and LOCA analyses performed for the non-site specific safety report (NSSR) for the ITER EDA. The analyses covered are an air ingress accident into the ITER cryostat, a vacuum vessel bypass accident, and a large ex-vessel LOCA. We conclude this paper by discussing ongoing modifications of the MELCOR code, making MELCOR more applicable for safety analyses of advanced magnetic fusion first wall, blanket and divertor design concepts and for inertial fusion energy applications. 2. Steam oxidation modifications Modifications were made to the MELCOR code to model the oxidation of PFC materials when exposed to a steam environment. In ITER, the PFC materials under consideration are beryllium, carbon, and tungsten. These materials chemically react at high temperatures with steam to produce hydrogen. The beryllium oxidation reaction is strongly exothermic, tungsten mildly exothermic, and carbon endothermic. When hot beryllium reacts with steam the following oxidation reaction occurs: H 2 O+Be BeO+H 2 (1) For fully dense beryllium, the following Arrhenius type oxidation rate relationships (kg beryllium per m 2 s) developed from measurements reported in [11] are used: R D ox = e 25,850/T T 1175 K (2a) R D ox =31.837e /T T 1175 K (2b) Neutron irradiation will induce porosity in the beryllium due to the production of helium and tritium bubbles. To account for the enhanced surface area associated with this porosity, the following oxidation rate was used for ITER safety analyses: R ox =P m R D P ox R ox (3) where P m is a steam pressure multiplier that accounts for the availability of steam near the PFC surface. This rate is the geometric mean rate between fully dense and porous (88% of full density) beryllium. The porous beryllium oxidation relationship (kg beryllium m 2 s) of Eq. (3) developed from measurements reported in [12] is as follows: R P ox =49.533e /T (4) Subsequent research on irradiated beryllium [13] has shown that Eq. (3) is conservative for beryllium irradiated to ITER fluences. Given the rate of oxidation, the chemical energy generated by this reaction is modeled as a surface heat flux for MELCOR heat structures. This heat flux is defined as the difference between the heats of formation of the reactants and products, times the oxidation rate determined from Eq. (4). Temperature dependent heats of formation were obtained from [14]. In addition, the reduction in heat structure thickness and hydrogen production is also determined from these oxidation equations. Similar oxidation equations for GraphNOL N3M graphite [15] and tungsten [16] have been incorporated into the MELCOR.

3 B.J. Merrill et al. / Fusion Engineering and Design (2000) Water freezing modifications Modifications have been made to the MEL- COR code that allow for water temperatures that are below the triple point temperature. These modifications were made in three specific areas: the equation of state (EOS), transport properties, and ice film buildup. The MELCOR code EOS for water is based on the polynomials that can be found in Appendix A of [17]. These polynomials relate pressure, internal energy, entropy and heat capacity to temperature and density. This EOS is accurate from near zero pressure to 100 MPa, and from 273 to 1573 K. However, if the water temperature drops below 273 K, as in the case of an ingress accident into a cryostat containing massive structures at 4 K, the water will readily freeze, and thereby drop below the temperature range of this EOS. To treat this occurrence, the water pressure at temperatures below the triple point temperature (T TP ) for a given density is determined as follows: p(, T)=p(, T TP )+ p T (, T TP) [T T TP ] (5) where the pressure p(, T TP ) and derivative of pressure with temperature (( p/ T)(, T TP )) are determined from the standard MELCOR code EOS. This approach represents a linear projection with temperature at a given density to estimate the system pressure when the temperature drops below the lower temperature bound of the MEL- COR EOS. If the temperature is above the triple point, then the standard MELCOR EOS is used. The specific internal energy [18] below T TP is defined by the following equation: du=c v dt+ T p T P n d (6) This equation is integrated for both phases assuming that the specific heat capacity decreases linearly with temperature below freezing [i.e. c v + c v TP (T )/T TP ; T T TP ]. The heat of fusion is included in the liquid or ice phase heat capacity over a 1 C temperature change below T TP [i.e. c v =(h f / ); T TP T T TP ]. Integrating Eq. (6) at a given or constant density gives the estimated ice internal energy as: u(, T)=u(, T TP )+ h f [T TTP ] (7a) for T TP T T TP and u(, T)=u(, T TP ) h f + c TP [T TP 2 ] n 2 T 2 1 2[T TP ] T TP 2 (7b) for T T TP. The specific entropy [19] below T TP is determined in a similar manner using the following equation: dt ds=c v T + p d (8) T v The viscosity of liquid water below the triple point is maintained at an arbitrarily large value, while the thermal conductivity is maintained at the value for ice at the triple point. The above approach is simplistic but allows the MELCOR to simulate all of the pertinent features of ice formation, i.e. a substance that will not move under pressure, conducts heat from it s surroundings, and releases energy at a constant temperature as it solidifies. Based on our experience in performing LOCA analyses for the ITER cryostat, we find that the MELCOR condensation model is more important during low water injection rates and the MELCOR choking model is more important during high injection rates than are the changes proposed here for the EOS. Therefore, given the lack of data for water injection into evacuated environments at cryogenic temperatures, and given the short period of time that low-pressure conditions exist in ITER LOCA analyses, we believe that this treatment is adequate at the present time. Water vapor that condenses on a surface at cryogenic temperatures will immediately freeze. As this ice thickens, it produces a thermal resistance to heat flow at this surface. The MELCOR code already models the thermal resistance of a liquid film on a given structure, but the maximum film thickness is a user specified input quantity. The MELCOR film resistance model was modified to account for freezing by solving the following time dependent conservation of energy equation at the structure surface to determine film thickness:

4 558 B.J. Merrill et al. / Fusion Engineering and Design (2000) h f t =q cond q conv c (h v h i ) (9) where, is the ice density (kg/m 3 ); h f, the heat of fusion (J/kg);, is the ice thickness (m); q cond, stands for heat flux conducted through ice (W/ m 2 ); q conv, heat flux convected to ice surface by atmosphere (W/m 2 ); c, is the condensation mass flux (kg/m 2 s); h v, represents vapor enthalpy (J/ kg); and h i, ice enthalpy (J/kg). The ice surface temperature of this model equals the minimum of the triple point, or vapor temperature. The maximum rate of growth of the ice layer allowed by this model equals the product of the surface area times the condensation flux. 4. Flow boiling heat transfer correlations Flow boiling heat transfer correlations were added to the MELCOR heat transfer package to improve predictions for transients involving cooling systems. The Chen [20] equations for nucleate boiling, the Biasi [21] correlation for critical heat flux, and the modified Bromley [22] correlation for film boiling were adopted. Chen s nucleate boiling correlation is based on the assumption that the total surface heat flux is composed of a nucleate boiling component and a single phase component. q =h nb (T w T sat )S supp +h l (T w T bulk )F (10) where q, is the surface heat flux (W/m 2 ); h nb,is the nucleate boiling coefficient (W/m 2 K); h l denotes the single phase liquid heat transfer coefficient (W/m 2 K); T w, represents wall surface temperature (K); T sat, stands for saturation temperature of the coolant (K); T bulk, is the bulk temperature of the coolant (K); S supp, two-phase suppression; F, flow parameter. The nucleate boiling heat transfer coefficient is evaluated using the following equation: h nb = k l c pl l l h lv v 0.24n T sat P sat (11) where k l, is the thermal conductivity of the liquid (W/m K); c pl, is specific heat of the liquid (J/kg K); l,v, stands for density of the liquid, vapor (kg/m 3 ); denotes surface tension associated with the fluid (N/m); l is the dynamic viscosity of the liquid (Pa s); h lv, latent heat of vaporization (J/ kg); T sat =T w T sat (K); p sat =p sat p sys (Pa); p sat stands for saturation pressure at wall temperature (Pa); p sys, denotes system pressure (Pa). The Dittus Boelter correlation is used to obtain the single-phase liquid heat transfer coefficient. The Biasi critical heat flux (CHF) correlation is used in this modification. This correlation is applicable down to a mass flux of about 200 kg/m 2 s. Below a mass flux of 200 kg/m 2 s, a linear interpolation with mass flux is performed between the Biasi correlation and the Roshenow [23] correlation for pool boiling. Once the surface heat flux exceeds CHF, a transition to stable film boiling occurs. The heat flux at which the transition is complete is predicted by the Zuber [24] minimum heat flux correlation. Beyond this heat flux; the correlation used for heat transfer is the modified Bromley film boiling correlation, which is as follows: q film =q conv +0.75q rad (12) where, q conv = c v D h (T surf T sat ) 3/4 4 q rad = sb (T surf T 4 sat ) and h fg = h fg + 0.5c pv (T surf T sat ) c = 2 surf 1/2 g( l v ) ( l v )gk v3 h fg v c 1/4 and where, g is the gravitational constant (m/s 2 ); sb, stands for Stefan Boltzmann constant (W/m 2 K 4 ); k v, denotes vapor thermal conductivity (W/m K); surf, is the surface tension between the liquid vapor interface (N/m); and c stands for Taylor instability wave length (m).

5 B.J. Merrill et al. / Fusion Engineering and Design (2000) Additional working fluids Two alternative versions of MELCOR were developed that substituted air or helium for water as the primary working fluid. EOS for these fluids were taken from polynomials developed by Reynolds [25]. These polynomials accurately predict thermodynamic properties of pressure, internal energy, enthalpy, specific heat capacity, and entropy for these fluids as a function of density and temperature, whether the fluid exists in a saturated or superheated (gaseous) state. Thermal properties of water, such as thermal conductivity, surface tension, and triple point temperature, etc., were replaced with those for helium or air. Structure heat transfer correlations applicable for water were assumed to be applicable for helium and air as fluids. 6. Aerosol deposition model improvements The standard MELCOR aerosol deposition model [2] accounts for four deposition mechanisms, i.e. thermophoresis, gravity, diffusion, and diffusiophoresis. Two additional aerosol deposition mechanisms were added to MELCOR, namely, turbulent and inertial deposition. In the case of turbulent deposition, a particle suspended in a fluid flowing in a pipe obtains momentum from the fluid in both the parallel and perpendicular direction to flow. The perpendicular momentum is gained from fluid turbulence. Since the particle density is larger than the fluid density, this momentum will allow the particle to penetrate the buffer layer and viscous sublayer of turbulent flow that are adjacent to the pipe surface and to impact this same surface. We have adopted a model proposed by Wood [26] for aerosol deposition in pipes due to fluid turbulence. When a fluid flows around a pipe bend, particles that are suspended in this fluid experience a centrifugal force that radially accelerates these particles, causing them to impact the pipe wall. This process is called inertial deposition. However, even in the event of surface impact produced by either of the above deposition mechanism, surface forces must be large enough to overcome the momentum associated with these particles if these particles are to adhere permanently to this surface. These forces include both a capillary force associated with a surface film, if present, and Van der Waals force. An expression for these forces [27] has been included with the turbulent and inertial deposition equations to determine if particles will adhere to the surface. The equations used to define the rate at which the aerosol deposition occurs involve thermal physical properties of the carrier gas, such as density, viscosity, conductivity, and particle diffusivity. The standard MELCOR model assumes that the carrier gas is air, which can result in deposition rates being more than a factor of five too low for a pure helium environment. Since in fusion, aerosol deposition can occur in atmospheres composed of a variety of gases, we have modified MELCOR to calculate the aerosol deposition coefficients by using the time-dependent properties of the gas that actually exits during a given calculation, for example, steam, hydrogen, air, helium, etc. or mixtures thereof. Mixture viscosity and conductivity were evaluated from MELCOR gas properties and specie mole fraction, and diffusion coefficients were obtained from a correlation by Wilke [28]. 7. Thermal radiation transport model First wall surface temperatures during accident conditions in ITER play a primary role in determining the amount of hydrogen produced through the oxidation reaction of beryllium with steam. This temperature depends on radiant heat transfer to cooler components within the vacuum vessel. The existing MELCOR radiation model does not allow for the direct exchange of radiant power between such components, or account for the presence of an atmosphere between these components that absorbs and re-radiates this power. A new thermal radiation heat transport capability was added to the MELCOR code. This new capability is an enclosure net thermal radiation model [29] similar to that of the CONTAIN code [30]. The radiant heat flux that leaves a surface in an enclosure is defined as follows:

6 560 B.J. Merrill et al. / Fusion Engineering and Design (2000) j q j = ( 1 j B j ) (13) j where, j, is the emissivity of surface j; j denotes radiosity of surface j (W/m 2 ); B j = T j4 is the Planck blackbody radiation of surface j (W/m 2 ); stands for Stefan Boltzmann constant (W/m 2 K 4 ); and T j is the temperature of surface j (K). The radiosity ( j ) of Eq. (13) is calculated by solving a set of linear equations simultaneously. These equations are: N j (1 j ) F j k (1 g,j k ) k k=1 N = j B j + F j k g, j k B g (14) k=1 where, N is the number of surfaces in the enclosure; F j k, denotes the view factor from surface j to surface k; g, j k stands for emissivity of the gas mixture in the enclosure; and B g = T g4 is the Planck blackbody radiation for the gas (W/m 2 ). In Eq. (14), the gas emissivity ( g, j k ) is a function of the mean optical path length (L j k ) between surfaces, and the radiative properties of the gas mixture are determined from the Modak radiative property model [31]. Fig. 1. Pressures for the cryostat air ingress accident scenario. 8. ITER accident analyses Cryostat air ingress accidents are unlikely (frequency, per year) events that have been postulated for the ITER design [32]. These accidents result from postulated breaches of the cryostat boundary, such as a metal bellows failure at a cryostat penetration. The consequences of these accidents are increased heat and weight loads for magnets due to air condensation, and a partial vacuum developing in adjoining rooms to the cryostat. Pressures from an air ingress accident scenario for a postulated 1.0 m 2 cryostat break are shown in Fig. 1, which contains the predicted cryostat, cryostat space room, and crane hall pressures. The cryostat space room is an adjoining room to the cryostat. The pressure of the cryostat space room drops to 90 kpa in 1.7 s following the initiation of the cryostat breach. This causes the vacuum breakers between the cryostat space room and crane hall to open, and the cryostat space room pressure to drop more slowly reaching a minimum pressure of 82 kpa in 225 s. From this point, the cryostat space room pressure begins to rise as it comes into near equilibrium with the cryostat pressure by 400 s. The cryostat pressurization rate was reduced by the magnets, which condensed the air that entered the cryostat through the breach. A peak pressure of 108 kpa is reached in the cryostat and cryostat space room by 965 s due to liquid air evaporation as heat leaks into the cryostat from the ambient. These pressures subsequently decay to about 100 kpa by 2050 s. The crane hall pressure drops to 90 kpa by 315 s, but recovers to 100 kpa after the vacuum breakers reseat at 400 s. The cryostat, cryostat space room, and crane hall pressures are well within the design limits for these enclosures. The total condensed air mass on the magnets for this study is 7615 kg by s. This condensed air mass and the increased heat loads associated with this air are not safety concerns for the magnets. An extremely unlikely accident (frequency between 10 4 and 10 6 per year) examined for the ITER [32] was a double-ended rupture of a single in-vessel first wall (FW) tube during a plasma burn ( m 2 total area). As the pressure

7 B.J. Merrill et al. / Fusion Engineering and Design (2000) Fig. 2. Airborne mass of dust, corrosion products, and tritium in generic bypass room (GBR) for in-vessel pipe break and vacuum vessel penetration bypass. Fig. 3. HTS vault and vacuum vessel pressures during an ex-vessel LOCA in ITER. builds in the vacuum vessel, a vacuum vessel penetration line (0.02 m 2 cross-sectional area) into an adjoining room designated as the generic bypass room (GBR) is assumed to fail as a result of the 100 kpa steam pressure in the vacuum vessel. At issue is the mobilization and possible release of the radioactive inventories contained within the VV. The radiological source terms involved are corrosion products in the coolant, and tritium and activated dust inside the plasma chamber. The corrosion product aerosol mass mobilized was 0.13 kg. The mass of tritium mobilized as HTO was 1.4 kg of tritium, with 0.8 kg mobilized immediately and 0.6 kg mobilized over a 6-h time period. The activated dust mass mobilized was 110 kg. Fig. 2 contains airborne aerosol masses in the GBR for this accident. As a consequence of stacking this mass via the ventilation system of the GBR and by GBR leakage, 22.5 g of HTO, 14.5 g of corrosion products, and g of the dust mobilized during this event are eventually released to the environment. These releases are a factor of five or more below the release limits defined for ITER extremely unlikely events. Finally, an extremely unlikely ex-vessel LOCA for ITER [32] was examined. This event considered a double-ended pipe rupture of the largest pipe ( m 2 area) in one of the four outboard baffle/limiter (OB/LIM) primary coolant loops during a plasma burn. In this event, coolant from the loop will be discharged into the primary heat transport system (PHTS) upper vault. The plasma burn was assumed to continue until a FW failure occurs at 1150 K, causing a plasma disruption. The FW failure involves ten coolant tubes (total break area= m 2 ) allowing steam and air to flow into the plasma chamber from the HTS vault through the failed cooling loop. Given the size of these breaks and the water inventory of an OB/LIM loop, this accident represents an enveloping ex-vessel LOCA. Fig. 3 contains the upper vault and vacuum vessel pressure for this event. The maximum upper PHTS vault pressure is approximately 170 kpa and occurs 130 s into the transient. This peak pressure is below the design pressure of 260 kpa. The VV pressure peaks at 110 kpa, which equals the setpoint for opening the bleed lines connecting the vacuum vessel to the pressure suppression system. Steam condensation on the vault walls and in the pressure suppression tank causes the maximum pressures in the VV and PHTS vault to decrease to sub-atmospheric in less than 24 h. Hydrogen generation in the ex-vessel LOCA is of concern since steam will be in contact with the beryllium FW surface. Because of the exponential

8 562 B.J. Merrill et al. / Fusion Engineering and Design (2000) dependence of the beryllium steam reaction rate on temperature, the hydrogen production can increase significantly as a function of temperature. Results show that the total hydrogen mass generated in the plasma chamber is well below ITER deflagration limits, and that the mass of hydrogen produced is reduced by a factor of two when the new radiation enclosure model described in Section 6 is used. 9. Conclusion The fusion specific modifications made to the MELCOR code as described in this paper have helped the INEEL fusion safety program to successfully participate in ITER EDA project. However, future magnetically or inertially confined fusion safety studies will require additional changes to the thermal hydraulics codes we use. For example, the capability of modeling a variety of coolants with a given computer code is required to analyze advanced magnetic or inertial design concepts. The proposed coolants range in nature from cryogens to liquid metals. A database is being developed based on the ATHENA fluid property package [33] that will be implemented in MELCOR. This database will be extended in the near future to include Flibe and SnLi. In addition, as data becomes available from fusion fluid flow and heat transfer experiments, we will continue to validate [34] the fusion specific modifications we are making to the MELCOR code. Acknowledgements This work was prepared under the auspices of the US Department of Energy, Office of Science, under DOE Idaho Operations Office Contract DE-AC07-94ID References [1] R.M. Summers, et al., MELCOR 1.8.0: a computer code for nuclear reactor severe accident source term and risk assessment analyses, NUREG/CR-5531 and SAND , USNRC Report, Sandia National Laboratory, January [2] R.O. Gauntt, et al., MELCOR computer code manuals, NUREG/CR-6119 and SAND ,USNRC Report, vol. 1 and 2, Rev. 1, Version 1.8.4, Sandia National Laboratory, July [3] D.L. Hagrman, B.J. Merrill, Initial modifications to the MELCOR code, ITER EDA US Safety Report, ITER/ US/95/TE/SA-18, June [4] D.L. Hagrman, B.J. Merrill, Additional of helium properties to the MELCOR code, ITER EDA US Safety Report, ITER/US/95/TE/SA-24, September [5] R.L. Moore, Documentation of new MELCOR flow boiling, EOS, and diffusion coefficient subroutines, ITER EDA US Safety Report, ITER/US/97/TE/SA-6, 12 May, [6] B. J. Merrill, An enclosure thermal radiation heat transport model for the MELCOR code, ITER EDA US Safety Report, ITER/US/97/TE/SA-04, 31 January, [7] MELCOR assessment: LACE aerosol experiment LA4, Sandia National Laboratory Report, SAND , September [8] MELCOR Assessment: FLECHT SEASET Natural Circulation Experiments, Sandia National Laboratory Report, SAND , December [9] Assessment of MELCOR using calculations for TMLB severe accident scenarios, AEA Technology Report, AEA RS 5484, March [10] MELCOR peer review, Los Alamos National Laboratory Report, LA-12240, March [11] G.R. Smolik, B.J. Merrill, R.S. Wallace, Implications of beryllium steam interactions in fusion, Fifth International Conference on Fusion Reactor Material, Clearwater, FL, November [12] G.R. Smolik, B.J. Merrill, R.S. Wallace, Reaction of porous beryllium in steam, Idaho National Engineering and Environmental Laboratory Report, EGG-FSP-10346, July [13] R.A. Anderl, et al., Steam chemical reactivity for annealed irradiated beryllium, J. Nucl. Mater (1998) [14] R.C. Weast, CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, [15] G.R. Smolik et al., Evaluation of graphite/steam interactions for ITER, Idaho National Engineering and Environmental Laboratory Report, EGG-FSP-9154, September [16] G.R. Smolik, Tungsten alloy oxidation behavior in air and steam, Idaho National Engineering and Environmental Laboratory Report, EGG-FSP-10116, March [17] S.H. Keenen, F.G. Keyes, P.G.I. Hill, S.G. Moore, Steam Tables, Wiley, New York, [18] G.J. Van Wylen, R.E. Sonntag, Fundamentals of Classical Thermodynamics, Wiley, New York, 1965, p [19] G.J. Van Wylen, R.E. Sonntag, Fundamentals of Classical Thermodynamics, Wiley, New York, 1965, p. 337.

9 B.J. Merrill et al. / Fusion Engineering and Design (2000) [20] J.C. Chen, A correlation for boiling heat transfer to saturated fluids in convective flow, ASME Paper, no. 63-HT-34. [21] L. Biasi, et al., Studies on burnout, part 3, Energia Nucleare 14 (9) (1967) [22] Y. Hsu, R.W. Graham, Transport Processes in Boiling and Two-Phase Systems, Hemisphere, Washington, 1976, p. 82. [23] W.M. Rohsenow, H.Y. Choi, Heat, Mass and Momentum Transfer, Prentice-Hall, Englewood Cliffs, NJ, 1961, p [24] N. Zuber, On the stability of boiling heat transfer, Trans. ASME 80 (1958) 711. [25] W.C. Reynolds, Thermodynamic properties in SI, Department of Mechanical Engineering, Stanford University Report, Stanford, [26] N.B. Wood, A simple method for the calculation of turbulent deposition to smooth and rough surfaces, J. Aerosol Sci. 12 (2) (1981) [27] M.B. Ranade, Adhesion and removal of fine particles on surfaces, Aerosol Sci. Technol. 7 (1987) [28] J.R. Welty, C.E. Wicks, R.E. Wilson, Fundamentals of Momentum Heat and Mass Transfer, Wiley, New York, 1969, p [29] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, third ed., Hemisphere, Washington, DC, 1992, pp [30] K.E. Washington, et al., Reference manual for the CON- TAIN 1.1 code for containment severe accident analysis, NUREG/CR-5715, USNRC Report, Sandia National Laboratory, May [31] A.T. Modak, Radiation from products of combustion, Fire Res. 1 (1979) [32] Technical basis for the ITER final design report, cost review and safety analysis (FDR), ITER EDA Series No. 16, IAEA Report, Chap. IV, December 1998, pp [33] K.E. Carlson, P.A. Roth, V.H. Ransom, ATHENA code manual, vol. 1 and 2, EGG-RTH-7397, Idaho National Engineering Laboratory, September [34] L.N. Tolpilski, et al., Validation and verification of ITER safety computer codes, 17th IEEE Symposium on Fusion Energy, San Diego, CA, September