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Technical Evaluation Rept INEEL/EXT-97-00779, Potential for AP600 In-Vessel Retention Thought Ex-Vessel Flooding
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Issue date:	12/31/1997
From:	Allison C, Knudson D, Rempe J; IDAHO NATIONAL ENGINEERING & ENVIRONMENTAL LABORATORY
To:	; NRC (Affiliation Not Assigned)
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	CON-FIN-L-2508 INEEL-EXT-97, INEEL-EXT-97-00, INEEL-EXT-97-00779, INEEL-EXT-97-779, NUDOCS 9803050237
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INEEUEXT-97-00779 l

December 1997 ii Idaho National Engineering Potential for AP600 in-Vessel

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Retention through Ex-Vessel

Flooding Technical Evaluation Report i

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J. L. Rempe D.L.Knudson C. M. Allison G. L. Thinnes C.L.Atwood l M. J. Cebull 1 4

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INEEUEXT 9740779 Potential for AP600 In-Vessel Retention through Ex-Vessel Flooding 4

Technical Evaluation Report i

J. L. Rempo D.L.Knudson 4

C. M. Allison

G. L. Thinnes

C.L.Atwood

. M. J. Cebull Published December 1997

) idaho National Engineering and Environmental Laboratory Nuclear Risk Management Technologies Dapartment Lockheed Martin Idaho Technologies Company Idaho Folls, Idaho 83415

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Prepared for the Division of Systems Safety and Analysis Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission

, Washington, D.C. 20555 Under DOE Idaho Operations Office Contract DE-AC07-941D13223 Job Code No. L2508

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Lontents Figures ...... ... ... ........................ ....................................................................................v-4 Tables .......... ............ ....................................................................................vil 1.- Introduction............................................................................................................................1-1 4 ,

1.1 Review of UCS B Study and M odel ..................................................... ...................... 1 - 1 1.2 Review of UCSB Study Peer Reviewer Comments . .................................................. 1-4 1.3 IndependentINEEL Assessments. .....................................................1-6

2. Methodology . .. ... .... . . .. .... .. . ..... . . .. ... ... .... . ... . . . . .. .. . .. ... . .. ... .. .. . .. . ... . . ... .. .. .. . .. ; .....................2I 2.1 Debri s Con fi gurations ....... ... .. ................................... .. ................................ ;21 2.2 : M ode l De sc ription . .... ... ... . . .. .. .. .. . . .. .. ... ... ... .... . . ... .... .. . ... .. . .. .. . .. .... . ... .. . .. . ... . .. . 2-5 2.3 Input Parameters and Uncertainty Distributions.......................................................... 2 7 2.4 Se nsitivity Studie s ..................... ....... ................................................... ..... . ................ 2-9

3. Results......................................................................................................................................3-1 3.1 Verification Calculation Results ........................................... .......................3-1 i-3.2 INi'EL Requantification of UCSB-assumed FIBS........................................ ............. 3-3 3.3 Altemate Debris Coufigurations ................................................................................, 3 10

4. CoDCIusions.............................................................................................................................4-I

5. References..............................................................................................................................5-1 Appendix A. VESTA Goveming Equations and Nomenclature ....................................... ................... A 1 A.1 VESTA Goveming Equation s ......... ........... ... ...... .. .......................... ....... .... . ............ .. A 2 A.2 - No me nclature . .. ..... . ......... ..... ............. .... .. .. . . . .. .. .... ... .. . ... . .... .. . ..... -. ... ... . . .. .. .. . .. . . .. . .. . .. . A- 1 3 Appendix B INEEL Input Uncertainty Distributions........................ .......................,.............B-1 B.1 Heat Transfer Assumptions .................................... ................................... ... .. .... ..........B- 1 B.2 Decay Heat Assumptions ...................................... .....................................................B B.3_ Mterial Property Assumptions .... ..............................................................................B-22

- Appendi x C - Li sting of Input ....... .............. .........................................................................................C- 1

' Appendix D - Benchmark Calculation Results......................... ........................................................... D-1 iii INEEL XT-97-00779

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INEEUEXT-974)0779 SV

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Figures 1 1. 1 UCSB strategy for demonstrating the effectiveness of AP600 IVR. .................... ...........1-2 e 21. UCSB assumed FIBS debris configuration..................................................... .................. 2 2 ' !

- 2 2. Altemate debris configurations evaluated by INEEL ......................................... ....... ... 2 3-2 3. _ -Impact of boiling on heat transfer frorr. a molten pool. ............... ................................... 2 10

31. UCSB (DOE /ID 10460) and VESTA (INEEL verification) heat fluxes assuming ~-

- UCSB FIBS and input distributions. .................................................................................. 3-2 3 2. :

UCSB (DOE /ID-10460) and VESTA (INEEL verincation) CHF ratio pdfs assuming UCSB FIB S and input distributions. .................................................................................. 3 2

- 3 3. _ Comparison of heat fluxes for UCSB-assumed FIBS........................................................ 3-4 3-4. Comparison of CHF ratios for UCSB assumed FIBS. ...................................................... 3-4 3-5. CHF ratio pdfs for UCSB assumed FIBS using INEEL input distributions...................... 3 5 3-6. CHF ratios assuming increased upward ceramic pool heat losses for UCSB FIBS. ......... 3-6 3-7. CHF ratio pdfs assuming increased upward cerarnic pool heat losses for UCSB FIBS.... 3-7 z3 8, CHF ratios assuming additional metallic layer heat source for UCSB FIBS. .................. 3-8 3-9.- CHF ratio pdfs assuming additiaal metallic layer heat source for UCSB FIBS.............. 3-8 3-10. CHF ratios assuming v6rious metallic layer steel masses for UCSB FIBS. ..... ................ 3-9 3 11.: CHF ratio pdfs assuming a 19,500 kg metallic layer steel mass for UCSB FIBS........... 3 10 3 12. Heat fluxe s for Configuration A. ....................... ............................................................. 3 12 3 13. CHF ratios for Configuration A. ................................................... ........................... ..... 3 12 3 14. - CHF ratio pdfs in the ceramic layer for Configuration A (4,187 kg steel mass). ............ 3-13 3-15. CHF ratio pdfs in the metallic layer for Configuration A (4,187 kg steel mass)............. 313 3 16. Heat fluxes predicted for Configuration B. ................................................ .............. ..... 3-15 3 17. CHF ratios predicted for Configuratan B....................................................................... 3 15 3 18. CHF ratio pdfs in the ceramic layers for Configuration B........ ...................... ............. 3-16 3 19. CHF ratio pdfs in the metallic layer for Configuration B. ............................................... 3-16 3 20. - Heat fluxes for Configuration C. ... ........... ............. ..................................................... 3- 18 3 21. CHF ratios for Configuration C. ........................................ ............................................, 3- 18 3 22. CHF ratio pdfs in the ceramic layer for Configuration C. ........................................ ...... 3-19 e 3-23. CHF ratio pdfs in the metallic layet for Configuration C. ....................... ................... . 3-19 t

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4 Tables l-1. UCSB Peer Reviewer comments requiring additional consideration. ........ .................... .1 5 j

2-1. Relocation masses predicted in Reference 3 SCDAP/RELAPS AP600 analysis ............. 2 3

2 2. Comparison of INEEL and iJCSE input assumptions. ............ ............................28

. 23. Sensitivity calculations pedormed to address phenomenological uncertainties,............... 2 9-

41. ERVC impact on Westingh Juse AP600 risk estimates. ..................................................... 4-4 1

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Yil INEEl/ EXT-97-00779

INEEIRXT.97-00779 VS

1. Introduction External reactor vessel cooling (ERVC) is a new severe accident management strategy that involves flooding the reactor cavity to submerge the reactor vessel in an attempt to cool core debris that has relocated to the vessel lower head. Advanced and existing light water reactors (LWRs) are considering ERVC as an accident management strategy for in vessel retention (IVR) of relocated debris, in the probabilistic risk assessment (PRA) for the AP600 design 1 Westinghouse credits ERVC for preventing ,

vessel failure during postulated severe accidents with successful reactor coolar.: system (RCS)

, depressurization and reactor cavity flooding. To support A Westinghouse position on IVR, the

> Department of Energy (DOE) contracted the University of Cal:f e4. Santa Barbara (UCSB) to produce

. the peer-reviewed report, DOE /ID-10460.2 To assist in the Nuclear Regulatory Commission's (NRC's) evaluation of IVR of core melt by ex-vessel flooding of the AP600, the Idaho National Engineering and Environmental Laboratory (INEEL) was tasked to perform the following:

An in-depth critical review of the UCSB study and the model that UCSB used to assess ERVC effectiveness.

An in-depth review of the UCSB study peer review comments and of UCSB's resolution method to identify areas where technical concems weren't addressed.

= /.n independent analysis effort to investigate the impact of residual concerns on the margins to failure and conclusions presented in the UCSB study.

His Technical Evaluation Report (TER) summarizes results from thase tasks. As discussed in Sections 1,1 and 1.2. INEEL's review of the UCSB study and peer reviewer comments suggested that additional analysis was needed to assess: (1) the integral impact of peer reviewer-suggested changes to input assumptions and uncertainties and (2) the challenge present by othe. credible debris configurations.

NRC tasked INEEL to perform an independent assessment to address this need. Section 1.3 summarizes the corresponding analysis approach developed by INEEL. De remainder of this report provides more detailed descriptions ofINEEL's analysis methodology, input assumptions, and results.

1.1 Review of UCSB Study and Model As noted in Reference 2, the objective of the UCSB study was to demonstrate the effectiveness of ERVC for an AP600-like design and to provide a readily adaptable path for demonstrating ERVC for other reactor designs. Figure 1-1 illustrates the UCSB approach for demonstrating AP600 vessel integrity for cases with complete RCS depressurization and ERYC. As indicated in this figure, the UCSB study attempts to demonstrate vessel integrity by proving two assertions:

Assertion 1: For all heat fluxes at or below the critical heat flux (CHF), the corresponding minimum vessel wall thicknesses are sufficient that the vessel remains intact.

Assertion 2: Heat fluxes from relocated melt to the lower head always remain below the CHF.

The above assertions assume that vessel heat fluxes exceeding CHF lead to vessel failure. Sections 3 and 4 of the UCSB report contend that the " boiling crisis is a sufficient condition for lower head failure," noting that once vessel heat fluxes reach CHF,"... vessel temperatures rise to values where the steel loses essen-tially all of its suength, and it becomes susceptible to creep, and structural instability..."

1-1 INEEUEXT 97-00779

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CHF Heat Fluxes ULPU data are appropriate w/o any1:ncertainty

No wall thickness efects .!

No surfsos degradation .

effects No counter current flow ,

oNects Madnum enoweWe heet sunse !

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f 1r 1r AssumDtions .. es o. . s-

- Material gc-; =:: - The two selected configurations i- -

Inner / outer vessel are bounding temperatures - Material proporties and uncertainties Stratified Laver Confinuration

%, - Oxidation of 26rosioy i

m . Debris decay heat / relocation time Heat flux distribution in ceramic pool

- Unoortainty gc-;- ; ^!_- s techrdques ir .- Radiation sink temperature Heat transfer from metallic pool i Annumtens Steady state configuration bounds

- Material properties and tranMloads uncertainties

- Time peM ofinternet Jet Imninnement Conflauration t- - Negligible end effects - Melt n ass

, Negligible radial stresses - Jet diameter p Possible failure modes L

- 161 melt Wture

- Negligible FCl-induced pressure rises struannel An*4*** **""*'

AneYew e nnewes ir 1r-Aasertion1 Assertion 2 i #

j~ The vessel remains Heat fluxes to intact if host fluxes are the vessel are .

at or below the CHF. below the CHF.-

i 1r Conclusion i '

Depressurtred b vesselwith ex vessel -

L cooling remains intact.

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, - Figure 1 1.' UCSB strategy for demonstrating the effectiveness of AP600 IVR.

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a Y ne UCSB study relied on various types _of information (analyses, experiments, and assumptions) to n L support each assenion. Starting at the top of Figure 1 1, the UCSB study applied CHF data from the UCSB -

ULPU tests to estimate a minimum vessel thickness for the structural analyses and provide bounding heat?

L . fluxes for the thermal analyses. For the minimum vessel wall thicknesses, structural calculations 4 I demonstrated that the vessel remains intact if heat fluxes are at or below values assumed for CHF -

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_(Assenion 1). Dermal analyses aNi data from UCSB sponsored experiments provided a basis for i estimating maximum possible heat fluxes for two debris configurations that were assumed to " bound" the thermal loads from all other debris configurathos that can " reasonably be expected". One configuration - ;j 1

was dominated by transient forced convectioni.J jet impingement effects, and the other was dominated l by natural convection in the final steady state, their postulated " Final Bounding State" or." FIBS". l e Analyses described in the UCSB report suggested that vessel failure would not occur due to jet i impingement and that thermal loads to the vessel for their assumed FIBS were more challenging. De

[ UCSB study found that heat fluxes (and associated uncenainties) for their FIBS were below values

} assumed for CHF (Assenion 2). Hence, the UCSB study concluded in Section 9 that " thermally-induced -

failure of an externally flooded, AP600-like reactor vessel is physically unreasonable." he UCSB study claimed that peer reviewer concurrence validated assumptions supporting their assertions. INEEL's review i - indicates that some peer reviewers did not concur with several UCSB analysis assumptions. Section 1.2 4

identifies key UCSB peer reviewer comments and the manner in which the, UCSB study addressed these comments.

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De INEEL review effort focussed on assessing the impact of residual uncenainties that were not considered in the UCSB study's integral solution. INEEL considered modeling assumptions, input values, uncertainty distributions, and experimental data peninent to the following aspects of the UCSB analyses:

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= Molten pool heat transfer (average and local values);

+ CHF estimates forheat transfer from a reactor vessel to a flooded reactor cavity;

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Molten metallayer heat transfer; I

Decay heat;

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Decay power split between ceramic and metallic melts;

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Heat addition due to oxidation and activation of metallic layer materials;

Melt progression (relocation timing, structural mass becoming molten);

Material propenies (melting temperatures, thermal conde:tivity, density, specific heat capacity, emissivity);

Structuralcalculations;

= Radiative heat transfer assumptions; ,

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* " Bounding" debris cocfiguration assumptions.

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. Tb quantify uncertainties in UCSB study conclusions,INEEL considered other nlevant experimental L ' data and severe accident analysis code calculations. For example, SCDAP/RELAP5,3 MELCOR,4 and 5

MAAP A?600 calculation resuhs were used to assess results presented. INEEL in the'also UCSB y6.

1- considered recent studies performed by the University of California - Los Angeles and the Royal Institute of Technology in Stockholm, Sweden.s As parc of their review, INEEL prepared questions for L Westinghouse; these questions were transmitted by NRC to Westinghouse as Requests for Additional-

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Information (RAls)?ll INEEL's evaluation -incorprated Westinghouse's responses to these questions.12,13 In addition,INEEL considered comments from the NRC Office of Research.34 Section 2.3 4

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summarizes k'ey fu.2.g. from INEEL's review of input values and uncertainty distributions assumed by UCSB. Appen' dix B provides more detailed information about INEEL's review.

l 1.2 Review of UCSB Study Peer Reviewer Comments .

Seventeen intemational " experts" reviewed selected sectio s of the UCSB study. Comments from these reviewers and the manner in which the UCSB authors addressed these comrnents are included as UCSB study sppendices. LNEEL reviewed these comments to determine if significant issues were adequately addressed. INEEL concluded that the UCSB study doesn't fully address many peer review comments.

l INEEL identified peer r: view comments that collectively hr.ve the potential to impact vessel 4

response and as such are considered outstanding items based on infonnation in DOE /ID-10460 Appendices O, P, S, T, U and V and responses to RAls. Table 1 1 summarizes these issues, the peer

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reviewers mentioning the issue, the approach taken in the UCSB study for resolution, and INEEL's )

approach for resolution. In some cases, INEEL judged that a peer reviewer comment about an issue j significantly impacting vessel response wasn't adequately addressed, although the peer reviewer may not !

have noted that the comment was an outstanding item in Appendix V. In other cases, INEEL may agree l with the reviewer that the comment wasn't adequately addressed, but INEEL omitted the comment from Table 1-1 because INEELjudged that the issue did not significantly impact vessel response, j l

As indicated in Table 1-1, INEEL found that the UCSB study typically addressed comments by l performing a sensitivity study where only one particular parameter was varied from i's base case value by l itself or with a limited number of other parameters. These sensitivity studies typically involved point ;

estimate calculations rather th'm requantification of input for their integral analysis. Although UCSB's response provides insights about the impact of a change in the varied parameter, their sensitivity calculations didn't reveal integral effects of the changes suggested by peer reviewers. Because integral effects may significantly impact estimated sessel failure margins,IhEEL developed a calculational t

model that could be used to independently address peer reviewer comments regarding input parameter uncertainty distributions in an integral manner (see Section 1.3).

Another key area identified in Table 11 is that the UCSB study dismissed the potential for the occurrence of other, more challenging, debris configurations. For example, several peer reviewers (Olander, Seiler, Sehgal, Tuomisto, and Turland) expressed concem that intermediate configurations were credible and could present more challenging heat loads to the reactor vessel. In addition, one peer reviewer (Schgal) noted in Appendix V that the UCSB authors failed to address comments by himself and other reviewers (Chu, Levy, Olander, and Turland) about the potential formation of a heavier, lower metallic layer. Because such configurations can not be excluded, INEEL evaluated heat loads from several alternate debris configurations.

Additional information about issues that INEEL considers as outstanding items may be found in Section 2.3. Section 3 calculation results demonstrate the impact of these issues on vessel respense.

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Table 1 1. UCSB Peer Reviewer comments requiring additional consideration.

Issue (Paraphrased Reviewer Comments *) UCSB Treatment INEEL Treatment Uncertainty Dutnhutinns Isroader uncer. Provided sensiuvity studies (Secuon 7.3, Used revised input distab9tions for tainty distnbutions for various input App. O. App. P and RAI 480.946 parameters described in Section 2.3 in an parameters (steel melt mass, steel emissiv- response) in which a limited number of independent requanti6 cation.' ,

ity, metal eutectic temperature, decay heat, parameters were varied.

l tircalav caidation fraction, convection heat transfer esfficients, CHF values) should be cor sidered. [Kress-2,3,4.$,b Olander 7,8; Seiler-4,9; and Wrland.

26,30] l Afterriate Dehris Confteurations or Inter- ~Provided sensitivity calculations (App. O, Performed uncertainty calculations for rrwsnte Debrit Staten Several credible App. P, and RAI 480.946 response) several debris configurations and inter-altemate debris con 6gurations or interme- assuming thinner metallic layers and mediate debris states (see Section 't.l.2).

diste states may be more challenging. ,

higher decay heat values. Although heat

[Cheur g.2 Chu-17, levy 9,14,15,32,

iuxes for some cases exceec d CHF, Olander 7,8,9,10; Schgal-$ 6. 28; Seller- concluded that such cases were anlikely 2, Spencer 3; Tuomisto 3; and Wrland- (referencing App.Oinformation).

25,268 ]

Power in the Metalhe Laver The metallic Provided sensitivity calculations (App. P Included appropriate amounts of metallic layer may contain volur.etric heat sources and RAI 480.946 response) assuming layer decay heat in irdepenoent requanti-from oxidation, metallic fission product that the ceramic pool's decay was trans- 6 cation. Also, performed sensitivity smd-retention, or dissolved uranium. [ Levy- ferred to the metallic layer lws considering additional metallic lay 33 Olander 1,3,6; Sehgal-6; and hear sources.

Turland-6 21)

Emin8vity of Metallic frer Assumed Performed sensitivity calculations (Sec. Used an emissivity input uncer'ainty dis-emissivity from the metallic layer was too tion 7.3, App P. and RAI 4*0.946 tribution based on unoxidized molten high. [Kress-16 and Seiler-8] response)in which emissivity was varied metal emissivity data in an independent with other selected inputs. requantincation.

Critient Heat Flui question applicabihty Asserted that CHF assumpions were Used SBLB-based CHF valuIand of ULPU data and impact of various pre- appropriate because ULPU fouling simu. uncertainty distributions in an indepen-nomena (insulation effects, surface fost- lates AP600reactorcavity condition:, dent requantification. When SBLB tests ing, uncertainty) on CHF. (Cheung- insulation didn't affect ULPU resuhs, and with insulation are completed, additional 4.5,6,7; Chi.-2,9,10,11: Dhir 2,3,4,5,9; assumed " minimum" ULPU values calculations may be needed to assess the Levy-2,3,4,5,6.7,8; Seiler-22; Tuomisto- require no uncertainty assumptions. Pro- impact ofinsulation.

8; and Thrland-30) vided one point estimate assuming 10%

lower vtlues (RAI 480.946 response).

Cavity Floodine 11mg question the impact Contended that AP600 design and proce- Assumed CHF values corresponding to of partially 6ooded cavities (less subcool. dure changes ensere that cavity Cooding earlier molten pool formation times pre-ing because of reduced gravity head). occurs prior to the ame that the) cheve a dicted by severe accident analysis codes

[14vy-12, Seiler 22, and Shewmon 1] molten pool occurs in the lower head. In independent requantification.

Decay Heat Izad High decay heat loads Performed sensitivity studies (Section Revised input distributions for decay heat (especially with earlier melt relocations) 7.3. App. P. and RAI 480.946 response) loads and other values described in may occur. [Kress 5,6,7 and Sehgal-4) assuming increased decay heat loads. Section 2.3 in an independent requantifi-cation.

Validity of ACOPO Correlations - Pmto- Responded that prototypic ACOPO tests included heat transfer correlation uncer-tynic Material Effects Prototypic material would only be useful for con 6rmatory tainties in an independent requanti6ca.

test results are needed to confirm the purposes. Performed sensitivity calcula- tion. Also, performed sensitivity applicability of ACOPO data. (Spencer. tions (Section 7.3, App. P. and RAI calculations to address some prototypic 6,8 and Wrland-7,15] 480.946 response) assuming different material effects, but recommended that correlations. prototypic RASPLAV test resuhs be used to resolve this issue.'

l.5 INEE1/ EXT-97-00779

Table 1 1. UCSB Peer Reviewer comments requiring additional consideration. (continued)

Issue (Paraphrased Reviewer Comments') UCSB Treatment INEEL Treatment Vahdity of ACOPO dunne Transient Time Asserted that time penods required for Did not address because additional data Periods Higher heat fluxes may occur at steady state behavior at the boundaries is are needed to specify heat flux distribu.

locations where CHF values are lower dur. much shorter than time periods required tion.

ing transient time periods. [ Levy 16 and for steady state bulk behavior.*nd Schgal-8,28) claimed that ACOPO reults resolved this -

Issue.

. VnMity of ACOPO Cnerelatinnt - Vann' Dismissed comment, contending that Performed sensitivity smdies to assess Trantnort E& cts Vapor from steel of there is no mechanism for entreeping sig- this phenomenon.

other lower boiling point rnaterials would nificant quantifies of steelin the oxidic rise up through oxidic pool nd enhance melt.

heat transfer). iOlander 10,i.evy 10.and Tuomisto.5 and UCSB response to Sch-gal 24)

Venet Watt Matrine Ternnerature Range Asserted assumed melting temperature is Estimated melting temperatures based on of possible cutectic temperatures wasn't cornervative for iron-rich compositions predicted metallic layer compositions in evaluated. [ Levy 17 and Olanderd,9) possible in metallic layer, but included an independent requentification, ser.sitiv-sensitivity studies (App. P) examining ity studies, and analyses of alternate higher tereperature, debris configurations, ceramie PoolI inutam Temneramre O.her Esmissed comment, contending that Assumed correct liquidus temperatures in possible ceramic pool lig'sidus tempera- ceramic poolliquidus temperatures an independent requutifcation, sensi'iv-ture should be considered. [ levy 32 and assumptions aren't important. ity studies, and anatses of alternate Olander.51 debris configurations.

a. Reviewers include: F. B. Cheung (Penn Su : T. Y. Chu (SNL). V. K. Dhir (UCLA). M. Epstein (FAI), R. E. Henry (FAD.T. S.

Kress (ORNL), S. Levy (Levy and Assoc.), F. Mayinger (U. Munich). R. E. Nickell (AST), D. R. Olander (UC4erkeley), R. C.

Schmidt (SNL), B. R. Sehgal (RIT), J. M. Seiler (CEN-0), p. Shewmon (OSU), B. W. Spencer (ANL), H. Tuomisto (IVO), B. D, Turland (AEA) b Designates Comments 2,3,4. and 5 from Reviewer Kress. Comment nurnbenng is consistent with numbenng provided in DOE /ID.

1040 Appendix T.

c. Because INEEL's raview indicated that metallic mass assumpuons should be treated as a discrete function, sensitivity calc ,lations were performed to address the impact of steel melt mass combined with other input parameter uncertainty distribution assumptions,

d. Also, see Turlai.!. s Additional Comment #3 in Appendix V.

c. Although RAsPLAV tests use a nonprototy~c geometry, data can be compared v tih other data from similar geometnes.

1.3 Independent INEEL Assessments In order to independently verify UCSB study results and to assess the impact of additional uncertainties and other debris configurations, INEEL developed the Vessel Statistical Thermal Analysis (VESTA) Code. VESTA is similar to the model used in the UCSB report. However, VESTA was developed in a more general fashion so that it could assess a wider range of conditions.

Section 2 of this report describes VESTA and de types of calculations that were performed with this code. Goveming equations encoded into VESTA and a nomenclature defining variables used in this

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document may be found in Appendix A. Results from VESTA calculations are presented in Section 3.

AppendixC lists input uncertainty distributions assumed for these calculations. Figures comparing VESTA and UCSB model benchmark calculation results may be found in Appendix D. Section 4 presents conclusions about the potential for vessel failure to occur for various debris configurations. Section 4 also discusses the impact of VESTA results on AP600 PRA results. -

INEEL/ EXT-97-00779 1-6

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2. Methodology-After evaluating peer review comments, INEEL concluded that additional study was needed to assess the integral effect of different input uncertainty distribut 8ons and the potential for other, credible

- debris configurations to present note severe challenges to_ vessel integrity, nis section des:ribes several-

' alternate debris configurations having the potewal to challenge vessel integrity, and the INEEL-developed ,

model for assessing the potential for_ vessel failure for these debris configurations. Input values and uncertainty distributions assumed in the UCSB study and in'the INEEL requantification for the UCSB-assumed FIBS are compared, and sensitivity studies to assesc the impact of phenomena significantly 2

c z different than assumptions for this case are identified.

2.1 Debris Configurations i ,

A key assumption in the UCSB_ study is their assumed debris configuration that is supposed to

" bound" thermal loads fram any other configurations that can " reasonably be expectad." INEEL's review i

- suggests that the UCSB FIBS doesn't bound possible thermal challenges from other debris configurations.

His section describes the UCSB FIBS and other possible, more challenging, debris configurations.

2.1.1 - UCSB MB$

> The UCSB I"IBS assumes a troiten ceramic pool lies beneath a metallic layer (Figure 2A). As E discussed in Section 5 of the UCSB study, this configuration assumes that the ceramic pool contains all of

! the oxidic core components (mainly UO2 and Z 0 ). 2 Heat transfer from the pool is governed by turbulent steady-state natural con aion associated with volumetric heat sources. Th molten pool experiences sufficient cooling that it is surrounded by thin crusts that impose uniform tempersture boundary conditions on the melt (i. e., its liquidus temperature), ne metallic layer is assumed to contain all unoxidized metallic components, and is thin compared to its diameter. It is heated from below and cooled from above and its L sides. However, only the side boundary temperature is fixed . at the metallic layer liquidus.

UCSB FIBS calculations invoked several key assumptions that may significantly impact estimated L vessel failure margins. Some key assumptions questioned by INEEL and/or peer reviewers include:

t All the decay heat resides in the ceramic pool;

No additional heat sources (due to oxidation or steel activation) exin in the metallic layer;

De probability _ density function (pdf) for relocated structurt! steel mass (UCSB Figure 7.5).

, applies;

UCSB Mini ACOPO rnoiten pool natural convection correlations apply; -

UCSB ULPU CHF lower bound correlations apply; _

a Emissivity from the raetallic layer may be represented by a point value of 0.45;

Metallic layer liquidus temperature may be represented by a point value of 1600 K;

The pdf for shutdown time applies (UCSB Figure 7.7);

Limited or no uncertainty distributions on heat transfer correlations, material properties, decay L _ heat, and radiation heat sink surface area aie yy.vy W

Density differences allow rapid separation of the ceramic and metallic components.

INEEL calculations presented in this study assess the Imr 1 of modifications to the above assumptions on f' the probability of vesse! heat fluxes exceeding CHF.

2-1 INEEUEXT-97 00779

y 1 > we b j

(' & u ShN r

Boihng to

?

4 l m

water-Med & , , .

o gUprer plenum w !

rector covtty gj structures @ .

w }g y ; 'm dm q . e 3

1 e] : w :g$

% o~

ggg f*

o . .

plenum structures Reactor P'"'W*

- "' k_k Metetc isyer 9)V lm@G(

oxidic crust Boiling 2 oxidepm -

\ water mee reeCtCr c4Vtty Figure 21. UCSB assumed FIBS debris configuration.

2.1.2 Alternate Debria Configurations As indicated in Table 1-1, several peer reviewers noted that the UCSB assumed FIBS is not necessarily the bounding or even the most plausible configuration for the str,.tification of frozen and molten material (see Section 1.2). These concerns were expressed by many peer reviewers in their original Appendix T comments, and several peer reviewers reiterated these concems in their final comments documented in Appendix V of the UCSB report. Figure 2 2 illustrates several possible axisymmetric configurations that may be more challenging than the UCSB-assumed connguration. 'Ihese corfi burations were selected by INEEL based on peer reviewer comments, experimental results, and severc accident code calculation results. Brief descriptions of each configuration are provided below. Section 3.3 and Appendix C provide additional information about INEEL calculations for these configuration.

ConAguration A. Configuration A is similar to the FIBS assumed in the UCSB study, but it is evaluated at an earlier time period, before all of the metallic and ceramic material relocates to the lower head. SCDAP/

RELAP5 calculation results 3provided the basis for the masses assumed to relocate in Configuration A.

Specifically, calculations assumed masses predicted to relocate by 12,047 seconds (see Table 2-1). This configuration is characterized by a large oxidic pool (-50% of the core inventory) with a small metallic component (-3800 kg of unoxidized zircaloy and ~2600 kg of stainless steel). Configuration A developed primarily as a result of a series of localized relocations through the reflector sidewall. The stainless steel component is associated with the melting of gray rods and she addition of lower plenum stmetures that melted as a result of being submerged by the debns. Although SCDADRELAPS results presenied in Table 21 indicate that this configuration will only persist for 13 minutes, this SCDAP/RELAPS analysis assumed that all relocations immedistely fall though perfarations 'n the core plate. If subsequent relocations were to be retained on the core plate, calculations suggest that Configuration A could persist INEEUEXT 97-00779 2-2

7, F , '%

) kD, [

N .y y uww mw b

bW .hQ q h W S we WG. ert vow w sowa.m) y :

f g 4; F, wen crust

.;; A k 3 % w M h

eYr"86)

,: L ~..L.

m *,2,%

v > v- ,.

^

a s

'2;.3 },{ ensenenre,me . ; j. x emnes) 4s c-r . pois > '

'..sW' '&~4,,,

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~

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., Ljg 4 " y l .s q

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Configurat*2n A ConAguraton B B B

'n

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's i@

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- = = ' _';p .n,,,,,

<=e-==

9* q.0;, i QQg%s .- '

Q gg&,; * ~~ ~1 Conngurnoon C -~

Figure 2 2. Altemate debris configurations evaluated by INEEL.

for more than an hour. Hence, this configuration could persist longe.r than the vessel thermal front penetration time (-10 minutes); and it is appropriate to consider Configuration A as a " quasi steady" state.

Table 21. Relocation masses predicted in Reli rence 3 SCDAP/RELAPS AP600 analysis Relocated Mass (kg)

UO2 ZrO2 Zr SS Ag In-Cd 10 970 714$ 807 822 556 11 106 8438 964 863 1342 11232 4559 525 464 157 11 513 10 478 1226 1Cu6 343 11891 956i 11987 60S 12 047 6596 792 638 205 12189 954 12 263 174 12 431 59 12 844 26 788 3278 1733 748 23 INEEIJEXT-97-00779

Because there are no experimental data proving that density differences overcome convective currents, SCDAP/RELAPS doesn't assume that density differences cause rt ett segregation to occur, if one assumes that materials segregate as postulated in the UCSB FIBS,8 the metallic layer would b -10 cm thick, which is well below the threshold of 15 cm given in the UCSB study as the thickness necessary to .

insure vessel integrity under ' focussed' heat Inads. Note that asymmetries could be expected in th, et te region as a result of the break location and the conditions that could develop in the vicinity of other major vessel penetrations. These asymmetries could significantly reduce reflector steel melting and, ultimately,

the thickness of the ' focusing' layer assumed in the UCSB study.

Several peer reviewers (Olander, Sehgal, Seiler, Tuomisto, and Turland) discussed concems about the potential for a Configuration A condition to present more severe challenges to the vessel. The UCSB authors added Appendix 0 to address such concems. However, several peer reviewers still expressed concerns about a thinner metallic layer in their final Appendix V comments. As observed by Peer Reviewer Sehgal "The fear that rome intermediate states may give higher thermalloading on the vesselis not cornpletely alleviated." Likewise, Peer Reviewer Seiler contends in Appendix V that he is still rat convinced that one should rule out an alternate scenario that would result in a thin metal layer due to the overlying steel core plate remelting before the oxidic debris remelts and a portion of the steel draining to fill porosity in the oxidic debris.

Configuration B, Configuration B represents a hypothesized endstate that is based on the same SCDAP/

RELAP5 calculations that formed the basis for Configuration A. At a time after Configuration A develops, SCDAP/RELAPS predicts a final relocation in which an additional 35% of the core materials relocates via a failure of the bottom crust of the in-core pool. These additional core materials are assumed to form a molten pool with an upper surface that submerges part of the lower core support plate. Specific masses assumed for this configuration correspond to masses predicted to have relocated by 12,844 seconds in Table 21. The masses in the initial metallic layer would be heated from below by the molten pool and above by the overlying pool and crust. Metal in this layer would become molten and eventually superheated, possibly resultig in a more severe vessel heat load than that postulated in the UCSB study.

In this configuration, the region of concem is the initial thin metallic layer that s sealed below the additional 35% of materials relocating to form a second molten pool. As in the UCSB assumed FIBS and Configuration A, this configuration assumes that less cense, metallic components have segregated from the ceramic components of the initial pour. As observed by UCSB authors in tneir response to Peer Reviewer Turland's comments in Appendix V, ceramic crusts form upon contact with metals because

" molten ceramic simply cannot exist in contact with a metallic melt." Hence, the metallic layer from the first relocations would be sealed by the upper and lower ceramic crusts. The boiling point for some components of the metallic layer is estimated to be around 3000 K (based on the boiling points of control materials and iron discussed in References 15,16, and 17). Hence, much of the metallic layer will trapped between these crusts, focussing its heat on the vessel wall.

Several peer reviewers (Levy, Sehgal) commented about the potential for multi-layered, intermediate ,

states to present more severe thermal challenges to the vessel. In addition, several analyses pmdicted geometries similar to Configuration B. For example, sensitivity analyses were performed by INEEL in

a. In Appendix O. UCSB authors refute peer review comments about the potential occurrence of a homoge-neous melt by stating, without ofering any evidence, that a ". . slurry consistency is impossible to maintain at these power densities and at macroscopic dimensions..."

INEEIJEXT-97 00779 2-4

- - _. -. - . _ _ - . . _ . - - ----- - - . ~

L which varying amounts of debris quenching was assumed for each of the debris relocations predicted by-

SCDAP/RELAP5 These analyses led to a Configuration B geometry where quenched, particulate ceramic

. debris is beneath and above the ' core ' plate. Calculations predict that the core plate will become molten lapproximately 2 hours2.314815e-5 days 5.555556e-4 hours 3.306878e-6 weeks 7.61e-7 months after it is sandwiched between ceramic debris. The " Lead-in Intermediate State" ,

l-

=

postulated in Appendix 0,of the UCSB study also considers a geometry where ceramic debris is beneath '

and above the core plate, However, the UCSB study postulates that their FIBS occurs because molten _

- _ ceramic debris above the core plate relocates sideways into the lower molten pool and lifts the core plate or

' because heat loads from the ceramic debris melt the core plate and core plate steel rises due to buoyancy i forces. Configuration B considers the heat loads occurring in the metallic layer during the transitional period before the UCSB assumed FIBS <

L CC- A C. Configuration C represents a case where sufficient uranium dissolves into unoxidized -

i' zirconium to form a heavier metallic layer, As in the UCSB-assumed FIBS and Configurations A and B.

this configuration assumes that more dense components have segregated from less dense components.- ,

l However, the metallic layer sinks in this configuration. Heat loads are " focussed" on the bottom of the l ' lower head where heat rejection is a minimum (see CHF values plotted in see Figure B-6).-

I For this analysis, INEEL assumed the same relocation masses assumed for Configuration A.

I However,INEEL assumcd that the metallic layer contained a sufficient amount of relocated uranium to be

heavier than the ceramic layer but remain below 40 wt% uranium. Tnis uranium mass (4291 kg) is less

- thaa half the number of moles of unoxidized zirconium that SCDAP/RELAP5 predicted to relocate during times when intermediate configurations could occur, i

[

[ Several peer reviewers (Chu, Levy, Olander, Sehgal, Turland) commented on the potential for this l configuration to occur. In- Appendix 0, the authors dismissed this configuration as "a non-confirmed ;

~

hypothesis..." However, a convincing probability argument against' this confi j experimental data refuting several sources of data l8 supporthg or calculations U Zr formatio illustrating that forces associated with turbulent natural convection overcome gravity forces that allow

melt stratification because of density differences.

l_

[ 2.2 Model Description

< In order to independently verify UCSB study results and to assess the impact of additional uncertainties and other debris configurations,-INEEL developed the VESTA code. VESTA contains

= equations similar to the equations reported in the UCSB study, However, VESTA was developed in a more general fashion in order to evaluate phenomena and debris configurations not considered in the UCSB

study.

VESTA allows consideration of several debris configurations, including the UCSB-assumed FIBS with a ceramic pool beneath a metallic layer (see Figure 21) and selected attemate debris configurations (see Figure 2 2). VESTA and the UCSB model include the following heat transfer processes:

senady- state turbulent natural convection within a volumetrically-heated (by decay heat), molten

' ceramic pool; 1 . * { convection within the metallic layer;

conduction through the ceramic crust surrounding the molten pool, upper plenum structures, and

- the vessel;'

25- INEEUEXT 97-00779 o

, , - , . , , < . . ,m-m.. --~ ,--.-.w .. mv

4 .g

radiation heat transfer from the upper surface of top metallic layers to the inner. surface of the.

~

upper plenum structures and the outer surface of the upper plenum structures to the vessel;

boiling heat transfer from the vesses outer surface ~(through an assumed outer surface temperature-boundary condition).

In both models, vessel wall heat fluxes are compared with critical heat flux correlations. In VESTA, the uncertainty distributions are Bayesian distributions, which are ultimately combined by a Monte Carlo sampling to yield a distribution on the probability of vessel heat fluxes exceeding CHF. Both models-presume that vessel heat Auxes exceeding CHF is a sufficient and necessary condition for vessel failure (see Sections 3 and 4 of the UCSB study). Once the boiling crisis is reached, the bubble density becomes so large that bubbles coalesce, forming a vapor film that blankets the vessel su. face. Although heat transfer

may still occur via conduction and radiation across the vapor film, neither of these two processes is very effective;Hence, heat transfer coefficients would decrease signi6cantly and the temperature of the outer vessel wall would increase to values where the steel essentially loses its strength and becomes susceptible to structuralinstability.

To address peer reviewer comments and INEEL concerns about limitations of the UCSB model, VESTA was developed to allow users to consider the following:

Selected alternate debris configurations (users may select either Configuration A, B, or C);

Decay heat power production associated with actinide and fission product heatmg;

Metallic layer heat sources based on the fraction of actinide or fission product decay heat and/or other heat sources in the metallic material; Material property (density, spec ic heat, viscosity, thermal conductivity, volumetric coefficient of thermal expansion, eutectic temperatures) uncertainties and dependencies on temperature and/or composition; Various metallic layer emissivitv uncertainty distributions; Various decay heat load uncertainty distributions (although VESTA includes a time-dependent decay power curve, the user may specify a decay power uncertainty distribution);

Various metallic layer heat transfer correlation uncertainty distributions (users may specify

constants and a sociated smcertainty parameters for their desired correlations);

7 4

Various molten pool heat transfer correlation uncertainty distributions (users may specify

-constants and associated uncertainty parameters for their desired correlation for estimating _

average and angular dependent heat traasfer coefficients); i

, * -Various CHF correlation uncertainty distr.butions (users may specify constants and associated -

uncertainty pararrieters for their desired CHF correlation);

Input parameter uncertain *ies [ users may designate the type of distribution (normal, log-normal,-

Student's r, uniSrm, user specified, or point estimate) and characteristic uncertainty distribution parameters (median value, standard deviation, degrees of freedom, etc.)).

Many of the capabilities implemented into VESTA were in response to unresolved UCSB peer review comments. For example, one peer reviewer (Olander) observed that the main solution in the UCSB 4

report neglected metallic layer heat sources associated with retained fission products. Furthermore, several

. peer reviewers (Chu, Levy, Olander, Sehgal.1bria..J) observed that there was the potential for uranium to -

dissolve into the metallic layer, creating a more dense layer with actinide decay heating. Appendix R was

- INEEUEXT-97-00779 2-6

added to the UCSB report to respond to Peer Reviewer Olander's comments, and Appendix P'of the UCSB_ - .

study presents results from a point estimate sensitivity study (UCSB Figure P.5) in which fractions of the decay heat are shifted to the metallic layer of their FIBS. Although UCSB authors concur that decay heat isi

. present in the metallic layer, no integral evaluation was performed to assess the impact of this energy shift i^ "

- with other uncertainties in model input parameters or to assess the impact of a heavier metallic layer with

-- intemal heat sources. INEEL developed VESTA in a general fashion so that users may'specify the fraction 1

of uranium tiissolving into the metallic layer, the decay heat associated with fissioa products and actinides, .

- - r.d the fraction of fission product decay heat retained by the metallic layer,

f. Appendix A lists VESTA modeling equations. Appendix B provides details about many of the

! modeling changes incorporated into VESTA. VESTA was verified using information presented in the L UCSB study, Results from these benchmark calculations are presented in Appendix D. l

_ 2.3 Input Paramotefs and Uncertainty Distributions

[ INEEL's review indicates that many of the uncertainty distnbutions assumed in the UCSB FIBS j < analysis should be modified. Many of these modifications may affect the estimated margin to failure for the' UCSB-assumed FIBS and-.other possiule, more challenging debris configurations identified in

. Section 2.1.2. 'Ihis section summarizes INEEL best estimate input uncertainty distn'outions for the UCSB.

E assumed FIBS. 'Ihe details regarding the development of INEEL uncertainty distributions are found in

! Appendix B. Where appropriate, Appendix B provides comparisons between input assumed by UCSB and i INEEL and other data available in the litentrre.

l. - Table 2-2 compares UCSB and INEEL analysis input for the UCSB-assumed FIBS For these

! calculations, both studies assumed the same debris configuration, i.e., a debris bed containing 88,870 kg of

) ceramic material beneath a metallic layer containing 79,600 kg of metallic material. However, other input parameters and uncertainty distributions differed significantly. Significant differences in input used by INEEL include:

Replacing the UCSB Mini-ACOPO (a 1/8th scale facility) molten pool natural convection heat L transfer correlations with correlations that INEEL derived using larger nale, ACOPO (a 1/2 scale

facility) data [ Sections B.l.1 and B.1.2);

i -- Replacing the UCSB ULPU CHF conelation with the Pennsylvania State University (Penn State)

Subscale Boundary Layer Boiling (SBLB) CHF correlations (both the UCSB study and INEEL

! nsumed input for tests without insulation) [Section B.1.3);

Assuming appropriate- uncertainties in heat- transfer conelations and decay power curves -

[ Sections B.! and B.2);

I -

Assuming a metallic layer heat source conesponding to the fraction of fission products residing in

the metalh layer [Section B.2.2); _

t Basing mL relocation times, which affects decay power density, on se' re accident analysis code 4 predictions rather than qualitative analyses [Section B.2.1];

Basing material properties and uncertainties on a wider range of published experimen'tal data o (parucularly, metallic layer emissivity) [Section B.3).

. Sec. tion 3 calculation results illustrate the impact of these input assumptions on the magnitude' and -

' distribution of heat fluxes predicted on the lower head.

4

^

2-7 INEEUEXT-97 00779 N " -

we'y

Table 2 2. domparison of INEEL and UCSB inpm assumptions.

Phenomena UCSB Input for FIBS INEEL Input for UCSB. assumed FIBS Requandficadon Heat Transfer Molten Ceranuc Poolikat Ccmlauons bued on Mmi-ACOPO data.no Correlanons and uncertamues for everage heat transfer bued on Transfer uncertainues. INEEL best-fit of ACOPO data.

Average Upward . UCSB Equanon 5.1I . thT.EL Equation (B-6)

. Average Dompard UCSB Equanon L28 . INEEL Equanon (B 7)

Localued Downmard UCSB Equations 5.30s and 5.30b . UCSB Equanons 5.30s and 5.30b, uncertainues from ACOPO data Cntical Heat Flux from a Ves. Cornlations based on ULPU data (UCSB Correlations and uncertainues based on Cheung SBLB data ses to a nooded Cavtry Equation E.3); no uncenainues. [(RC=3) curve INEEL Figure B 7]-

Mohen Metal byer Heat Correlations based on MELAD data (UCSB Conclations based on MELAD data (UCSB Equations 5 40 and Transfer Equauons 5 40 and 5 41); no uncertainues. $ 41); uncertaintws from MEL AD data.

Decay Power Density Ceranus Pool Statistical cornbinauon of decay power curve Statasucal combinanon of UCSB decay power curve (UCSB (UCSB Figure 7.1), zirconiurn oxidanon Figure 7.I) with ANS $ 1 Standard-recomntaded uncertainty dis-frecuon pdf (UCSB Figure 7.3), and melt tnbuuon. UCSB nrcoruum oxidation fraction pdf(UCSB Figure relocation time pdf(UCSB Figure 7.7). ).3), and 1NEEL recommended sM. of I hour in the UCSB-pro-posed meh relocation time curve (UCSB Figure 7.7). Resulung pdf reduced by rnetallic layer decay heat fraction Metalhc Layer No heat sources in the metallic layer. Tarne. dependent finion product 6 ay power fractions and uncer-taints. sociated with urconium. niobiurn, telluns gmup, and noble rnetals group.

Material Properties Ceranuc Pool and Crust specific Heat Capacity Mass avease UCSB Table 7.1 values; no Mass ave sge UCSB Table 7.1 values; unwrtainnes associated with uncenamnes each component's value and with mass everaging.

Thermal Conducuvity UCSB Table 7.1 values; reduced Composition dependent values; uncensintws from UCSB Appendix L uncertainties Appen&x L Melting Temperature 2973 K; no uncertainues 2830 K; no uncertainties Volutnetnc Coemenent of UCSB Table 7.1 value; reduced Appendix L UCSB Table 7.1 value, uncertainues from UCSB Appendix L.

Expansion uncertainues Density Volurne average UCSB Table 7.1 values; no Volume average UCSB Table 7.1 salues; uncertainties associated uncertaintic: with each compo1ent's value and with volume averagtng.

Metalhc Layer Specific Heat Capacity Mass average UCSB Table 7.1 alues; no Mass average UCSB Table 7.1 values uncertainues associated with uncertainues each component's value and with mass everagmg Thermal Cone . *ivtry UCSB Table 7.1 values; reduced Appendix Composition-dependent values; uncertamnes from UCSB L uncertainuca Appen&x L Volurnetne Coefficient of UCSB Table 7.1 value; reduced Appendtx L Volume aserage UCSB Table 7.1 values; uncertamtie. associated Expansion uncertainues with each component's value and with volume averaging Density volume average UCSB Table 7.1 values; no Volume averste UCSB Table 7.1 values; uncertainties associated uncenainues with each component's value and with volume averaging Emissivtry 045 (UCSB tests); no uncenainties Me&an value of 0.29; standard deviation of 0 04 (based on pub-Itshed data) hsel Wall Thermal Conducuvity point estimWs based on UCSB Figure L.3 Median values and uncertainties based on UCSB Figure L.3.

Upper hl; Not clear Upper wall:412 IW/mK; Lower Wall: 32 V7m2K;no uncertainties tower Wall:32 2 2 W/mK .

Melting Temperature 1600 K; no uncertainties Zr Fe phase &agram; no uncertainues Upper Internal Structures ThermalConducuvtry 30 W/mK; no uncertainties Temperature dependent values; standard deviation of 0.6 W/mK (based on published data)

Emissmty 0.8, no uncenamties Medtan value of 0.85; standard deviation of 0.03 (based on pub-lashed data) 2-8 INEEllEXT-97-00779

?

$5 2.4 : : Sensitivity Studies e

INEEL identified phenomenological uncertainties associated with some parameters that would be better addressed _ by performing sensitivity studies or additional calculations. Table 2 3 summarizes ~

calculations that were completed to addres+ these uncertainties. This. section provides additional information on these phenomena. In addition, this section discusses phenomenological uncertainties that INEEL and NRC deemed aws rquiring additional investigation. ,

3 Table 2-3. Sensitivity calev'stions performed to address phenomenological uncertainties.-

Phenomena Effeet c"W _

4 Vapot transport effects on natural incrossed upward becaosses from Uncertaly analyses assuming a nector of 101acrease convection mohen ceramic pool. In upwerd heet trenefer, Additional metallic layer heat ,,,g;, Uncensinty analysis assuming additional heat in g 9 sources (due to stool activation or metallic layer that encompasses steel structure taidation).

hIw' activation and oxidation Most best " focussed" from metallic Poirt estimates assuming various metallic masses; gy;, g ,,,,

leyer, unconsinty analysis for mass yieldins q/4CHF=1.0 l -2.4.1 Vapor Enhanced Upward Heat Transfer from the Ceramic pool i-If the temperature in the ceramic pool exceeds the boiling temperature of one or more metallic

components, vaporization and pool boiling may occur, enhancing upward heat transfer from the molten L pool Phenomena and/or mechanisms that could result in the presence of lower boiling temperature components in the ceramic pool were identified by several peer reviewers (1.4vy,- Olander, Tuomisto). As

noted in Tuomisto's peer review comments, the question of steel boiling was identified in a March 1994 Grenoble Workshop on "Large Molten Pool Heat Transfer." However, UCSB study authors indicated that the quantities of metallies that they believed would exist in the ceramic pool were too small to impact heat transfer, l_

As observed by Peer Reviewer Olander, the presence of such lower vaporization temperature materials is su d by voids measured in exans .tions of debris from the Three Mile Island Unit 2 (TMI 2) vessel. I Voids were also observed in severe fuel damage tetts, such as the INEL Loss of Fluid Test LP-FP-2 (LOFT LP-FP-2)22 and the SNL Damaged Fuel 4 (DF-4) test.23 (Poros ties of approximately 20% were typically measured in debris specimens.) Using correlations based on experiments performed by Greene, et al.,24 INEEL performed cr.lculatiota to estimate the impact of vapor on heat transfer to the

. side walls.25 As shown in Figure 2 3, Reference 25' calculations indicate that boiling significantly -

17 increases upward heat transfer for pool Rayleigh numbers of interest (1034 < Ra p ' < 10 ).

Peer Reviewer 1.4vy c' ommented that there is the paeential for additional metallies to fall into the molten ceramic pool at later times, citing mechanisms such as melting upper plenum metallic structures. .

Although such transient mechanisms would eventually cease if heat fluxes from the vessel remain below .l CHF, it is possible for this transient state to exist for sufficierit times that it is appropriate to characterize it j as a quasi-steady st ?.e. Hence, INEEL performed a' sensitivity calculation to determine if the enhanced ' _

i E - heat transfer associated with vaporization and pool boiling was sufficient to cause vessel heat fluxes to

~

- exceed CHF. Because of the limited data available for assessing the impact of vapors on heat transfer, .

INEEL assumed a factor of 10 increase in the upward heat transfer correlation for this sensitivity i

l 29- INEE1JEXT 97 00779

, i

, , . , n , . - , ~ .- , . . _ - - .,, . . _.,,n. _ _ - . , ,. . , _ _

l i

?

.. i calculation. 'Ihis factor of 10 bounds she increase in heat transfer shown in Figure 2 3 for void fractions -

, and Rayleigh tiumbers ofinterest.

-10' . , , ,

Void Fraction.e a=0- -

10* . . . . . a = 0.1 -

- . .- a = 0.2 *

... - a = 0.6 10' - -

g , e*** u gsh, ,

10* -

gsN' -

10' 10 ' 1b' 15 1b" 10'8 1b 10" 1b5 10 1b" 105 Rayleiph number -

Figure 2-3. Impact of boiling on heat transfer from a mohen pool.

1 2.4.2 Additional Metallic Layer Heat Sources There is a potential for the metallic layer to contain additional heat sources due to activation of -*

stainless steel and oxidation of materials in the metallic layer. Although there is considerable uncensinty associated with the magnitude of such heat sources, INEEL performed a sensitivity study to investigate the effects of additional metallic layer heat sources.

INEEL performed scoping ORIGEN2 calculations to estimate the magnitude of the additional heat source associated with stainless steel activation.26These calcul:.tions suggest that the isotope of concern is

- Manganese-$6,' which has a 2.578 hour0.00669 days 0.161 hours 9.556878e-4 weeks 2.19929e-4 months half-life. For time periods of interest (between 2 and 6 hours6.944444e-5 days 0.00167 hours 9.920635e-6 weeks 2.283e-6 months after

-' shutdown) ORIGEN2 calculations suggest that thdent source associated with activation of stainless steel

- may lie between 4 and 8 percent of the core's power. At later times (between 6 and 12 hours1.388889e-4 days 0.00333 hours 1.984127e-5 weeks 4.566e-6 months ), the heat source is smaller (between 2 and 4 percent of tk core's power). For a FIBS point estimate ralentadon, this ,

translates into the me:allic layer heat source being increased from approximately 17% to a maximum of 25% of the core's power. It should be noted that these calculations are scoping. There was considerable uncertain:y associated with several input assuinptions,'such as the flux distribution, the composition of .

-SS304, and activation libraries for ORIGEN2.

Peer Reviewer Olander observed that there is also the potential for heat sources associated with -

^

oxidation of materials in the metallic layer. Using equations in Reference 27, INEEL performed scoping.-

- calculations to bound the energy released 60m oxidation. For a steam environment, these calculations -

2-10 INEEUEXT-97-00779

, q - w - e- < - ~

m-, - ,

i p indicate that il MW will be released during the first few seconds of oxidation. In cases where the upper

'=

surface ~ of the ' metallic layer isn't disturbed by turbulent convection or addi:ional structurd material,

(calculations indicate that within fairly short time periods (< 5 minutes), the oxidation energy rapidly '

i decreases to less than 1% of the melten pool's decay heat; Although higher amounts of en;rgy (~ $ MW)

~

may be' released when zirconium or stainless steel reacts with air, it isn't clear that there will be a continuous source of air into the reactor vessel. Hence, INEEL considers that the metallic layer hest source -

assumed in this sensitivity case bounds the energy addition associated with metallic layer oxidation.- ;

- 2.4.3. Reduood Metallic Melt Mass l' INEEL's review indicates that a key assumption for the UCSS assumed FIBS is the mass of L relocated vessel intemal structures (reflector, core barrel, core plate, etc.) in the metallic layer. Because

- this layer has a higher thermal conductivity, the mass of metals assumed in the metallic layer significantly affects the estimated magnitude of the heat fluxes " focussed" toward the adjacent vessel sidewall. Lerger metallic masses result in lower heat loads to the vessel wall because the heat in the metallic layer is

' dissipated over larger surface areas, f Figure 7.5 of the UCSB report illustrates their assumed pdf for the amount of structural steel that

melts As noted in Section 7 (p. 7 5), the minimum value in this pdf corresponds to all of the core plate ,

! (-25,000 kg), all of the reflector (-40,000 kg), and all of the lower internal structures (-2,000 k2) forming ]

the metallic layer,' In addition, the pdf considers the potential for lower por* ions of the core barrel and l some of tne upper intemal structures to be included in the metallic layer. Seven.1 peer reviewers (Kress, L - Olander, Sehgal, Seiler, Tuomisto, and Turland) specifically auestioned the UCSB pdf for metallic layer ,

mass, observing that th: UCSB-assumed FIBS doesn't neccesarily bound challenges to the vessel wall !

from postulated intermediate states. Several analyses (SCDAP/RELAP5,3 MELCOR,4 MAAP,5 and I expert opinion34) estimate smaller steel masses (-6,000 27,000 kg) than the minimum mass (67,000 kg) i shown in the Figure 7.5 pdf for relocated steel.

l Differences in metallic melt mass assumptions are due to cunent limitaticc., in modeling core melt progression and relocation, uncertainties inherent in code calculations, and differences in opinion about j how melt progression would proceed in the AP600. Many severe' accident analysis codes contain models that allow localized reflector and/or cose plate failure. 'Ihese models were developed based on pst-accident examinations of materialin the TMI-2 vessel. 'Ihe UCSB study provides qualitative arguments as a basis for assuming that the massive steel reflector and core plate delay relocation of ceramic material,

= and therefore, that it is not possible to get substantial relocation of ceramic material without including the mass of the core plate and the reflector. However, the UCSB study doesn't provide any data or detailed, transient thermal hydraulic analyses to substantiate their AP600 melt progression assumptions. ,

1 The large impact that steel melt mass has on analysis resub (see Section 7 of the UCSB report) suggests that a single pdf that considers the entire range of postulated melt masses possible et various times in the transient would not yield meaningful results. Hence, INEEL performed a series of VESTA point

'estimau colculations in which the metallic mass assumed for the UCSB-assumed FIBS was reduced until

. - vessel heat fluxes were predicted to equal CHF. For the case in which the assumed metallic mass resulted

, n. Steel structural mass estimates by UCSB and INEEL differ. INEEL estimated that the core plate mass is 21,000 kg. the reflector is 52,000 kg, and the lower iriternal structure 'nass is 2,400 kg.

I 2-11 INEEIJEXT 97-00779 d- - r S. egys- - - , , . . , - - -gs c. - , w-er r 4 w r e-

w us- W-w -- ee=-- 's- # *-'~4-- --

w- - - - - - - < e-w-- i- e-

i l

[ in q"(9)/q"(9)c, = 1.0 at some locations, INEEL applied VESTA to obtain a typical pdf for CHF i j ratios exceeding unity at other locations. !

2.4.4 Additional Uncertainties not Addressed try INEEL Sonettivity Studies .

As discussed above, there were several uncertainties identified by UCS,B study peer reviewers and l' 1 by INEEL as having the potential to affect UCSB study results that were not addressed by additional ;

- INEEL caleu!ations. These uncertainties are discussed belowi i

2.4.4.1 Tranelent Natural Convootion i

j_ _ Heat fluxes to the vessel wall from a_ volumetrically heated ceramic pool with fully developed

steady state natural convection vary with angle (see Section B.I.2) Near the base of the h enisphere, the heat fluxes are consideraMe smaller, approximately 1/10th the average downward flux and near the top .

heat fluxes are larger, nearly twice the average downward heat flux. IAewise, CHF values vary in a [

_ similar manner with angle (see Section B.I.3). Variations in angle between vessel wall heat fluxes from i

the ceramic pool and CHF values result in a minimum margin-to failure near the top of the pool. However,

! a fully developed steady state heat flun profile may not exist at certain tirnes in the molten pool. For j example, there are intermediate states that exist before steady state natural convection is established. If {

upper plenum structures continue to melt into the pool, these intermediate states may contir.ue for

[ ' significant time periods. Several peer mviewers discussed the irnpact of these transient time periodt (Levy,

, Schmidt, and Sehgal), observing that the challenges to the lower head may be more severe at certain -

locations than heat fluxes predicted for the UCSB assumed FIBS. Because heat flux profiles (for heat l transfer nom the pool to the RPV wall) may be flatter before steady state turbulent natural convection is established, it may be possible for vessel heat fluxes at the bottom of the vessel to exceed CHF during such intermediate states. Hot enr. there are little data available for quantifying such transient heat flux profiles.

Hence, no additional calculations were performed to address this plenomena.

l 2.4.4.2 Metallie Layer Natural Convection J

As discussed above, several peer mviewers (14vy, Olander, Schgal, and Turland) noted that there may be volumetric heat sou/ces present in the metallic layer, and thes , heat sources were included in the l

INEEL nquantification, in the UCSB study, heat transfer to the vessel wall due to natural convection

{ within the metallic layer is modeled using heat transfer cornlations for fluids witicut volumetric heat sources. However, conelations considering the presence of volumetric heat sources may t% more _

i appropriate for the metallic layer. Although many o' the natural conve: tion cornlations for pools with volumetric heating were obtained for pools witi Rayleigh numbers similar to values predicted for the

- metallic layer, few tests were performe* with other relevant boundary conditions existing in the metallic layer, e.g., a heated lower suiface and constant sidewall tergrat uss. As discussed in Appendix B (see Section B.1.4), turbulent natural convectica et,ralations developed for pools with volumetric heat sources yield comparable or lower values than heat transfer coefficients predicted with the corniat'ons assumed in - ,

l the UCSB study. Hence, no additional calculations were performed to investigate this phenomena; and the I-UCSb assumed conelations were retained in the INEEL requantification (although INEEL considered E uncenainty associated with these correlations). '

L

^

2 12 INEEUEXT 97 00779

- + - . .- - . . - -

l 2.44.3 Upper Monum Surface Area ne upper mternal structure surface ares defines the surface area to which heat is transferred from the upper surface of metallic layer (see Equations 6.10 and 6.12 of DOF/ID 10460). This area varies with the mass of molten ceramic and metallic material in the molten pool. For the range of core barrel masses suumed to melt in the UCSB study (see page 7 1 of DOE /ID 10460),INEEL calculations indicate that the

. internal surface area of the core barrel may range frcm 26 to 56 m2 ,

In their responus to RAI questions 480.459 and 480.965,8 Westinghouse indicated that a single 4

value was assumed for the upper internal structure surface area above the melt of 75.36 m2 . The I

Westinghouse response to RAI 480.966 includes a limited number of point estimate calculations in which 2

the upper plenum surface area was varied from approximately 40 to 75 m . These point estimate l calcula'Jons indicate that the ratio of q"(9)/q"(9) cur decreased by less tb 10% when the upper intemal )

structure surface area decreased by o":r 45%. Although INEEL believes diat the area assumed for upper intemal structure surface should be decreased h the main solution for the UCSB assumed FIBS, nnsitivity studies indicate that this area did not significantly impact results. Hence, the INEEL requantification assumed 75.36 m2 and no additional calculations were performed to address this uncenainty.

2.4.4.4 Structural Analyses he UCSB study includes several analyses to provide insights about vessel integrity when the vessel i wallis reduced to CHF limited thicknesses:

.

Section 4.1 uses a " basic principles" approach to determine that the vessel must be at least 0.15 mm thick in order to support dead loads (without considering thermal stresses) when the vessel is at full strength.

Section 4.2 applies " basic principles" to determine that the load carrying capacity is govemed by the wall thi:kness under tension, which is considerably larger than 0.15 mm (- 5 mm).

De Section 4 Addendum uses a finite element, elastic perfectly plastic thermal stmetural analysis to provide a more rigorous indication of the ablated section's structural etpacity.

Appendix 0 presents a finite element structural creep analysis for a vessel with an internal prenure of 400 psi to provide additional insights.

De Section 4 structural analyses only consider dead loads and buoyancy forces in a completely depressurized, thin walled hemispherical vessel. De vessel is assumed to have a linear temperature distribution through its thickness, with an outside wall temperature of 400 K and an inside temperature of 1573 K (the liquidus temperature of their assumed iron /zircaloy eutectic composition),

a. The UCSB study did not document what value was assum4 for this surface area. In the response to RAI Question 450.459. Westinghouse indicated that 57.4 m2 was rasumed. However, their response to RAI 2

Question 480.965 indicates that a value of 75.36 m was assumed and cites the dimensions used to estimate this number (a cylinder for the core barrel with inner diameter = 2 m; and height = 5 m topped by a disk with radius = 2 m). Hence. INEEL assumed that there is a typographical error in the Westinghouse response to RAI Question 480.459, 2 13 INEE1/ EXT 97-00779

In their1nitial comments, the UCSB study peer reviewers questioned several aspects of the UCSB l structural analyses. Two peer reviewers requested that additional analyses be performed to investigate ductile tearing at the inside surface of the vessel due to reversed longitudiaal bend" 2. UCSB study authors added the Section 4 Addendum to address these peer review questions. IN6EL's evaluation of final peer -

review final comments in Appendix V indicates that the peer reviewers typically believM that their '

questions on the structural analysis were addressed.

However, INEEL identified the following concems about the UCSB structural analyses:

INEEL observed that the UCSB study neglected the radial stress component in their solution for thermal stresses in a cylinder (Equation 4.1 of DOE /ID 10460). INEEL calculations indicate that this radial stress, calculated clastically, is about 10 MPa, which is considerably less than clastic tangential stresses of around !$00 MPa. Therefore, INEEL calculations confirm that it was appropriate for UCSB to neglect radial stresses.

Section 4 implies that an inner region of the vessel wall remains elastic and is available, with the outer segment in the vessel wall that is in tension and slightly yielded due to thermal stress, for some additional load carrying capacity. Because there is no additienal tensile load carrying capacity in a material that is assumed to be clastic perfectly plastic and previously tension-yielded, INEEL's review indicates that the load capacity margin of the vessel may be less than inferred in the UCSB study.

Although the elastic perfectly plastic thermal stmetural analysis documented in the Addendum to Section 4 gives a good idea of how thermal stress would redistribute and confirms the existence of a vessel wall mner segment that could be called on for longer term dead weight loading capacity, the analysis appears to neglect creep effects and doesn't include details about assumed boundary conditions, mechanical loading, or mechanical nroperties.

The UCSB study lacks a finite element analysis of the ablated region of the vessel in which creep and thermal stresses are simultaneously considered and boundary conditloas, mechanical loads, and mechanical properties are clearly specified.

In summary, more defensible estimates of the vessel's margin could be obtained if the Appendix 0 UCSB model was modified to consider thermal creep stresses and applied to the ablated region of the vessel. Although INEEL's review indicates that the load capacity margin of the vessel is less than inferred in the UCSB study, margins predicted for the vessel for the various structural analyses presented in the UCSB study suggests that no additional structural analyses are needed.

2 14 INEEl> EXT 97 00779

l

3. Results This section presents VESTA calculation results. As shown in this section, VESTA benchmark calculations verify UCSB study results. VESTA results for the UCSB ass imed FIBS with INEEL input demonstrate the impact of uncertainty distribution assumptions. Results from VESTA calculations considering altemate debris configurations identified in Section 2.1.2 indicate that heat fluxes induced by some credible debris configurations may exceed CHF.

3.1 Verification Calculation Results In addition to verifying UCSB study results, benchmark calculations indicate that INEEL correctly irderpreted equations applied in the UCSB analyses and correctly encoded these equations into VESTA.

Results from VESTA wers compared with results presented in DOF1ID 10460 Appendix Q. Appendix D of this document contains a complete set of figures comparing benchmark calculation results. This section summarizes these results.

Input distributions used by INEEL for these benchmark calculations are lista.d in Columns 2 and 3 of Table C 1 in this report. Note that this is INEEL's interpretation of UCSB input based on information in the UCSB study and Westinghouse's responses to RAls The distributions assumed for some input parameters in the UCSB study aren't well documented, and UCSB study results suggest that some of their calculations may have assumed inconsistent FIBS input parameters. For example, the three sets of FIBS results included in the UCSB study differ in venel wall heat fluxes predicted at locations within the metallic layer. [For locations adjacent to the metallic layer, Appendix P (Figure P.5) suggests heat fluxes to the water are 550 W/m2 and that the ratio of q"(0)/q"(0) cur is 0.4; Appendix Q (Figure Q.1) suggests heat fluxes to the water are 500 W/m2, and Section 7 (Figure 7.10) suggests that the median value of the ratio of q"(0)/q"(0) cur is 0.49).

Figure 3 1 compares point estimate vessel wall heat fluxes predicted by VESTA (designated INEEL verification) and the UCSB model (designated DOE /ID 10460), and Figure 3 2 compares CHF pdfs predicted by each model at selected locations along the vessel lower head. Figure 31 indicates that the VESTA and UCSB model predictions differ by less than ten percent at locations adjacent to the ceramic pool (between 0 and -76'*) and by approximately twenty percent at locations adjacent to the metallic layer (greate.r than -76'). However, the CHF ratio pdfs t'nwn in Figure 3 2 appear to match fairly well in both the ceramic and metallic layers. As discussed above, the three sets of FIBS results included in the UCSB study differ in vessel wall heat fluxes predicted at locations near the metallic layer. Hence, differences in Figure 31 heat flux results may be due to undocumented differences in UCSB input assumptions.

a. INEEL calculations indicate that point estimate UCSB assumptions would yield a ceramic pool that has a maximum depth of 1.52 m, which corresponds to an angle of 75.9*.

31 INEE1/ EXT-97 00779

n 800' ,

DOE /ID.10460 i '

700 ........... INEEL . verification - '

,'i 600 ..

..- l .

e 500 i

~m) g ,,, .... .......................

E j 300 f200 ....... .. .........

~

100 0

0 20 40 80 80 100 Angle (degrees) ==

Fl pure 31. UCSB (DOE /ID.10460) and VESTA (INEEL verification) heat fluxes assuming UCSB F13S ar ) input distributions.

60

30' DOE /ID 10460

.----- INEEL . verification 50

u. 40 30 5, 85' g. ,

\ ,

20

/

\

. i o ,

Q. 10 !

j

) '

/ i 0 N '

~-

0.1 0.2 0.3 0.4 0.5 C (8)%(8)

Figure 3-2. UCSB (DOE /ID-10460) and VESTA (INEEL-verification) CHF ratio pdfs assuming UCSB FIBS and input distributions.

INEEUEXT.97 00779 32

l l

3.2 INEEL Requentification of UCSB assumed FIBS As discust'd in Section 2.3, some peer reviewers questioned several input parameter distributions assumed in the UCSB study. Derefore, the UCSB assumed FIBS was evaluated using INEEL input uncertainty distributions discussed in Section 2.3. (Specific input values used for these benchmark calculations are listed in Columns / anu 5 of Table C 1 of this report). As discussed in this section.

calculations assuming INEEL input parameter distributions confirm that heat fluxes are below CHF for the UCSB assurped FIBS but indicate that the heat flux distribution is significantly different than predicted in the UCSB study. In addition, INEEL performed sensitivity calculations to assess the impact of phenomenological uncertainties associated with input parameters. Sensitivity studies indicate that some phenomenological uncertainties identified in Section 2.4 can significantly reduce margin to failure estimates.

3.2.1 INEEL Input Uncertainty Distributions When the UCSB assumed FIBS is evaluated using INEEL input uncertainty distributions, the distribution of vessel failure margins differs significantly. Figure 3 3 compares point estimate values for vessel heat fluxes predicted assuming INEEL input (the curve labeled INEEL) with the UCSB input (the curve labeled DOE /ID 10460). Vessel heat flux to CHF ratios predicted for these cases are compared in Figure 3 4. CHF ratio pdfs predicted with INEEL input distributions are plotted in Figure 3 5.

As shown in these figures, INEEL input uncertainty distributions significantly affect heat flux predictions. INEEL calculations predict that the margin to failure is smallest at vessel locations adjacent to the metallic layer (above -76.2'). In addition, Figure 3 5 indicates that INEEL input distributione decrease the margin to failure in the metallic layer and broaden uncertainty distributions predicted for CHF ratios.

As shown in Figure 3 5, the pdf for q"(0)/q"(0) cur t 85' a extends from 0.3 to 0.6 and is centered around 0.48. For UCSB input, Figure 3 2 indicates that the pdf for q"(0)/q"(0)cu, at 85' extends from 0.22 to 0.32 and is centered around 0.28.

Differences in results are primarily attributed to differences in assumptions related to metallic layer heat sources, metallic layer emissivity, and CHF correlations. Modeling decay heat sources in the metallic layer and reducing metallic layer emissivity increased vessel heat flux estimates at vessel locations in contact with the metallic layer. Assuming the Cheung SBLB CHF correlations decreased CHF estimates at vessel locations in contact with the metallic layer (see Figure B 7). De net effect of these changes led to increased CHF ratio predictions at vessel locations near and in contact with the metallic layer (at angles greater than -76.2'). Note that the allocation of some decay heat to the metallic layer reduces ceramic pool heat sources and that assuming Cheung SBLB CHF correlations decreases CHF estimates at locations where the vessel is adjacent to the ceramic pool. However, INEEL's assumed increase in decay heat (due to an assumed earlier core relocation time) partially offsets reductions predicted for the heat flux and heat flux ratio at vessel locations adjacent to the ceramic pool. Finally, the pdfs predicted with INEEL's recommended input tend to be less peaked because INEEL input considers uncertainties in many parameters that UCSB calculations assumed as point estimate parameters.

33 INEEUEXT 97 00779

... -- -_. _ . - . _ .-.. - _ _ . . . _ - . - - . - . _ - - - - . - . - - ~ . . . - . .

400

j

> DOEllD 10460

INEEL

beet estimate input ,

700 a

i 6M I 0

500 .

',e' i

. 400 .

300 .

f

/ '

,/

200 ,/

0 0 20 40 60 80 100 Angle (degrees)

Mgure S 3. Comparison of heat fluxes for UCSB assumed FIBS.

0.6 ,

DOE /ID 10400

--- INEEL . boot estimate input 0.5 .

f 0 .4 ',

E -

.t

/,'

{0.3 l

l (T '

O.2 . <

N ,'

% ~~~~..

0.1

[ .

L 0.0 .

0 10 20 30 40 50 60 70 80 90 100 Angle (degrees) l l Mgure 3 4. Comparison of CHF ratios for UCSB assumed MBS.

t l

' INEEUEXT 97-00779 ; 3-4

i 20 i

60' 1

30. O.

is

- 4 ;

, j

[ s,,1 i

l

, fI 1 1I .

1l L 10 .

1 I

'5'

l' 'i l J

[ l 76.2' 8

i' i 1 :

5 g ;

j l'c :

l 0

0

) '! \ 'N 0.2 0.4

\ 0.6 0.8 1 q~, (8)/q'c,(8) = = "

P6gure 34. CHF ratio pdfs for UCSB assumed FIBS using INEEL input distributions.

3.2.2 Sensitivity Studios As discussed above, VESTA predicts that CHF ratios remain below unity when INEEL input

uncensinty distributions are assumed for the UCSB FIBS. However, there are several input parameters for 4

which phenomenological uncensinties precluded input uneenainty distributions from being conclusively i

defined. Section 2.4 identifies sensitivity calculations that were defined to investigate phenomenological uncertainties. This section presents results from these sensitivity calculations. Note that INEEL sensitivity -

. studies look at the integral effect of varying an assumed input parameter distribution or modeling l assumption. In these ca'culations, INEEL input parameter uncenainty distributions for the UCSB FIBS (Columns 4 and 5 in Table C 1 of this document) were assumed except for the parameter (s) or equations that were modified to assess the phenomena ~of interest. Modifications required for each analysis and ,

results from each analysis are discussed below.

3.2.2.1 ' Vapor 4nhatsood Upward Heat Transfer in the Molten Ceramic Pool As discussed in Section 2.4.1, vaporization and boiling of lower vaporization temperature materials.

such as metal structures or control materials, enhance upward heat losses from the molten ceramic pool in the lower head. Although it is recogniaod that nwchanisms introducing lower vaporization temperature metallics into relocated melt are a transient stage, such mechanisms may exist for sufficient time periods that it is appropdate to characterine this transient stage as a quasi steady state (see Section 2.4.1)._ INEEL -

. assessed the impact of enhanced upward heat losses by increasing the upward heat transfer correlation by a ;

factor of 10. Specifically, INEEL increased the median value of the input variable, C6 . to 24.42 (Table C - ;

1 Column 4). '

35 INEEl./ EXT.97-00779 l

_=. -

Results from this analysis are summarized in Figures 3 6 and 3 7. As shown in Figure 3 6, the heat aux from the vessel at locations adjacent to the ceramic pool are reduced signincantly (below -76.2').

Typically, increased upward heat losses decreased downward heat fluxes by a factor of six. Hence, the heat auxes from the vessel at angles below ~76.2' are dominated by the heat flux associated with heat -

generation in the crust surrounding the molten pool. At vessellocations in contact with the metallic layer (at angles above ~76.2'), heat fluxes from the vessel are nearly 63% higher than values estimated for the base case, liigher predicted heat fluxes are due to the increased heat input from the ceramic pool into the metallic layer. Uncertainty calculation results in Figure 3 7 indicate that the probability of vessel heat Auxes exceeding unity is small at locations adjacent to the metallic layer. At an angle of 76.2',

approximately 0.13% of the CIIF ratios at locations exceed unity, or pdf[q"(0)/q"en,(0))d[q"(0)/q"en,(0)) = 0.0013. (31) i llence, the probability of the vessel heat fluxes exceeding CIIF for this case is approximately 0.13%.

1 INEEL best estimate input 0.9 . --- INEEL . increased upward heat transfer 0.8 : -

0.7 -

l c

0.6 .

I l

.$ l E 0.5 I a

') OA >

I 0.3 I i

0.2 l 0.1

% _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ s!

0 20 40 60 80 100 Angle (degrees) "'"'"

Figure 3 6. CIIF ratios assuming increased upward ceramic pool heat losses for UCSB FIBS.

I INEEllEXT.97-00779 3-6

... ~ -

. +

4 .

60 4

1 50' 50

] f 30'

! i i 30 ! .

0' f

20 )

i s N 10 f 0

0 0.2 0.4 0.6 0.8 1 I 9*, '""'"

(8)/ 4*cw (8)

Figure 3-7. CHF ratio pdfs assuming increased upward ceramic pool heat losses for UCSB FIBS.

3.2.2.2 Addhlonal Metallie Layer Heat sources i

As discussed in Section 2.4.2, additional heat sources may be present in the metallic layer because of stainless steel activation. To address the impact of these heat sources, a sensitivity caleviation was performed assuming " upper bound" estimates for stainless steel activation heat sources. Specifically, '

j INEEL assumed an additional heat source in the metallic layer that corresponded to 8% of the core's power at times between 2 and 6 hours6.944444e-5 days 0.00167 hours 9.920635e-6 weeks 2.283e-6 months after shutdown and to 4% of the core's power at times between 6 and 12 hours1.388889e-4 days 0.00333 hours 1.984127e-5 weeks 4.566e-6 months after shutdown (see Section 2.4.2). 'Ihis additional heat source was implemented into a !

VESTA calculation by adding a time-dependent variable to the parameter, fw in the first term of ;

Equation (A Il7). As discussed in Section 2.4.2, this sensitivity study also addresses the impact of additional heat sources associated with oxidation of material in the metallic layer.

Results from this analysis are summarized in Figures 3-8 and 3 9. Additional heat sources only affect metallic layer results. Point estimate calculations for the INEEL requantification of the UCSB assumed FIBS indicate that approximately 17% of the core's power is allocated to the metallic layer. Hence, the metallic layer heat source will be increased up a maximum of 25% of the core's power. As shown in p Figues 3 8, this additional heat source increases heat flux ratios at locations adjacent to the metallic layer by approximately 15%. Comparisons between Figures 3-5 and 3 9 uncertainty distributions indicate that additional heat sources in the metallic layer broaden the uncertainty _ distributions for the pdfs in the metallic layer (at angles above ~76.2').

L 37 INEEIJEXT 97 00779 "

i 0.6

INEEL . best estimate input ---- ~~~~

- - - INEEL . additonal rnetallic layer host source i .+

0.5 -

1 -

_ 0.4 -

E :

.5 :

R 0.3 -

a :

,I -

er -

0.2 -

0.1 n,n , , , , , ,,,,,,,,,,,,,,

0 20 40 60 80 100 Angle (degrees)

Figure 3 4. CHF ratios assuming additional metallic layer heat source for UCSB FIBS, 18

O' 50' 16 :

}. \ .

14 :

i e

n l\i l); .

1 Ii \

12 I j { r, iI i

lk i -

10 3 ! I

, i

~

j V\\\

\

\lt. }

8s-ti . 76.2' 6 e t -

E il p(\ /\ I 4 :

; '\

Ii , \t \

2 i- l fk.g s k \ / .~.'s\g

~

5 , ,I ,1, u , , , , i b.

, , i , , , ,

o 0 0.2 0.4 0.6 0.8 1 q',,(6)/q', (6) '

Figure 3-9. CHF ratio pdfs assuming additional metallic layer heat source for UCSB FIBS.

INEEUEXT 97-00779 38

3.2.2.3 Reduced Metallic Layer Mass ,

For point estimate calculations, the UCSB study apparently assumed that the metallic layer contains approximately 9,600 kg of unoxidized ritcaloy cladding and approximately 70,000 kg of vessel intemal i

structure steel. As discussed in Section 2.4.3, a key assumption for UCSB's FIBS is the mass of vessel intemal structures in the metallic layer. Because steel melt mass assumptions significantly impact analysis results, a single pdf that encompasses the entire range of postulated melt masses possible at various times in the acclJent would not yield meaningful results. Hence, INEEL perfonned a series of VESTA point ,

estimate calculations to determine the mass of relocated stainless steel in the UCSB assumed FIBS that would produce q"(9)/q"(0) cur = 1.0 at some vessellocations. In these calculations,INEEL varied the median value for the steel mass, M .a (Table C 1, Column 4). For the steel mass yielding a CHF ratio of unity, a VESTA uncertainty calculation was performed to determine the associated probability of vessel ,

heat fluxes exceeding CHF at other locations.

Results from these calculations are summarized in Figures 310 and 311. Reductions in the steel relocation mass only affect metallic layer results because ceramic pool heat fluxes are independent of metallic layer mass assumptions. As shown in Figure 310, CHF ratios at vessel locations in contact with the metallic layer approach unity for steel melt masses equal to 19,500 kg. Uncertainty distributions in Figure 311 suggest that this less than a factor of four reduction in steel melt mass (from 70,000 to 19,500 kg) results in non. negligible probabilities of the vest,el heat fluxes exceeding CHF in the metallic layer. For example, at an angle of 85', VESTA results indicate that there is a 52% probability of exceeding CHF (based on Equation (3 1)). Similar to UCSB study results for their MBS, Figure 3 11 shows a double-hump at an angle of 76.2' because input parameter uncertainties result in some trials predicting that this position is in the oxidic pool and other trials predicting that this position is in the metallic layer.

1.6 Metalliclayer Metaniclayer Steel maan (kg) maan (kn) helaht (m) 1.4 .. .* * * ** * *

10,000 19,600 0.25

- 19.500 29,100 0.36 .............. ****

--- 30,000 39,600 0.47 1.2

- - - 70,000 79,600 0.93

$ 1.0

.8 --~~~

{0.s

.E cr 0.6 -

c..._.._..-

0.4 0.2 0.0 0 20 4tl 60 80 100 Angle (degrees)

Figure 310. CHF ratios assuming various metallic layer steel masses for UCSB FIBS.

39 INEEUsXT 97 00779

. i to 0 50' SV \

15, pg ,si , , ;

II *\l.

I li II tl lj.! .

[

10 .

Jt-lt il l-lt.l' l

L il s 76.2*

5 i l lt I. 85' o .s \*

6.lt '

0 0

-i l'i.'k.4 0.2 0 0.6

- f % --

0.8 1.0 1.2 1.4 q",,, (6)/q *e, (6) c ""

Figure 3-11. CHF ratio pdfs assuming a 19,500 kg metallic layer steel mass for UCSB FIBS.

3.3 Alternate Dc6ris Configurations Section 2.1.2 describes three debris configurations having the potential to challenge the integrity of the vessellower head Configuration A represents an intermediate configuration with less metallic material relocating to form a thinner metallic layer than assumed for the UCSB FIBS. Configuration B conesponds to a case where a limited amount of relocated metallic melt is trapped between ceramic materials before the massive amounts of steel structures relocate. Configuration C considers a case where a more dense metallic layer, consisting of uranium dissolved in zirconium, sinks below the oxidic pool. As discussed in Section 2.1.2, these debris configurations were investigated to' address unresolved peer reviewer comments. VESTA was applied to each of these configurations. As discussed in this section, each of these configurations have the potential to produce vessel heat fluxes that exceed CHF.

3.3.1 Configuration A

- As discussed in Section 2.1.2, Configuration A conesponds to an intermediate state where approximately 50% of the core inventory forms a ceramic pool with a small metallic component associated with melting of gray rods and submerged lower plenum structures. As discussed in Section 2.1.2, SCDAP/

RELAPS calculations assuming that melt relocations immediately traveled through core plate perforations predict that this configuration would only persist for 13 minutes. However, calculations assuming that relocations .were retained by the core plate suggest that Configuration A could persist for more than an .

hour. Hence, this configuration could persist longer than the vessel thermal front penetration time

(~ 10 minutes); and it is appropriate to characterin it as a quasi steady stata configuration.

INEE!JEXT.97-00779 3 10

VESTA equations allow this configuration to be analyzed by modifying a select number of input parameters: relocated metallic material mass, relocated ceramic material ma ., oxidation fraction, decay heat, fraction of decay heat produced by actinides, metallic layer emissivity, and CliF correintion coefficients. Specific input values used in this VESTA analysis are listed in Table C 2 of Appendix C.

Metal and ceramic material masses, zirconium oxidation fractions, debris relocation time, and debris decay roduced by actinides) were ba.ed on a SCDAP/RELAP5 AP600 heat assumptions 3DE analysis.3 (power and fra:

Several referencesl32 i tion p# ndicate that the location of relocated control mat known, although experimental data suggest that relocated cadmium would be vaporized, relocated silver would be retained by tirconium, and relocated indium would be split between oxide and mettilie debris.

lience,INEEL performed two Configuration A calculations: a case in which none of the control material was retained in relocated material (simulated with a 0.10 m-) thick metallic layer containing 2,603 kg of steel); and a case in which all control material was retained in the metallic layer (simulated with 0.13 m-thick metallic layer containing 4,187 kg of steel).' Metallic melt emissivity and ClIF correlation coefficients were selected to reflect conditions expected at earlier time periods when intermediate con 0gurations occur. Specifically, the ClIF Cheung (ll/R=2) curve values were selected to correspond to time periods before the reactor cavity becomes fully flooded (see Section B.1.3) and the metallic melt errissivity was lowered to reDect the presence of steam in the reactor vessel (see Section B.3.3)

Configuration A point estimate calculation results are shown in Figures 312 and 313. Depending on control material relocation assumptions, peak heat fluxes in Figure 312 range from 2.5 to 3.5 times larger than predicted for the UCSB assumed FIBS in Figure 3 3. These higher heat Duxes a,e primarily due to the reduced metallic mass in the icwer head, causing heat to be " focussed" on a smaller area of the vessel sidewall. In addition, the reduced metallic layer emissivity and higher decay heats (associated with earlier relocation times) increase metallic layer vesscl heat Dux predicilons. Figure 313 results indicate that the ratio of the vessel heat aux to CIIF values typically range from 1.5 to 10 at vessel locations in contact with the metallic layer (at locations above -59'). This result is primarily due to increased vessel heat Dux predictions. Although CliF values are also slightly reduced for the Cheung (ll/R=2) curve (relative to the 11/R=3) curve, Figure B 7 indicates that Cheung (11/R=2) CIIF values are not significantly different from ULPU ClIF values at locations where the vessel is adjacent to the metallic layer (at beations above ~59').

Plots in Figures 312 and 313 indicate that the increased mass associated with control material in the metallic layer would decrease peak heat fluxes and associated CliF ratios. liowever vessel heat fluxes cxceeded CIIF irrespective of assumptions pertaining to control material location.

Uncertainty calculation results are presented in Figures 314 and 315 for the Configuration A case in which all control materials are assumed to be retained within the metallic layer (a steel mass of 4,187 kg). Figure 3 14 illustrate that Cl!F ratios remain below unity at vessel wall locations adjacent to the ceramic pool.11owever, results presented in Figure 3-15 indicate that the probability of vessel heat Duxes exceeding CIIF at locations where the vessel is in contact with the metallic layer is significant. At an angle of 59', VESTA calculations indicate that appmximately 65% of the CliF ratios predicted are above unity, or that the probability of vessel heat fluxes exceeding CIIF for Configuration A debris conditions is approximately 85% [ based on Equation (31)). It should be noted that the standard deviation for this pdfis much larger at veswl 'ocations in contact with the metallic layer. This is due to the larger uncertainty associated with input r ameters for this configuration.

a. A more exact app ach would have required that control material properties be added to VESTA. Ilow-ever, this approach simulated the effects associated with an increased metallic layer mass.

3-11 INEEUEXT 97-00779

&A- p +--#-^-em- 1 c. - J.M-- +++-n 2-h---e--.wA W- *~-- 2.,L---'L-4M

. a- + - a >-~a,_ 4-d. .

l i

i 2500 ' ,

Sinal mass (kg) Total mass (kg) Height (m) - '

.4187 6021 0.13 ,

2S03 6437 0.10 2000 1500 5 '

1000 500 0

0 20 40 60 80 100 ,

Angle (degrees)

Figure 312. Heat fluxes for Conaguration A.

2.5 Sul mass (kg) Total mass (kg) Heightim) 4187 6021 0.13 2003 6437 0.10 2.0 .

1.5 -

~

.5 k

.Icr 1.0 .

0.5 .

0.0 0 20 40 60 80 100 .

Angle (degrees) ;

Figure 313. CHF ratios for Configuration A.

INEEIAXT 97 00779 3 12

i 30 15'

u. 20

,i

\ 30' [T 4s' i

\

10

\

\ \

0 0 k1- I2 0. 0.4 0.5 o_m <6)

Figure 314. CHF ratio pdfs in the ceramic layer for Configuration A (4,187 kg steel mass).

1.0 i

5 0.8 .

} ,f i r 0.6 .

l 0.4 .

N 0.2 . b [

0.0 --

0 1 2 3 4 q',,, (6)/q*e,, (6) ==

- Figure 315. CHF ratio pdfs in the metallic layer for Configuration A (4,187 kg steel mass).

3 13 INEEUEXT 97 00779 ,

Finally,'it should be noted that VESTA (or UCSB model) heat flux predictions exceeding CHF are beyond the ran'se of applicability for these models. In a detailed transient analysis, heat nuxes in excess of CHF would cause vessel temperature 6 to rise to values where the steel loses its strength, experiencing creep structural instability. Because governing equations in VESTA (and the UCSB model) are limited to cases where heat fluxes are below CHF, heat flux predictions exceeding CHF should merely be viewed as an indicator of the probability of vessel failure.

3.3.2 CortfiguMtion 5 As discussed in Section 2.1.2. Configuration a corresponds to a debris configuration that occurs sometime after Configuration A (which involved approximately $0% of the core), it assumn that an additional 35% of cc,r materials relocate to form a molten pool with an upper surface that submerges part of the lower core support plate. '!he initial 0.13 m-thick metallic layer (containing 8,021 kg) would be heated from below by the molten pool and above by the ovulying pool and crust.

Equations incorporated into VESTA allow this configuration to be analysed by modifying a select

- number of input pa ameter distributions: the mass of n etal as sumed to relocate into each layer, the mass of ceramic materials assumed to relocate into each laya. th6 oxidation fraction of zirconium and uranium in each layer, the decay heat, the amount of decay heat produced by actinides, the metallic layer eminivity, and CHF correlation coefficients. Specific input values used in this VESTA analysis are listed in Table C.

3 of Appendix C. Metal and ceramic material masses, zirconium oxidation fractions, melt relocation time, ons (;:ower and fraction produced by actinides) were based on SCDAP/

and RELAPS debris decay calculation results.heat assupCHF correlation coefficients were selected to ref the earlier time periods when this intermediate configuration occurs. Specifically, the CHF Cheung (H/

R=2) curve values were selected to correspond to time pwiods before the reactor cavity becomes fully flooded (see Section 2.1.2).

Configuration B pht estimate calculation results are shown in Figures 316 and 317, and uncertainty calculation results are shown in Figures 318 and 319. Peak vessel heat fluxes shown in Figure 3 16 occur at locations where the vessel is in contact with the metallic laya and are approximately a factor of 4.5 times larger than predicted for Configuration A (see Figure 312). '!hese higher heat fluxes are primarily due to the combined heat load to this metallic layer from the upper and lower ceramic pools.

Figure 3 17 results indicate that the ratio of the vessel heat flux to CHF values are predicted to typically be approximately 25 at vessel locations adjacent to the metallic layer (at locations above ~$9*). As shown in

. Figure 3 18, VESTA predicts that CHF ratios remain below unity at vessel wall locations adjacent to either cwamic pool. For locations where the vessel is in contact with the metallic layw, results presented in Figure 3 19 indicate that all of the CHF ratios will exceed unity.

Because two-dimensional heat transfer effects might dissipate the focussing effects from the thin layer assumed in Configuration B, INEEL also performed sensHvity calculations in which the mass of the

-. stainless steel was increened. VESTA predicts that even if the stainless : teel mass were increased to the -

mass assumed in the UCSB point estimate FIBS analyses (a 0.93 m thick metallic layer containing

= 70,000 kg of steel), CHF ratios of approximately 3.9 will occur at locations ahere the vessel is in const ,

with the metallic layer.

INEBLAXT 97 00779 3 14 ,

. . - _ . . . .. - - - _- . . .- - - ~ _ - . - _ - -. . _ . - -_ ._.

l l

30000 - ,

26000 t i ;

a 20000.

i E l g 16000-10000 6000.

0 0 20 40 60 80 100 Angle (degrees)

Figure 3-18. Heat Auxes predicted for Configuration B.

30 8

n 20 .

S,

.B h '

i

.I 7

10 t

0 0 .20 40 $0 80 100 a' *"

Angle (degrees)

Figure 317. CHF ratios ' predicted for Configuration B.

3 15 INEEUEXT 97 00779 s ++yr --w---yw----- - - - - - - - --r '- *7 -

y

l i

30

15' /, I f .,

20 45' 30' 10

\

0 O 0.2 0.4 0.6 q*(6Fq*e,.(6) a' ~ '

Figure 318. CHF ratio pdfs in the ceramic layers for Configuration B.

0.20 0.15 l

0.10 0.05 0.00 -

D 5 10 15 20 25 30 35 40 4*.(4F4*c.,(6) a'"'

Figure 319. CHF ratio pdfs in the me'.allic layer for Configuration B. .

INEEIAXT 97 00779 3 16

. . f a

As discussed in Section 3.3.1, VESTA (or UCfB model) heat flax predi:tions exceeding CHF are !

beyond the range of applicability for theu models. In a detailed transiem analysis, heat fluxes in excess of - !

- CHF would ceuse venet temperatures to rise to values where the steel loses its strength, experiencing

creep structural instability. Because governing equations in VESTA (and the UCSB model) are limited to f

cases where heat fluxes ce below CHF, heat flux predictions exceeding CHF should merely be viewed as .

j an indicator of the probability of vnul failure. l L ,

3.3.3 Cortflgutstion C i 4

As d4cuned in Section 2.1.2. Configuration C corresponds to a case where a more dense tretallic l layer, consisting of uranium dinolved in zirconium, has sunk below the oxidic pool. Heat loads from the ,

j lower metallic layer are " focussed" to the bottom of the venel lower head where heat rejection is a ;

j minimum (see CHF values plotted in see Figure B 6). ;

Equations incorporated into VESTA allow this configuration to be analyzed by modifying a select ;

j number of input parameters: the mass of nlocated metal in each layer, the mass of relocated ceramic j

. . materials in each layer, the oxidation fraction of zirconium and uranium in each layer, the decay heat, the

amount of decay heat produced by actinides, the metallic layer emissivity, and CHF correlation- 1 coefficients. Specific (apat values used in this VESTA analysis are listed in Table C 3 of Apper dix C.

Metal and ceramic insterial maswt tirconium oxidation fractions, melt relocation time, and debris decay .

! bat anumptions (power and frar, tion produced by actinides) were based on SCDAP/RELAP$ calculation

tesults.3 CHF correlation coefficients were selected to reflect conditions expected at earlier time periods ?

! when this intermediate configuration occurs. Specifically, the CHF Cheung (H/R=2) curve values were

, selected to correspond to time periods before the reactor cavity becomes fully flooded (see Section 2.1.2).

De uranium oxidation fraction and amount of unoxidized uranium assumed to be present in the lower .

layer were specified by determining the mHmum mass of uranium that would cause the metallic layer to !

l:

4 become more dense, nen, metallic layer constituents won checked to insure that the mass fraction of ,

! uranium remained below tid maximum 40 wt% uranium cited isy Peer Reviewer Olander in his comments.

The 4,291 kg of unoxidized uranium assumed to be dissolved into the metallic layer is less than half the

, number of moles of unoxidized zirconium that SCDAP/REU P5 predicted to relocate during times when

! intermediate configurations could occur, his dissolved uranium mass resulted in a total metallic layer ,

'~

mass of 12,112 kg, which results in a maximum metallic layer height of 0.50 m.

! Configuration C point estimate calculation results are shown in Figures 3 20 and 3 21. As shown in i Figure 3 20, peak vessel heat fluxes occur at locations where the vessel is in contact with the metallic layer :

c (at locations below - 42'). As shown in Figure 3 21, the ratio of the vessel heat flux to CHF values range from 4 to 3 at locations adjacent to the metallic layer (at locations below - 42'), but remain below unity at locations adjacent to the overlying ceramic pool (at locations above - 42'). '!his nauh is due to high heat flutes from the' metallic layer (due to decay heat from finion product and actinides in the metallic layer) and to lower heat rejection rates possible at lower angles (see SBLB CHF values plotted in Figure B 7),

p Configuration C uncertainty calculation maults are shown in Figures 3 22 and 3 23. As shown in Figure 3-22, VESTA predicts that CHF ratios remain below unity at vessel wall locations adjacent to the L ceramic pool. However, results presented in Figun 3 23 indicate that CHF ratios exceed unity at locations when the vessel is in contact with the lower metalhe layer. - ,

i i

3 17 INEEUEXT 97 00779

~ . _ _ . _____..__s_ _ _._.=___

i l

. i 6000 4000 e

1-5 2000 1000 I 20 40 so so 100 Angle (degrees)

. Figure 3 20. Heat fluxes for Con 6guration C.

10 8

E'

,B K

a

') <

t 0

0 20 40 60 80 100 Angle (degrees)

Figure 3-21. CIF ratios for Con 6guration C.

L DGEUEXT 97@779 . 3 18

30 ', ,

e 25 45' Ig

u. 20 60' 15 10 5

1

/ \.. . .

,0 0.1 0.2 0.3 0.4 0.5 q',,, (6)/q *, (6) c=*

Figure 3 22. CHF ratio pois in the ceramic layer for Configuration C.

1.0 0.8 0.6 4

l0.4 O*'

rf(%lc-fi '.

,w" kr 0.0 6 8 10 0 2 4 q',,, (6)/q', (6) en m Figure 3 23. CHF ratio pdfs in the metallic layer for Configuration C.

3 19 - INEEUEXT 97 00779

As discossed in Section 3.3.1, VESTA (ce UCSB model) heat flux predictions exceeding CHF are beyond the rarige of applicability for thew models. In a detailed transient analysis, heat fluxes in excess of CHF would cause vessel temperatureA to rise to values where the steel loses its strength, experiencing creep structural instability. Becauw governing equations in VESTA (and the UCSB model) are limited to cases where heat fluxes are below CHF, heat flux predictions exceeding CHF should merely be viewed as an indicate of the probability of veswl failure.

4 INEEUEXT 97 00779 - b20

1

4. Conclusions Results presented in Section 3 confirm that the vessel will remain intact for tne UCSB. assumed !

FIBS, but suggest ther failure margins are smaller than predicted by UCSB at some vessel locations. ,

Furthermore, Section 3 results demonstrate that a key assumption in the UCSB approach (we Figure 1 1), l that the UCSB assumed FIBS bounds all credible thermal challenges to the vessel wall, isn't val;d. For all alternate debris configurations and for several unsitivity studies analyud in Section 3, INEEL found that 1 the heat load to the vessel could exceed CHF, His uction summarizes sonw of the key findings from i INEEL's review and discusses the impact of these findings on AP600 PRA results. !

4 i UCSB study approach and peer review comments

" sll the assumptions were valid in the UCSB approach, it is logical to make the assertions and ass > s cot.clusion identified in Figure 11. However, INEEL found that several key assumptions invw . s in the UCSB study weren't valid. Specifically, INEEL's review and evaluation determined the 4 following:

The UCSB-assumed FIBS doesn't bound all credible thermal challenges to the vosoel.

Independent INEEL omloulations Indloats that host flunes from the vessel for several alternate debris configurations could exceed CHF.

Independent INEEL coloulations indicate that heel fluxes from the vessel for the UCSB.

assumed FIDS are below CHF. However, the margins to CHF for the UCSS assumed FIBS are overestimated at some locations in the UC85 study for the formwing reasons:

. The preconoe of fission product deoey hea\ In the metallic layer is neglected;

- The deoey heet estimated for the ceramic pool differs from values recom-monded by saleting standards and severe acclient code predictions;

. Some UCSB-assumed material property assumptions amn't suppetted by the existing databooe;

. Uncertainties associated with host transfer corraletions, decay heet, and some material properties are neglooted.

The UCSS study typloally addressed peer reviewer comments by senaltivity studies, but didn't assess integral effects associated with changes ataggested by peer review-erS.

4 INEEL assessed the impact of these and other deficiencies on UCSB study conclusions.

Vessel integrity foi' UCSB assumed FIBS Using the INEEL-developed VESTA code, INEEL performed three types of calculations considering the UCSB assumed FIBS. First, INEEL performed benchmark calculations essuming input parameter uncertainty distributions consistent with values assumed in the UCSB study. Second, INEEL performed calculati(ns assuming revised input parameter distributions that reflected UCSB study peer reviewer and INEEL review comments. Finally, INEEL performed several unsitivity studies to address phenomenological uncertainties associated with several UCSB input assumptions. Dese calculations provided several important insights.

41 IhT.ELEXT 97 00779

Agreement between UCSB and INEEL calculation results when UCSB input distribu.

tions are assumed (soe F6gures 31 and 3 2). This agreement suggests that goveming equations listed in the UCSB study were correctly encoded into both models.

Analysis of the UCSB assumed PIBS with INEEL Input uncertainty distributions (Fig. .

uros 3 3 through 3 5):

- oonfirm UCSB prodletions that the vessel remains intact; .

- Indioste that margine to fallure are smaller than pre &ted by UCSB at some vessel locations; and

. Indloats that ml ' mum margine to failure occur at vessel locations that are in con-tact with the metallic layer (in contrast, the UCSB study prodlots that minimum mar.

gins occur at vessel loostions adjacent to the oeramic pool near the metallic layer and ceramic poolinterface).

Sonettivity calculations indioste that certain phenomenological uncertainties signifl.

cently impact vosoel heat flux estimates. Spoolfloally,

- Increased upward heat fluxes associated with vaporlastion and bolling of lower vaporlastion temperature materials, such as metal structures or control materials, increased vessel heat flux estimates by 83%;

- additional metallic layer heat sources due to etsinless steel activation or oxidation did not significantly impact vessel heat fluxes;

- less than a factor of four doorense in relocated steel mass results in a 52% probabil-

- Ity of the vessel heat fluxos exceeding CHF for the UCSB assumed FIBS.

Vessel Integrity for alternate debris configurations VESTA was applied to consider thermal challenges presented by three altemate debris configurations. Configuration A is an intermediate state, similar to the UCSB assuined FIBS in which less ceramic and less metallic materials have selocated to the lower head. Configuration B is an intermediate state in which the thinner metallic layer evaluated for Configuration A is sandwiched between two ceramic pools. Configuration C considers the impact of unoxidized uranium dissolution into unoxidized tirconium causing the metallic layer to sink beneath the ceramic pool. VESTA analyses of these attemate configurations indicate:

The UCSB assumed FIBS doesn't bound all heat loads. Specifically, vessel heat fluxes associated with all three postulated configurations (Configurations A, B, and C) are pre-dicted to exceed CHF.

The formation of these alternate debris configurations is hypothetical. Additional analyses and experimen-tal data are needed to substantiate w hether such configurations are viable. However, based on the current state of knowledge, these configurations cannot be ruled out.

Imwot of AP600 risk assessment results A straightforward approach for estimating the impact of INEEL calculation results would be to multiply the probability of vesse! failure for each postulated debris configuration by the probabihty of the debris configuration to occur. However, there are insufficient data available to estimate the probability of INEEUEXT 97 00779 42

1 I i

l various proposed debris configurations to occur. Hence, INEEL applied a bounding approach to l l investigate the impact of calculation results on the AP600 risk assessment. This bounding approach l

! attempted to answer tie quotion, i t

i l Whar is the maximwn increase in AP600 plant rid yell cavity)looding scenarios lead to vnselfailure?

4 3

1 In the Westinghouw PRA, the six releau categories summarized in Table 41 are used to estimate ;

plant risk. Representative releans for five of these six releam groups (all twat the BP release category) are j

based on variations of the 3BE accident class in which successful cavity flooding is assumed to preclude j

! vnsel failure. Howeyw, in the CFE and CI release categories, the reduction in source term associated with ;

ERVC is ineffective because other events (hydrogen detonation and failure of containment isolation) cause

! containment failure. ,

In order to bound the maxirnum increase in plant risk associated with ERVC failure, ERVC failure ;

was conservatively assumed to result in vessel and containment failure.' The impact of this conservative ,

assumption was estimated by transfemns the estimated frequency of the IC. CFI, and CFL release groups i in which ERVC prevented vnsel failure to the CFE releau category (see Table 4 1). Because CFE release estimates are band on a 3BE transient in which early vnsel and containment occurs because of severe

accidest phenomena, CFE releases were essumed as a reasonable bound for doses predicted for the ;

remaining release groups, which were also based on 3BE transients. (Cl teleases provided an unrealistic i uppe: bound for the IC, Cfl, and CFL releases because containment isolation failure occurs e.arly in Cl ,

transients). ,

4 Section 49 oi A PRA prewnts two types of 24 and 72 hour8.333333e-4 days 0.02 hours 1.190476e-4 weeks 2.7396e-5 months dow estimates (mean effective 1

committed dow (EDE) and acute whole body dow) that can be used to estimate plant risk. Table 41 summarius PRA estimated 24 hour2.777778e-4 days 0.00667 hours 3.968254e-5 weeks 9.132e-6 months doses and release probabilities for the six release group. As indicated in Table 41, plant risk will increase by a factor of twenty if ERVC is u isuccessful (inespective of the type of oose considered). Table 4-1 indicates that the sum of the pmbabilities of events with releases exceeding 4

25 rem would equal 1.6x10 7 events per reactor year, which is still a factor of 6 below the 1 x10 events oal from the Electric Pown Rewarch Institute Advanced Light

' per reactor year Westinghouse design g?0 Wata Rea~ Requirements Document f

i i

- a. This is a conservative assumption. Howme, as oburved by Watinghouse in their raponw to RAI 720.388, no signincant beneAt is achieved by assuming that the containment doesn't fall at early times . ,

harma there is so much uneenainty associated with ex vessel debris spreading, coolability, and hydrogen ;

generation and combustion.

1=

E 43 INEEUEXT 97-00779 2 . -- . . . . . .-a_._. - - - - - - - . - _ - . - . - . . . . - .

. _ . . - _ . - .- -- .. . - . - - - - - - . - . ~ , _ . . - . . - . . . - - - .

Table 41. ERVC impact on Westinghouse AP600 risk estimates.

Westanghouse AP600 Eaumans Maximum Rist (Assunung Sumsful ERVC) (Assuming Unsucensful ERVC)

Relene Caugwy Mean Mean Done Rak(rem pr Mean Rak (rem pet Fmquency (rom)%an mactw year / Faguency nector parl .

(pr routor- Populauon Ekme person rom per (per reactw. prion-sm pr par) (penon rom) nactos year) year) nactw year)

IC Coniaantnent nowhy maintamd througemt 1.310 07 4.lWL+00/ l.60E.47/ 000E+00 0 00R+00/

the accident; selease of redaauon to the environ. 2.12E+02 4.71E4$ 000E+00 meat is due to nominalleakage.

BP Passa products release from the RC$ to the 1.12D08 2.32E+02/ 2.60E4F l.12E46 2 60D06/

environnwnt via the secondary sysum or other ).720+04 417E 04 417E 04 inwifactng system bypass, containment failwe occurs pnw to onset of core danese Cl Punion product release occurs thrt.,9 e fauwe 3 61E 10 846E+01/ L20E-06/ 161E 10 320E46/

of the system et talves that close the peeetro- 2.05e+06 7.40E44 7 40E44 tions botmoon tenteinment and the environnent; commanment feslure occurs prior to enset c4 core damage.

CPE Fusion prodect release occurs through a con. 6 63E49 3.72E+03/ 3.79E 05/ 1.$$E47 9,02DO4/ ,

talarment failwe caused by some dynanne sevore 9.25E+0$ 6.13D03 146E-01 accident phencmene (hydropea detonation, hydropa diffusion flame, swam emplosions.

vessel fallwe, etc.) occomng nLt the onset of core damese but petor to core solocation Crl Passion product release occus through a con- 1JIDll 1.54E+03/ 2.02D06/ 000E+00 0.00E+00/

tainment failure caused by some dynamic sevore 3.35E+0$ 4.39E46 0 00E+00 accident phenomena (hydropea detonation.

hydropa d:ffusion flama,etc.) occumag aner core miocanon but before 24 hours2.777778e-4 days 0.00667 hours 3.968254e-5 weeks 9.132e-6 months .

CPL Passion product release occws through a coe. IJIDil 2.5tE+00/ 3 90 Dill 0.00E W 0.00E+00' tainement fallwe caused by some dynarnic sevore 1.05E+0e 1.59E 00 0 00E+00 accident phenomenn, such as containment heat mmoval fallwe, occur..ng ther 24 hours2.777778e-4 days 0.00667 hours 3.968254e-5 weeks 9.132e-6 months Total R6sk som per reactor year 439E-05 9.0tE04 person rem per mactor year 7.HE 03 147D01 4

9 INEEUEXT 97-00779 4-4

5. References

1. Westinghouse Electric Corporation, AP600 Probabilistic Risk Assessment, Revision 8, September i 1996.

l 2. T. G. 'theofanous st al., in Vessel Coolabillry and Retention of a Core Melt, DOEllD 10460 Revised October 1996.

3. D. L. Knudson, A SCDAP/REL4P3.%Iysis ofAn AP6003BE Transient with Ex vessel Flooding,

! _ Aptil 26,1996, Attachment to letter from D. Knudson. INEL, to Y. Chen, NRC RES," Transmittal of Task 181.4tter Report under JCN L2330, DLK 2 96.

4 4.- M. T.14onard et al.,"MELCOR Calculations Supporting the NRC/NRR AP600 Design Certi6ca-tion Review," Sandia National Laboratories Preliminary Draft Report, TTS/SNL 95-006, August

1995.

5. 1 etter from B. A. McIntyre, Wednghouse, to T. R. Quay, U. S. NRC, NSD NRC-96 4687, DCP/

NRC0493 Docket No: SM 52 003, April 4,1996. 4 Kastenbarg, W. E., Editor, A Frameworkjor the Assessment ofSevere Accident Management Strat. ;

6.

egles, NUREG/CR-6056, September 1993. ;

7. Lim, H. 'The Impact of Phenomenological Uncertainties on an Accident Management Strategy, University of California . Los Angeles Doctoral Dissertation,1994.

I

8. B. R. Sehgal, et al., " Heat Transfer Processes in Reactor Vesul Lower Plenum during Late Phase of tn Vessel Core Melt Progression," to be publishedin Advances in NuclearSchnce and Technol-ogy, %lume 27.

9. Letter from J. Sebrosky, U.S. NRC, to N. J. Liparulo, Westinghoose, followon Questions Regard.

Ing Reactor VesselIntegrity during Severe Accident Core Melts, November 7,1996.

10. Letter from J. Sebrosky, U.S. NRC, to N. J. Liparulo, Westinghouse, followan Questions Regard.

i ing Extemal Reactor Vessel Coolingfor the AP600, February 24,1997.

11. Letter from J. Sebrosky, U.S. NRC, to N. J. Liparulo, Westinghouw, followon Questions Regard-ing External Reactor Vessel Coolingfor the AP600, March 10,1997.

[ 12. 1.etter from B. A. McIntyre, Westinghouse, to T. R. Quay, U. S. NRC, NSD NRC-96-4913, DCP/

NRC0683, Docket no: STN 52 003, December 13,1996.

13. - 1.4tter from B. A. McIntyre, Westinghouse, to T. R. Quay, U. S. NRC, NSD NRC 97 5067 DCP/

NRC0683 Docket no: SW 52 003, April 15,1997.

i 14. A. Rubin, et al., Review of "in %ssel Coo ability and Retention of a Core Melt, DOFJID 10460 July 1995, Attachment to letter from M. W. Hodges, U.S. NRC RES, to 0. M. Holahan, NRC-NRR, " Review of DOE Report, In Wssel Coolability and Retention of a Core Melt, DOE /ID-10460, July 1995." May 19,1997.

15, . R. R. Hobbins, D. A. Petti, and D. L. Hagrman, " Fission ProJuct Release from Fuel under Severt Accident Conditions," Nuclear Technology, Vol.101, March 1993,

16. O. Kubaschewski and C. Alcock, Merellurgical Thermochemirrry,5th Edition, Pergamon Press.

1979.-

17. Y. S. Touloukian and C. Y. Ho, Properties of Selected Ferrous Alloying Elements," McGraw HiW CIND(5 Data Series on Material Properries, whme 11101,1981.

51 INEEUEXT 97 00779 e

l ,

18. G. Wl Parker and S. A. Hodge, "Small Scale BWR Core Debris Eutectics Formation and Melting Experiment," Nuclear Engineering and Design,121,1990, pp 341-347.

19. K. T. Kim and D. R. Olander, " Dissolution of Uranium Dioxide by Molten Zircaloy," Journal of Nuclear Materials,154,1988, pp. 85 101. -

20. P. J. Hayward, and I. M. George, " Dissolution of UO2 in Molten Zircaloy-4, Part 4: Phase Evolu-tion during Dissolution and Cooling of 2000 to 2500 'C Sp cimens," Joarnal ofNuclear Materi-als,232,1996, pp 13 22,

21. D. W. Akers, S. M. Jensen, and B. K. Scheutz, Examination of Relocated Fuel Debris Adjacent to the Lower Head of the TMI 2 Reactor Vessel. MUREG/CR-61995, TMI V(92)EG10, July 1992.

22. S. Jensen, D. Akers, B. Pregger, Postirmd stion Examination Data and Analysisfor OECD LOFT Fission . Product Experiment LP FP 2, OECD LOFT 3810, Vol.1, December 1989,

23. R. G untt, et al., The DF-4 Fuel Damage Experiment in ACRR with a BWR Contml Blade and Channel Box, NUREG/CR-4671, S AND86 1443, November 1989.

24. G. A. Greene, O. C. Jones Jr., C. E. Schwartz, and N. Abuaf, Heat Removal Characteristics of Vol-ume Heated Boiling Pools with inclined Boundaries, NUREG/CR-1357 BNL-NUREG-51157, 1980.

25. C. M. Aliison, J. L. Rempe, and S. A. Chavez, Design Report on SCDAP/RELAPS Modelimprove-ments - Debris Bed and Molten Pool Behavior, INEL-94-0174. November 1994.

26. J. Stephen Herring, Notes on the Activation ofSS304 in the AP600, Unpublished notes, dated April 18,1996.

27. C. Allison et. al., SCDAP/RELAP5/ MOD 3.1 Code Manuals, Volume 4: MATPRO- A Library of Materials Propertiesfor Light Water Reactor Accident Analysis, Idaho National Engineering Lab-oratory Repott, NUREG/CR 6150, EGG-2720, June 1995.

28. Personal conversation betweer. J. Rempe, INEEL, and D. Petti, INEEL, September 1997,

29. Personal conversation between J. Rempe, INEEL, and R. k. Hobbins, RRH Consulting, Septem-ber 1997.

30. Electric Power Research Institute, " Advanced Light Water Reactor Requirements Document," Wl-urae III, Annex B of Appendix A to Chapter 1. "PRA Key Assumptiocs and Groundrules," Revs. 5

& 6, December 1993.

31. T. G. Theofanous et al., "The First Results from the ACOPO Experiment," Transaction:from the International Topical Meeting on Probabilistic Safety Assessment (PSA '96), Park City, Utah, Seg-tember 1996.

32. S. Angelini, "ACOPO Data Discrepancies," emsil from S. Angelini, to S. Sorrell, US DOE, December 8,1997.

33. E B. Cheung, H. K. Haddad, and Y. C. Liu, "A Scaling Law for the Local CHF on the External Bottom Side of a Fully Submerged Reactor Vessel," prese :ted at the J9% Light Water Reactor -

Safety information Meeting, 0ctober 1996.

34. E B. Cheung, K. H. Haddad, and Y. C. Liu, Critical Heat Flux (CHF) Phenomenon on a Down. .

ward Facing Curved Surface, NUREG/CR-6507, PSU-ME-NRC-06-95, June 1997.

35. Personal conversation between J. Rempe, INEEL, and M. Leonard, ITS, April 1997.

i INEElJEXT-97-00779 5-2 1

,1 6

- 36.' Personal conversation between J. Rempe, INEEL, and J. Scobel, Westinghouse, April 1997.

37. Personal conversation between J. Rempe, INEL, and T. Y. Chu, SNL, April 1996.'

Personal conversations between J. Rempe, INEEL, and F. B. Cheung, Penn State, April 1997.

38.

39. Personal conversation between Cory Atwood, INEEL, and J. Rempe, INEEL, October 1997,

40. S. Globe and D. Dropkin, " Natural-Convection Heat Transfer in Liquids Confined by Two Hori-4 zontal Plates and Heated from Below," Transactions of the ASME, p. 24, February 1959.

41. G. Fies, " Experimental Investigations of Heat Dansfer Charac: eristics in Liquid Layers with Inter-nal Heat Sources," Pmceedings of the ANS ENS InternationalMeeting on Fast Reactor Safety and Related Physics," Chicago, USERDA Report CONF-761Cel .4,1976, pp. 2047-2055.

42. E A. Kulacki and A T Nsuyea Hydedynamic Instability and Thermal Convection in a Norizontal L layer of Two immiscible Fluids with internal Heat Generation, NUREG/CR 2619R3,1980.

43. J. L. O'Toole and P. L. Silverston, " Correlations olConvective Heat Transfer in Confined Horizon-tal Layers l' AIChE, Chem. Engng. Pmgr. Symp. Ser., 57(32) , pp 81 86,1961.

-44 T. C. Chawla and S. H. Chan, " Heat Transfer from Vertical / Inclined Boundaries of Heat Genreat-ing Boiling Pools," J. ofHeat Transfei; Tmnactions of the A5ME, Vol.104, pp. 465-473,1982.

1 45. American Nuclear Society Standard ANS1/ANS 5.11979, " Decay Heat Power in Light Water Reams",1979.

46. " Residual Decay Energy for Light Water Reactors for Long Term Cooling," Auxiliary and Power Conversion Systems Branch echnical Position Paper, APCSB9 2, p. 9.25-8, November 11,1975.

47. D. R. Olander, Fundamental Aspects of Nuclear Reactor Fuel Elements, Technical Information Center, Energy Research and Development Administration,1976.

48. Personal conversation between J. Rempe,INEEL, and J. Sienicki, ANL, April 9,1997.

49. Personal conversation between J. Rempe, INEEL, and B. Schnitzler, INEEL, April 8,1997.

50. T. R. England and W. B. Wilson, TMI 2 Decay Pdwer: lASL Fission Pmduct and Actinide Decay ,

. P6wer Calculationsfor the Pnsident's Commission on the Accident at Three Mile Island, LAS.

8041 MS, Revised, Informal Report, March 1980.

51. J. K. Fink and L. Leibowitz,"An Analytis of Measurements of the Thermal Conductivity of Liq.

uid Urania," High Temperatures Nigh Pnssures,1985, Volume 17, pages 17-26, pp 17-26.

52.' C. S. Kim, et al., Measurement of Thermal Diffusivity of Molten UO ,2 Pmceedings of the Seventh 4

Symposium on thennophysical Pmpenies, ed. A. Cezairliyan, ASME, New York p. 338, May 10-12,1977.

53. K. A. Romberger, C. E Bates, Jr., H. H. Stone," Phase Equilibrium Studies in the UO 2 -ZrO 2 Sys-tem, Journal ofinorganic and N,wlear Chemistry, 29,1966, pp.1619-16*K).

54. - " Density'of Liquid - Uranium Dioxide,' International Nuclear Safety Center Database, //

www.inse. ant. gov /index.html, April 1997.

> 55. . Y. S. Touloukian and D. R DeWitt, "Ihermal Radiative Properties - Metallic Elements and

~

Alloys," Thermophysical Pmpenies ofMatter, Volume 7, IFI/ Plenum, New York,1970.

5-3 INEEUEXT 97-00779

56. A. J. Rulison med W. K. Rhim, " Constant Pressme Specific Heat to Hemispherical Total Emissiv-ity Ra~tio for Undercooled Liquid Nickel, Zirconium, aru 5ilicon." Metallurgical and Materials Transactions B, Volume 26B, June 1995, pp 503 508.

57. S. Krishnan and P. C. Nordine, " Spectral Emissivities in the Visible and Infrared of Liquid, Zr, Ni, and Nickel based Binary Alloys," Joumal of Applied Physics, Volume 80 (3), August 1995, pp ,

1735 1742. .

58. D. L. Hagrman, ISS, personal conversation with J. L. Rempe, INEEL, April 7,1997.

59. R. A. Moen, Thermophysical Pwperties of Fermus Structural Alloys, Haniord Engineering Devel-opment Laboratory Report HEDL-TME 78-47, UC-79b,h, April 1978.

60. Pelton, A.D., L. Leibnowitz, and R. A. Blomquist,1994, Journal ofNuclear Mance, 210,1994, pp 324-332.

61. Nuclear Systems Materials Handbook, Volumes I and 2, Property Code 3112, Revision 3, August 1,1977.

62. General Electric Company, Chart of the Nuclides, Twelfth Edition, Schenectady, NY,1977.

63. J. R. Welty, C. E. Wicks, and R. E. Wilson, fundamentals ofMomentum, Neat, and Mass Transfer, Second Edition, John Wiley & Sons, New York, NY,1976.

64. P. J. Haywarti, and I. M. George, " Dissolution of UO2 in Molten Zircaloy-4, Part 4: Phase Evolu-tion during Dissolution and Cooling of 2000 to 2500 'C Specimos," Journal ofNuclear Materi-als,232,1996, pp 13 22.

65. J. H. Min and F. A. Kulacki, Steady and Transient Natural Convection with Volumetric Energy Sources in a Fluid layer Boundedfmm Below by a Segment of a Sphere Annual Report 6, July 1976- September 1977, NUREG/CR-0006, February,1976.

66. J. T. Bittel, L. H. Sjodahl, and J. F, White, "Cxidation of 304L Stainless Steel by Steam and Air,"

Cormston 25, pp. 714,1969.

67. L. Leibowitz, et al., " Solidus and Liquidus Temperatures in the Uranium-Plutonium-Zirconium System" Journal ofNuclear Materials,154,1988, pp 145-153.

(

l L

l INEEL/ EXT 97-00779 5-4

Appendix A- VESTA Governing Equations and Nomenclature in order to independently verify UCSB study results and to assess the impact of additional uncertainties and other debris configurations, INEEL developed the Vessel Statistical Thern.al Response Analysis (VESTA) model VESTA governing equations are listed in Section A.1, Variables used in Section A.) equations and in other sections of this report are defined in Section A.2.

Figure A 1 illustrates the generalized geometry of the lower head and debris assumed for this model.

As indicated by this figure, VESTA is more general than the UCSB model. VESTA includes equations for predicting three debris configurations: Configuration A contains a molten ceramic pool beneath a molten metallic layer; Configuration B contains a molten metallic layer sandwiched between two ceramic pools; and Configuration C contains a molten metallic pool beneath a ceramic layer Section 2.1 provides additional details about each of these debris configurations.

VESTA is written in MODULA 2 using SAGE libraries and was compiled using the Stoneybrook compiler, it is designed to run on an IBM or IBM-compatible PC with MS Windows 95/NT operating systems. The model requires 16MB RAM and 2 MB diskspace. On a P120 (Pentium computer with a 120 MHz processor), VESTA can perform an uncertainty calculation with 1,000 iterations within approximately 1 minute.

l J

L <R lg e

(3) l

,. 7 _____ 7 _.

~

V' ' Layer' 2 2fpsi

.T' ;0;(1)

/

( "

{- H (3)

T.

' / qqysydfyQ $;pl'/ f~' H (2)

- H,(1)

@WL*e(1)y y

'" V-t

_s.

uaop'MQM @w/ /. _ _ _ _ _ $_ _

8,,,(0)

I woc Figure A 1. Geometry assumed for VESTA analyses. I l

1 l

i A1 INEEUEXT-97-00779

l l

A.1 VESTA Governing Equations

.A.1.1 CHF from Vessel Outer Surface For point estimates calculations:

q" cur (0) = Ci + C 20 + C3 0' + C4 0' + C3 0' (A1) .

For calculations considering uncertainties:

4" cup (0) = exp(Ccur)(C i + C 20 + C 30* + C40' + Cs0*) (A 2)

A.1.2 initiallzstion and Material Properties A.1.2.1 Ceramic Regions Muo,(n) = Muo,-i.if. -ufuo,(n) . (A3)

For Muo,(n)> 0:

Mz,(n) = f,..z,Mz,....fz,o,(n) (A-4)

"' (A 5)

Vuo,(n) =

Puo,

'" (A-6)

Nuo,(n) =

vo, Nz,(n) = (A-7)

N(n) = Nz,(n) + Nuo,(n) (A 8) fu.uo,(n) = Nuo,(n)/N(n) (A-9) fx z,o,(n) = Nz,(n)/N(n) (A 10)

Mo,(n) = Nz,(n)2Zo (A11)

Mz,o,(n) = Mz,(n) + Mo,(n) (A12)

M(n) = Mz,o,(n) + Muo,(n) (A-13) f uo,(n) = Moo,(n)/M(n) (A14) .

f..z,o,(n) = Mz,o,(n)/M(n) (A-15)

Vz,o,(n) = Mz,o,(n)/pz,o, (A-16)

V(n) = Vuo,(a) + Vz,o,(n) (A-17)

INEEIJEXT 97-00779 A-2

V, = [V(n); for V(n)> 0 (A18) f,.co,(n) = Vuo,(n)/V(n) (A 19) f..zro,(n) = Vzro,(n)/V(n) (A 20) p,(n) = (fv-vo,(n)p .co, + Iv-zro (n)pp.z,o,)e' (A21) p 9 (A 22) c,.,(n) = (f..uo,(n)c,,, + f..z,o,(n)c,,,)e k,(n) = (fu.vo,(n)k,.co,+ fw.zro,(n)k,.zio,-0.4fs.uo,(n)fu.z,o,(n))e# (A 23) k,,(n) = (f N.uo,(n)k,,.uo, +NI zro,(D)N s ,-z,o,- 0.4 fw.vo,(n)fx.z,o,(n))e#" (A 24) u,(n) = k,(n)/p,(n)c,.,(n) (A 25)

A.1.2.2 Metallic Regions M.,(n) = M,.. .,f.,(n) (A 26)

For M.,(n) > 0 :

Mz,(n) = (1 - f ..z,)Mz,...,fz,(n) (A 27) b (A 28)

. Mv(n) = Muo,.i.i(1 -f...u)fu(n)7voi M(n) - Mz,(n) + M,,(n) + Mu(n) (A 29) f z,(n) = Mz,(n)/M(n) (A-30)

f. ,(n) - M.,(n)/M(n) (A 31)

(A 32) f..u(n) = Mu(n)/M(n) 2'("} (A 33)

Nz,(n) =

Zz, ,

" (A 34)

N,,(n) =

u(n) (A-35)-

Nu(n) =

N(n) = Nz,(n) + N .(n) + Nu(n) (A 36)

(A-37) I fu.z,(n) = Nz,(n)/N(n) fu ,(n) = N.,(n)/N(n) (A-38)

(A 39) fx.u(n) = Nu(n)/N(n) l A3 INEEUEXT-97-00779

Vz,(n) = Mz,(n)/pz, (A-40)

V ,(n) = M,,(n)/p,, (A-41)

Vu(n) = Mu(n)/Pu (A-42)

V(n) = Vz,(n) + V,,(n) + Vu(n) (A 43) - .

(A-44)

Vi = [V(n): for V(n)> 0 f,.z,(n) = Vz,(n)/V(n) (A 45) f,..,(n) = V,.(n)/V(n) (A-46) fv-u(n) = Vo(n)/V(n) (A-47) pi(n) = (f,.z,(n)pz, + f,..,(n)p., + f.-u(n)Pu)e "' (A-48) 5' (A-49) c,.i(n) = (f..z,(n)c,,,, + f. .,(n)c,, + f,,,.u(n)c,,)e For UCSB-assumed FIBS and Configurations A and B:

ki (n) '= (f,,,.z,(n)ki .z, + f...,(n)ku.. - 0.72f z,(n)f,,. ,(n)lkpz,-k i .,,l)e# (A-50)

For Configuration C:

k (n) = (fu.z,(n)kz, + fx...(n)k,, + fN .u(n)ku)e '-' (A-51)

(n) = (f.-z,(n) z, + fv. ,(n) ,, + f,.v(n) u)e (A-52) a (n) = (A-53)

A.1.3 Geometry 3

(A-54)

V .. = fxR -

V,,,(n)= V(z) (A-55) 3e]

For V,,,(n) s V.,,,,:

Obtain H,,i(n)l,,i,3 by iteratively solving:

V,,,(n) = (1/3)xH,.,(n)'(3R-H,,,(n)) (A-56)

R,.,(n)= .xH,,,(n)

'*'(") -

(" (A-57) 3 .

0,,,(n) = art <in(Ri .,(n)/R) (A-58)

S,,(n) = xR,,,(n)" (A-59)

INEEUEXT 97 00779 - A-4

- - - . _ . ~ . - . . - - - . -

H(1) = +1,,,(1) (A 60)

H(2) = H,,,(2)- H,,i(1) (A-61)

H(3) = H,,i(3)- H,,,(2) (A-62)

So,(1) = 2xRH(1) (A 63)

S,i,,(1) = 0.0 (A 64)

For n= 2 and n=3:

S,i (n)' = xH(n)[R,.,(n) + R,,,(n- 1)) (A-65)

S.,(n) = S,,(n - 1) (A 66)

For V,,,(2) s VS ., and V,,,(3) > Vn..:

Obtain H,. (n)l,,i,3 by iteratively solving:

V .,(n) = (1/3)xH,,,(n)'(3R - H,,i(n)) (A 67) l For n=1 and n=2

'*' "'*'(" } (A 68)

R,.,(n) = .xH,,,(n) -

3 .

-- S.,(n) = xR ,(n)*

i (A-69) 0,,,(n) = arcsin(R,.,(n)/R) (A 70)

' Estimate H(3) by applying:

H3, = R - H,,,(2) (A 71)

H 33 = 1(Y2 io

,(3)-V .) S (A 72) xR H(3) = H3 ,+ H3 , (A 73)

H(1) = H,. (1) (A-74)

H(2) = H,. (2)- H,,,(1) (A-75) _

H,,,(3) = H(3) + H,,,(2) (A-76)

S,i,,(2) = xH(2)[R .,(2) + Ri ,(1)] (A 77) -

S,i,,(3) = 2nhH 3 ,(R,,,(2) + R) + RH ,

3 (A-78)

A5- INEEUEXT-97-00779

Ri o,(3) = R (A 79)

So,(1) = 2xRH(1) (A-80)

For n= 2 and n=3:

S,,(n) = xR,,,(n - 1)* (A 81) .

A.1.4 Deosy Heat fo,..,4(t,,i) = Mo,,,,4(t,,i)t,,i + Bo,,,,4(t,,i) (A-82) fo,..,6(t,,i) = Mo,,,, .(t,,i)t,,i + Bo,,,, (t,,i) - (A-83) fz,a m(t,,i) = Mz,a m(t,,i)t,,i + Bz,a m(t,,i) (A 84)

Im.i.i = (1 - f. .ze)lforo,p 4(t,,i) + fz, a m(t,,i)) + fa,,,, .(t,,i) (A 85)

P.,,,,. .i(t,,i) = e '"P, y ucsa(t,,i) (A 86)

P 4 ...y. r,(t,,i) = (1 - fACT(I,el))P 4 ...,. .i(t,,i) (A-87)

P,,,,,.4c7(t,,i) = f 4cr(t,,i)P 4 .,,y . .,(t,,i) (A-88)

For ceramic materials:

Q(n) = , v pdecay-FP(t,,i)(1 - f..i,3) + P ..y.4c7(t,,i)] (A 89)

For metallic materials:

"" -**~"

Q(n) = P 4.e.y.r,(t,,i) **")+P...y.act (A-90)

A.1.5 Heat Transfer A.1.5.1 Equations for Ceramic Pools For n with Muo,(n) > 0:

T,(n) = T,, (n) + 0.5T,...i(n) (Initially assume T,...i(n) = 0) (A-91) 1 (A-92) p,(n) = 1.5868x10"exp(T,(n)30 + C, . ,

u,(n) = p,(n)/p,(n) (A-93)

Ra,(n)' = I "("

(A-94) n,(n)u,(n)k,(n)

INEE1JEXT-97 00779 A 6-

1 S'up..,(n) = C,[Ra,(n)'#')[10 """ )* (A-95).

Nu,. .(n) = Ce[Ra,(n)J(H(n)/R)';25(10 '"* )* (A 96)

R(n)' = Nu,..,(n)/Nu,.e,(n) (A 97)

Ssg= @ (A-@

N ' " " (S,ig,(n) + S , S ,(n)R(n)'). n*

T,...i(n)= 9 **I") = T,,,,,(n) - T, .(n) (A 99)

H(n)

"'I")

Check pool temperature assumption for calculating viscosity T,(n) = T,,,,(n) + 0.5T,.4,i(n) (Repeat until estimates for T,(n) are within 10 K). (A 100)

" "'* (" d' " .(A101) q",. .,(n) =~ " ~ 9 ' j' For [0(.1)/0,,,(n) s 0.1) q",.e,(0, n)/q",..,(n) = Max [0.01, (Ci ...i + q",..,[0.10,,,(n)]/q",.. (n))) (A-102)

For [0.1 < 0(n)/0,,,(n) $ 0.6]

4",.4,(0, n)/q",...(n) =

Max [0.01, (C i ...i +i C o + C (0(n)/0,,,(n)) + i2 C (0(n)/0,,,(n))' +33C (0(n)/0,,,(n))')] (A 103) l ii For (0.6 < 0(n)/0,,,(n) s 1.0) q",.4,(0, n)/q",...(n) = C ...i i + Cu + Ci3(0(n)/0,,,(n)) + Ci .(0(n)/0,,i(n))* (A-104)

For n, such that n > 1 and Muo,(n) > 0:

e,,,< , - i >

2 4",.e.(n)l,,, = 3 ,

q",.,,(0, n)sinecosede (A-105) o

a. As described in Section B.1.1, u o ,,,,(Ra,(n)') and o n ,,,,(Ra,(n)') are given by:

Gw,, ,,(Ra,(n)') = [sec ,+ sec ,(log (Ra,(n)')- 15.0148)*] T

=+

U Ne,..(Ra,(n)') = [sec , + se'c,(log (Ra,(n)')- 14.9701)'] T -

A? INEEUEXT-97-00779 :

5 For n with M(o,(n) > 0: ,

If n = 1, for 0(1) s 0,,,(1), or if n > 1, for 9,,,(n - 1) < 0(n) s 0,,,(n) 5 x/2, the heat Aux to the vessel wall, q",,,(0), is obtained from the following equation, where either the vessel wall temperature, T,,,(0), _ ,

or vessel wall thickness, 8,,,(0) and the crust thickness, 8,,(0, n), are unknown.' - ,

First, assume 8,,,(0) = 0.15_ m and solve for 5,,(0, n) and T,,,(0) using: ,

0=

' " + 5,,(0, n) " ""

2k,,(n) - ( 'k',','I (n) 0' " } + k, . 6 s

(-Tr(n)) + 9"*(0, n)6,,,(0) ;

k ,. . . -

'T,,,(0) = ' ' ' ' '" "'"('"

+ T. (A.107) k,. . . .

' If T,,,(0) > T,.,,,,,, then solve for 6,,(0, n) and 8,,,(0) using 0 = DI"} "I + 6,,(0, n)(9~'{'*f-Tr(n) '" + T,.,,,, ,,, (A.108) 2 8,,,(0) = k,,,.6 "" *

(A 109) 9",.4.(0, n) + Q(n)6,,(0, n)

Then, obtain the heat Aux to the vessel wall, q",,,(0), using q",,,(0) = q"p.e.(0, n) + Q(n)6,,(0, n) (A110)

A.1.5.2 Equations for the Metallic Layer - UCSB-assumed FIBS and Configuration A Iteratively solve the next equations to obtain T i.iop(2), Ti .boi(2), Ti . bulk (2), T,.i Teo, and T.,

First, solve for Aj.iop(2),- A.w(2), i and A..w(2) i by evaluating at the appropriate temperatures

--(initially assume metal layer is at its liquidos temperature and upper plenum structures are at 1000 K).

5m Sn.i(2) = 1.1081x10"exp + C,.i (AIll)

Tn.i(2)s vn.i(2) = Pn. (2)/pi(2) (A112)

. k,(%) = (1.4154x10'*{ + 9.9214)e#"' (A113) e c gSi(2) Ti' - .

. Ai .i.,(2) = Cne *ki(2)[vn .i.,(2)/ai(2)) i,r ),

(A ll4)

. Ai .v.,(2) .= Cne #"k:(2)[Un.m.,(2)/(ai(2))]

i(2)

Vn.m. (

~ f a. For n=3, calculate 5 ,(0,3) for 0 s 0(3) s 0,.,(3).

INEEUEXT.97-00779 A8 Y w , --

- ,- ,, , =-. - ,r,,, - .

.~ . .- - - . . _ - _ - _ - - . - - - - . . . .

=

e Ai .,i ,(2) = Cz *ki(2)(""**SSi(2) ',,(2)ai(2) _

r e gj92 '86'37 1+. l s ,dun .,ie,(2)/ai(2)) s Second, assume T,.i and solve the next equation for iT.g(2)

< 8 f,,,i,iQ(2)V(2) + S,,(2) 9 ~' ' "( =

I -I)~ -'I II ' 8"(2) ]+

.H(2 )*'" ~ '. 1 + 1 - E,'S.,(2)) 'H (2 )" ' 's

rr 3 . 3c .i r 1 Ai . i,.(2)S,,,,(2) o[T-'",(2) -),T,' il

, , c ,, . + Ti . ,,,(2) - T ,,(

t 2) (A Il7)

Third, use T,.i and Ti .g(2) to estimate T,, from e 3 6, o [T'. ..,(2 ) - T'. i]

T .. = T,.i .- (All8) k,(T,) 1( S._'y 1 -t, (EAS,,(2)) e, s Fourth, use the following two equations to estimate T.

k,(2) - *28 T,,, =

'I.,, . . 3 ,g (T, . i - T, . .)_ (A 119)

T,,, = k (i",)6k... . ,6, I ' T, . .) + T. (A 120)

When both equations yield tiie same Tm, use the following equations to findi T.w(2) and Ti .wg(2) 4 r 3 - 1 o[T' ,,'(2)-T' il r 1 3

T-6*ik(2)=

I 3 , t, es,,(2)' 'A i .,,,(2)H(2)'""' 's "'

l

.< ti e, < S, >> .

i

~

q *"( 1 ) G T i .6,i(2) = + Ti ...in(2) (A.122)

.Ai . .,(2)H(2)3e".i .

Then, re evaluate above equations using i

Tn.,,,(2) = $ lT i. .,(2) + T .i ,36(2)) . (A-123)

-1 Tn.6,i(2) = 3[T .6.,(2) i + Ti ...in(2)) (A-124) 4 A-9 INEEIKKT 97 00779 -

l Tn.,ie.(2) = f[Tt ,,(2) + iT .6,ig(2)) (A 125)

T = f[T,.i+ T ..] (A 126) ,

Once these steps are completed, the heat flux to the side wall from the metallic layer [q"i. i4,(2), or q",,,(0), for 0,,i(1) < 0 s 0,,i(2)) and sidewall vessel thickness are estimated using .

q~i..ia,(2) = Ai .,i (2)[Ti .. ii(2)- Tt.,.(2))#' (A 127)

B.,,,(2)= k '" - "

i - - _ t -(A 128) q" ..ia.(2)[T ,,(2)- T,]

he existence and thickness of a crust between the ceramic pool and the metallic layer is verified by solving the following quadratic equation:

0=2 ' I'6sn(l)-[T,,,,(1)- T i...i(2)] (A 129)

)6*.n(l ) +

In the metal layer, the crust thickness, Sun (1), should satisfy the following relationship in order to be considered thin 0 < """ s 0.03 (A 130) q", . ,,( 1 )

ne ratio of the crust volume to the pool volume should be calculated to verify that it is small using A 3 nhl80g 6n(0,1)2nRsined0 P j

+ f nR i .,(1)'63n(l) s 0.05 P

(A 131)

A.1.5.3 Equations for the Metallic Layer Configuration B The heat flux to the vessel wall, q"i.,i4,,(2), is obtained from the following equation, where either the vessel wall temperature, Ts,,,(2) or vessel wall thickness, Bi .,,,(2) is unknown.

First, assume i B .,,,(2) = 0.lb m and solve for Ts,,,(2) using Q(2)V(2) + q",,,,(1)S,,(1 ) + q",.4,(3)l: i,2 8a(3)= d (Ti .,,,(2)- T,) (A-132)

If Tu,,,(2) > T ,,(2),t assume Tp,,,(2) = T ,n(2) t and solve Equation (A 132) for Si .,,,(2) .

The heat flux to the side wall from the metallic layer [q~i..i .(2), or q",,,(0), for 9,,,(1) < 0 5 0,,,(2)]

is then estimated using k" (A-133)

- q~s.,i4..(2) = iS .,,,(2)(Ti .,,,(2)- T )

Estirute a minimum h ia,,(2) 9 ' - '" 9 ' ' '" '

h **"(2) 2. Min .T,, ,( 1 ) - T .,,,( 2 )' T,, .(3 ) - T .,,,(2 ). (A-134) i i INEE1AXT-97-00779 A 10

Because bl .dn(2) isn't known, compare possible values

Ti .6,a(2) = 0.25[T,..(1) + T,,,(3) + 2Ts,,,(2)) (A-135)

5776 pi(2) = 1.1081x10 xp Ji 6,n(2))s + C,.i (A 136) vi(2) = pi(2)/p (2) (A-137)

' '"( (A 138)

Rai(2) = vi(2)ai(2)k 8 '( } (2) ,

' 2) hs.a./Acoro(2) = 0.1857 H "(2)n2m (ACOPO) (A 139)

Rai(2) = I '( }

( ' *( ' * ' "( }' ~ '" "'( ' "( (A 140) vi(2)ai(2) hi .4,,co(2) = 0.1 ai(2)"' (Globe-Dropkin) (A141)

Then, verify that the crust above and below the metallic layer is thin by applying the following equations:

0= 3,,(1 )' + q",. ,(1 )l, ,,369,,(1)- k,,(1)[T,,,(1)- T i.6,a(2)] (A 142) 0 < "' " 5 0.03 (A-143) q",..,(1)

)

3,,(3)' + q",,,,(3)l3 2 69,(3)- k ,(3)(T,,.(3)- T i . ,n(2))

0= (A 144) 0< ( I- 5 0.03 (A 145) q",...(3)l3,3 Finally, calculate the ratio of the crust volume to the pool volume to verify that it is small using x 0 Ajl) 3 y 6,,(0,1)2xRcosede +y xR .,(1)'6 9,,(1) s 0.05 (A-146)

\ 0 )

3

'I 0 A!3) '

6,,(0,3)2xRcosede + y(I3)xR.,W 34 ,,Q) M.M M-W) y(3) \ ,

o >

A.1.5.4 Equations for the Metallic Layer Configuration C

- The heat flux to the vessel wall, q"i. (1), is obtained from the following equation, where either the vessel wall temperature, Ts,,,(1) or vessel wall thickness, S i .,,,(1) is unknown.

First, assumei 6.,,,(1) = 0.15 m and solve for T.,,,(1) i using d

c- Q(1)V(1) + q",..,(2)l2,,S (2) = "'- *(Tu,,,(1 ) - T.) (A 148)

_ )

A-11 INEEllEXT-97 00779 ,

1 If T.,,,(1) i > T,,(1),i assume T.,,,(1) i = T,,(1) i and solve Equation (A 148) for 6.,,,(1). 3 ,

ne heat Aux to the side wall from the metallic layer [q"i. ;.,(1), or q",,,(0), for 0 $ 0,,,(1)) is then .

estimated using

l q"i.,,(1 ) = 6 i....(1 )(T .,,,(1 i ) - T.) . (A 149) '

! Estimate a minimum hi4(1) hi .,%(1) 2 T -

'M I^'I50}

l Because h3#(1) isn't know, estimate possible values:

Ti .s,a(1) = 0.5(T,,,(2) + Ti .,,,(1)) (A151) pi(1) = 1.1081x10"exp(T 5776 .s,a(1))+

) C,.i '(A 152) '

i vi(1)= i(1)/(pi(1)) (A153)

Ral(l) = vi(1)ai(1)k 8 '(1)Q(1)H(1)si(1)

(A 154) hi ...,4co,o(l) = 0.1857 al(l)*** I)f (ACOPO) (A 155)

Rai(1) = 8 '( }I * *( } ~ '-'"(

}I"( }

(A156) vi(1)ai(1) hi . .,oo(l) = 0.1 R"'(1) 8 (Globe Dropkin) (A157) r H

Then, verify that the crust above the metallic layer is thin by applying the following equations:

2 0= 1- (7):, q,,. ,(2)l3,,6i ,(2)-k ,(2)(T,,,(2)-Ti . a(1)) (A-158) 0< s 0.03 (A-159) q", ..,(2)l, , , .

Fmally, calculate the ratio of the crust volume to the pool volume to verify that it is small using N2) . 3

,,(0,2)2nRainede + nR,,,(1)'6 i ,(2) s 0.05 (A-160) -.

2 .

< o. ) .

L j' (

INEEUEXT-97-00779 A-12

^

., ta . . -, . -. .- - -, -..--._..=---._..:-..-.--

i- 1 i

A.2 Nomenclature- .

1 c,(n)- = , Specific hat capacity of rr.:lt in layer n [may be further designated by the

'. subscript (1) for metallic layer, (p) for ceramic layer, (ss) for stainless steel, (U) for uranium, (UO2 ) for uranium dioxide, (Zr) for zirconium, or (ZrO2 ) for zirconium dioxide)(J/kg K) f(n) = Mass fraction of total relocated species in layer, n [may be further designated by the subscript (ss) for stainless steel, (U) for unoxidized uranium, (UO2) for -

oxidized uranium, (Zr) for unoxidized zirconium, and (ZrO2 ) for oxidized zirconium) i E ' f(t,,i) = Fractional contribution to decay power (contribution may be further designated i P the subscript (ACT) for actinide, (Group 4) for Group 4, (Group 6) for Group

! c. or (Zr & Nb) for zirconium and niobium) f .i = Fraction of fission product decay power residing in the metallic layer f,(n)' = Mass fraction in layer n [may be further designated by the subscript (ss) for stainless steel, (U) for uranium, (UO2 ) for uranium dioxide, (Zr) for zirconium, I

or(ZrO 2) for zirconimn dioxide]

fx(n) = Mole fraction in layer n [may be further designated by the subscript (ss) for stainless steel, (U) for uranium, (UO2 ) for uranium dioxide, (Zr) for zirconium, or(ZrO 2) for zirconium dioxide]

f., = Fraction of species oxidized [may be further designated by the subscript (U) for uranium, or(Zr)for zirconium) f,(n) . = Volume fraction in layer n [may be further designated by the subscript (ss) for stainless steel, (U) for uranium, (UO2 ) for uranium dioxide, (Zr) for zirconium, or(ZrO 2) for zirconium dioxide) 2 3 = Gravitational acceleration (9.8 m/s )

hi .. (n) = - Heat transfer coefficient froin the bottom of metallic layer n [may be further designated by the subscript (min) for minimum value, (ACOPO) for value predicted by correlation based on ACOPO data, or (GD) for correlation based on Globe-D opkin data)(W/m2K) .

-k(n) - =- Thermal conductivity in layer n [may be further designated by the subscript (cr) -)

for ceramic crust, (cr-UO2) for ceramic crust uranium dioxide, (cr-ZrO2) for -

ceramic crust zirconium dioxide, (1) for metallic layer, (p) for ceramic melt, (p-UO2) for ceramic melt uratiium dioxide, (p ZrO2 ) for ceramic rrdt zirconium dioxide, (1 ss) for metallic layer stainless steel, (1-Zr) for metallic layer j zirconium, or (1-U) for metallic layer uranium) (W/mK)

A-13 INEEUEXT 97 00779

- -- - . - ~ . . - . . - . _ __ - -. - - . . . -

k,(T.) = Upper plenum structure thermal conductivity (W/mK) k ,, , = Vessel wall effective thennal conductivity [may be further designated by the ,

subscript (c) for cooler locations above the metallic layer or (h) for hotter locations near the ceramic or metallic layers) (W/mK) q"(0) = Angular -dependent heat flux [may be further designated by the subscript (CHF) 2 for vessel surface critical heat flux or (ves) for heat flux to the vessel) (W/m )

q",,,,(0, n) = Angular dependent downward heat flux from melt in ceramic layer n (W/m2 )

q"(n) = Average heat flux in layer n [may be further designated by the subscript (1-d i) for downward heat flux from metallic layer, (1-side) fcr sidewall heat flux from metallic layer, (p dn) for downward heat flux from ceramic layer or (p-up) for upward heat flux from ceramic layer) (W/m2 )

tai = Debris relocation time (s)

A i (n) = Coefficient for estimating heat transfer from the surface of metallie layer [may ,

be further designated by the subscript (bot) for lower surface, (side) for side surfaces, or (top) for upper surface) (W/m24 K)

B (t,,i) = Constant for estimating fractional contribution to fission product decay power

[may be further designated by the subscript (Group 4) for Group 4 contribution, (Group 6) for Group 6 contribution, or (Zr & Nb) for zirconium and niobium contribution] ,

C, = Constants [may be further designated by the subscript (1 5) for estimating critical heat flux, (6-9) for estimating ceramic layer heat transfer, (10-16) for estimating local heat transfer from the ceramic layer, or (17-22) for estimating heat transfer from the metallic layer)

C = Uncertainty parameter [may be further designated by the subscript (bot) for estimating metallic layer lower surface heat transfer, (c p p) far estimating ceramic layer specific heat, (cp -1), for estimating metallic layer specific hea',

(dec) for estimating decay heat, (k-cr) for estimating ceramic crust thermal conductivity, (k-1) for estimating metallic layer thermal conductivity, (k-p) for estimating ceramic layer thermal conductivity, (k-s) for estimating upper plenum structure thermal conductivity, (local) for estimating angular-dependent downward heat fluxes, (side) for estimating metallic layer side surface heat ,

transfer, (top) for estimating metallic layer upper surface heat transfer, (CHF) for estimating critical heat flux, ( 1) for estimating metallic layer coefficient of thermal expansion, (p-1) for estimating metallic layer densia/, or (p-p) for '

estimating ceramic layer density) l INEEUEXT 97-00779 - A-14

l

+ 1 C, = Uncertainty parameter for estimating viscosity [may be further designated by the subscript (1) for the metallic layer or (p) for the ceramic layer) (Pa s) -

H(n) =- Height of layer n [may be funher designated by the subscript (3a) for height of layer 3 below the hemisphere,(3b) for height of layer 3 above the hemisphere,-

(tot) for cumulative height of relocated debris up through layer n) (m)

M(n) = Mass of relocated debris in layer n [may be funher designated by the subscript (0 2) for oxide, (UO 2) for tiranium dioxide, (U) for uranium, (Zr) for zirconium, (ZrO2) for zirconium dioxide)(kg)

M(t,,i) = _Coemcient for estimating fractional contribution to fission prod 9ct decay power

[may be further designated by the subscript (Group 4) for Group _4 contribution, (Group 6) for Group 6 contribution, or (Zr & Nb) for zirconium and niobium contribution)(s'3)

M = Mass (may be funher designated by the subscript (1) for metallic layer, (1 Zr) for metallic !ayer zirconium, (p) for ceramic layer, (p-Zr) for ceramic layer zirco-nium, (ss) for metallic layer etainless steel, (ss tot) for total relocated stainless steel, (tot) for total relocated debris, (U) for uranium, (UO2 -tot) for total relo-cated UO2 , or (Zr tot) for total relocated zirconium) (kg)

N(n) = Number of moles in layer n (may be further designated by the subscript (ss) for i staintess sieel, (U) for uranium, (UO2 ) for UO2 , or (Zr) for zirconium)

Nui = Metallic layer Nusselt number [may be funher designated by the subscript (horz) for horizontal, (vert) for vertical, or (up) for upward)

N7p(n) = Average Nusselt number for molten material in ceramic layer n [may be further designated by the subscript (up) for the upward direction or (dn) for the downward direction)

Nu,. (0, n)= Nusselt number in the downward direction at the angle, 0, for molten material in ceramic layer n P...,(t,,i) = Decay power (may be funher designated by the subscript (tot) for total decay power, (UCSB) for decay power shown in DOE /ID-10460 Figure 7.1, (FP) for decay power associated with fission products, or (ACT) for decay power associated with actinides)(W)

Pri = Metallic layer Prandtlnumber

. Q(n)- = . Heat generation rate in layer n (W/m3 )

I R = Vesselradius(m)

'b,(n')_ = Upper radius forlayer n (m) i A 15 INEEl> EXT-97-00779

. _ . _ . _ _ . . _ _ . _ . . . _ _ . _ _ . , _ . _ _ _._ _. _ ~ .. __ _

R'(i./ = Ratio of upward to downward heat fluxes in ceramic layer n Rai(n) = Rayleigh number based on temperature difference of melt in metallic layer n ,

Ra(n)' = Rayleigh number based on u,lumetric heating of melt in layer n [may be further designated by the subscript (1) for metallic layer or (p) for ceramic layer) ,

S(n) = Area of volume n (may be further designated by the subscript (dn) for lower 2

surface, (side) for side surfaces, or (up) for upper surface) (m )

2 S, = Upper plenum nructures' surface area (m )

Tn(n) = Film temperature at surface of metalFe layer n (may be further designated by the subscript (bot) for lower surface, (side) for side surfaces, or (top) for upper surface)(K)

T,(n) = Average temperature of molten material in ceramic layer n (K)

T(n) i

= Temperature of metallic layer n (may be further designated by the subscript (bot) for lower surface, (bulk) for bulk, (m) for liquidus, or (top) for upper surface) (K)-

Ti .,,,# ) = Vessel steel inner surface temperature at locations adjacent to metallic l layer n (K) >

T,(n) = Liquidus temperature of molten material in ceramic layer n [may be further designated by the subscript (m) for liquidus or (max) for maximum) (K)

, T,.,,i(n) = Difference between maximum and minimum temperature in ceramic layer n (K)

T, = . Upper plenum structures average temperature (K)

- T, = Upper plenum structures' temperature [may be further designated by the a' subscript (i) for inner surface or (o) for outer surface] (K) -

T,,,(0)

= Angular dependent vessel temperature on inner vessel surface at locations -

adjacent to ceramic layers (K)

T,,, = -Average vessel temperature on vessel inner surface at locations above the metallic layer (K) ,.

T,_,,,, , = - Vessel steel liquidus temperature at locations adjacent to the ceramic layers (K)

T, . = Vessel temperature on outer surface (K)_

INEELEXT-97-00779 A 16

=.- .

V(n)- *= Volume of layer n (my be further designated by the subscript (ss) for stainless steel, (U) for urar. lum, (UO2 ) for uranium dioxide, (Zr) for zirconium, or (ZrO2) 3 for zirconium dioxide)(m )

V% = Volume of vessel hemisphere (m3 )

-V = Total volume of metalliclayers (m3 )

Vp = Tbtri volume of ceramic layers (m3) -

V ,(n)- = Cumulative voldme of relocated debris up hrough layer n (m3) 2 . Molecular weight (may be further desigt.ated by the subscript (02) for oxygen (15.994 kg/kg-moles), (ss) for stainless steel (55.066 kg/ks moles), (U) for uranium (238.029 kg/kg moles), (UO2 ) for UO2 (270.02 kg/kg-moles), or (Zr) for zirconium (91.22 kg/kg moles))

a(n) =- Bermal diffusivity in layer n (may be further designated by the subscript (1) for metallic layer or (p) for ceramic lapr] (m2 f,)

$(n) = Volumetric coefficient of thermal expansion in layer n (may be further designated by the subscript (1) for metallic layer or (p) for ceramic layer) (K*l)

$ = Volumetric coefficient of thermal expansion (may be further designated by the subscript (ss) for stainless steel, (U) for uranium, or (Zr) for rirconium) (K*l) 8,,(0,n) = Angular-dependent thickness of crust along lower and side surfaces of ceramic layer n (m) 8;..,(n) = Crust thickness on upper surface of ceramic layer n (m)

Bi.,,,(n)= nickness of vessel wall near metallic layer n (m)

- 8, = nickness of vessel wall to estimate heat transfer from metallic layer (m)

- 6,. ,(6) = - nickness of crust on lower surface of ceramic layer (m) 6, = nickness of upper plenum structures (m) 6,,,(0) = nickness of vessel wall adjacent to ceramic layers (m)

-t = - Emissivity [may be further designated by the subscript (1) for metallic layer or (s) for upper plenum structure) 8' .= Angle from the bottom center of the vessel lower head (degrees) >

9(n)l .= - Angle from the bottom center of each layer n (degrees)

A 17 INEEIJEXT-97-00779 -

]

- _2.__

b(n) = Maximum angle from upper surface of volume, Via(n), with upper radius, Np(n), and height, H ,(n)(degrees) i p(n)- = Viscosity of molten material in layer n [may be further designated by the subscript (A side, fi top, or fi bet) for metallic layer Alm temperature at the side, upper, or lower surfaces, (1) for metallic layer at the bulk temperature, (p) for ,

ceramic layer at the bulk temperature) (Pa-s) p(n) = Density of layer n [may be further designated (1) for natallic layer or (p) for ceramic layer)(kg/m3) p = Density [may be further designated by the subscript (1 ss) for molten stainless steel in metallic layer, (1 Zr) for molten zirconium in metallic layer, (1 U) for molten uranium in metallic layer, (p-ZrO2 ) for molten zirconium dioxide in 3

ceramic layer, or (p UO2 ) for molten uranium dioxide in ceramic layer) (kg/m )

2d o = Stefan Boltzmann constant (5.672x10-8 W/m K )

o,m = Standard devia' ion for estimating the average Nusselt number for molten material in ceramic layer n [may be further designated by the subscript (dn) for downward or(up) for upward) i V(n) = Kinematic viscosity of material in layer n [may be further designated by the subscript (6-side, fl top, or fl-bot) for metallic layer film temperature at the side,

" 2 upper, or lower surfaces, (1) for metallic layer or (p) for ceramic layer) (m j,)

4 5

INEE!JEXT 97-00779 A _ _

3 I

, Appendix B - INEEL Input Uncertainty Distributions

. VESTA calculations use Baye'sian uncertainty distributions, which are ultimately combined by a :

Monte Carlo sampling to yield a distribution on the probability of vessel heat fluxes exceeding CHF. As

- discussed in Section 2.3, INEEL determined that many of the input uncertainty distributions assumed in ,

g the UCSB study should bel modified. Collectively, these modifications affect results for the UCSB- ,

assurned FIBS, Table B 1 compares INEEL and UCSB assumed input, and Section 2.3 summarizes '

INEEL input uncertainty distributions for the UCSB assumed FIBS. This appendix provides additional .

information used to derive INEEL input uncertainty distributions.

! B.1 Host Transfer Assumptions i

s 1.1 Average Convection Heat Transfer from a Molten Pool l

~

DOE /ID 10460 Approach.In DOE /ID-10460, comlations for predicting average heat transfer from a molten pool containing a fluid that is volumetrically heated with turbulent natural convection were based

. on data from the UCSB Mini ACOPO tests. Purther testing was subsequently carried out in the ACOPO facility, which is a larger scale version of Mini-ACOPO (Mini ACOPO is a 1/8th scale facility; ACOPO is i a 1/2 scale facility).3 Comlations obtained from the Mini ACOPO and ACOPO tests differ, Although DOE /ID-10460 Appendix V suggests that correlations based on ACOPO are more appropriate, it

concludes that differences in these comlations don't impact their conclusions because the upward to downward heat loss ratio is preserved. No uncertainties are considered in the Mini ACOPO comlations, l although sensitivity studies were performed in the UCSB study to assess the impact of assuming a limited number of other comlations.

INEEL Approach.The Mini ACOPO and ACOPO facilities use a unique approach to obtain natural consection heat transfer data for high Rayleigh number, volumetrically-heated molten pools. Rather than trying to produce uniform volumetric heating in a fluid, the Mini ACOPO and ACOPO tests simulate j volumetric heating by suddenly cooling the boundaries of a system containing preheated fluid and

- interpreting the transient system -:ooldown as a sequence of quasi-stationary natural convection states.

Figures B 1 and B 2 compare comlations obtained ' rom the Mini-ACOPO tests with various comlations from facilities containing volumetrically heated fluids (see Reference 25 for references describing the tests e

and facilities from which other correlations were obtained). Each correlation in Figures B 1 and B 2 is plotted over the Rayleigh number for which it was obtained. Although Mini ACOPO correlations differ from correlations obtained from other natural convection tests, the authors of DOE /ID-10460 maintain that

~

. their comlations are the most appropriate because higher Rayleigh number fluids were tested in a 1 hemispherical facility in the Mini ACOPO tests.

1 d

i~

< l l

B-1 INEEUEXT-97-00779 l l

Table B 1. Comparison ofINEEL and UCSB input assumptions.

Phenomena UCSB Input for HBS INEEL Input for UCSB assumed FIBS Requentification lleat T ratufer Molten Ceratruc Pool Heat Correlanons based on MinbACOPO dua, Correlanons and uncertamues for average heat trarafer bued on Transfer no uncertainues INEEL best. fit of ACOPO data

. Average Upward UCSB Equation 511 . INEEL Equation (B 6)

Average Dawnward . UCSB Equation 5 28 INEEL Equanon (B-7) lacahud Downward . UCSB Equanons 5.30s and 5 30b . UCSB Equanons 5.30s and 5.30b; uncertainnes from ACOPO data.

Cnucalllent Mua from a Corrtisuons based on ULPU data (UCSB Correlanons and uncertamoes based on Cheung SBLB data Vessel to a nooded Cavity Equauon E.3), no uncertainues. [(WR=3) curve INEEL Rgure B 7).

Mohen Metal Layer Heat Cornlmions based on MELAD data (UCSB Correlations based on MELAD data (UCSB Equations 5 40 and Transfer Equanons $ 40 and 5 41), no uncertainnes 5 41); uncertamues from MELAD data.

Decay Power Denalty Ceranuc Pool Stausucal combinanon of dec4y power Stausucal combinauon of UCSB decay power curve (UCSB curve (UCSB ngure 7.1) zirconium oxida- Figure 7.1) with ANS 5.1 Standard-recommended uncertainty dis-non fraction pdf(UCSB Rgun 7.3), and tnbution. UCSB zirconium oxidanon fraction pdf(UCSB Mgure rnett relocanon urne pdf(UCSB Egure 7.7). 7.3), and INEEL recommended shift of I bour in the UCSB pro-posed rnett relocanon tirne curve (DB Figure 7.7). Resulting pdf reduced by metalhe layer decay heat frecuon.

Metalhc IJyer No heat sources in the metalhe layer. Tame dependent fission product decay power fractions and uncer.

tainues associated with zircotuum, niobium, tellunum group, and noble metals group Material Properties Ceramic Pool and Crust

. Specific Heat Capactry Mass everage UCSB Table 7.1 values; no Mass everage UCSB Table 7.1 values; uncenainues assocised with uncertainoes. each component's value and with mass averaging.

. Thermal Conducavity UCSB Table 7.1 values; reduced Composinon-dependent values; uncertatnties frorn UCSD Appendix L uncertsnces Appendix L Melung Temperature 2973 K; no uncertamues 2850 K; no uncertainues

.Volumetnc Coefficient of UCSB Table 7.1 value, reduced Appendix L UCSB Table 7.1 value; uncertainnes from UCSB Appendix L.

Expansion uncertamnes Density Volume averge UCSB Table 7.1 values; no volurne averige UCSB Table 7.1 values; uncenannties associated uncertainoes with each component's value and with volume averaging.

Metalhc layer

.Speafic Heat Capacity Mass everage UCSB Table 7.1 values; no Mass average UCSB Table 7.1 values; unceruunnes associated with uncertainues each component's Salue and with mass averagmg Thermal Conductivity UCSB Table 7.1 values; reduced Appendix Composition dependent values; uncertainties from UCSB L uncertamucs Appendta L Volumetric Coefficient of UCSB Table 7.! value; teduced Appendix L Volume average UCSB Table 7.1 values; uncertaint.es associated Expansion uncertamnes with each component's value and with volume averaging Density Volume average UCSB Table 7.1 values; no Volume average UCSB Table 7.15alues; uncertainnes associated uncertainues with each component's value and with volume averaging Enussivity 0.45 (UCSB tests), no uncertamties Median value of 0.29, standard deviation of 0.04 (based on pub-hshed data)

Vessel Wall

. Thermal Conductivity Pomt esumates based on UCSB Figure L3 Median values and uncertaitties based on UCSB Rgure L3.

Upper Wall: Not clear Upper wall:41 i IW/mK; Lower Wall: 32 W/m 2K; no uncertainties lower Wall:32 2 2 W/mK .

Melting Temperature 1600 K; no uncertamties Zr Fe phase diagrarn; no uncertamnea i Upper internal Structures Thermal Conductiviry 30 W/mK; no uncertainues Temperature dependent values; standard deviation of 0.6 W/mK (based on pubbshed data)

Ennssivity 0 8, no uncertainnes Median value of 0 85, standard deviation of 0.03 (based on pub-hshed data) l l

l INEEL/ EXT 97 00779 B-2

10' . . . . . . . . .

108 -

I 2 .

10 f .

O e .....

..... .~.~ % Mint-Acopo 101 - ~ ~ . . . _ . . , ~ ~ . ~ .

10' -

10 ' - - - - - . . .

10 7 10' 10' 10 10" 1 052 10'8 10" 10'6 10 10" CW7 00s 1 Ra'P Figure B 1. Comparison of Reference 15 and Mini ACOPO downward heat transfer correlations.

104 . . . . . . . .

DOEllD-10460 Mini-ACOPO .

102 .

f ~ .

10t ..~._

10' 10 10'- 10' 10' 10 10" 1 012 10'8 10" 10'5 10 10" Ra'p Figum B-2. Comparison of Reference 25 and Mini-ACOPO upward heat transfer conclations.

B-3 INEEUEXT-97-00779

In Refetence 31, the authors present data from several ACOPO tests and correlations based on a

" typical" ACOPO run (Run 5/28/96). INEEL digitized data from the four ACOPO tests presented in Reference 31 (Figures 13 and 15) and determined that ACOPO data were better fit with the following correlations:' ,

two.1s -

Nu,.o = 0.1857Ra'lm (31) ,

N7,.., = 2.4415 Ra','"2' (B2)

Since the time that INEEL completed this analysis, a revised version of DOE /ID 10460 was published with ACOPO data added to Appendix V. The new Appendix V ACOPO run (Run 5/28/96) data and corre-lations differ from Reference 31 data and correlations.b Recent information32 indicates that UCSB study authors believe that the data presented in Appendix V are more accurate. In Reference 12, UCSB study authors assett that mini-ACOPO data were confirmed by the ACOPO data. However, Figures B-3 and B-4 indicate that Mini-ACOPO correlations differs from ACOPO data and correlations presented by UCSB in DOE /ID-10460 Appendix V and Reference 31 (PSA '96) and from INEEL best fit ACOPO correlations for Rayleigh numbers ofinterest (-101810 ),4Nevettheless, UCSB-recommended ACOPO correlations .

presented in Appendix V and in Reference 31 predict similar Nusselt numbers for Rayleigh numbers of interest. Because the two UCSB correlations yield similar Nusselt numbers and because INEEL consid-ered uncertainties in their correlations, INEEL did not modify the conelations based on Reference 31

[ Equations (B 1) and (B 2)) data to consider revised Appendix V information.

INEEL digitized ACOPO data from Reference 31. (Figures 13 and 15) were used to obtain appropriate uncertainty distributions for predicting upward and downward heat transfer. For these correlations, there are uncertainties associated with the method selected for simulating natural convection in the AP600 reactor vessel, the reproducibility of the tests, the variability asw:iated with performing tests in different facilities, and experimental instrumentation error. Comparisons with results obtained from other experimentalists investigating natural convection phenomena suggest that there is typically 20 to 30% uncertainty in the abtisty of their correlations to predict data from their tests.25 The scatter in the data plotted on log plots (Figures B-3 and B 4) appeared uniform. Hence.- l

' logarithms were used. Base 101ogarithms were selected because the data were taken from the log-log plots i shown in Figures 13 and 15 of Reference 31. A straight line was fitted to the obtained data. 'Ihe random !

scatter around the true straight line was assumed to represent measurernent error, and to be normally distributed with constant standard deviation. The fitting line was estimated using least squares. The form of the fitting line can be written i

a. The Mini-ACOPO and ACOPO tests only considered cases with H=R. However, the Westinghouse '

response to RAI 480.961 Indicates that UCSB assumed that the Mayinger correction factor H/Ra25, may be

. applied to their correlation. Because previous experimental data suggest that correlations should be modified to consider cases with H < R, this factor was included in the INEEL correlation.

b. Appendix V (Figures V.13 and V.15) contain data from Ave ACOPO tests at 200 second intervals; whereas Reference 31 (Figures 13 and 15) only contains data from four ACOPO tests at 400 second intervals. How-ever more data from Run 5/28/96 appear in the Reference 31 figures, and different correlations are recom-mended by UCSB in Appendix V and in Reference 31. J

-97 O I-4

10000 . . i DOE /ID-10460 Mini-ACOPO

...... INEEL ACOPO-best f;t (Eqn. B 1)

...... DOE PSA '96 ACOPO

- - DOE /ID 10460 ACOPO 1000 -

m ACOPO data (PSA '96) . ,,g e M'* "

s *,,,, ,

Z ..... " , ,:~. -

2"*,,.....,......"' -

100 10 10 10" 10" 10" 10

, ce nisi Figure B-3. Comparison of ACOPO and mini-ACOPO downward heat transfer correlations.

10000 . .

DOEllD-10460 Mini-ACOPO

. ...... INEEL ACOPO-best fit (Eqn. B 2)

- --- DOE ACOPO-PSA '96

- - DOEllD-10460 ACOPO a ACOPO da'a (PSA '96)

$ 1000 -

99n9N'

e. , ,... . #;....

100 10

10" 10" 10" 10" ceca Figure B-4. Comparison of ACOPO and mini-ACOPO upward heat transfer correlations.

B-5 INEE1 EXT 97-00779

l 4

I l

logN7, = C(+ C (logRa,'-logRa',)

-(B3).

wh;te

. , - . . . _ . . ~.

3- Ci =. Thimeted as ":,'181 for modeling downward heat transfer, and estimated as - -

2.9TJ5 fm testdirig upward heat transfer.' i 2

.C: = Estimated as 0.2304 for modeling downward heat transfer, rnd estimated as ,;

, 0.1722 for modeling upwani heat transfer. - 4 log Ra', =- The average oflogio fothe ceramic pool Rayleigh number. Estimated as 14.9701 for modeling downward heat transfer and estimated as 15.0148 for modeling upward heat transfer, 1lthitstir4 the nominal values for C and i C into 2 Equation (B 3) yields Equations (B-1) and (B-2). How-ever, the average, log Rn',, is subtracted it Equation (B 3)in order to allow the equation to be expressed in a form so that the estimators of the p ..m:s Ci and C2 are statistically i%adant. The usual confi-dence interval for log Nu is based on the fact that the quantity Estimator oflog Eis,-true log NIs, (B-4)

[se' + se*(log Ra/ - log Ra',)')"'

has a Student's t distribution with degrees of freedom equal to the number of data points, n, minus the number of estimated parameters, 2 (C , C2 ). Here, sei and se2 are the standard etron of Ci and C 2.

respectively. Writing the above expression as T and rearranging terms yields the recommended Bayesian uncertainty distributions for log Nu.

Estimator of log Nu, + [se' + se'(logRa,'- logRa',)*]" T (B-5)

, where Thas a Student's t distribution with n - 2 degrees of freedom. This distribution was selected because it accounts for the error in estimating the true variability from the observed scatter in a limited amount of data. The Student's t yields uncertainty intervals that are numerically the same as the usual confidence intervals.

~

. . Therefore, VESTA applies the following uncertainty distribution for log Nup.4.

loge,. . = 2.7181 + 0.2304(logRa,'- i4.9701) + [0.0023' + 0.0040'(logRap '- 14.9701)') T (B-6) where 7 has a Student's distribution with 22 degrees of freedom (corresponding to the number of data points displayed in Figure 15 of Reference 31 minus the 2 estimate parameters). For apward heat transfer, VESTA applies the following uncertainty distribution for log Nup.r,,

2 log Nu,~.., = 2.9735 + 0,1722(logRa/- 15.0148) + [0.0021 + 0.0035'(103 R a,'- 15.0148)') T (B-7) where T has a Student's t distribution with 53 degrees of freedom (corresponding to the 55 data points displayed in Figuins 13 of Referer3:e 31 minus the 2 estimate parameters).

DEEUEXT-97 00779_ B-6 l

s

o B.1.2 Local Heat Transfer from a Volumetrically Heated Molten Pool DOE /ID 10460' Approach.ne UCSB study applied data from UCSB Mini-ACOPO tests to obtain the following equations (Equation 5.30s and 5.30b_of DOFAD 14060) for pr'edicting heat transfer as a function of angle along the bottom of the hemisphere.

"!.d * = 0.1 + 1,06(1 -4.5 + 8.6(0,,a 0.1 s( 00,,, 5 0.6 (B-8)

' N up. 4. 0,,o A,o

} 0--

J = 0.41 + 0.35 +I0 -- ;

0.6<[0,,,s1.0 (B 9)

Nu,.4. @,,, 50,,, <

where 0 = Angle from bottom of the ceramic pool, deptes 0,,, = Maximum angle at upper surface of ceramic pool, degrees

, Nup.4,(0)= Pool Nusselt number in the downward direction at angle. O P N7,.4. = Average ceramic pool Nusselt number in the downward direction The UCSB study neglected uncertainty in the above correlations.

,- In Appendix V (Figure V.11) and in Reference 31 (Figure 11), location-dependent Nusselt data from a " typical" ACOPO run (Run 5/28/97) are compared with Mini-ACOPO correlations.* At shown in Figure B 5, ACOPO data vary from the Mini ACOPO correlation, However, the authors conclude in Appendix V that the Mini ACOPO correlation " represents a fair representation through the middle of Jie data."

INEEL Appmech.The UCSB approach did not consider any uncertainties. In general, there are uncertainties associated with the ability of an experiment to simulate the situation of interest, the reproducibility of the data, and experimental measurement techniques. In this case, the Mini-ACOPO and ACOPO texts used a hemispherical facility, whereas the UCSB FIBS analysis assumed cersmic melt-masses that resulted in a pool maximum angle of only -75* Although no data are presented to support this

assertion, UCSB authors claim that the normalized angle in their correlation makes it valid for such cases.

' It is difficult, if not impossible, to appropriately account for all of the uncertainties associated with applying the Mini ACOPO,co relation. In VESTA calculations, INEEL used the variability between ACOPO data- and the Mini-ACOPO correlation as an estimate for uncertainty. DOFAD-10460 Appendix V data suggest that the uncertainty in localized heat transfer is normally distributed with a standard deviation of 0.12. His standard deviation describes scatter of the data around the Mini-ACOPO correlation, not uncertainty in the value of the curve. However, it is probably a conservative bound on the

- standard deviation corresponding to uncertainty in the curve because the standard deviation of data is typically greater than the standard deviation of the fitted mean. Mini-ACOPO and ACOPO data indicate

- a. Data displayed in Figure 11 of Reference 31 and Figure V.ll of Appendix V appear identical.

B-7 INEE!JEXT-97-00779

2.5 , , , , , , . . .

s ACOPOdata Mini-ACOPO correlations (DOE /ID 10460 Eqns. 5.304 and 6.30b) -

2.0 ,

m ,

a 1.5 3 .

1.0 -

s s

0.5 .

e a I be ! , , , , ,

0 10 20 30 40 50 60 70 80 90 100 Angle (degrees)

Figure B 5. Comparison of typical ACOPO data (Run 5/28/96) with Mini ACOPO correlation.

that the values for 9/0, s 0.6 and 9/0, > 0.6 are related. Hence, VESTA simulates uncertainty for these relationships by including in each equation a new variable, which is normally distributed with a median value of 0.0 and a standard deviation of 0.12. Because the value for Nu,,(0) must be positive, VESTA limits the minimum value of Nu,,(0) to a small number (0.01).

8.1.3 Critical Heat Flux from a Vessel to a Flooded Cavity DOFAD 10460 Approach. 00FXs 10460 predicts CHF using a " lower 1,ound" correlation based on data from the UCSB ULPU Cos.tiguration11 tests without insulation (see Figure B 6). Natural circulation occurred in these tests. The gravity head tint existed in these tests resulted in a water depth to vessel radius ratio of approximately 4 (H/R = 4). This gravity head is estimated to result in approxirnately 14 K subcooling at the bottom center of these tests. Tov UCSB study assumed zero uncertainty in this correlation because it is supposed to be a lower Wnd correlation for ULPU Configura' ion 11 data. In the Reference 12 response to RAI Question 480.448. Westinghouse states that the uncertainty in the CHF is below the 20% uncertainty normally associr.ted with experimental tests because of advantages in the ULPU facility that allowed them to " sero in" on the CHF value by successive runs. After the UCSB report was issued, addition.ai testa were completed in ULPU to assess the impact of reactor vessel insulation on ,

ex vessel heat transfet. 'the ULPU dats shown in Figure B-6 suggests that there are no distinct differences between ULPU Ccafiguration II and Configuration III data.

INEEUEXT 97-00779 B-B

_ _ _ _ . _ _ _ _ _ _ _ _ _____ _ _ _ _ _ _ _ . ~ . _ _

k s T 1 I I y I E I i

i [

1.5 ,

! ! E l 1.0 I

i 1r a

0.5 I -

o e utpu.ll FulFlowData(w/oinsulanon)

ULPU ill Copper CHF (w insuletion)

- DOE /ID 10400 Eqn. EJ a i 1 a 1 e i 1 O 10 to 80 40 60 to 70 80 80 ,

Angle (dogrees) ei- - .

1 Figure 3 4. Comparison of UCSB lower bound" CHF correlation (DOFl!D 10460 Eqn. E.3) with ULPU Configuration 11 and 111 data.

t

, -INEEL Approach.Cheung et al. developed a scaling law for estimating CHF as a function of several parameters, such as coolant pressure, local coolant subcooling (associated 'C.th gravity head), coolant velocity, vessel size, and position.33 In Reference 33, Cheung demonstrates that this scaling relationship ,

successfully predicts data from the Subscale Boundary Layer Boiling (SBLB) tests 34 and the ULPU

- Configuration 11 tests. Figure B 7 compares results from this scaling relationship applied to an AP600 reactor vnsel with coolant at atmospheric pressure. '!hree cases are shown to reflect the difference in CHF due to local coolant subcooling associated with gravity head (denoted by the ratio of the reactor cavity coolant height to vessel radius, H/R). As shown in Figure B 7. CHF increases with coolant height (because of increased subcooling associated with coolant head). 'lhe lower bound ULPU Configuration 11 correlation, which is also plotted in Figure B-7, ranges between correlations with water depth to vessel

radius ratios between 1 and 3 (1 s H/R S 3) for angles less than 75' from the bottom of the vessel and exceeds H/R for angles greater than 75'.

4 B INEEUEXT 97 00779

_ _. .. _ . _ . . _ . . ~ , ._ __ -. , _ _ . _ . _ . . . _ . . _ , . . _ _ _ , _ _

1.6 . . . , , ,

1.4 -

.r,,..." -

f ,7 '

/ -

1.2 -

g' "

1 11- ,,..*"

0.0 -

0.6 , ....... DOE /ID 10440 Egn. E.3 -

, Cheung CHF Soehn0 Law Kb1 0.4 -

nm2

gg3 0 to 20 30 40 60 60 ho 80 90 Angle (degrees) a.

Figure B.7. Comparison of ULPU and Cheung SBLB correlations.

Figure B 8 illustrates time dependent cavity water levels bued on information presented in Section 39 of the AP600 PRA.3 This figure shows cavity water levels for cases in which one and two cavity flooding lines are assumed open. Figure B 8 water levels assume that water in the cavity prior to operator-initiated flooding (due to water exiting the break) causes the cavity water height to initially be near the top of the hemisphere of the vessel.' SCDAP/RELAP5,3 MELCOR,4b and MAAP4 536 calculated times for when molten pools would occur in the lower head for AP600 3BE type transients are plotted in Figure B-

8. In Appendix 0 of the UCSB study, the authors estimate that their assumed FIBS occurs at approximately 120 minutes after the operator initiates flooding. Differences in estimated molten pool formation times are primarily attributed to differences in assumptions pertaining to failure of the reflector, failure of the co e plate, and debris quenching during relocation. Although estimated molten pool a; A review of MAAP4 calculations for cases with one cavity flooding line and no IRWST gravity injection found that coolant exiting the RCS cauwd the cavity water to be near the top of the hemisphere. However.

- there was considerable variation in MAAP4 predictions for the time between the point where the initial water exited the break and the time when the operator initiated cavity flooding and in predictions for the cperator initiated cavity nooding fill rates. Because Westinghouse has initiated an AP600 Severe Accident Management Guideline (SAMO) change that would reduce the time till the operator initiates cavity flooding, cavity Couding rates were based on information in Section 39 of Reference 1 (which assumes that cavity flooding is initiated near the time of the break).

' b.These calculations were performed assuming no material interactions or eutectic formation.35 Earlier mol-een pool formation times would be predicted if materials interaction models were invoked.

INERIJEXT 97-00779 B 10

l

~

fonnation times differ, the ratio of the water height to the vessel radius varies between -2 and 4.4 (the maximum flooding height) for time periods when these references predict molten pools are present in the lower head. ,

6 - -

One cavity floodmg kne, no IWRST grevny dreh6ng

..... Two cevny flooding lee, no fWRST pfavny drahing

,7,$.

- ~

3 g, . .. ...... -

- ~

T l 1 0 -

M% ic g .

.M '

?

" l&"E

1 0 N 100 160 200 Time after operator initiates cavity flooding (min.) ===

Figure B 8. Comparison of predicted molten pool formation times with cavity flooding rates shown in the AP600 PRA.

In addition to uncertainties associated with estimating coolant height (and associated subcooling) at the time of relocation and molten pool formation, experimental errors contribute to uncertainties in 38 estimating CHF.37 Cheung indicates that there is typically 7% uncertainty in his conclations for predicting SBLB CHF data [because of uncertainties associated with instrumentation, reproducibility of results, geometry, surface conditions, heat flux (power shape) assumptions, etc.).

In light of the calculated molten pool formation times shown in Figure B 8, INEEL assumed the Cheung (H/R=3) correlation for analyzing the UCSB ansumed FIBS and the Cheung (H/R=2) correlation for analyzing various intermediate states postulated to occur following initial molten pool formation.

Discussions with Cheung38suggest that the relative uncertainty in his correlations is constant, with 95th.

percent uncertainty limits of 10% (20/p = 10%). In this case, the standard deviation describes scatter of the data around the line, not uncertainty in the value of the curve. However, it is probably a consenative

- bound on the standard deviation corresponding to uncertainty in the curve because the standard deviation of data is typically greater than the standard deviation of the fitted mean.

l B 11 INEE1/ EXT 97 00779

. - - - - - - . - _ _- = . - - - _ . _ - - - - . . .

i ne nattaral logarithm of this correlation was used in order to obtain an absolute standard deviation that is indeperident of the magnliude of CHF. It can be shown, using a Taylor series approximation that3 '

c(In x) =

I*} '

(B10)

As noted above, Cheung reports that o/g = 0.05. nerefore,INEEL chose to work with natural logarithms, and assigned 0.05 as the standard deviation of in (q" cur ).

INEEL neglected insulation effects. As discussed above, data from ULPU Configuration III (with insulation) don't differ significantly from data fiom ULPU Configuration II (without insulation). ;

Preliminary results from SBLB tests with insulation suggest that the presence of insulation will increase heat removal.38 However, heater dimeulties prevented CHF from occurring in these tests. When SBLB tests with insulation are successfully completed, the impact ofinsulation should be considered.

3.1.4 Heat Trenefer from a MoHen Metallic Layer DODID.10460 Approach.To predict heat losses from the metallic layer to the vessel wall, DOE /ID-10460 Section 5 states that the following fonn of the Churchill and Chu correlation (Equation 5.35 of DOE /ID 10460)is used:

Nui..,,,, = 0.076Rai 8 (B11)

DOE /ID 10460 Section 5 also states that heat transfer across the horizontal surfaces of the metallic layer is modeled using a " specialized" version of the Globe Dropkin correlation:40' Nui.,,n = 0.15 Rae (B12)

Section 6 (Equation 6.11) of the UCSB study implies that the following, more general, forms of the above correlations were applied so that the fluid's Prandtl number could be explicitly modeled.

Nui.s.,, = 0.069RaiPri" (B.13)

Nu 0.825 + 0387Rai OBRai

"= ,

(B14)

. [ t + (0.492/Pri)']". [l + (0.492/Pri)'f'"

In Appendix N the authors of the UCSB study acknowledge that there was no information in the literature that validated the application of these correlations to cases in which horhontal and vertical heat transfer occur simultaneously. Tojustify their approach, the au hors conducted the MELAD (Metal Layer Demonstration) tests in which heat transfer was measured from water contained in a rectangular box (50 .

cm long,10 cm wide, and 10 cm in height) with one side surface insulated, one side surface and the upper surface cooled, and the lower surface heated. In Appendix N of DOE /ID.10460, the authors compare

n. Information in the UCSB study suggest that this specialization was performed by redefining the tempera-ture difference as the difference between the temperature in the upper (or lower) surface and the temperature at the midplane of the metallic layer. -

INEEIAXT 97 00779 B 12

MELAD data to values predicted by their Chu-Churchill / localized Globe Dropkin model and conclude that theit model is adequate. De UCSB study applies these conelations without uncertainties.

INEEL Approach. Although Appendix P of the UCSB study considered a sensitivity case in which heat was transposed to the metallic layer and Appendix R of the UCSB study acknowledges that a fraction of the fission products (and their associated decay heat will be retained by the metallic layer), the UCSB study neglected the impact of volumetric heat sources on heat transfer from the metallic layer.

Funhermore, neither the Globe Dropkin, the Chu-Churchill, nor the MELAD tests considered heat transfer from a fluid layer above a volumetrically heated fluid. Herefore, INEEL evaluated the irapact of volumetric heating within and below the metallic layer on heat transfer and used MELAD data to quantify appropriated uneenainty for the metallic layer heat transfer correlations.

For the various debris configurations analyzed by INEEL, volumetric heat sources within the metallic layers resulted in Rayl'eigh numbers ranging from 2 x 10 8 to 3 x 1012. As discussed in Section 5 of the UCSB study, many of the turbulent natural convection heat transfer correlations developed for pools with Rayleigh numbers within this range. lience, INEEL compared Nusselt numbers estimated from selected natural convection heat transfer conelatinns described in Reference 25 with values obtained from the Globe Dropkin and Chu-Churchill conelwns assumed in the UCSB study. In general, the values predicted from correlations based on volumetric heat sources were comparable to or lower than values predicted with the conelations assumed in the UCSB study.

As documented in Reference 40, the Globe Dropkin tests considered a single layer fluid confined between two horizontal plates with the lower plate heated. Several references have developed conelations from tests in which an intemally heated fluid layer existed below a second unheated, immiscible fluid layer. Correlations based on several of these tests [Fiegd3 and Kulacki/Emara,42 which vary with the ratio of the unheated layer height to the heated layer height (L 3 /L 2 )') are compsed with the Globe Dropkin correlation in Figure B 9, As shown in this figure, the Globe Dropkin correlation predicts higher upward heat losses than the Fieg or Kulacki/Emara conelations.

The above information suggests that there is considerable uncenainty in assumptions related to heat transfer from the metallic layer because of the presence of volumetric heat sources within the metallic layer and within the lower ceramic layer. Additional experimental tests are required to reduce the uncertainty associated with heat transfer from the metallic layer. liowever, the various correlations typically yielded Nusselt numbers with the same order of magnitude for the pool Rayleigh numbers investigated by INEEL.b Although the UCSB sponsored MELAD A tests neglected the impact of volumetric heat sources, these tests did consider simultaneous heat transfer in the horizontal and venical directions. Therefore, INEEL used MELAD A test data to estimate heat transfer from the metallic layer. It 8

is interesting to note that recent FoyalInstitute of Technology calculations indicate that MELAD A test data agree with the correlations recommended by two other references for predictinE heat transfer from an d3 unheated layer above a volumetrically heated layer and from a volumetrically heated boiling pool."

a. Although many of the Reference 42 correlations were developed in te ins an internal Rayleigh number based on the heights of both layers, the Kulacki/Emara correlation compared in Figure B 9 was developed in terms of a modified Rayleigh number based on the upper layer's height and a maximum possible tempera-tu:e difference across the unheated layer (see Figure 4.7 of Reference 42).

b. *Ihe manner in which INEEL formulated the Configuration B and C analyses did not require that the metallic layer heat transfer coefficient be assumed. Hence, these values were only required for the UCSB-assumed FIBS and Configuration A calculations.

B 13 INEE1/ EXT 97 00779

i i

i l

300 . .

Globe Dropkin '

pg ,

20 . .. . ...KulaciWEmers

.. . L,/L, = 0.111

~

........ ..... L,/L, m 0.433 i & ~

ug eme

' l

% 4 l

~ .,

. . .~ . " "

j l 'so .,,,......

~ ~ " " " . ". .*. ". , . . . . . . .

" . ." .. ~. .. .. ... .. .. .. ... .. .. .. .. ... .. .. ....~.

80 ~~ u m:w::.... ..............

em.

~

~,,,,

,____.-..---~~ -~~~~

0 10' 10 10" i

, Ra, est em FigWfe S 9. Comparison of correlations for predicting upward heat transfer from the metallic layer. !

Similar to the apptrach followed in the UCSB study, INEEL assumed Prandtl number dependent versions of the " specialized" form of the Globe Dropkin correlation for venical heat transfer and the Chu. - ,

Churchill correlation for horizontal heat transfer. MELAD A test data presented in DOE /ID 10460 Appendix N were manipulated to obtain the Nusselt number versus Rayleigh number plots shown in Figures B.10 and B ll. Variances between MELAD data and comlation predictions were calculated for e.ach heat transfer direction. For horizontal heat transfer, the relative standard deviation (c/g) was found to equal 8.8%; for venical heat transfer, the relative standard deviation (c/p) was found to equal 15E Here, the standard deviation describes scatter of the data around the assumed comlations, not comlation uncensinty. However, it provides a conservative bound on the o comsponding to comlation uncenainty because the standard deviation of data is typically greater than the standard deviation of the fined mean.

'the natural logarithms of these heat transfer comlations [ Equations (B 13) and (B 14)) were used so that an absolute standard deviation could be obtained [see Equation (B.10)]. Because there were limited data for measuring heat transfer, INEEL used a Student's t distribution to represent the uncertainty in these contations. As discussed above, a Student's i distribution accounts for the error in estimating the true variability from the observed scatter in a limited amount of data and yields uncenalnty intervals that are numerically the same as the usual conrulence intervals. The assumed comlations were developed -

independently from MELAD data. and there were no estimated parameters (see discussion about degrees of freedom in Section B l.1). Hence, three degrees of freedom were assumed for estimating uncensinty in ,

horizontal heat transfer (consponding to the three data points in the horizontal direction). For venical-heat transfer, six degrees of freedom were assumed (consponding to the three data points taken in the upward direction and the three points taken in the downward direction).

INEEUEXT 97 00779 : B 14 -

. ,-._-.a. - - - - , - . = - . , , . . .

260' o MELAo wr surface e McLAD upper surface Giwe/Dropkin correlabon 'specialitof Upper surface

Lower surface O ,

gog . .

e DC

160 9

I 10' 10' 10*

Ra, cc ==

Figure B 10. Comparison of MELAD A data with " specialized" Globe Dropkin correlations.

160 m MELAD side surfeos Chu/Churchillcorrelabon side surface 160 140 gg . D .

339 4

110 o

100 o -

10' 10' 10*

Ra, ev Figure B 11. Comparison of MELAD A data with the Chu-Churchill conelation.

B 15 INEEUEXT 97 00779

I 1

B.2 Decay Heat Assumptions 8.2.1 Decay Power Density DOE /ID.10460 Approach' .The pdf assurned for the decay power density in the UCSB analysis was derived by statistically combining the decay power curve (which included some treatment of volatile fission products) shown in DOMD-10460 Figure 7.1 and pdfs for the fraction of zirconium oxidized ..

(DOMD 1040 Figure 73) and the core relocaticn time (DOMD 10460 Figure 7.7). DOMD 10460 Figure 7.8 illustrates the pdf obtained by statistically combining their assumed values.

INEEL Approach. For timeframes of interest during a reactor accident, decay heat is primarily produce 2 by fission products and actinides present in core rnaterial. It appears that the UCSB approach is basically sound. However, their decay power density pdf does not appropriately account for uncertainties in the decay powet curve or core relocation time. Consequently, the edge of spectrum value (with an assigned probability of zero), was non-conservatively limited to only 1.4 MW/m 3. INEEL imposed two changes in the UCSB method for estimating decay power density. First,INEEL considered ANS 5.1 recommended uncertainties in the decay power curve shown in Figure 7.1 of the UCSB study. Second, INEEL reduced the melt relocation time shown in DOMD-10460 Figure 7.7 by one hour. Reasons for these recommendations are discussed below.

The decay power remaining in relocated melt is influenced oy irradiation history, heatup transient, cooling time, enrichment, and neutron spectrum. Although decay power may vary more because of assumptions pertaining to these factors, INEEL believes that, as a minimum, the UCSB study should have considered the uncertainties in calculating decay heat for the particular power history and cooling time.

According to the 1979 ANS 5.1 Standard," decay power predictions for a particular irradiation history and cooling time may be assumed to be normally distributed with a relative standard error of 5%. In order to capture ~95% of the decay porer uncertainty, one should apply error bands of 10% (2 o/p). This 10%

uncertainty is consistent with the decay power uncertainties recommended by NRC."

Table B 2 compares the decay power used in DOE /ID 10460, the decay power one would obtain by accounting for pertinent uncertainties associated with the ANS Standard, and the discrepancy relative to what was used to evaluate IVR. In their Reference 12 response to RAI Question 480.452, Westinghouse asserts that the decay power curve used to evaluate IVR is similar to an ANS decay power cune with a reported adjustment of +2a. However, it appears that the UCSB study non-conservatively limited a by only considering uncertainties associated with mU, while the 1979 ANS Standard also provides a methodology for considering three-group (*U,mU,mPu) behavior. As indicated in Table B 2, the UCSB study used a decay power that was generally consistent with their interpretation of the ANS 5.1 Standard and 10% lower than values that one would obtain if appropriate upper bounds on uncertainties were considered.

For the UCSB assumed FIBS, INEEL applied the DOMD 10460 Figure 7.1 decay power cune (that includes volatile release). However,INEEL assumed that values from this curve were median values a of normally distributed data with 95th-percent uncertainty limits of 10% (20/p = 10%). Note that the INEEL decay power demity (Column 4 of Table B 2) is later reduced by the fraction of decay heat estimated to exist in the metallic layer (see Section B.2.2). '

INEEUEXT 97 00779 B 16

l l

Table B 2. Comparison of decay powers.

Decay Power, Decay Power, Decay Power,1979 DOMD 10460 nieaftn DOMD 10460 1979 ANS 5.1 ANS 5.1 Standard Decay Power Shutdown (s) re 11 WW) Standard (MWf +10% (MW) Discrepancy (%)

200 62 55.9 61.5 0.81 500 48 46.8 $1.5 7.29 1000 40 40.1 44.1 10.3 2000 33 33.2 36.$ 10.6 3000 29 29.3 32.2 11.0 5000 25 25.0 27.5 10.0 10000 21 20.4 22.4 6.67 20000 17 16.9 18.6 9.41 40000 14 14.0 15.4 10.0

a. According to information contained in the Reference 12 response to RAI Question 480.452.

The edge of spectrum value should also bound estimated relocation time uncertainties. A high probability (-90ck) was assigned to core relocation times between 4 and 5 hr in DOE /ID 10460 Figure 7.7.

(The remainder of the distribution included a probability of -10% for core relocation times between 5 and 6 hr.) However, existing code calculations 3AJ indicate that core relocation in an AP600 3BE transient occurs earlier. For example, both SCDAP/RELAPS and MELCOR calculations3A suggest that significant amounts of core material relocate ~3 hr after shutdown. 'Iherefore, INEEL shifted the Figure 7.7 distribution -1 hr earlier. Using values published in the UCSB study (i.e., a decay power of 20.7 MW at 3 hr and a decay power of 19.2 MW at 4 hr), a 1 hr core relocation shift increases decay power by -8ck.

In Reference 12, Westinghouse provided arguments regarding the timing of core relocation in their response to RAI Questions 480.105,480.453, and 480.454. In these responses, Westinghouse stated that:

(1) core relocation could not occur earlier than 4 hr after transient initiation because the reflector is massive (implying that a substantial part of the reflector must melt before core relocation), and (2) SCDAP/RELAP5 results showing core relocation at ~3 hr were not reliable because the analysis didn't include the :ffect of the reflector on melt progression. The SCDAP/RELAPS code calculations do model the reflector. However, SCDAP/RELAPS considers the potential for localized reflector failures and corresponding side ways relocations. Specifically, at some point during asymmetric core degradation, molten materials could spread to the reflector boundary. At that time, a localized region of the reflector will be subjected to very high heat fluxes from the core side with only stagnant steam cooling on the downcomer side. SCDAP/RELAP5 calculations indicate that the reflector will melt through under those conditions in a matter of minutes. Some amount of reflector steel could be entrained following localized melt through/ ablation and carried with the core debris into the lower head. However, it is also possible that the hole in the side of the reflector could be relatively small, adding only insignificant amounts of stainless steel to the debris bed.

B 17 INEEUEU 97 00779

4 . j r

s VESTA' statistically combined distributions for decay power and relocation time with the pdf for rirconiurn oxidation shown in Figure 7.3 of DOE /ID 10460. Results, shown in Figure B.12, suggest that the most probable values for decay power density increase by 9% and that the edge of spectrum decay power density increases from 1.4 to 1.7 MW/m3.

f 6 . . l DDE/ID 10400 7 . .......lNEEL -

6 -

6 j<,

4 4 ,

\

3 - \ -

I

\

2 - -

l ,

/

1

/ \'

~

/ .

n _... , \'.._

0.6 1.0 1.6 2.0

~

Decay power density (MW/m')

Figure B.12. Comparison of DOE /ID 10460 and INEEL pdfs for decay power density.

3 it is worth noting that a decay power density of 1.7 MW/m agrees with the adjusted value calculated by SCDAP/RELAP5 at the time when peak thermal loads occur on the lower head 3 (7he SCDAP/

RELAP5 value was adjusted for a +10% uncertainty in decay power and the segregation of metallies consistent with the approach used in DOE /ID 10460.) Finally, it should be noted that in an independent review of DOE /ID.10460," NRC RES also concluded that the decay power density should be higher than 1.4 MW/m3.

B.2.2 Power Iri Metallic Layer DOE /ID.10460 Approach. For the FIBS analysis, the UCSB study neglected heat sources associa:ed with ,

the presence of decay heat from fission products in the metal layer and any heat addition associated with ox6dation or activation of the metal. In Appendix 0, the UCSB study states that uranium dissolution into a zirconium is a "non-confirmed hypothesis (by Powers)." However, DOE /ID 10460 Appendix R indicates that 5% to 10% of fission product decay heat may be present in the metallic layer. In Appendix P l (Figure P.5), UCSB presents results from sensitivity studies in which various fractions of the ceramic pool's decay heat (from 0 to 50%) was transferred to the metall:e layer and the vessel. As discussed in Appendix P, even a 50% shift wasn't adequate to " compromise integrity in the Base Case." However, INEEUEXT.97 00779 B418

Figure P.S indicates that the ratio of q"(6)/q"(6) cur went from 0,4 (wi 5 no power in the metallic layer) to 0.7 (with 50% of the power shifted to the metallic layer). ,

In the Refwence 12 response to RAI Question 480.456, Westinghouse nsponded that there is .

approximately 100 kg of mesm present in the RCS that is available for oxidatics. However, Wutinghouse !

also observed that an oxide layer will form on top of the maallic layer, noting that this oxide layer will l inhibit further oxidation and transfer heat more efficiently becaun of its higher emissivity. !

INEELC#The INEEl developed VESTA code considers several types of volumetric heat ;

sources in the metallic layw in conjunction with uneenannties associated with other input parameters. i VESTA allocates the fraction of dway heat in the metallic layer by utimating the contribution to decay i heat associated with actinides and fission products that was retained in the_ metallic layer. INEEL j determined which species were retained in the metallic layw using information in Appendix R, comments by Peer Revieww Olander in Ap#'48 Mix V, and other pertimat references discussing the most prob chemical states of these species. INEEL als considered the impact of energy sources due to l metallic layer oxidation and structural material activation. However, INEEL mgluted oxidation energy !

source because scoping calculations suggest that this additional energy source will only be non negligible for small periods of time (< $ minutes). Bwause scoping calculations suggest that the onwgy source usociated with structural material activation isn't negligible,INEEL posformed sensitivity calculations to !

assess the impact of this additional heat source. Additional information about the INEEL approach is provided below- t r

Section 2.1 describes an alternate debris configuration (Configuration C) that considers the potential for uranium to dissolve into unoxidized tircaloy in the metallic layer, his dissolved uranium increases the metallic layw density and introduces volumetric heat sources associated with actinide decay heat !

production. VESTA allows decay heat to be separated into two contributions, decay heat usociated with l actinide heating, Ph M), and decay heat usociated with fission products, Pm l INEEL calculations, th.wr was is optien (I only invoked for Configurations A, B, and C. Sd.pp(t DAP/RELAPS calculation results quantifying the fraction of decay heat associated with actinide heating weren't available i for other calculations. In calculations based on the UCSB assumed FIBS, the decay heat was based on the ,

curve shown in DOE /ID 10460 Figure 7.1. Information in Figures 7.1 and 7.2 suggest that the UCSB study l assumed that this decay heat was entirely due to fission product heating. Hence, INEEL invoked a similar -

assumption in calculations for the UCSB assumed FIBS.

in Appendix R, the UCSB study presents decay heat fractions usociated with various fission product relmse groug for the 'IMI 2 reactor. Dese decay heat fractions, which were obtained from CINDER 10 calculations, correspond to two different operating histories for the TMI 2 reactor (96.2 effwtive full power days, which is the actual TMI 2 history at the time of the accident and 26,000 hours0 days 0 hours 0 weeks 0 months at full pown). j Although Appendix R acknowledges ti,at the '!MI 2 and AP600 reactors have different fuel enrichments, ;

fuel burnup, and neutron spectrum, UCSB study authors state that these data are adequate for estimating i the order of magnitude of the decay heat tha; may exist in the metallic layer. Of the six fission product groups idesatified in'Appendia R, UCSB authors conclude that only the decay heat associated with the Noble Metals Group (Group 6, containing Ru, Mo, Pd, Rh, and Tc) should be allocated to the metallic layer, in Appendix V, Peer Reviewer Olander commented that the metallic layer decay heat should also include contributions from the Tellurium Group (Group 4, containing Te, Se, and Sb) and Rare Earth Group (Group 7, containing 14. Nd, Eu, Y, Ce, Pr, Pm, Sm, Zr, Nb, etc.). Peer Revieww Olander noted l

that several references indicate that tellurium is stable in the preseixe of aircaloy and is only released when ;

i B 19 INEEUEXT 97 00779 3

m,--.e e-- enw--a,e --- - ,- - - u- - - - --"

the zirceJoy Is oxidized. Likewise, he observed that the zirconium decay heat contribution should be partitioned according to the fraction of zircaloy that is oxidized. After reviewing several references that discuss the most probable chemical state of various species,dW INEEL estimated the metallic layer decay heat source by considedng contributions associated with all of the Noble Metal Group, all of the Tellurium Group (multiplied by the fraction of zirconium that is not oxidized), and the zirconium and niobium species of the Rare Eanh Group (multiplied by the fraction of rirconium that is not oxidized). Discussions '

with James Sienicki, one of the authors of Appendix R,48 indicate that he concurs with INEEL's approach.

Fission product fractional decay heat contributions depend on the reactor's fuel enrichment, burnup, neutron spectrum, heatup transient, and irradiation history. INEEL investigated these sensitivities by comparing the fractional decay heat contributions for the two Appendix R TMI 2 CINDER 10 calculations with values estimated from an ORIGEN2 calculation for an AP600 fuel assembly aesumed to have operated for 99,530 hours0.00613 days 0.147 hours 8.763227e-4 weeks 2.01665e-4 months . Fractional contributions for the species and groups of interest are summarized in Table B 3. As shown in this table, the various analyses predict similar decay heat fractions for the different reactors and operating histories.

Because the AP600 operating history prior to the accident is not known and because thi. fractional decay heat for longer time periods are similar, INEEL estimated the decay heat associated with each species by averaging the AP600 and TMI 2 values shown in Table B 3. Specifically, TMI 2 anu AP600 results were used to obtain mean values and standard deviations for the contribution of species ofinterest.

Because the fractional decay heat contribution of each species varies with time, the fractional contributions were fit to lines with the y intercepts and slopes indicated in Table B 3. Then, the following steps were used to estimate the decay heat present in the metallic layer.

Select the fraction of zirconium oxidized, fo x.3, ard the melt relocation time, tg.

Find the tr.elt relocation time, tm, and the fractional decay power contribution (see Table B 3) for each group at the selected relocation time [foroup 4(t,,1), foroup 6(t,,i), fb & Nb(t,,i)).

Estimate the fractional decay power in the metallic layer, fmew, by applying f..,,i = (1 - f,. .z,)[fo,,,, .(t,,i) + f ,2 a m(t,,i)) + fo,,,,,(t,,i) (B.!5)

Multiply the fission product decay power in the oxide pool, 4 P . ., rr(t,.i), by (l me f w). Assume a metallic layer fission product decay heat source equal to fmew Pe...r rr(t,,i).

INEE11 EXT 97 00779 B 20

I J

Table B 3. Fractional contributions of fission product decay heat associated with various species.

Time, seconds Group 4' Group 6' Zs & Nb 7M12 (Actually power history; 96.2 effective full pomer deys) r

, 7200 0.0440 0.046( 0.1111 [

16,000 0.0273 0.0$76 0.1428

28.800 0.0267 0.0626 0.152$

4 TMI 2 (26,000 hours0 days 0 hours 0 weeks 0 months ) j

7200 0.0477 0.0965 0.1209 18.000 0.0316 0.1110 0.1477 28,800 0.0300 0.11$2 0.1544 AP600(99.$30 hours) .

5 7200 0 0481 0.09$1 0.1348 18,000 0.0321 0.1045 0.1462 28,800 0.030$ 0.1101 0.l$31 Mean Value:

2 7200 0 0466 0.0777 0.1223

(

l8,000 0.0307 0.0910 0.1456 28,800 0.0291 0.0960 0.1533 Pararreters for estimatin8 between 7,200 and 18,000 seconds Slope of Line,(3 .l.473x104 1.236:104 2.154x104 Y.intenopt 0.0$72 0.0688 0.1068 Standard Devistion 0.0025 0.0244 0.0070 Parameters for estimating between 18,000 and 28,880 seconds Slope of Line, s'l .l.502:10 7.197x10

4.! } s107 Y Intercept 0 0334 ' oM28 0.1326

$tandard Devlation 0.0025 0.0284 0.0070

a. Tellurium group; includes Te. Se, $b.

b. Noble Metals, includes Ru, Mo, Pd, Rh, Tc.

B 21 INEEIAXT 97 00779

4

'. B.3 Material Property Assumptions B.S.1 Ceramic Pool and Crust t

. i B.S.1,1 Spoolfic Heat Capacity DOE /ID.10460 Approach. In Section 7, the UCSB study indicates that material properties were assumed .

to be normally distributed with the mean and 20 values corresponding to values provided in Appendix L.

However, the Table 71 entry for specific heat indicates that point estimate values for the specific heat of UO 2(485 JAgK) and ZrO (815 2 JAgK) were averaged based on the mass fraction of these materials in the ,

ceramic pool. Although Appendix L cites uncertainty distributions for UO2 and ZrO2 specific heats Table ;

71 suggests that the UCSB study neglected uncertainties in the specific heat for UO 2 and ZrO2 and uncertainties associated whb mass averaging.

l INEEL Approach. VESTA simulates uncertainties in individual specific heats and uncertainties !

associated with mass averaging by applying the following relationship, 4"

c, , = (f=-vo,cr y + f iii-reo,cru,)e (B.16) !

where e,,, = Ceramic pool melt specific heat capacity, jag K c,g = UO2specific heat capacity, jag K e,,, = ZrO2specific heat capacity, jag K f,,,.v o, = UO2mass fraction in the molten pool f .z,o, = ZrO 2mass fraction in the mohen pool C,, , , = Uncertainty parameter for estimating molten ceramic specific pool heat.

This experimentally validated approach is consistent with the approach recommended it. the MATPRO materials library.27 Based on information in Appendix L and Reference 27. INEEL assumed that c, has a mediari value of 485 jag K and a standard devlation of 5 jag K and that c, ' has a median value of 815 jag K an/ a standard deviation of 14 jag K. Note that the median values 70r' these specific heats are consistent with the values cited in DOE /ID 10460 Table 71. Based on information in Reference 27 INEEL assumed that C,,, has a median value of 0.00 and a standard deviation of 0.10 B.3.1.2 Thermal Conductivity e

DOE /ID 10460 Approach.In Section 7, the authors state that material properties were assumed to be normally distributed with the mean and 20 values cornsponding to values provided in Appendix L However, it appears that the UCSB study assumed thermal conductivity uncertainty distributions that -

correspond to a specific melt composition. For the crust in tie oxide pool, Table 71 indicates that 2.8 i 0.4 W/m K was assumed as the mean and 20 values; whereas Appendix L presents a range of uncertainty distributions (2.0

0.3 W/m K to 6.2 i 0.5 W/m K) that depend on crust composition and temperature.

INEEUEXT 97 00779 B 22

1 For the moltenoxide pool. Table 71 suggests that 5.3 W/m K was assumed as the mean and that 1.6 was assumed as 2c;whereas Appendix L presents a range of lo uncertainty distributions (4.7 i 1.7 W/m K to 5.311.6 W/m K) that depend on the molten pool's composition, assumed cutectie temperature, and estimation method.

INEEL Approach in VESTA, INEEL applied the approach and uncertainties presented in Appendix L.

Appendix L presents several possible approaches for estimating the thermal conductivity of a mixed oxide crust and molten pool. It is determined in Appendix L that the various approaches yield similar values.

Hence, INEEL ap lied the first approach described in Appendix L, which is from the SCDAP/RELAPS MATPRO library,p7 because it can easily be incorporated into VESTA (note that Appen appear to prefer this approach in their discussion about corium crust thermal conducthity).

Specifically, VESTA estimates oxide thermal conductivity using the following relationship:

k,,(T) = [fu.co,k,,.co,(T) + fu.rso,k...z,o,(T)-0.4fs.co,fu.zro,lc '" (B17) where k,,(T) = Temperature dependent ceramic material thermal conductivity, W/mK k...uo,(T) = Temperature dependent thermal conductivity for UO2 , W/mK k,..t,o,(T) = Temperature dependent thermal conductivity for Z:02 , W/mK fw.vo, = Mole fraction of UO2 fu.z,o, =

Mole fiuction of ZrO2 Cn,, = Uncertainty parameter for estimating cuamic material thermal conductivity When the above relationship is applied to the molten ceramic material in the pool, the subscript, (ox), is replaced with p; when this relationship is applied to the ceramic crust, the subscript, ox, is replaced with cr.

Based on information in Appendix L, INEEL assumed a median value of 0.00 and a standard deviation of 0.05 for C .,$ and C ..,.i Reference 27 and Appendix L recommend the temperature-dependent relationships for solid UO2 and 2 0 solid 2 thermal conductiviev shown in Figures B 13 and B 14. For molten ZrO2, INEEL concurs with Appendix L that the therma, 3ductivity may be assumed to have a normal distribution with a median value of 3.25 W/mK and . standard error of 1.85 W/mK. As acknowledged in Appendix L, there are no direct measurements to support this value. For molten UO2 .

INEEL also concurs with Appendix L that a mean value of 5.6 W/mK with a standard error of 1.1 W/mK may be assumed. This value is based on a numerical analysis, which evaluated several experimental test results using the THTB (Transient Heat Transfer, Version B) code.83 The THTB analysis rerulted in a much lower estimate for the thermal conductivity of molten U02than the 11.5 W/mK measured by Kim, et alf 2 (the MATPRO library currently assumes the Kim, et al. value).

B.3.1.3 Molting Temperature DOE /LD 10460 Approach. DOE /ID 10460 Figure 6.2 illustrates how the melting point of (U,Zr)O2 compounds vary with composition, and informatinn in Appendix L suggests that the melting temperature of the cerans material should be estimated as a function of composition. However, Table 71 suggests B 23 INEEl/ EXT 97-00779

e to . .

e- .

2 le s-1 I 4. .

u. .

b 1000 16o0 s000 s000 so00 sto0

v. iu,. <m -

Figure B 13. Temperature-dependent thermal conductivity of solid 0.98 TD U0 2(Reference 27).

t s.0 s.6 - -

30 - .

i.6- -

"o so0 1000 16o0 3o00 asco son 0 T.mp.teture (q i '

Figure B 14. 'kmperature-dependent thermal conductivity of solid 2:0 2(Reference 27).

INEEUEXT 97 00779 - B 24

~ - _ _ _ . _ _ _ . . . _ . . . _ . . . . _ _ _ . , . . - . ---._----.----.---)

that the (U,Zr)O 2rr. citing temperature was assumed as 2973 K triespective of composition, The UCSB study also neglected any uncertainties in melting temperature.

INEEL Approach.The MATPRO r aterials library27 assumes solidus and liquidus temperatures for (U,2s)0 using 2 the phase diagram recommended by Romberger et al.83 As shown in Figure B 15, these temperatures remain fairly constant for the (U,2 )O2 compositions expected in a ceramic pool forming in an AP600 vessel lower head (between 0.10 and 0.85 ZsO2 ). Hence, INEEL assumed a single melting temperature,2850 K. rather than the 2973 K value cited b Table 7 1. This higher temperature is consistent with the values shown in Figure B 15. Because no uncertainties in melting temperature were cited in either the UCSB study or the MATPRO reference manual. INEEL neglected uncertsinties in (U.Z )O2 compound melting temperatures.

3400 3700 g

s000

~ -

2600

u. / N.

$ 2400 Ub 2200 2000

wooonal 1600 goo

- I. weponet wegonet (ub)o, 1400 4

muc(ub)o,

" enanocid (ubp, "u 0 0.2 04 06 08 1.0 U..O.., Atomic frec*on Zr..O.., Zr O..,

Figure B 15. Quasi binary phase diagram for ZrO2 UO system 2 (Reference 53).

B.3.1.4 Volumetric Coefficient of Thermal Expansion DOE /ID 10460 Approach.In Section 7, the authors state that material properties were assumed to be nonnally distributed with the mean and 20 values corresponding to values provided in Appendix L. In both Sect'on 7 and Appendix L, the authors indicate that the volumetric coefficient of thermal expansion 4

for material in the molten pool should be assumed as 1.05 x 10 K'I. However, there appears to be a discrepancy between the uncertainty values cited in Section 7 and Appendix L, In Section 7, the volumetric coefficiem of thermal expansion is assumed to have an uncertainty distribution chrracterized by 2e = 0.12 x 10 d K'l whereas in Appendix L, the volumetric coefficient of thermal expansion is assumed to have an uncertainty distribution characterized by o = 0.12 x 10 4 K*l.

B 25 INEEUEXT 97 00779

i INEEL Apprbach. In VESTA calculations, INEEL assumed uncertainty distributions recommended in Appendix L. Namely, INEEL assumed that the pool volumetric coefficient of thermal expansion has a d d normal distribution with a median value of 1.05 x 10 K*3 and a standard deviation of 0.12 x 10 K*l.

i 3.3.1.5 Density DOE /ID.10460 Approach. Table 71 of DOE /ID 10460 indicates that the ceramic pool melt density was .,

estimated based on the UO 2 and ZrO2 volume fractions and the density of UO 2 and ZrO 2 at their liquidus temperatuu Although Appendix L recommends uncertainties for estimating the density of molten ceramic material, Table 71 suggests that the UCSB analysis neglected these uncertainties.

INEEL Approach. VESTA applies the approach recommended in Appendix L for estimating the ceramic pool density. Namely, VESTA estimates the ceramic pool melt density using UO 2 and ZrO2 volume fractions with the following equation:

4 (B 18) p, = (f,.ve,p .co, p + f..z,o,pp.z,o,)e "

where f, . co, = UO2volume fraction in the molten pool f,.z,o, = ZrO 2volume fraction in the molten pool pp.vo, = Molten UO 2density in the ceramic pool, kg/m3 p p.2,o, = Molten ZrO 2density in the ceramic pool, kg/m3 C,., = Uncertainty parameter for estimating the density of the ceramic pool.

Although the density of molten UO2 decreases with temperature, these decreases are small for temperatures of interest.88 Hence, INEEL evaluated each constituent's density at its melting temperature.

The uncertainty specifications in Appendix L are somewhat ambiguous. Based on information in Reference 27. INEEL assumed that the parameter, C,., , has a normal distribution with a median value of 0.00 and a standard deviation of 0.02.

B.3.2 Metallic Layer B.3.2.1 Specific Heat Capacity DOE /ID 10460 Approach.In Section 7, the authors state that material properties were assunwd to be normally distrii>uted with the mean and 20 values corresponding to values provided in Appendix L.

However, the Table 71 entry for specific heat indicates that point estimate values for the specific heat of Zr (458 JAgK) and Fe* (835 JAgK) were averaged based on their metallic layer mass fractions. Although Appendix L cites mean values and standard deviations for Zr and Fe specific heats, Table 7 1 suggests that metallic layer specific heat uncertainties were neglected. .

a. The UCSB study assumed that iron properties could be used to estimate the properties for stainless steet in l

the n.etallic layer.

l l

INEEUEXT 97-00779 B 26 l

l -

. . l INEEL Appreest. VESTA estimates uncenannties in individual specific heats and uncenalntles i suociated with mass averaging using the following relationship. l 9

c,.i = (f..g,c,, + (. . .,cr . + f=-uc ,,)e (B 19) l where !

c,.i = Metallic layer melt speel6c heat capacity, JAs K l c,. = Zirconium specine nut capacity, jag K

c,, = Uranium specine heat capacity,343 K c,, = Stainleu steel specine hw..t capacity, jag K

f. . x, = Zirconium mass fraction in the metallic layer .,

i

f. . ., = Stainteas steel mass fraction it Ihe metallic layer i.

f..u = Uranium mass fraction la the metallic layer Cy .i =. Uncertainty parameter for estimating the n etallic layer specific heat.

Although an additional term was added to consider cases where uranium dissolves into the metallic layer, this approach is consistent with the approach suggested in Appendix L. Based on information in Appendix L and References 27 and 55, INEEL assumed that c,, has a normal uncertainty distribution ;

with a median value of 458 JAs K and a standard deviation of 14 JAs K, that c,, has a normal uncenalnty distribution with a median value of 835 jag K and a standard deviation of 25 jag K and that c,, has a normal distribution with a median value of 157 J43 K and a standard deviation of 8 jag K. '

Note that the median values for these specific heats are consistent with the values cited in Table 71 of the UCSB study, Based on infonnation in Appendix L and Reference 27, INEEL assumed that the uncenainty r parameter, Cg.i, has a normal distribution with a median value of 0.00 and a standard deviation of 0.10.

i B.3.2.2 Thermal Conductivity ;

DOE /ID 19460 Apptwoch.In Section 7, the authors state that material propenies were assumed to be >

normally distributed with the mean and 20 values conosponding to velues provided in Appendix L.

However, it appears that the UCSB study assumed values and uncertainties that correspond to a specific melt composition. For the metallic layer, Table 71 indicates that 25 i 6.3 W/m K was assumed as the mean and 2a values; whereas Appendix L presents a range of to uncertainty distributions (24.8

6.3 W/

m K to 32.8 i 50 W/m-K) that depend on the composition and estimation method.

INEEL A;;:7A For a two component mixture, VESTA applies the Filippov equation piesented in Appendix L because it has been extensively tested on many types of two-component mixtures, For a ,

metallic layer containing stainless steel and tircaloy, this equation may be written as:

i B 27 INEEUEXT 97 00779 I

e ,

k i is (f,,,.z,knz, + f,,,,,kp., - 0.72 f,.-reI,....lkk r,- kp.,l)e# (B20) where ki = Metallic layer melt thermal conductivity, W/mK ,

f ,, . . , = Stainless steel mass fraction in the metallic layer f, . g, = Zirconium mass fraction in the metallic layer kg., = nermal conductivity for stainless steel in the metallic layer, W/mK kpz, = nermal conductivity for zirconium in the metallic layer, W/mK C6.3 = Uncensinty parameter for estimating metallic layer thermal conducti ity For three component mixtures, VESTA estimates thermal conductivity using the following approach recommended by Reference 27 ki = [fu.z,k,.z, + fu..,ki , + fu.ok i.u]e#

where ki = Metallic layer melt thermal conductivity, W/mK fu . ., = Stainless steel mole fraction in the metallic layer fu . g, = Zirconiem mole fraction in the metallic layer fu.y = Uranium mole fraction ir, the metallic layer k g., = Thermal conductivity for stainless steel in the metallic layer, W/mK ksz, = hermal conductivity for zirconium in the metallic layer, W/mK ki .u = nermal ccnductivity for uranium in the metallic layer, W/mK Cg. = Uncertainty parameter fer estimating metallic layer thermal conductivity For malten zirconium, INEEL assumed the thermal conductivity distribution recommended by Reference 27 and Appendix L (e normal uncenalnty distribution with a mean value of 36 W/mK and a standard error of 5 W/mK). For mohen stainless steel INEEL assumed the distribution recommended by Appendix L (a normal distribution with a median valu. o(24.1 W/mK and a standard deviation of 4.3 W/mK). For molten uranium,44 EEL assumed ti.e thermal conductivity distribution tocommended by Reference 55 (a normal

uncenainty distribution with a mean value of 49 W/mK and a standard error of 4.9 W/mK)c Based on -

information in Appendix L. INEEL assumed that C . has a normal uncenalnty distribution with a median ,

value of 0.00 and a standard deviation of 0.05.

INEE1AXT 97 00779 - B 28 -

B.3.2.3 . Volumetric Coefficient of Thermal Expansion DOE 4D.10460 Approach.In Section 7 the authors state that material propenies were assumed to be normally distributed with the mean and 20 values conespondtng to values provided in Appendix L in Section 7 the authors indicate that the volumetric coefficient of thermal expansion for the metallic layer should be assumed as 1.1 x 10 4 K*l with an uncenainty distribution characterized by 2e equal to 0.18 x d

10 K*l; whereas in Appendix L, the authors indicate that the volumetric coefficient of thermal expansion should be bued on the volume fractions of materials in the metallic layer.

INEEL Approach. Although an additional tenn was added to consider cases where uranium dissolves into the metallic layer, VESTA applies an approach consistent with the approach recommended in Appendix L. Namely, VESTA estimates the volumetric coefficient of thermal expansion using the following equation 0: = (f..z,@r, + f... S.. + f..uEu)e '*' (B21) where p, = Molten metallic layer volumetric coefficient of thermal expansion, K*l z, = Zirconium volumetric coefficient of thermal expansion. K*l p, = Stainless steel volumetric coefficient of thermal expansion, K*l 4

pu = Uranium volumetric coefficient of thermal expansion, K*l f, . z, = Zirconium volume fraction in the metallic layer f,.si = Stainless steel volume fraction in the metallic layer

f. . e = Uranium volume fraction in the metallic layer Cp = Uncensinty parameter for estimating the metallic layer coefficient of thermal expansion.

Based on information in Appendix L, References 27 and 55, INEEL assumed that ,, has a normal 4

distribution with a mean value of 1.20 x 10d K*l and a standard deviation of 0.17 x 10 K*l, z, has a d 4 normal distribt. tion with a mean value of 0.54 x 10 K* land a standard deviation of 0.11 x 10 K*l, p 4

has a normal distribution with a mean value of 8.61 x 10 K*l and a standard deviation of 0.60 x 10 d K, and the uncenalnty parameter, Cp, has a normal distribution with a median value of 0.00 and a standard deviation of 0.02.

B.3.3 Emissivhy DOE /ID.10460 Approach. Table 71 of DOE /ID.10460 indicates that a value of 0.45 was assumed with no uncertainties. As documented in Appendix ! of DOE /ID 10460, this value was based on UCSB measurements performed with carbon steel materirJ inductively heated in an inen environment. In the Reference 12 response to RAI Question 480. 449, Westinghouse states that the emissivity was considered '

B 29 INEEI/ EXT.97-00779

as an "intanjible in the ROAAM analysis" and that the " lowest possible value" was assumed.

Westinghouse 'also notes that a sensitivity analyses was performed to assess the impact of lower errJssivity assumptions. However, no uncertainty analysis was performed that incorporated the effects of emissivity uncertainty. Although UCSB authors cite one reference in which the emissivity of molten iron was .'

rneasured as 0.4, no attempt was made to determine the impact of differences in melt composition (iron versus stainless steel) or compare UCSB emissivity data with other data.

INEEL Approach. Several references" report considerably lower emissivities for molten drconium (ranging from 0.29 to 0.33). Although no data could be found for molten stainless steel, Reference 55 summarizes several sources of emissivity data for unoxidized solid stainless steel and zirconium. Figure B-16 compares data from References $6 through 55 with data provided in Appendix ! of the UCSB study. As .

shown in this figure, the emissivity of the carbon steel material measured in the UCSB study is typically higher than emissivities measured for stainless steel or zirconium. Higher emissi itles may have been measured at low temperatures because the UCSB tests used oxidized material, which many references cite as having emissivities ranging between 0.5 and 0.9. Furthermore, the UCSB study acknowledges that the higher emissivities measured for the test with zirconium at higher temperatures may be due to oxide being retained in the melt. Because all of the UCSB study measurements appear to be higher than available references for stainless steel and zirconium, INEEL estimated the emisshity using the zirconium and stainless steel data shown in Figure B 16 (out of the six groups of data points in this figure, the four non.

DOFAD 10460 groups of data points).

1.c , , ,

e im.unomseedb B Toulouleen.teenalmedas i + oopmoeso. ine.n ro.a.e onet n ew a oonmaano.% e,-

4

/a ,a O.s -

,,an as one v -

X Knshnan end Nor$ne . unomdeed monen b e a.on.,. .. uno ,n no ,

{

. 4, 06 -

4 -

w l

+

0.4 -

, *N

. # 4 ', .

$"" e

, m ,a % %' I 0.2 -

i l

I k 1000 1600 2000 2600-Temperature (K) ,

Figute B 16. Co.nparison of UCSB emissivity data with unoxidized stainless steel and zirconium data.

INEEi/ EXT 97 00779 B40

l

'Ihere is considerable scatter in the unoxidized strantess steel and zirconium data in Figure B 16.

Although stainless ; teel emissivities typically appear somewhat lower than tirconium emissivities, these differences are comparable to scatter in the data. Funbermore, there appears to be no distinct temperature dependence in emissivity, in the case of tirconium, there isn't even a distinct difference between emissivities measured above and below melting. Discussions with Donald Hagrman, a major contributor to the SCDAP/RLLAPS material propenies package (MATPRO),38 indicate that there are no experimentally validated relationships available for estimating the emissivity of a compound. Therefore, estimated the emissivity of the molten metallic layer by considering all of the unoxidized stainless steel and rirconium data in Figure B 16. Assurnbg that these data are nonnally distributed, this approach yields a median value of 0.29 with a standa d deviation of 0.N. Note that this uncertainty encompasses some of the lower emissivity values measured in the UCSB study.

As discussed in Section 3.3.1, calculations for Configuration A required that an emissivity be assumed for cases where steam may be present in the reactor vessel. Although the upper surface of the metallic layer may be oxidized in such conditions, radiation heat transfer from this surface would be reduced because of the thick cloud of vapor in the RCS. Hence, Configuration A calculations assumed an emissivity distribution with a mean value of 0.2 and a standard deviation of 0.1.

B.3.3.1 Density DOE /ID 10460 Approach. Table 71 of DOFJID IN60 indicates that the melt density was estimated using the volume fractions of Zircaloy (assumed to be primarily Zirconium) and Iron (Fe) in the metallic layer and the density of Zr and Fe at their liquidus temperatures. Appendix L recommends that median values and uncertainties for the metallic layer density be estimated using Zr and Fe densities and associated uneenainties. However, Table 71 suggests that the UCSB analysis neglected Appendix L-recommended uncenainties.

INEEL Approach. Although an additional term was added to consider cases where uranium dissolves into the metallic layer, VESTA applies an approach consistent with the approach recommended in Appendix L for estimating the density of material in the metallic layer. Specifically, VESTA applies the following equation to predict an uncenainty distribution for the linear superposition of these densities.

Pi = (f,. t Pi-z, + f, . . Pi-. + f. - u Ps . u)e "' (B 22) where f, . g, = Zirconium volume fraction in the metallic layer f, . s = Stainless steel volume fraction in the metallic layer f,- u = Uranium volume fraction in the metallic layer Pi-ss = Stainless steel density, kg/m 3

p. _, = Zirconium melt density, kg/m3 pi.y = Uranium melt density, kg/m 3 C,.i = Uncenalnty parameter for estimating the metallic layer density.

B-31 INEElJEXT 97-00779

Because' density data for rircaloy, stainless steel, and uranium above their liquidus temperature are ilmited and no data were found for the density of a SS/Zr/U or a SSf4r mixture,INEEL evaluated the density of each constituent at its meltig ternperature. Based on information in Appendix L and References 27 and $5, INEEL assumed that p,.z, is normally distributed with a median of 6,130 kg/m'and a standard -

3 3 deviation of 180 kg/m , p,.ss is normally distributed with a median of 7,020 kg/m and a standard deviation of 90 kg/m 3, and p,- u is normally distributed with a median of 17,500 kg/m 3and a standard deviation of 1,750 kg/m .3 Median values for the stainless steel and z.irconium densities are consistent with the values cited in DOE /ID 10460 Table 71. Based on Appendix L, INEEL assumed that the uncertainty parameter C,.i. is normally distributed with a median of 0.00 and a standard deviation of 0.02.

5.3.4 Veeeel Well .

5.3.4.1 Thermal ConductMty DOE /ID 10460 Approach. Table 71 of the UCSB study implies that a single value,32 W/m2 g, was assumed for the vessel wall effective thermal conductivity with no uncertainty. The Westinghouse response to RAI 480.448 notes that this effective thermal conductivity was obtained from Figure L.3 (by considering a vessel wall with temperatures ranging from 130 to 1300 *C), llence,32 W/m2 K should only be assumed as the vessel effective thermal conductivity at locations where the vessel inner surface is in contact with either ceramic debris or molten metal and the vessel outer surface is cooled by water. The UCSB model also requires that an effective vessel thermal conductivity be estimated for much cooler locations above the metallic layer, where heat transfer from the upper plenum structures is radiated (see Equation 6.12). Although the UCSB study uses the same variable name, k,, for the bulk average vessel wall thermal conductivity at both locations, INEEL calculations suggests that a higher thermal conductivity, approximately 41 W/m 2K, was applied for the effective vessel thermal conductivity at cooler locations (i.e., in Equation 6.12). This higher thermal conductivity is consistent with values shown in Figure L.3 over the range of temperatt.res predicted for the vessel wall at locations above relocated ceramic or metallic material (130 to 260 'C). ,

As discussed in Appendix L, vessel steel thermal conductivities were estimated using SA508 low temperature data and iron high temperature data. Information in the UCSB study and discussions with Westinghouse indicate that either SA533B1 or SA508 steel will be used for the AP600 reactor vessel (most operating reactors use SA533B1 vessels). Appendix L recommends uncertainties for vessel thermal conductivities, but information in Section 7 and the response to RAI 480.448 suggests that no uncertainties were considered for the vessel thermal conductivity in the UCSB calculations.

INEEL Approach. INEEL assumed two distinct values for the effective vessel wall thermal conductivity; one for hotter locations in contact with the ceramic debris / molten metallic layer and one for cooler locations significantly above the relocated melt (for modeling radiation heat transfer from upper plenum stmetures). Using SA533B1 thermal conducthity data" and values shown in Figure L.3, INEEL 2

estimated that the venel thermal conductivity was 32 i 2 W/m K at locations near the relocated melt and 2

41i1 W/m K at locations above the relocated melt. Uncertainties in these values are based on .

AppendixL. Namely, INEEL assumed that the data were normally distributed with 95th percent uncertainty limits of 4% (2 alp = 4%) for temperatures between 150 and 1300 K and 10% (2o/p = 10%)

for temperatures above 1300 K.

INEEUEXT 97 00779 B 32

-_ _ _ _ -_ . _ _ _ _ _ _ _- __ __, _ _ _ _ ~ _ _ - . _ _

B.3.4.2 Melting Temperature DOrJID 10460 Approach. ne UCSB FIBS assumes study all of the core plate, all of the reflector, lower portions of the core barrel, and all of the lower internal structures have melted. Ilence, the UCSB study presumed that it is only possible to obtain metallic layers with high iron mass fractions. The 1600 K vessel wall melting temperature assumed in the UCSB study corresponds to the minimum liquidus temperature

. for iron / zirconium cutectics that have high (more than $5%) iron mass fractions (see Figure B 17)." The UCSB study neglected uncertainties in this temperature. In the Reference 12 response to RAI Question 480.448, Westinghouse reiterated their position that it is not possible to get zirconium rich compositions.

Ilowever, no experimental data were supplied to support this position.

a.am ,

i ,- ,- ,- ,- , ,. i i ,

2.000 h ,g 1946 t"*

/s > ~ ;

K 0 mis 1YW

,4

, sm "

1687 :duas im ;7 7 g t e0 7 oou :, , .

J..........t"t....J... :

1.4m 7

, sees irti -

0 644 ];, 1M q,gg Y 1112 \

,o itse x) i136 3,a 7

l f 1068 067q a-.

...........0U................ ,"

i .,

I

.i i ., i. i , .i i

,O 01 02 0.3 04 0.s 06 07 0.8 OD 10 Mole traction Zr --

Figure B 17. Iron. zirconium phase diagram.

INEEL Approach. VESTA considers melt compositions that may occur prior to the UCSB. assumed FIBS. SCDAHRELAPS. predicted melt compositions suggest that a broader melting temperature range (1400 to 1900 K) should be considered. De SCDAP/RTiAP5 calculations consider time-dependent relocations that occur as a result of localized reflector melting and sideways reiocation cf molten core materials. Rese calculations considered time periods before the coolant in the lower head has boiled off (prior to 12,720 seconds). In light of the fact that asymmetries may occur during core melt, that stagnation points may develop in the molten metallic layer, and that there are uncertainties in SCDAPiTGl.AP5 calculations, VESTA considers the entire range of liquidus temperatures shown on the iron /tirconium phase diagram (1200 to 2l00 K) by simply picking the temperature that corresponds to the mole fraction of zirconium in the metallic layer. Applying Peer Reviewer Olander's recommendations (DOFJID.10460 Appendix T), VESTA estimates the vessel wall melting temperature by applying the following steps:

Calculate the metallic layer tirconium mole fraction for the assumed mass of unoxidized tirconium and structural steel.

B 33 INFIIEXT 97 00779

In the* metallic layer, select the inner vessel wall temperature (for locations where the vessel steel is predicted to melt) based on the mole fraction of zirconium in the metallic layer and Figure B 17.

+ in the ceramic pool, assume the inner vessel wall temperature (for locations where the vessel steel is predicted to melt) as 1809 K (corresponding to 100% iron in Figure B 17). '

The above approach was not orly applied to two-component, stainless steel and zirconium metallic layers, -

but also to three-component metallic layers containing dissolved uranium. Ahhough it is recognized that the presence of dissolved uranium could impact the vessel melting temperature, information in Reference 67 suggests that impact was minimal for the mole fractions of dissolved uranium considered.

B.3.5 Upper Plenum Structures B.3.5.1 Thermal Conductivity DOE /ID 10460 Approach. Although the UCSB study did not document what upper plenum structure thermal conductivity was assumed, the respo ise to RAI 480.965 indicates that a value of 30 W/m2K was assumed with no uncenalnties. Their response implies that the UCSB assumed thermal conductivity was based on propenies shown in Figure L.3.

INEEL Approach. INEEL estimated the thermal conductivity of the upper plenum steel stmetures using temp.:rature-dependent information for stainless steel. UsinE stainless steel information in Reference 61 INEEL implemented the following rela.lonship into VESTA for predicting the uneenainty distribution for the upper plenum stmetures' temperature-dependent thermal conductivity, k,(T,) = (1,4154x 10'87, + 9.9214)e' (B 23) where k,(f.) = Upper plenum stmetures thermal conductivity, W/mK.

T, = Upper plenum structures average temparature (0.5 T,.i + 0.5 T ), K.

C., = Uncenalnty parameter for estimating upper plenum structure's thermal conductivity.

Based on information in Reference 61. INEEL assumed that the uncenainty parameter, Cg.,, has a normal distribution with a median value of 0.00 and a standard deviation of 0.05.

B.3.5.2 Emissivity DOE /ID.10460 Approach.In Section 7, the UCSB study indicates that an upper plenum structure emissivity of 0.8 was assumed. Because of the large areas involved, the UCSB study concluded that -

emissivity uneenainties may be neglected.

INEEL Approach. Based on oxidized stainless steel data,55 INEEL assumed that the upper plenum .

structure emissivity has a normal distribution with a mean value of 0.85 and a standard deviation of 0.03 (a = 0.03).

INEE1 EXT 97 00779 B 34

Appendix C - Listing of input The main report discusses results for several debris configurations ^ .'CSB assumed HBS and three alternate con 0gurations that were based on masses predicted by SCDAnRELAP5 and peer review er comments (Configurations A, B, and C of Section 2.1.2). This appendix lists input assumed for each connguration. Table C 1 compares input values used by UCSB (based on information in the UCSB study and responses to RAls) and by INEEL for analyzing the UCSB assumed FIBS. The UCSB input was used in the benchmark calculations reported in Appendix D. Table C 2 through Tab'; C-4 list which Table C 1 INEEL input assumptions were modified for analyzing Configurations A through C. Variables in these tablet are defined in the Nomenclatr *

this report.

Table C 1. Comparison ofINEEL and UCSD input uncertainty distribut ions.

UCSB assumed FIBS INEEL Requantineatie i of UCSB assumed FIBS Median Wlue Distribution Median W1ue Distribution US Point estimate 835 Normal e,* , ;4 g.g o = 25 485 Point estimate 485 Normal c, ** , Jag.g o=5 NA NA 157 Normal c, , Jag.g a=8 '

cp ,J/kg K 458 Point estimate 458 Normal o = 14 t15 Point estimate 815 Normal c,,9, JA= K o m 16 fASt,,if NA NA NA NA NA NA 1.000 Point esumate foi-U f,, , g, 0.5 Figure 7.3 0.5 Figure 7.3 f,,(1 ) NA NA 0.000 Point estimate f,,(2) NA NA 1.000 Point estimate fg(j) NA NA 0.000 Point estimate (p(2) NA NA 0.000 Point estimate NA NA 1.000 Point estimate fuo,(7 :

fgg(2) NA NA 0.000 Peint esumate (g,(1) NA NA 0.000 Point estimate fg,(2) NA NA 1.000 Point estimate NA NA 1.000 Point estimate fg,o,r,1 )

NA NA 0.000 Point estimate fg,o,(2) 2.8 Normal NA NA k,, , W/mK 20 = 0.4 C-1 INEEUEXT 97-00779

_,_a._a_ A__,6 _ .aa_

w Ah..--,-4q wA._Am%_.__.4,uu-- . _ .

ae e 4- _ 4 4.wa.. -A.3 - 44, m.# :s~g z.

Table C 1, Comparison ofINEEL and UCSB input uncertainty distributions,(continued)

, UCSBd.ssumed FIBS INEEL Requantification of UCSB assumed FIBS Med;an Value Distribution Median Value Distribution * '

k,,- voi, W/mK NA NA 2.41 Normal o = 0.2 ,

k,, . z,o, , W/mK NA NA 2.48 Normal o = 0.25 k i , W/mK 25 Normal NA NA.

2a = 6.3 k i... . W/mK NA NA 24.1 Normal o = 4.8

, ki .v . W/mK NA NA 49.0 Normal o = 4.9 k i .z,, W/mK NA PIA 36 Normal o=5 k, , W/mK 5.3 Normal NA NA 20 = 1.6 k,. vo,, W/mK NA NA 5.6 Ne a al o m 1.1 kp.z,v,, W/mK NA NA 3.25 Norn,al o = 1.85 k,(T ), W/mK 30 Point estimate Temperature-dependent Uncertainty treatedin values (Equation (A 113)) Cg...

k,,,,, , W/mK 4lb Point estimate 41 Normal o=1 k,,,, n , W/mK 32 Point estimate 32 Normal o=2 4 Figure 7.7 t,,i , s 1.62x10 1.26x10 4 Figure 7.7 values at one hour earlier For 0 5,n < 18,000 seconds Bo,,,,4(t,,i) NA NA 0.0572 o x Student's t (6 d.f).

o = 0.0025 Bo,,,, e(t,,i) NA NA 0.0688 o x Student's t (6 d.f.)

o = 0.0284 by a %(t,,i) NA NA 0.1068 o x Student's t (6 d.f.)

o = 0.0070 Mar..,4(t,,i) , s 1 NA NA -1.473x104 Uncertainty treated in B Ma,,,,.(t,,i),s 4 NA NA 1.236x104 Mz, a %(tr .i), s I NA NA 2.154x104 For 8,000 seconds s t,,i < 28,880 second ,

Bo,,,, 4(t,,i) NA NA 0.0334 o x SUent's (6 d.f.)

o = 0.0025 INEEUEXT 97-00779 C-2

Tablo C 1. Comparison of INEEL 6nd UCSB input uncenainty distibutions. (continued)

UCSB-assumed FIBS INEEL Requantification of UCSB assumed FIBS Median Value Distribu. ion Median Value Distribution l Boroep 6(1,es) NA NA 0.0828 o x Student's (6 d.f.)

o = 0.0284 Bg, a S(t,, ) NA NA O.1326 o x Student's t (6 d.f.)

o = 0.0070

~

Mo,,,, (t,,i) , s 1 NA !E 1.502x10-7 Uncenainty treated in B

-- parameters Mo,,,, (t,,i) , s 1 NA NA 4.572x10'7 Mz, a %(t,,i), s l NA NA 7,197x10-7 Cw NA NA 0.000 o x Student's t (6 d.f.)

o = 0.088

~

Cmp NA NA 0.0 Normal o = 0.05 Ce, NA NA 0.000 Normal o = 0.05 Cg.,, NA NA 0.000 Normal o = 0.05 NA NA 0.000 Normal Cg.p o = 0.05 Cg.: NA NA 0.000 Normal o = 0.05 Cg., NA NA 0.000 Normal o = 0.05 C;w NA NA 0.00 Normal o = 0.12 NA NA 0.000 Nonnal C,,,, o m 0.10 NA NA 0.000 Normal C,, . , o m 0.10 C,ie NA NA 0.000 o x Student's (3 d.f.)

o m 0.15 Cwp NA NA 0.000 o x Student's t (6 d.f.)

o = 0.088 NA NA 0.000 Normal Cp . ,

o = 0.02 r C,.3, Pa s NA NA 0.000 Normal; c = 1.1 x10'3 NA NA 0.000 Normal; o = 2.5 x10-3 C, . , , Pa-s NA NA p.000 Normal C,. :

i o = 0.02 NA NA 0.000 Normal C,.,

o = 0.02 4

C3 INEEl/ EXT-97-00779

Table C 1. Comparison ofINEEL and UCSB input uncertainty distributions. (continued)

UCSB assumed FIDS INEEL Requantification of UCSB-assumed FIBS Median Value Distribution Median Value Distribution '

C ,W/m 2 4.90x105 Point estimate 5.864x'05 Uncertainty treated in CCHF C2 , W/m 2 3.02x10 4 Point e' stimate 2.081x10 4 *

~

C3 ,W/m 2 8.88x102 Point estimate -1.467x102 C4 ,W/m2 1.35x10 1 Point estimate 1.361x10'3 C5 ,W/m 2 -6.65x10 2 Point est i mate 4.000x10 5

~

C6 0.345 Point estimate 2.4415 Uncertainty treated in O Nu,,,,(Ra',) d C7 0.233 Point estimate 0.1722 Uncertainty treated in ou,,,,,(Ra',) d Cs 0.0038 Point estimate 0.1857 Uncertainty treated in O Nu,,,,(Ra',) d C9 0.35 Point estimate 0.23M Uncertainty treated in U Nu,,,,(Ra',) d Co i 0.1 Point estimate 0.1 Uncutainty treated in Cai 1.08 Pc. int estimate 1.08 Cioc#

C12 -4.5 ioint estimate -4.5 Ci3 8.6 Point estimate 8.6 C i4 0.4 i Point estimate 0.41 Csi 0.35 Point estimate 0.35 C16 1.00 Point estimate 1.00 Ci7 0.170 Point estimate 0.170 UncertaintytreateoinCio ,

Cei 0.074 Point estimate 0.074 and Cw.

Cgi 0.3333 Point estimate 0.3333 C20 0.150 Point estimate 0.150 Uncertainty treated in C2 0.3333 Point estimate 0.3333 C,ie.

Mz, . .. . kg 19,200 Point estimate 19,200e Point estimate M,, , ,,, , kg 70,000 Figure 7.5 70,000s Figure 7.5' Muo,-i.,, kg 75,900 Point estimate Point estimate 75.900s P4.c.y-ucsa(t,,i),W Time-dependent Point estimate Time-dependent values Uncertainty treated in values shown in shown in Figure 7.l f Cdee -

Figure 7.l f R,m 2 Point ertimate 2: Point estimate INEEllEXT 97-00779 C-4

Table U-1. Comparison of INEEL and UCSB input uncertainty distributions. (continued)

UCSB-assumed FIBS INEEL Requantification of UCSB-assumed FIBS Median Value Distribution Median Value Distribution S. , m 2 75.36 Point estimate 75.363 Point esumate 1600 Point estimate Figure 6.1 value based on Point estimate Tu,K Zr mole fraction -

2973 Point estimate 2850 t'oint estimate T,, ,,, , K T, , K 400h Point estimate 400s Point estimate T,.,, ,, , , K 1600 Point estimate 1809 Point estimate 91.22 i Point estimate 91.22 1 Point estimate Zz,, kg/kg moles Zo,kg/kg moles 15.994 1 Point estimate 15.994 1 Point estimate Z,,, kg/kg moles NA NA 55.0663 Point estimate Zu,kg/kg moles NA NA 238.029 1 Point estimate Zuo,,kg/kg moles NA NA 270,02 1 Point estimate 5, K1 NA , NA 1.20 x 10-4 Normal d

o = 0.17x 10 l- U , g l NA NA 8.61 x 10-4 Normal d

o = 0.60 x 10 sz,, K 1 NA NA 0.54 x 10-4 Normal d

o = 0.11 x 10 4 Norms' NA NA

,, K 1 1.10 x 10 d

2a = 0.12 x 10 1.05 x 10-4 Normal 1.05 x 10-4 Normal

, , K*l d d i 20 = 0.18 x 10 a = 0.12 x 10 6, , m 0.2032' Point estimate 0.2032 Point estimate 6, , m 0.0508 Point estimate 0.0508 Point estimate 5,,,(0) , m 0.15' Point estimate 0.15 1 Point estimate 0.45 Point estimate 0.29 Normal E

o = 0.04 0.8 Point estimate 0.85 Normal E,

o = 0.03 pi. .. . kg/m3 7020 Point estimate 7020 Normal o = 90 Pi-U , kg/m 3 NA NA 17,500 Normal o = 1750 pi. z, , kg/m3 6130 Point estimate 6130 Normal o = 180 i

C-5 INEEUEXT-974)0779 l

- _m._

Table C-1. Comparison of INEEL and UCSB input uncertainty distributions. (continued)

UCSB assumed FIBS INEEL Requantification of UCSB assumed FIBS Median Value Distribution Median Value Distribution p p z,o,, kg/m 3 5990 Point estimate 5990 Normal o = 100 ,

Pp-voi, kg/m 3 8740 Point estimate 8740 Normal o = 200 o,W/m 2g4 5.672x 10-8m Point estimate 5.672x10 8m Point estimate

a. It appears that the UCSB study assumed that all decay heat was produced by fission products. Hence, this parameter wasn't used in INEEL's assessment of the UCSB assumed FIBS.

b. Consistent with Appendix L recommendations for temperatures at this location.

c. For the UCSB assumed FIBS reassessment, INEEL assumed values correspond to a cavity water height to vessel radius ratio of three.

d. A4 described in Appendix B,uo ,,,,(Ra',) and cy,, (Ra',) are given by:

2 8 o u ,,,,,(Ra',) = [0.0021 + 0.0035 (log (Ra,')- 15.0148)2]T where 7 has a Student's t distribution with $$ degrees of freedom, and 2

ou,,,,(Ra',) = [0.0023 + 0.0040'(log (Ra,')- 14.9701)') T where Thas a Student's t distribution with 22 degrees of freedom

e. This mass distribution was used for the UCSB-assumed FIBS, it does not represent an expected mass dis-trioution,

f. For time periods of interest, the following equation was used P...., ucss = (- 0.000333t,,i + 19.5)l0'

, g. This value was used te be consistent with values assumed by the UCSB study for their base case analysis.

l

h. Not explicitly stated in DOE /ID 10460. Nomenclature suggests that water saturation temperature was used. However, Response to RAI 480.446 suggests that 400 K was used.

i. Frorra Reference 67.

j, Estimated from Reference 62, assuming composition of 0.05% C 2.00% Mn,1.00% Si,10% Ni,0.04% P, 0.03% S,19.00% S, and 67.88% Fe.

k. This s alue is based on AP600 plant vessel drawings. It is consistent with value specified in RAI 480.459, but differs from the value specified in RAI 480.965,

1. For loc.itions where vessel melting doesn't occur.

m. From Reference 63.

l INEEL/ EXT-97 00779 C-6

l 1

Table C-2. Configuration A input assumptions.*

Parameter Value Uncertainty C ,W/m 2 5.211x10 5 Uncertainty treated in Cap Corresponds to SBLB (H/R=2) 4 C2 ,W/m 2 1.743x10 C3 ,W/m 2 7.311x108 C4, W/m2 7.643x10'l C3 ,W/m 2 4.180x10'3 0.2 Normal; o = 0,1 g,

Phe UcssN1), W B.5x106 Uncertainty treated in Cee. Conesponds to S/R5 results.

t,,i, nec 12,047 Point estimate. Corresponds to S/RS results.

Mz,.i.i kg 7,027 Point estimate. Conesponds to S/R5 results.

2,603/4187' Point estimate. Corresponds to S/R5 results.

M., _ ,,, , kg 37,207 Point estimate. Conesponds to S/R5 results, Muo,-ion kg fox.2, 0.4544 Point estimate. Corresponds to S/R5 results, FACT (t,,1). 0.123 Point estimate. Corresponds to S/R5 results.

a. Only those input values differing from those assumed in the INEEL analysis of the UCSB assumed FIBS are listed. Input for Configuration is based on Reference 3 SCDAP/RELAP5 calculations for a relocation time of 12,047 seconds.

b. The stainless steel mass has been increased to include the mass of control material that might be present in the metallic layer.

C-7 INEEIJEXT-97 00779

Table C-3. Configuration B input assumptions."

Parameter Value Uncertainty Ci ,W/m 2 5.211x105 Uncertainty treated in Ccup Corresponds to SBLB (H/R=2)

C2 , W/m 2 1.743x10 4

C3 , W/m 2 -7.311 x103 C4 , W/m 2 7,643x10 3 C5 , W/m 2 4.l B0x10'3 Po,e.vesg,W 14x10 6 Uncertainty treated in C dec. Corresponds to S/R5 results.

t,,i, sec 12,844 Point estimate. Corresponds to S/R5 results.

M z, . ,,, , kg 11.188 Point estimate. Corresponds to S/R5 results, fg,(] ) 0.0000 Point estimate. Corresponds to S/R5 results.

fg,(2) 0.6887 Point estimate. Corresponds to S/R5 results.

(zr(3) 0.0000 Point estimate. Corresponds to S/R5 results.

fg,(4) 0.3113 Point estimate. Corresponds to S/R$ results.

fg,g( } } 0.5682 Point estimate Corresponds to S/R5 results.

fg,o,(2) 0.0000 Point estimate. Corresponds to S/RS results, fg,o,(3) 0.4318 Point estimate. Corresponds to S/R5 results.

fz,o,(4) 0.0000 Point estimate. Corresponds to S/R5 results.

fox .z, 0.5024 Point estimate. Corresponds to S/R5 results.

M., . ,,, , kg 6121.7* Point estimate. Corresponds to S/R5 results.

f,,( } } 0.000 Point estimate. Corresponds to S/R5 results, f,,(2) 0.6840 Point estimate. Corresponds to S/R5 results.

f,,(3) 0.000 Point estimate. Corresponds to S/R5 results.

f,,(4) 0.3160 Point estimate. Corresponds to S/R5 results.

63,995 Point estimate. Corresponds to S/R5 results.

Muo:-i., , kg fuo,(1) 0.5814 Point estimate. Corresponds to S/R$ results.

fg,g(2) 0.0000 Point estimate. Corresponds to S/R5 results, fug(3) 0.4186 Point estimate. Corresponds to S/R5 results.

fuo,(4) 0.0000 Point estim.te. Corresponds to S/R5 results.

fu(1) 0.0000 Point estimate. Corresponds to S/R5 results.

INEEUEXT 97-00779 C-8

Table C 3. Configuration B input assumptions.* (continued)

Parameter Value Uncertainty 0.0000 Point esumate. Corresponds to S/R5 results.

fu(2) fg(3) 0.0000 Point estimate. Corresponds to S/R5 results.

0.0000 Point estimate. Corresponds to S/R$ results.

fu(4)

FACT (Irel) 0.125 Point estimate. Corresponds to S/R5 results.

a. Only those input values differing from those assumed in the INEEL analysis of the UCSB-assumed FIBS are listed. Inprt for Configuration B is based on Reference 3 SCDAP/RELAPS calculations for a relocation time of 12,844 seconds.

b. The stainless steel mass has been increased to include the mass of control material that might be present in the metallic layer.

C-9 INEEIJEXT 97 00779

.-_ - .. - _. . - . - . . _ - - - _ . _ . _ . . . - - - . . . - . . _ . . _ - _ - ~

O Table C 4. Configuration C input assumptions.*

Parameter Value Uncertainty N C3 , W/m - 2 5.211x10 5 Uncenainty treated in Cogy Corresponds to SBLB (H/R=2) values.

C2, W/m2 1.743x10' '~.

C,W/m 3

2 7.311x103 C,W/m2 4 7.643x10 3 C3, W/m2 4.180x10'3 PA.Ucss, W 8.5x106 Uncenainty treated in C 4,,, Corresponds to S/R5 results, tut, see 12.047 Point estimate. Corresponds to S/R5 results.

M z,... kg 7,027 Point estimate. Corresponds to S/R5 results.

f2,(}) 1.0000 Point estimate. Corresponds to S/R5 results.

fzr(2) . 0.0000 Point estimate. Corresponds to S/R5 results, fg,g(1)_ 0.0000 Point estimate. Corresponds to S/R5 results.

fg,g(2) 1.0000 Point estimate. Corresponds to S/R5 results.

M, . ... , kg 4187' Point estimaie. Conssponds to S/R5 results, f,,(1 ) 1.000 Point estimate. Corresponds to S/R5 results.

f,,(2) 0.000 Point estimate. Corresponds to S/R5 results.

37,207 M uoi-i.,, kg Point estimate. Corresponds to S/R5 results, fuo,(1) 0.000 Point estimate. Corresponds to S/R5 results.

fuo,(2) 1.000 Point estimate. Corresponds to S/R5 results.

E fu(I) 1.0000 Point estimate. Selected to address peer reviewer comments, fu(2) 0.0000 Point estimate. Selected to address peer reviewer comments.

fos .2, 0.45445 Point estimate. Corresponds to S/R5 resulu.

f. .y 0.8692 Point estimate corresponding to the minimum value making the metallic layer denser than the ceramic layer.

(Acr(lien) 0.123 Point estimate. Corre: pads to S/R5 results.

a. Only those input values differing from those assumed in the INEEL analysis of the UCSB assumed FIBS

- are listed. Input for Configuration C is based on Reference 3 SCDAP/RELAP5 calculations for a relocation

- time of 12,047 seconds. However, a fraction of the uranium is assumed to dissolve into the metallic layer to ,

address peer reviewer comments,

b. The stainless steel mass has been increased to include the mass of control material that might be present in the metallic layer.

INEEIJEXT-97-00779 C-10

Appendix D - Benchmark Calculation Results Figures presented in this appendix demonstrate that equations documented in the UCSB study are correctly implemented into the INEEL-developed VESTA code. Dese figures compare VESTA results to

~ UCSB model results for their assumed FIBS and sensitivity calculations presented in Appendix Q of the UCSB study. Figures D-1 through D 14 compare point estimate model results, and Figure D-15 presents uncertainty analysis results. As shown in these figures, the UCSB and VESTA results typically differ by less than one percent.

Differences between model predictions are attributed to slight differences between UCSB and INEEL input assumptiens. Table C 1 lists the input distributions that INEEL assumed for the UCSB.

assumed FIBS benchmark calculations. Note that this is INEEL's interpretation of UCSB input based on information in the UCSB study and Westinghouse's response to RAls. De three sets of UCSS assumed FIBS results included in the UCSB study differ in vessel wall heat fluxes predicted at locations near the

- metallic layer. [For locations adjacent to the metallic layer Appendix P (Figure P.5) suggests heat fluxes to the water are 550 W/m2 and that the ratio of q"(0)/q"(0) cup is 0.4; Appendix Q (Figure Q.1) suggests heat fluxes to the water are 500 W/m 2, and Section 7 (Figure 7.10) suggests that the median value of the ratio of q"(0)/q"(0)cu, is 0.49.) Hence, it appears that input for the UCSB assumed FIBS must have differed for some calculations and that the VESTA results presented in this appendix appear to match most FIBS results presented in the UCSB study.

800 DOE /ID 10460 700 - lNEEL

^ ,

, '}i 'l E ,-

?

{ 600 '

E 500 ,-

2 ..- \

g 400 i-2 5

lii g 200

~

.........- - -- - s 100 0

0 20 40 60 80 100 Angle (degrees) c=

Figure D-1. INEEL VESTA and UCSB model predictions for heat flux distribution.

D-1 INEEUEXT 97 00779

. c 8

DOEllD.10460 '

7 -lNEEL

,,6 -

5 I

jg ~~..' ...

jE 4 ,

N\

3 1 . .. .,

%m

. 0 0 20 40 60 80 100 Angle (degrees) -

Figure D 2. INEEL VESTA and UCSB model predictions fur oxide crust thickness, 20 DOE /ID-10460

........... INEEL n 15 - -- -

8

';r s.

E 10

.u: '

f , ....,'

=

~ ...~ ~....-

0 0 20 40 60 80 100 Angle (degrees) -

Figure D-3. INEEL VESTA and UCSB model predictions for vessellower head thickness.

INEEllEXT.97 00779 D2

l 1

I 310d

@ DOE /lD-10460

........... INE EL ..',..

E 3095 3r$0 3085 -

.l3080 -

{

,g 3075 -

22 x

o 3070 0.9 1.0 1,1 1.2 1.3 1.4 Decay heat power density (MW/m') ==

Figure D 4. INEEL VESTA and UCSB model predictions for oxidic *; x>l maximum temperature.

0.65 DOE /ID 10460

.......... . IN EEL 0.6 0.55

)I

[0.5 o.

0.45 0.4 0.9 1.0 1.1 1.2 1.3 1.4 Decay heat power density (MW/m') ==

Figure D-5. INEEL VESTA and UCSB model predictions for energy flow split.

D-3 INEEUEXT-97-00779

0.9 DOE /ID.10460

........... INEEL m 0.8 .

g .

f0.7 '.....,,,,,

.f ..,,,,,

0.6 -

. . . . . . .. .. . ~

0.5 3-0.4 -

0.9 1.0 1.1 1.2 1.3 1.4 Decay heat power density (MW/m') a, -

Figure D 6. INEEL VESTA and UCSB model predictions for oxidic pool top crust thickness.

1680

...",,,"... DOE /ID-10460 g

.,,, ........... INEEL 1670 - .....,....' " ....

1660' E

.S I 1650 .

I 1640 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 Metal pool height (m) a' " '

Figure D-7. INEEL VESTA and UCSB model predictions for metal layer bulk temperature.

INEEUEXT.97 00779 D-4

9 1660 DOE /ID 10460 g .... ......, ..... ........... INE EL 1650 .........' " ....,

1640 N I

1 g 1630 1620 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 Metal pool height (m)

Figure D-8. INEEL VESTA and UCSB model predictions for metal layer top temperature.

1740

- DOE /ID-10460 E ........... IN EEL E $73o

.2 7"~.s..,,~.....,

" ~ ~ .......,,,,,,

- 1710 '

I 3 1700-

I 1690 0.8 0.85 0.9 0.95- 1.00 1.05 1.1 -1.15 Metal pool height (m)

Figure D-9. INEEL VESTA and UCSE model predictions for metal layer bottom temperature.

D.5 INEEUEXT.97 00779

_. _ _ _ . _ . . _ ~ . . . .- -

. c

$1200 DOEllD.10460 .i

........... INEEL 1100 *'

j1000 -

g ................... .. . .. . ..... .. . ..

'E 900 .

A b

8@0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 Metal pool height (m) .,

Figum D.10. INEEL VESTA and UCSB model predictions for core barrel inner surface temperature.

{1200 DOE /ID.10460

........... IN EEL E

1100 .

2 3 -1000 e

5 8 ...... . .. .. .

900 -

3 8e0 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 Metal pool height (m) ==

Figtere D 11. INEEL VESTA and UCSB modei predictions for core barrel outer surface temperature. .

INEEUEXT.97 00779 D.6

P 800 DOE /ID 10460

........... INEEL

$ 700 600

$ 500 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 Metal pool height (m) ==

Figure D 12. INEEL VESTA and UCSB model predictions for vessel temperature.

600

{

s DOE /ID-10460

........... INEEL 3 550

. 6 u

ai!

500 1! 450

....'......,~.

400

....."*" ~....., ,,,,

350 1

300 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 Metal pool height (m) ==

FiguN D 13. INEEl. VESTA and UCSB model predictions for vessel heat flux.

D-7 INEEUEXT 97 00779 I _

14 13 .

12 :

^

[ 11 l10 2 .

] g ,,... ....

h .......

7 DOE /ID 10460 6 ... INEEL 5

0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 Metal pool height (m)

Figure D 14. INEEL VESTA and UCSB model predictions for vessel wall thickness.

60 g

.; 30* DOE /lD 10460

INEEL . vertfication Lf 40 1

3 30

$ " i85' g. ,/'

\

k l 2 20 1

j ,

b O.

l 10 <

j \

0 -

O.1 0.2 0.3 0.4 0.5 4* (6)/ 4cw(6) '

Figure D-15. INEEL VESTA and UCSB model predictions for CHF ratio pdfs.

INEEUEXT 97 00779 D-8

.. _ _

ML20203K795

Text

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