Text

Forwards Plan Providing Hydrogen & Steam Release Histories to Containment for Spectrum of Accident Sequences Using MAAP for Mechanistic Portion of Calculation
	ML20151Q166
Person / Time
Site:	Mcguire, Catawba, McGuire, 05000000
Issue date:	07/28/1988
From:	Tucker H; DUKE POWER CO.
To:	; NRC OFFICE OF ADMINISTRATION & RESOURCES MANAGEMENT (ARM)
References
	NUDOCS 8808110063
	Download: ML20151Q166 (62)
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Duxn POWER GOMPANY P.O. HOX 33180 CHAMLOTTE, N.O. 28249

!!AL H. Tt'CKER Tzt.ernown vice razeisswt (704) 373-4tW31 avet. san reonte July 28, 1980 Us'S'.tNucleareRegulatory, Commission Attention: Document Control Desk l Washington, D. C. 20555 l

Subject:

Catawba Nuclear Station Docket Nos. 50-413 and 50-414 McGuire Nuclear Station Docket Nos. 50-369 and 50-370

Dear Sir:

On May 13, 1988, a telecon was held between representatives from Duke Power Company (Duke) and the NRC Staff to discuss the resolution of issues concerning equipment survivability during deliberate ignition of hydrogen in containment.

from this meeting, we committed to provide hydrogen and steam release histories into containment for an appropriate selection of degraded core accident sequences using similar methodology to the Mark III Containment, Hydrogen Control Owners Group (HCOG).

We were unabic to calculate release histories via mechanistic methodologies while t.cmplying with the 75 percent metal-water reactor (MWR) requirements of 10 CFR 50.44. Therefore, release histories, which were compromised of a mechanistic portion, and a non-mechanistic portion for extrapolation to 75 percent clad oxidation, were developed. The attache' document provides hydrogen and steam release histories to containment for a spectrum of accident sequences using MAAP, i- Version 3.0B, for the mechanistic portion of the calculation, and the HCOG nethodology for the non-mechanistic extrapolation to 75 percent clad oxidation.

In order to facilitate the review process, the format of the attached information resembles the HCOG licensing submittals HGN-034 (May 17, 1985), HGN-052 (August 1, 198.G , and HGN-096 (July 30, 1986). The attached results will form the basis for analyzing the response of containment and its associated systems to the accident. sequences pending NRC approval.

Very truly yours, JW W n Hal B. Tucker PGL/35/sbn ?005 5

Attachments j 8808110063 080728 DR ADOCK 0 %

,.J.' . , . -.,

i U.'S.' Nuc1str Rigulatory' Commission July 28, 1988 Page Two-

. xc: Dr.-J. Nelson Grace, Regional Administrator U. S. Nuclear Regulatory Commission-Region II

-101 Marietta Street, NW, Suite 2900 Atlanta,' Georgia 30323-Mr. P..K. Van:Doorn

~

NRC. Resident Inspector Catawba Nuclear Station I

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A,

-s' ' U. 'S. Nuclear Ragulatory Conniscion

-July 28, 1988 Page Three IT bxc: (w/o-attachments).

H. D. Brewes L. T. Burba

' B. J. Dolan R. L. Gill' C. D. Ingram R.-W. Ouellette N.-A. Rutherford-J. G. Torre File: CN-801.01-R.M. Glover R; 0. Sharpe 4

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f DUKE POWER COMPANY Catawba Nuclear Station 4

Phase I Submittal for the Plan to Resolve-Issues Concerning .

Control of Combustible Gases in Containment as Outlined by -

10CFR50.44.

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The first phase in the plan to resolve issues concerning equipment survivability during deliberate ignition of hydrogen in containment is the selection of specific accident sequences to be analyzed. A spectrum of accident sequences that envelope the range of hydrogen and steam release rates have been studied.

Since steam flow through the core is the limiting factor for clad oxidation, primary system pressure is the parameter of importance due to its effect on steam availability. Therefore, the following sequences were analyzed:

SD (low primary system pressure)

SD (intermediate primary system pressure)

T U (high primary system pressure)

As a result of NRC Staff interest over sequences involving ECCS failure in the recirculation mode, S2H will also be investigated. These accident cequences envelope the possible primary system pressure conditions under which hydrogen could be developed in the primary system, the release rates of that hydrogen to containment, and conditions in containment at the time of hydrogen release. For each sequence, FCCS was not recovered until hydrogen production had reached its peak value for the case of simply boiling away the remaining water inventory in the core region (an unmitigated case). consistent with the HCOG methodology.

Primary system breaks were assumed to occur in the hot leg in order to allow minimum holdup time of hydrogen as it's produced in the core. It was assumed that oxidation could take place on both sides of the Zircaloy fuel cladding to account for steam ingression after clad rupture.

MAAP, Version 3.0B, was used to analyze the four degraded core sequences. MAAP is a computer code developed by the Industry Degraded Core Rulemaking (IDCOR)

Program. It is designed to provide realistic thermal-hydraulic assessments for severe core damage accident sequences.

The model diviles the primary system into fifteen nodes as shown in Figure 1.

Nodes exist for the core region, upper plenum, reactor "dome" (upper head),

downcomer and lower head, pressurizer, and five nodes in each modeled coolant loop. Two coolant loops are represented and are denoted the "broken" and "unbroken" loops. The unbroken loop consists of all the coolant loops except one. This primary system nodalization permits a detailed accounting of the water / steam which is available for cooling the core and for reacting with the Zircaloy fuel cladding. In addition, this arrangement allows the user to track hydrogen through the primary system and thereby calculate release rates to the containment. The core is further divided into a user selected number of subnodes; a 4 radial X 17 axial nodalization is used for the Catawba analysis.

The safety systems considered in this analysis include the charging pumps (NV),

safety injection pumps (NI), low pressure injection pumps (ND), cold leg accumulators, auxiliary feedwater, and containment sprays. These are shown in Figure 2 along with other systemc important to accident progression, such as the pressurizer and steam generator safety and power cperated relief valves. In order to model individual accident sequences, all of these systems can be enabled or disabled by the user through the use of MAAP "event codes." For a complete description of the relevant MAAP models used in this calculation refer to Appendix 5.

1

The four sequences analyzed are discussed below:

S yD SEQUENCE The S D sequence was modeled as a 6-inch diameter break on the hot leg followed 3

by failure of the emergency core cooling system (ECCS). The auxiliary feedwater system was assumed to function properly and provided secondary side heat removal. Within 6 minutes the primary system pressure had dropped below the cold leg accumulator (s) initial discharge setpoint (646 psia), resulting in rapid depletion of accumulator (s) inventory. The loss of primary system inventory through the 6-inch diameter break on the hot leg eventually led to cere uncovery and a loss of decay heat removal (0.51 hrs.).

The core continued to heat up, and subsequent oxidation of the Zircaloy cladding began at 0.64 hours7.407407e-4 days 0.0178 hours 1.058201e-4 weeks 2.4352e-5 months . By 0.73 hours8.449074e-4 days 0.0203 hours 1.207011e-4 weeks 2.77765e-5 months the hottest core node had reached the UO 2

-Zr-Zr02 utectic melting temperature of 2500 *K. ECCS was recovered at 1.22 hours2.546296e-4 days 0.00611 hours 3.637566e-5 weeks 8.371e-6 months with all NI and NV pumps available. The majority of the hydrogen gas was expelled through the break by 1.92 hours0.00106 days 0.0256 hours 1.521164e-4 weeks 3.5006e-5 months .

The total fraction of the clad oxidized was 25.5%. Appendix 1 contains relevant plots for the S D3 sequence, which consists of the following parameters as a function of time:

FIGURE NUMBER DESCRIPTION 1.01 H2 Flow Out of Hot Leg Break (kg/s) 1.02 Water / Steam Flow Out of Hot Leg Break (kg/s) 1.03 Integrated Mass of H7 Genersted in the Core (1b) 1.04 Mass of H in the Primary System (lb) 1.05 Mass of H in the Pressurizer (1b) 1.06 Water Temperature in the Core (*F) 1.07 Primary System Pressure (psia) 1.08 ECCS Flow to Cold Legs (1b/hr) 1.09 Accumulator (s) Flow to Cold Legs (1b/hr) 1.10 Reactor Vessel Water Level (ft) 1.11 Accumulator (s) Pressure (psia)

As previously stated, the core is divided into 4 radial X 17 axial nodes.

Rather than submit core node temperatures for all 68 nodes 3 representative axial cross-sections will be presented as follows:

1.12 Top of Active Fuel Axial Node X 4 Top Radial Nodes (*F) 1.13 Middle of Active Fuel Axial Node X 4 Middle Radial Nodes (*F) 1.14 Bottom of Active Fuel Axial Node X 4 Bottom Radial Nodes (*F) l 2

l

S D SEQUENCE 2

The S,D sequence was modeled as a 2-inch diameter break on the hot leg, followed by failure of ECCS injection. Auxiliary feedwater was assumed to operate during this sequence. The core uncovered at 0.61 hours7.060185e-4 days 0.0169 hours 1.008598e-4 weeks 2.32105e-5 months , and subsequent oxidation of the Zircaloy cladding began at 0.72 hours8.333333e-4 days 0.02 hours 1.190476e-4 weeks 2.7396e-5 months . By 0.90 hours0.00104 days 0.025 hours 1.488095e-4 weeks 3.4245e-5 months the hottest core node had reached the UO 2

-Zr-Zr0 2

utectic neiting temperature. The primary system pressure dropped below the cold leg accumulator (s) initial discharge setpoint at 1.03 hours3.472222e-5 days 8.333333e-4 hours 4.960317e-6 weeks 1.1415e-6 months , thereby introducing a discontinuous reflood source to the reactor vessel. ECCS was recovered at 1.20 hours2.314815e-4 days 0.00556 hours 3.306878e-5 weeks 7.61e-6 months with all NI and NV pumps available.

The majority of the hydrogen gas was expelled through the break by 2.08 hours9.259259e-5 days 0.00222 hours 1.322751e-5 weeks 3.044e-6 months .

The total fraction of the clad oxidized was 23.1%. Appendix 2 contains relevant plots for the S D2 sequence, which consists of the following parameters as a function of time:

FIGURE NUMBER DESCRIPTION 2.01 H2 Flow Out of Hot Leg Break (kg/s) 2.02 Water / Steam Flow Out of Hot Leg Break (kg/s) 2.03 Integrated Mass of H, Generated in the Core (lb) 2.04 Mass of H in the Primary System (lb) 2.05 Mass of H in the Pressurizer (lb) 2.06 Water Temperature in the Core (* F) 2.0/ Primary System Pressure (psia) 2.08 ECCS Flow to Cold Legs (1b/hr) 2.09 Accumulator (s) Flow to Cold Legs (1b/hr) 2.10 Reactor Vessel Water Level (f t) 2.11 Accumulator (s) Pressure (psia) 2.12 Top of Active Fuel Axial Node X 4 Tcp Radial Nodes (* F) 2.13 Middle of Active Fuel Axial Node X 4 Middle Radial Nodes (*F) 2.14 Bottom of Active Fuel Axial Node X 4 Bottom Radial Nodes ('F)

TMLU SEQUENCE The TMLU sequence was modeled as a station blackout. As a result of loss of power, main feedwater failed, ECCS failed, and the MSIVs closed. It was also assumed that the auxiliary feedwater system failed and the pressurizer PORVs failed to open.

Initially, the decay heat from the core was removed by boiling the water remaining in the steam generators. However, as the secondary side inventory was depleted, heat transfer from the primary system to the secondary system decreased, and at 0.98 hours0.00113 days 0.0272 hours 1.62037e-4 weeks 3.7289e-5 months the pressurizer safety valves lifted relieving pressure to the Pressurizer Relief Tank (PRT). At 1.42 hours4.861111e-4 days 0.0117 hours 6.944444e-5 weeks 1.5981e-5 months the PRT rupture disk blew out and began the release of steam to containment. By 1.45 hours5.208333e-4 days 0.0125 hours 7.440476e-5 weeks 1.71225e-5 months the steam generators had boiled completely dry.

3

. .=_ _-. .- -_

At approximately 1.88 hours0.00102 days 0.0244 hours 1.455026e-4 weeks 3.3484e-5 months , the core began to uncover, and at 2.41 hours4.74537e-4 days 0.0114 hours 6.779101e-5 weeks 1.56005e-5 months the hottest core node had reached the UO,-Zr-Zr0 2 utectic melting temperature. At 2.80 hours9.259259e-4 days 0.0222 hours 1.322751e-4 weeks 3.044e-5 months the EC ' was restored with the NV pumps providing cooling water by pumping against the high primary system pressure. Because primary system pressure remains elsvated, the cold leg accumulator (s) never discharge during this sequence. The release of hydrogen gas was controlled by the presst rizer safety valves and the pressurizer PORVs (after power restoration) by relieving pressure to the PRT and, therefore, the majority of hydrogen gas escaped slowly from the primary system over a five hour period. Auxiliary feedwater was not restored when power became available in order to expedite the discharge of hydrogen gas from the primary system to containment.

The total fraction of the clad oxidized was 31.6%. Appendix 3 contains relevant plots for the TMLU sequence, which consists of the following parameters as a function of time:

FIGURE NUMBER DESCRIPTION 3.01 H2 Flow Out of the PRT (kg/s) 3.02 Water / Steam Flow Out of the PRT (kg/s) 3.03 Integrated Mass of H9Generated in the Core (1b) 3.04 Mass of H in the Primary System (lb) 3.05 Mass of H in the Pressurizer (1b) 3.06 Water Temperature in the Core (* F) 3.07 Primary System Pressure (psia) 3.08 ECCS Flow to Cold Legs (1b/hr) 3.09 Downcomer Water Level in the Steam Generator (s) (ft) 3.10 Reactor Vessel Water Level (ft) 3.11 Top of Active Fuel Axial Node X 4 Top Radial Nodes (*F) 3.12 Middle of Active Fuel Axial Node X 4 Middle Radial Nodes (*F) 3.13 Bottom of Active Fuel Axial Node X 4 Bottom Radial Nodes ( *F) '

S2H SEQUENCE The S2 H sequence was modeled as a 2-inch diameter break on the hot leg with successful ECCS injection but failure of ECCS to operate in the recirculation mode.

i The sequence began with a 2-inch diameter break on the hot leg. By 64.3 secords the primary system pressure had dropped to the ECCS set point of 1860 psia, 2nd all high head pumps began injection of cooling water into the primary system.

Containment sprays were initiated automatically at 85.0 seconds causing 5:apid depletion of Fueling Water Storage Tank (FWST) inventory. At 0.67 hours7.75463e-4 days 0.0186 hours 1.107804e-4 weeks 2.54935e-5 months the FWST was empty, and ECCS failed to switch over to the recirculation mo6e of core coalir.g.

'l The loss of primary inventory resulted in the core being uncovered at 1.10 hours1.157407e-4 days 0.00278 hours 1.653439e-5 weeks 3.805e-6 months . Hydrogen production from Zircaloy oxidation began at 1.22 hours2.546296e-4 days 0.00611 hours 3.637566e-5 weeks 8.371e-6 months . By 3 1.43 hours4.976852e-4 days 0.0119 hours 7.109788e-5 weeks 1.63615e-5 months the hottest core node had reached the UO 2

-Zr-Zr0 utectic melting temperature. The primary system pressure dropped below the2 cold leg 4

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

accumulator (s) initial discharge setpoint at 1.51 hours5.902778e-4 days 0.0142 hours 8.43254e-5 weeks 1.94055e-5 months , thereby introducing a discontinuous reflood source to the reactor vessel. ECCS was restored at 1.79 hours9.143519e-4 days 0.0219 hours 1.306217e-4 weeks 3.00595e-5 months with all NI and NV pumps operating in the recirculation mode. The majority of the hydrogen gas was expelled through the break by 2.80 hours9.259259e-4 days 0.0222 hours 1.322751e-4 weeks 3.044e-5 months .

The total fraction of the clad oxidized was 25.2%. Appendix 4 contains relevant plots for the S H2 sequence, which consists of the following parameters as a function of time:

FIGURE NUMBER DESCRIPTION 4.01 H2 Flow Out of Hot Leg Break (kg/s) 4.02 Water / Steam Flow Out of Hot Leg Break (kg/s) 4.03 Integrated Mass of H9Generated in the Core (lb) 4.04 Mass of H in the Primary System (lb) 4.05 Mass of H in the Pressurizer (1b) 4.06 Water Temperature in the Core (*F) 4.07 Primary System Pressure (psia) 4.08 ECCS Flow to Cold Legs (1b/hr) 4.09 Accumulator (s) Flow to Cold Legs (1b/hr) 4.10 Reactor Vessel Water Level (ft) 4.11 FWST Water Level (ft) 4.12 Ac~2sulator(s) Pressure (psia) 4.13 "op of Active Fuel Axial Node X 4 Top Radial Nodes (*F) 4.14 Middle of Active Fuel Axial Node X 4 Middle Radial Nodes (* F) 4.15 Bottom of Active Fuel Axial Node X 4 Bottom Radial Nodes ('F)

Altbrugh injection of ECCS into the vessel should rapidly quench the core and tGrminate hydrogen production, the improbable case which results in continued oxidation equivalent to 75% MWR has been considered. Since a completely mechanistic model is not capable of predicting hydrogen production equivalent to the amount mandated by 10CFR50.44, a non-mechanistic model similar to the HCOG methodology has been utilized.

The non-mechanistic codel that is being used to predict hydrogen production is based upon an energy balarice in a severely damaged core which no longer retains an intact geometry. The core is assumed to have deformed into a debris bed which is postulated to form following injection of ECCS into a severely overheated core. To assure that the damaged core is coolable it is necessary that energy losses from the damaged core are at least adequate to remove decay energy in the core; plus energy produced by continued oxidation of Zircaloy in the core; plus excess stored energy in the core. It is additionally assumed that termination of the Zircaloy oxidation at 75% MWR requires a quenched core at that time.

This can be presented in equation form ast (1) Q1 ,,, a Qdh + O ox +O s where:

5

Qy , = Energy loss rate from the damaged core to surrounding water; Qdh a Rate of core decay heat; Q ox =

Rate of exothermic energy produced by oxidation of Zircaloy in the damaged core; *

-Q s = Release of excess energy stored in the damaged core = '

E (T) - E (T ) over some time period; E = Energy stored in the core and associated structures as a function of temperature. I If the losses from the debris bed do not exceed the sum of the decay heat, the oxidation energy and the excess stored energy, then the debris will continue to overheat and will eventually challenge the integrity of the lower vessel head.

The limiting case would, therefore, be a severly deformed core in which the long-term sum of the decay energy, the oxidation energy, and the excess stored energy approaches the maximum heat loss from the debris bed.

Hydrogen production would occur over the extended period of time t12 * *2 ~ "I where t 2= time when 75% WR is achieved and the core is quenched; t 1= time when the mechanistically produced hydrogen has been released to containment.

(The sequence dependent parameters referenced in the following discussion apply

, to the S D I sequence.)

The decay heat can be expressed ast (2) Qdh = 349.6 t-0.253 (g),

which is a curve fit to the decay heat history for Catawba reload cycles of 390 days, using 3.8 w/o enrichment Westinghouse Optimized Fuel Assemblies (See Attachment 6). This curve fit is accurate to +1.6%, -2.8% over the required time span (approximately 6912 to 16068 seconds following scram).

The total amount of energy of each term in Equation (1) can be determined for the problem time span (t12). Equation (2) can be integrated to find the total decay heat:

t 2

(3) Qdh12 " 9dh(t) dt 1

or (4) Q dh12 = 468.0 t 2

~#

1 (W-s e c) .

6 t

, _ . _ , , . . . . . _ _ , . . ._,.,,,,,m_ ,m.-.. . . _ _ . . - _--,,-..y-

L For the Zircaloy oxidation energy term, Q we know that 75" MWR = 1496.6 12 lbs. of hydrogen, and that the ECCS reflood ca,se produced 508 lbs. (25.5% MWR) of hydrogen. Therefore, the remaining mass of hydrogen to be generated, M is: HU' (5) MH12 = 1496.6 - 508 - 988.6 lbs. of H 2 From the NRC-sponsored thermal properties package MATPRO-11, we have:

(6) Q = 66.68 MW-sec/lb of H2 Produced.

Combining Equations (5) and (6) yields:

4 (7) Q od2 = 6.59 X 10 gy_ ,

The energy storage term can be stated as:

1 (8) Qs12 " 9(

s dT sat When the average temperature of the debris bed exceeds 2173 'K, the Zircaloy in the debris bed will exceed the Zircaloy melting temperature, and the existence of a debris bed is no longer assured. The energy stored in the core will be maximized if the average debris bed temperature is assumed to equal 2173 *K.

For the S j D sequence, the equilibrium primary system pressure is approximately 60 psia af ter core recovery. Assuming that the core will quench to approximately T,,e for 60 psia system pressure ( m 418

K) we have the following equation for the energy storage term 2173 (9) Q s12 "

9s(T) dT g

The energy storage term in the fuel, cladding, baffles, and formers can be readily calculated based upon known masses of the core components, and their corresponding specific heats as a function of temperature. The total stored energy which must be removed in t 12 as the core cools from 2173 *K to 418 oK ist 4

(10) Q s12 = 7.03 X 10 MW-see The maximum heat loss which can occur from the severly deformed core is controlled by the size of the assumed debris bed, and the heat transfer assumed to occur. The model which has been used assumes that the deforned core occupies the entire core region of the inside of the core barrel. The model conservatively evaluates heat losses from the top, bottom and sides of the debris bed. Heat loss from the top of the bed is assumed to be lim pool boiling critical heat flux which is calculated to be 2.13 MW/m{ted forby theS D the 3

sequence. Heat loss from the bottom surface of the core is conservatively assumed to be controlled by horizontal upward plate film boiling. This represents a conservative maximized treatment of heat transfer from the lower surface, since downward heat transfer into a pool of water is likely to be much smaller than the maximum heat transfer which would orcur due to film boiling. 2 The downward heat transfer for the S gD sequence is calculated to be 0.223 MW/m .

7

Heat transfer through the side of the debris bed is assumed to be controlled by

-conduction through the stainless steel core barrel. For the S D sequgnce, heat 3

transfer through the sides of the core is calculated to be 0.507 W/m . The total amount of heat which can be removed from the core is:

III) 91oss " 9 top + 9 bottom + 9 sides Based upon the assumed size of the debris bed (i.e., the entire core region area inside the core barrel), the maximum heat loss from the severely deformed core is calculated to be:

(12) Q1 , = 48.0 W The full energy balance will now be expressed as an equality by incorporating the production time span, t12, into Equation (1) and substituting Equations (4),

(7), (10) and (12) into the resulting equation:

( }

91oss "12 " 9dh12 + Nox12 + Os12 or (14) ' 0 747 g ,,,c 48.0 (t ~2 *1) MW-sec = 468.0

~

t 2 ~ *1 ~

4

+ 6.59 X 10 W-see + 7.03 X 10 4W-s e e Combining like terms, and since t occurs when the majority of the hydrogen gas was expelled through the break (1.g92 hours (6912 seconds) for t eh S D sequence) gives the following equation I (15) 0.102564 t2 " *2 + 261.7 which, when solved iteratively, yields:

t 2= 16068 seconds Therefore, for the S D g sequence, the average rate of hydrogen production over the time span of t 12 t reach a total hydrogen production equal to 75% WR is:

988.6 lbs "H12 "

H12 "

t 12 16068-6912 secs or h = 0.108 lbm/see H12 for a period of 16068-6912 secs = 9156 eees (2.54 hrs.)

Since the non-mechanistic model description given for the S D 3 sequence also applies to the S D, TMLU, and S H sequences, the results for the remaining three sequences will be2 presented in an 2 abbreviated format.

8

S D Sequence 2

(1) Qy,,, 2 Qdh + Oox +Os (2) Qdh = 349.6 t-0.253 (g)

This curve fit is accurate to +1.6%, -2.8% over the required time span (approximately 7488 to 13192 seconds following scram).

2 (3) Qdh12 " 9dh(t) de

1 0 747 0 747 (4) t (W-se e ) .

Qdh12 = 468.0 .2 ~ "1 i (5) MH12 = 1496.6 - 460 = 1036.6 lbs. of H 2 (6) Q,x = 66.68 W-sec/lb of H 2Produced.

(7) Q ox12 = 6.91 X 10' W-sec.

T (8) Qs12 " 9s(T) dT sat For the S,D sequence, the equilibrium primary system pressure is approximately 210 psia af ter core recovery. Assuming that the core will quench to approximately T for 210 psia system pressure ( = 470 *K) we have the following equatf$$ for the energy storage term:

f 2173 (9) Q s12

9s(T) dT 4

(10) Q s12 = 6.86 X 10 g ,,,,

(11) Qy,,, = Qgop + Qbottom + Osides Upward heat loss = 3.02 W/m 2 2

Downward heat loss = 0.314 p /m Side heat loss = 0.487 W/m (12) Q 1oss = 58.1 W (13) Q3 ,,, t12 ~9dh12

Nox12 + Os12 ,

(14) 58.1 (t 2~ *1) W-sec = 468.0 t 2 ~ *1 #~ * * +

6.91 X 104 W-sec + 6.86 y 10' W-see t goccurs at 2.08 hours9.259259e-5 days 0.00222 hours 1.322751e-5 weeks 3.044e-6 months (7488 seconds)

(15) 0.124145 t2 " *2 + 440.1 9

if

4 i

l which, when solved iteratively, yields:

t2 = 13171 seconds Therefore, for,the S D2 sequence, the average rate of hydrogen productirsn over 12 t reach a e tal hydrogen production equal to 75% MWR is:

the time span of t ,

M H12 " 1036.6 lbs "H12 "

t 12 13171-7488 secs i ur 12 = 0.182 lbm/sec l for a period of 13171-7488 secs = 5683 secs (1.58 hrs.)

TMLU Sequence (1) Q 1oss E 9dh~+ Sox +O s (2) Qdh = 366.1 t (W) '

This curve fit is accurate to 10.005% over the required time span (approximately 24480 to 28501 seconds following scram).

2 (3) Qdh12 " 9dh(*) d' '

t 1 ,, .

(4) Q dh12 = 492.7 t 0 743 , g 0.743 (MW- s e c) .

2 _

(5) M H12

= 1496.6 - 630 - 866.6 lbs. of H 2 >

t (6) Q, = 66.68 MW-sec/lb of H2 produced. ;

(7) Q ox12 = 5.78 x 10' MW-see T

(8) Qs12 " 9s (T) dT sat For the TMLU sequence, the equilibrium primary system pressure is approximately 2335 psia after core recovery. Assuming that the core will quench to approximately T for 2335 poia system pressure (:: 621 *K) we have the following equatI$n for the energy storage terms I

2173 (9) Q s12

Os (T) dT g

10

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

4 (10) Qs12 = 6.35 X 10 W-s e c (II) Sloss " 9 top + 9 bottom + Ssides Upward heat loss = 2.95 W/m 2 2

Downward heat loss = 0.504 p/m Side heat loss = 0.429 W/m (12) Qy,,, = 5 6.9 W

( }

91oss #12 " 9dh12 + Oox12 + 9s12 ,

(14) W-s e e +

56.9 (t2 ~ "1) MW-sec = 492.7 t 2 ~ *1 J 4

5.78 X 10 W-see + 6.35 X 10 0W-s e e t yoccurs at 6.8 hours9.259259e-5 days 0.00222 hours 1.322751e-5 weeks 3.044e-6 months or 24480 seconds 4

(15) 0.115486 t 2 * *2 + 1249.9 which, when solved iteratively, yields t 2= 28501 seconds ThetJore, for the TMLU sequence, the average rate of hydrogen production over the time span of t 12 t reach a total hydrogen production equal to 75% WR is:

~

"H12 "

866.6 lbs "H12 t

12 28501-24480 secs or higgy = 0.216 lbm/see for a period of 28501-24480 sees = 4021 sees (1.12 hrs.)

S H Sequence 2

(1) Qy ,,, ;t Qdh + Nox *S s (2) Q dh = 224.0 t-0.206 (g)

This curve fit is accurate to +2.1%, -1.1% over the required time span (approximately 10080 to 15339 seconds following scram).

2 (3) Qdh12 " 9dh(t) de

1 (4) Q dh12 = 282.1 t 2 ~ *1 (#-8'C)*

11

(5) M H12 = 1496.6 - 502 = 994.6 lbs. of H 2 (6) Q ox = 66.68 W-sec/lb of H 2Produced.

0 (7) Qox12 = 6.63 X 10 W-se e T

(8) Qs12 " Os (T) dT sat For the S,H sequence, the equilibrium primary system pressure is approximately 200 psia after core recovery. Assuming that'the core will quench to approximately T at for 200 psia system pressure ( :: 467 *K) we have the following equation for the energy storage terms f2173 (9) Q s12 "

Os (T) dT 4

(10) Qs12 = 6.87 X 10 W-se c (II) 91oss " 9 top + 9 bottom + 9 sides Upward heat loss = 2.99 W/m 2 Downward heat loss = 0.310 P9"i Side heat loss = 0.488 W/m' (12) Q1 ,,, = 5 7. 7 W (13) Q3 ,, , c12 " 9dh12 + Oox12 + 9s12 (14) ' W-s e e +

57.7 (t ~2

1) W-s e c = 282.1 t 2 ~ *1 4

6.63 X 10 W-sec + 6.87 X 100 W-s u .

t goccurs at 2.80 hours9.259259e-4 days 0.0222 hours 1.322751e-4 weeks 3.044e-5 months (10080 seconds)

(15) 0.204537 t2 " *2 0 794 + 1031.1 which, when solved iteratively, yields t 2= 15339 seconds Therefore, for the S H sequence, the average rate of hydrogen production over the time span of t 12 2 t reach a total hydrogen production equal to 75% WR ist b12 " 994.6 lbs b12 " t 15339-10080 secs 12 or M

H12 = 0.189 lbm/see for a period of 15339-10080 sees = 5259 sees (1.46 hrs.)

12

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10CFR50.44 ANALYSIS

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S1D SEOLlENCE -
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i APPENDIX 5 :
r The following: documentation describes the models HEATUP and ACCUM which are-currently incorporated within the MAAP 3.0B computer code. . Complete documentation for the remaining MAAP models can be found in 7DCOR Technical Report 16.2-3, MAAP (3.0) Modular Accident Analysis Program User's Manual - Vol.
II,_ February 1987.
-I-HEATUP/Pd CORE-COOLANT INTERACTIONS 1.0 J INTR 00'CTION The HEATUP subroutine predicts the behavior of the reactor core during and after uncovery, as it is heated by fission product decay and by Zircaloy oxidati e The HEATUP subroutine includes models for calculating the steaming rate from the: core, hydrogen formation rates, fuel melting, natural circulation flows, and upper head injection cooling from external accumula-tors.
The HEATUP subroutine was originally intended to substitute for the detailed PWR heatup code (EPRI PWRCHC) while that program and the MAAP code were under development. Another reason for developing this HEATUP subroutine was to provide a core heatup model with an execution time comensurate with the main PWR MAAP code. This has baen achieved through several simplifica-tions and assumptions described in detail in the model descriptions. The main simplifications are:
1.
The core is divided into a maximum total of 70 nodes.
1
~~2. Only the heatup of the fuel rods is considered. Other struc-tural materials such as grids and control roos se ignored.~~
~~3. The boiled-up water level is assumed to be uniform across the core. '~~
4.
Radial temperature gradients in the fuel rods are usually neglected.
~~5. Axial radiation heat transfer is neglected.~~
~~6. The melting model for the fuel rods is simplified in its representation of material interactions and internal heat transfer processes.~~
i
1 4
HEATUP/PWR These simplifications reduce the computationa.1 complexity while still pro-viding a realistic overall description of the core behavior, t i
In accordance with the computaticnal procedure of the main MAAP program, the HEATUP subroutine calculates rates of change of the core state variables. These rates are detennined from mass and energy balances and are integrated externally to provide updated values of the state variables at the next time step. The main core state variables include the nodal masses of UO 2 , Zr, and Zr0 2 , the internal energies-of the core nodes, the cladding strains (ballooning model), and the fraction of the decay energy in each node which is not associated with fission products tracked by the fission product routines. The rates of steam and hydrogen production and the rate at which molten corium leaves the core boundaries, which drive many of the processes modeled in the rest of the MAAP code, are the most significant outputs of the subroutine.
2.0 NODEL DESCRIPTION 2.1 General Core Model i
The reactor core is assumed to consist only of fuel rods and coolant flow channels as shown in Fig. 1. The fuel rods contain UO2 pellets, which generate decay heat, clad in Zircaloy. The coolant channels may be partially covered by a water pool. Steam generated in the pool boils up the pool and flows in the uncovered part axially along the coolant channels and radially between them. Since there are no barriers for radial flow in the core, and the steam flow velocities are small, a unifonn boiled-up water level is assumed across the core.
When the cold leg nozzles are empty, the core and the downcomer are j hydraulically disconnected from the rest of the primary system. In this case, water may flow from the downcomer to the core, or vice versa, to equalize the static liquid heads in both regions. Thus, during core uncovery the water level in the downcomer essentially equals the collapsed water level of the core.
.p,,
STEAM AND HYDROGEN o COOLANT y af n q -
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/
r' l l 2 / , BLOCK AGE OF l l 0 /
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~
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-DIVERTED STEAM
/
l
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o- BOILED-UP o o
/ ol o ol COOLANT LEVEL
/ o* C l oo 'o o oloe *$
/ o c ol oo o I o, o*lo l o
~~d *,l ._.,~~
l0 Ol LOWER PLENUM Fig. I Schematic description of a PWR core during uncovery.
HEATUP/PWR During "nonnal" boildown of the core, the heat generated in the covered part of the core is transferred into sensible and latent heat of the water pool. Hence, the temperature of this part is limited to the pool saturation temperature. In the uncovered part of the core, on the other hand, heat can be removed by convection to the gas stream, and by pin-to-pin radia-tion across the core. This heat removal rate is generaily less than the decay heat generation and thus the temperature in the uncovered region increases.
As the uncovered core heats up, differences in gas density across the core can cause natural circulation flows to be set up between the core and the upper plenum. Eventually, the Zircaloy reacts with steam in the flow channel to fonn Zr02 and hydrogen. This reaction is exothermic and results in further heating of the uncovered part. Ballooning and clad rupture may further contribute to the oxidation rate as the surface area increases and as the inner clad surface becomes exposed to steam. When the temperature at any location in the core reaches the Zircaloy melting point (2100 K) or a higher temperature if the Zircaloy reacts with oxygen or U0 2, Zircaloy may melt and refreeze as it slumps or drains on the outer cladding surface. The flow channels thus msy become blocked, and the steam and hydrogen mixture flowing below the blockage are then diverted to all the remaining unblocked channels.
Wien the temperature in the uncovered core reaches the melting temperature (e.g. 2500K for typical U-Zr-0 eutectics), the molten core components, namely UO 2 , Zr, and Zr02 (corium) leave the original node boundary.
When water frem an external accumulator is injected into the upper part of the reactor pressure vessel it may quench the core by entering from the top or it may bypass the fuel rods to mix directly with the water pool.
Both processes will cool the core.
Some accident sequences may involve very rapid injection of water into the core through the downcomer after the core has been uncovered for an extensive period (such as in THI-2). In this case inverted annular flow can result where a film of steam would cover the not fuel rods while water would be present in the central part of the flow channels. In this case, the covered part of the core can be at substantially higher temperatures than the water pool and may therefore oxidize.
I
.s . . - ~ _ . _ _ _ _ . -
HEATUP/PWR A detailed description of the models used to calculate these pro-cesses are described in the following subsections.
2.2 Calculational Structure The HEATUP subroutine primarily calculates the rate of change of the mass and energy of the major components of the core. These components are UO2 , Zr, Zr0 2, water (and steam), and hydrogen. The first three components are the major constituents of the "core material" while the other components are present in the flow channels.
The mass and energy rate of change of the core material components are calculated for cach node in the core. Nodal temperatures are determined by subroutine TNODE from the core material masses and energy in the node. The masses of all the solid components are sunined up to a total core mass. The water pool is treated as a lumped mass and energy control volume. The overall pool rates of change are determined by all the inlet and outlet flows and by the overall pool energy source tenns. Similarly, water energy and mass balances are computed for the downcomer.
Steam and hydrogen are assumed to flow along the uncovered (and unblocked) ficw channels, and the mass flow rates and enthalpies in each channel are calculated by tracking the generation and consumption of each component at each axial level.
The channel exit values are summed to form a total steam and hydrogen flow from the core and an overall gas enthalpy.
When subroutine HCATUP is called for the first time ir PWR-MAAP the following major user-specified definitions are made:
1. Number of radial rings and axial rows. All nodal variables are dimensicned to a total maximum of 70 nodes. The maximum number of rings is 7 and the maximum number of rows is 20. Any combination of the number of rings and rows which (a) does not exceed the corresponding maximum limits of 7 and 20, and (b) yield an overall number of nodes not exceeding 70, is accept-able. For example, 7 rings x 10 rows or 3 rings x 20 rows are
~~HEATUP/PWR acceptable; 5 rings x 16 roxs (more than 70 nodes) or 8 rings x 8 rows (more than 7 rings) are unacceptable. The top node in each. ring represents the unfueled upper fission gas plena.~~
~~2. Fuel rod and channel geometry.~~
~~3. Power and flow area fractions are normalized, if not already done so by the user.~~
~~2.3 Physical Pror. esses Modeled The major models used by tne HEATUP subroutine are:~~
~~1. Heatup and steam generation in the water pool,~~
~
~~2. Zircaloy oxidation and hydrogen femation, i 3. Core-upper plenum natural circulation,~~
~~4. Radial radiation model,~~
~~5. Heatup of an uncovered node.~~
~~6. Corium nelt model .~~
~~7. Upper head injection.~~
l 8. Clac ballooning.
l The models are formulated with the primary concern of providing a realistic overall description of the dominant physical processes while minimizing the computational complexity. A lumped control volume approach is used for all mass and energy balances. The model is quasi-steady in the sense that the l
exit flows are determined by the inlet flows and steaming, i.e. changes in internal core flow rates due to pressure changes are neglected, j 2.3.1 Heatup of the Water Pool and Covered Nodes The covered part of the core extends from the bottom of the core to the location of the boiled up level. Since the boiled-up water level is assumed to be unifonn across the core, its location is detemined by relating the boiled-up water volume ta the free volume in the reactor vessel. This boiled-up vnlume is obtained from the water mass, density and the average void 1
j HEATUP/PWR l
l fraction in the pool. The boiled-up water level is calculated externally to HEATUP (in PRYSIS) by subroutine VLEVEL by specifying the water mass in the cere, the water and steam specific volumes, the height at which the inlet flows became saturated in the last time step, and the steam flow rates below and in the core. These flow rates detemine the average void fractions in the lower plenum and in the core.
In the lower plenum, steam is generated by interaction of water with the molten corium. This steam flow, W 'ttem, is calculated by subroutine s
PLSTN, and the resulting veld fraction is applied to the entire lower plenum.
In the covered part of the core, steam can be fomed by boiling and also by flashing if the pressure in the RPV changes with time. Steam genera-tion by boiling is assumed to take place only when the pool is saturated. The boiling steam f N rate, Wst b, is detemined from the heat transferred to the water pool, Qw ;png), by:
N st;b * (O w; pool' Osub)/hfg (1) where h fg is the latent heat and Q sub is subcooling of the inlet flow.
The time scale for the heat transfer from the fuel rods to the pool during "nomal" core boildown, is much smaller than the core heatup time scale. Thus, Q pog) is evaluated in this case by:
P00I U
cover -U cover ,fg gw; pool , r pag) c DCN g where U P is the cover is the internal energy of all the covered nodes, U ,0g internal energy of all covered nodes if they were at the poci temperature, i
pog) is the relaxation time set to the maximum time step allowed, f c is the fraction of the node which is covered, and Q is the decay heat in the node.
DCN For partially uncovered nodes, if the water level is decreasing, Q,; pan) is limited to the last tem since including the other tem would artificially couple the covered and uncovered parts of the node; this algorithm improves
HEATUP/PWR I
the accuracy of the code when relatively few axial nodes are used by not delaying the onset of node heatup until the node is fully uncovered. When the pool is subcooled, Q,;pooj is applied to increase the sensible energy of the pool.
However, ininediately following a scram, the fuel is still hot *nd covered with water. In this case, the heat transferred into the pool is detennined by the overall fuel-to-coolant heat transfer resistance rather than the internal heat generation. This resistance is the sum of an effective conduction heat resistance in the fuel and a convective heat resistance in the coolant:
h=x 1 (3) 95 In Eq. (3) kfis the fuel thennal conductivity, h eis calculated using Oittus-Boelter correlation and x is an effective conduction thickness. Some side calculations of the fuel-to-coolant heat transfer rates using an effective thickness and a detailed heat conduction model through the fuel pin, showed good agreement for x = 0.3 rpellet, where rpellet is the radius of the fuel pellets. The heat transfer to the water pool is calculated as the sum of all the individual covered node heat transfer rates:
QCN = h ACN (TCN - Tpag)) (4) where A is the heat transfer area and subscript CN denotes covered nodes.
The actual heat transfer to the water pool is taken as the minimum f Ow; pool (Eq. 2) and IQCN (Eq. 4).
In the case where the core is recovered from below after an exten-sive period of being uncovered, the heat transfer rate from the hot fuel pin into the pool is limited by two-phase hydrodynamic stability considerations.
A maximum gas superficial velocity exists beyond which liquid droplets would 1
. _ _ __ ____- _ _ _ _ . . _ __ . _ _ . _ _ _ ~ . . . . _ _ _ _ _ , . , . _ . . _ . _ _ . , . _ . _ , . . _ _ _ _ _ _ _ . _ _ _ -.__ __ .
HEATUP/PWR ,
be entrained in the gas stream and be carried out of the pool. This maximum velocity is [1]
4 o g(o -o) jE
K 3 (5) 9 where o is the surface tension, 9 is the acceleration due to gravity, ogand og are the liquid and gas densities respectively, and X is the Kutateladze number. This number is taken as 3.0 when the original geometry is intact, and a user-specified number (default: 0.3) when the core has collapsed. The resulting maximum steam flow rate is Nst; max " dEA fog (6) where A is the total area inside the core barrel. The maximum heat that can f
~~be transferred to the pool is~~
~
.25 o
1 + 0.1 h* - h D Ow ; max " Nst;mxhfg (7) where h, is the enthalpy of saturated water and hp is the enthalpy of the water pool. The second term in the parenthesis of Eq. (7) is a ccrrection for the case where the pool is subcooled (h p
< hg ). When the pool is saturated h,
=h p and this tenn is zero.
If Q,;pogj is larger than Q ; max or if the total w
steam flow from the covered core exceeds Wst; max, the heat transferred from each covered node to the pool is reduced by Q,;pngj/Qw ; max so that Q,; pag) is always less than or just equal t S; max' Steam generation by flashing, Wst,f, is calculated in subroutine POOL and RATES, (called from PRISYS) as:
U w
-M g h y 3, st.f , (8) n fg . rf
HEATUP/PWR l
where U, is the energy of the water, hw; sat and hfg is the water saturation enthalpy and latent heat corresponding to the current system pressure, respec-tively and Tf is the flashing time scale.
The void fraction in the covered pool is detennined from the total steam flow out of the pool by functions VF5 PAR and VFVOL (in subroutine VLEVEL). However, in the case of core recovery from the bottom, large amounts of steam could be generated from the top of the pool due to the quenching process. This would lead to high average-void fractions and numerical oscil-lations in the boiled-up level. To avoid this unrealistic average void fractions, the steam generation from the just-recovered nodes is not accounted for in the void fraction calculation during recovery.
The steam flow rates described above contribute to the pool mass and energy balances and detennine the void fractions in the pool.
The pool mass rate of change, gA is:
bw" - (Nst;cm
~~Nst;b + Nst,f) + N ;de w~~
N w;ps + N w;up (9) where W is the sum of water flow rates from the rest of the primary ps system Ww ;de is the water flow rate from the downcomer, and W yp is the flew rate from the core upper plate due to UHI flows.
The pool energy rate of change includes all the heat content of the various streams described by Eq. (9), and the heat transferred from the fuel.
l The energy rate of change of core material in a covered node is l 0=Qdecay 3 - Q ;wpool + 0 reaction ~ Omelt (10) l where Q decay is the decay heat generated in a node, Q reaction is the heat generated in a node due to clad oxidation and Q melt is the energy rate carried with the melting fuel. Oxidation and melting can occur in the covered part
. _ _ _ . . _ __ _ . ~- ___. . _, _
l HEATUP/PWR 1
1 only during recovery from core degradation and is discussed in the next i sections.
I 2.3.2 Zircaloy 0xidation and Hydrocen Formation Zircaloy may react with steam according to the following chemical reaction:
Zr + 2 H2 O + Zr02+2H2 + aHg, (11) where oH R
is the heat of reaction per mole of Zr. This oxidation takes pl-ace at the Zr/Zr02interface leading to an increase in the oxide layer thickness.
The reaction rate equation proposed by Cathcart, [2] is used for Zircaloy temperature. T, up to 1850 K and the Baker-Just equation [3] is used for higher temperatures. The rate of change of the oxide layer thickness, i is n
thus:
8
~~0 , 294 exo(- 1.654 10 /RT) 400 < T < 1850 K (12) x 2 oZr o 3 8 10 exo(- 1.884 10 /RT)~~
~~o , 3.33 2 T > 1850K (13) 2DZr *o where R is the gas constant, and Zr is the Zircaloy density.~~
~~Zircaloy oxidation is assumed to be tenninated if either:~~
~~a. The node has less than a user-specified non-fuel fraction due to accumulation of once-molten material from higher nodes.~~
~~b. The' node is melting.~~
HEATijP/PWR This logic is intended to represent the diversion of steam away from nodes with little flow area and small hydraulic diameters, and the decrease in oxidation rates due to reductions in surface to volume ratios.
For uncovered nodes the radial temperature gradient is small and therefore T in Eqs. (12) and (13) is taken as the riade temperature. In the covered part of the core, during recovery of hot nodes, a significant radial temperature gradient may exist. Hence, the cladding temperature, rather than the node temperature, should be used. The cladding temperature is calculated iteratively by 0 reaction- OCN Tclad = TCN
CN Nf /*
A where Q CN is the heat transfer to the water, N
Zr0.
0 reaction = aHR MW Zr0 2
l MW Zr0 is the Zr02 molecular weight and WZr0 is the rate of Zr02 generation.
2 2 This rate is calculated from Eq. (13) as W
Zr0 Zr0 ^0* O ( }
2 2 where A is the oxidation area of a node computed in subroutine GN0DE.
ox Normally this area should equal the outside surface area of the cladding.
However, if a flow channel (possibly ballooned) is ruptured, the area may be
! increased by a user-specified factor.
For a covered node, oxidation may continue after the onset of melting if the user defeats the submerged blocking model with IEVNT(202) = 1.
The actual oxidation rate is limited by either the rate at which Zr may oxidize, Eq. (16), or by the availability of steam. The latter limit is l
HEATUP/PWR based on the channel steam flow and the stoichiometry of Eq. (11). The rates of hydrogen and Zr02 fonnation, steam and Zircaloy consumption, as well as the heat generated by the reaction are all calculated from the actual oxidation rate and the stoichiometry of Eq. (12).
2.3.3 Core-Upper plenum Natural Circulation Work by various investigators have shown that natural circulation flows can be set up between the upper plenum and the core. Such flows could alter the progression of a severe core accident by delaying the onset of core oxidation, supplying steam to prolong the oxidation process; heating the upper plenum and revolatilizing fission products, and perhaps causing the primary system to fail due to high temperatures prior to core slump into the lower plenum and failure of the reactor vessel lower head. These considerations lead to the conclusion that a model for the phenomenon should be integrated into subroutine HEATUP.
To make the problem tractable, the geometry of the flow pattern was set a priori based on the results of available detailed hydrodynamic calcula-tions and experiments.
Two different flow patterns are considered. In Fig. 2, the flow pattern for Westinghouse-type reactor vessel geometries is schematically illustrated. As shown, it is assumed that the flow consists of one large "loop" coupling the core to the upper plenum. The return leg from the upper plenum is assumed to flow down the outer, cooler flow channels and to occupy half the total core flow area. In Babcock and Wilcox reactors, on the other hand, a significant flow area exists through the core baffle as shown in Fig. 3. There is therefore a potential for the return flow to pass down the core barrel-baffle annulus and through the baffle into the core. Rather than determining by detailed calculations which of the two flow patterns would be established in such reactors, the approach taken was to allow the user to select either pattern and perfonn sensitivity calculations.
The flow rate is derived by assuming the flow patterns outlined above. The flow rate W) in some channel j in a nodalized core is given by
HEATUP/PWR l
l l
l l
J i W + Ws W O p l
UPPER I d i dL JL UNCOVERED NODES l -
I l a i I
d I
LOWER UNCOVERED NeJES l I
" Ws i
SUBMERGEDI NODES I
~~CORE l BAFFLE Fig. 2 Flow pattern when through-core-baffle resistance is high.~~
l l
HEATUP/PWR g W + Ws w I
I u UPPER u u i k o n UNCOVERED l NODES I
I a --
l .
^
LOWER l \CORE UNCOVERED! \ BARREL NODES N
CORE l BAFFLE I d w, SUBMERGED l NODES I
I Fig. 3 Flow pattern when the through-core-baffle resistance is moderate.
l l
l l
l k ..
HEATUP/PWR 2
-d P 20 A 43 43 o43 43 Wj lW 3 l = ,.,dZ f fl7) where dP y= denoted axial friction (ij) pressure gradient in channel j at row i, Djj = hydraulic diameter at (i.j) oq) = gas density at (i.j)
A43 = flow area at (i.j) in the x-y plane f = friction factor for axial flow At this point, the P.ssumption is made that the friction pressure gradient in all up-flowing channels and all-down flowing channels are equal in a row. As discussed in the appendix on subroutine REMIX, this is not strictly true. Small differences in hydrostatic head 'betweer. channels cause flow redistributions which lead to d<fferences in the friction. The assumption of equality will be made here nonetheless on the basis that it should provide a reasonable estimate for the total flow; the distribution of the total flow among the different channels is treated by subroutine REMIX.
Under this assumption, the total up or down-flow is obtained by suming over the appropriate channels. If the down flow is denoted W, the up-flow will be W + W where W is the total flow which arises from the s s covered nodes. Performing the sumations we obtain 2
dP down 20 43 og3 A W= dZ 93 (18) f i
down channels at elevation i l
l
HEATUP/PWR M+W 3 = Id 3 Id
, l l (19) up channels at elevation i
If we now solve for the pressure gradients and sum over rows we obtain 6P (20) down " mws [ 2D 43 o43 A 2h2 43 kdown channels aZ (W + Ws )2 AP =-
[ (21) rows 2
[ [2 D93 o4343 A p
channels where AP is the total pressure drop across the down channels and similarly down for APup; aZ is the axial height of each node. Define the flow resistance in row i for down flow as S " f aZ 2D '2 (22) 2 D A
$3 o93 j3 dawn channels and similarly for the up flow resistance. Denote the sum over rows of these l terms as SD and SU respectively, e.g.
SD = S 2D (23) rows i 1
HEATUP/PWR Substituting Eqs. (22) and (23) into Eqs. (20) and (21), and subtracting the resulting two equations yields AP =
SD + (W +3 W ) h (24)
In the limiting case of only one up-channel and one down-channel, the tems on the right hand side of Eq. (24) are easily interpreted as the pressure drops across the two channels induced by the flows.
Note that we have so far neglected the pressure drop induced by. the downward moving flow as it turns and moves across the fuel bundles. This pressure drop can be calculated by an expression of the form [4]
nf W 2 AP eross fl w " 2 2, where f x= friction f actor for cross flow (s .25 .45),
n = number of tube rows crossed by the fluid.
Ax = minimum flow area as the fluid crosses a row of tubes, o = density of the sideways-moving gas.
For the case represented by Fig. 2, the assumption of equal up- and down-flow areas delineates the radial boundary between the up and down portions of the flow loop. This is used to estimate the average number of rows crossed by the fluid. By consulting published hydrodynamic calculations of the flow, the axial extent of the horizontal portion of the loop is estimated to be approxi-mately 0.5 m; this along with the tube pitch defines the area A . Users x
wishing to investigate the sensitivities to these reasonable, but admittedly rather rough assumptions, can vary f . Thus, to account for the radial x
HEATUP/PWR pressure drop, the following expression for the cross flow resistance is added to the term SD in Eq. (24) nf x A2,*
The total pressure difference aP across the core caused by the fluid motion is balanced by the difference in hydrostatic head between the up and down chan-nels:
AP={(oi,down~bi,up) g aZ (25) rows where g is the acceleration of gravity. Equation (25) is solved by area-averaging the densities in the up and down channels at esery row.
i Equation (24) is solved in the code by substituting Eq. (25). It is instructive to derive from Eq. (24) the conditions necessary for positive natural circulation flow. RewritingEq.(24)
W2( + ) + W (SV)(W3 ) + W - aP =0 s (26)
For positive W, we require the last term be negative, i.e.
2 W
3
< aP (27)
The first tenn in Eq. (27) is just the pressure difference across the up l channels due to the steaming flow W . Thus , Eq. (27) confims that the s
requirement for natural circulation is that the pressure gradients due to i buoyancy exceed th'ose due to the forced flow.
The only other unknown which must be detemined to solve Eq. (24) is the row number in Figs. 2 or 3 where the flow from the down channels turns horizontai and enters the up channels. At present, this is established by i
HEATUP/PWR finding the row where the temperature in the downward moving fluid reaches the temperature of the upward moving fluid in the lower nodes. This algorithm is consistent with observations made in EPRI-sponsored natural circulation {
I experiments on a 1/7 scale model of a PWR at Westinghouse. For further information on these experiments as well as a comparison of the MAAP natural circulation model to the experimental results, the reader should consult Ref.
[43 After reactor vessel failure, natural circulation between the upper l plenum and the core is assumed to be replaced by the overall unidirectional natural circulation patterns which are set up in the primary system around the coolant loops. Thereafter, the inlet flows to the core consist in part of the downcomer to core flow rate computed in subroutine FLOW. Such flows persist until the core has completely melted.
2.3.4 Radial Radiation Heat Transfer Model Typical radial power profiles in LWRs exhibit a significant reduc-tion in the power generation in the outer core region fuel assemblies.
Therefore, in an accident involving core uncovery, high temperatures may be obtained at the central core assemblies while the temperatures of the outer core assemblies may be much lower. This represents a large potential driving force for radial radiation heat transfer in the core. However, the fuel pins in the outer assemblies will act as radiation shields between the hot inner assemblies and the colder core shroud and the reactor vessel. For example, hand calculations show that in order to allow for radial heat losses from the core of 1 MW with an 8 x 8 fuel assembly, the temperatures of the fuel pins in the outer subassembly would decrease from 1200K at the inner row to 600 K at the outside of the core. For the inner regions of the core, on the other hand, the power generation distribution is more uniform. Therefore as the fuel pins in the inner assemblies become hot (say more than 1200 K), the radiation heat transfer would . tend to further flatten the radial temperature profile.
This concept is incorporated in MAAP by an approximate radial radiation model which compares favorably with a more detailed calculations.
HEATUP/PWR The detailed model is discussed in Ref. [4] along with a comparison of the two models.
Consider the radial heat transfer between two nodes containing only fuel pins as shown in Fig. 4. Node i contains N (i) fuel pins in the axial R
slice while node i + 1 contains NR (i + 1) pins. Let j indicate the fuel pin index between the nodes as shown in Fig. 4. With this notation T 3,3 = T3 and Tj =m = T$ ,j.
~
The model assumes that a given row of fuel pins acts as a radiation shield. Specifically, a fuel pin sees neighboring fuel pins with a view factor of 1 and does not see beyond the aojacent row of pins. If we further assume an emissivity of one, the radial heat fluxes between the fuel pins are:
4 4 91 -2 = (T 4 -T2) 4 4 q) 3 ) = o(T3 - T3 ,7 ) (28) 4 9m-1 m = (T,,j -T) )4 Therefore, in view of the assumption that the heat fluxes between the pins are equal, the heat transfer rate is 4 4 cA(i)(T 4 -T93 )
Orad (i) " m (29) where A(i) is the outer surface area of node i. The number of reflective surfaces between the centers of the two nodes, m, is NR (i) NR (I+I) m= * -1 (30) 2 2 l
l
\
HEATUP/PWR 1

Nodei Node i+1 Nn(l) radiation resistances Nn(l+1) radiation resistances i I l 9I o o 'opoo-- =oo

- *t ,- I - I ta. O e W o * - 4: 1 e w i e o e e
d ~

I ' l 'g c3 g g g g g g g o 3 3 j 0.0 1.0 2.0 3.0 4.0 5.0 i TIME SEC x10 3 Fig. 7 HEATUP code comparison: hydrogen generation history for a reference accident simulating a large break I.0CA. x 9 E .l ,l11,1I ' 4

~~uN e e I3 %5 4~~

O l x ~ I 2 1 r o f ~ , y _ r . oA tC 1 sO 1 . iL 1 h k na oe ir tb a rl el na em gs 0 1 1 na e p C gg u E on t S ri a dt ya e C hl H H E u P C M ;i m A R I T ns A W 0 o 1 st M P 9 in - I re R ad H pi W P mc oc P E ca

~~ce d c on 0 ce r a~~

~~8 P e~~

~~Uf T e Ar~~

- El ia 8 _ g - - - - - 0 i 7 F _ *N " e'e o:, e- O "o.* Ox xwOOEO>X uO we<2 i11 l( 1';l' c. o M e N~ , O M * ; PWR-MAAP Heatup ~ 6 ,9 - - EPRIPWRCHC e O sr a >- e - I ; - u. 4 O m u) < J - e 2 y o 9 - , 9 ___e I i I 7.0 8.0 9.0 10. I 1. TIME SEC x10 3' Fig. 9 ilEATUP code comparison: hydrogen generation history for a reference accident simulating a PWR transient. 5 D E E = r - l . - 39 HEATUP/PWR The execution time of the PWR-MAAP stand-alone heatup model is at least an order of magnitude smaller than the PWRCHC. On a VAX 11/750 computer with a floating point accelerator, the execution times are about 1 t,v0 minute for the PWR-MAAP and about 100 CPU minutes for the PWRCHC.

~~4.0 REFERENCES~~
~~1. S. S. Kutateladze, "Elements of the Hydrodynamics of Gas-Liquid Systems,"~~
~~Fluid Mechanics - Soviet Res., 1, 4, 29, 1972.~~
~~2. J. V. Cathcart, et al. , "Zirconium Metal-Water Oxidation Kinetics IV.~~
~~Reaction Rate Studies," ORNL/NUREG-17, August 1977.~~
~~3. L. Baker, Jr. and L. C. Just, "Studies of Metal-Water Reactions at High Temperatures III. Experimental and Theoretical Studies of the Zirconium-Water Reaction," ANL-6548, May 1962.~~
~~4. Fauske' & Associates, "Technical Support for Issue Resolution," IDCOR Report 85-2, July, 1985.~~
~~5. H. K. Fauske, "Boiling Flow Regime Maps in LMFBR HCDA Analysis, Trans.~~
~~ANS, Vol. 22, pp. 385-386, 1975.~~
~~6. Meltdown Accident Response Characteris-R.~~
tics)O. Wonten, Code et' aland Description . , Use "MARCH 2 (P s ManuaT," NUREd7CR-3988, ,
September,1984.
~~7. P. Hofmann and D. K. Kerwin-Peck, "Chemical Interactions of Solid and Liquid Zircaloy-4 with UO,, Under Transient Nonoxidizing Conditions,"~~
~~Paper presented at the Ittternational Meeting on Light Water Reactor Severe Accident Evaluation, Cambridge, Massachusetts, August,1983.~~
8. S. Hagen and S. O. Peck, "Temperature Escalation of Zircaloy-Clad Fuel Rods and Bundles Under Severe Fuel Damage Conditions," Paper presented at the International Meeting on Light Water Reactor Severe Accident Evalua-tion, Cambridge, Massachusetts, August, 1983.
9. T. Y. Han, P. I. Nakayama, and R. G. Stuart, "Analysis of In-Vessel Core Melt Progression " User's Manual and Modeling Details for the PWR Core Heatup Code (PWRCHC)," Final Draft Report, EPRI/NSAC, December 1982.
l
P. '.
-l-ACCUM ACCUMULATOR FLOW RATE Subroutine ACCUM calculates the pressure in the accumulators and the flow rate from the accumulators to the primary system. This flow is driven by the pressure difference between the accumulator and the primary system, and by the flow area and the hydraulic resistance of the connecting pipes. Flow from the accumulators will therefore result only if the accumulator pressure P, is larger than that of the primary system Pp3, and if the connecting pipes are not blocked by the operator. '
Assuming an isothermal expansion of the gas space in the accumul'ator due to the depletion of water, the pressure in the accumulstor is:
V -mv P
a"V a my P
p (1) where V is the volume of the accumulator, m and y are the mass and specific a
volume of water, and subscript o denotes a nominal operating value as supplied by the user.
The water flow rate through a unit area based on the driving pres-sure difference W), is determined by calling WFLOW. This call requires that values be passed to WFLOW for accumulator pressure, primary system pressure, void fraction, accumulator temperature, and a loss function (CD based on the overall loss coefficient for flow between the accumulator and primary system.
This loss function is calculated in ACCUM as, t f
CD = (f L/D + K)-1/2 (2) !
where f is the friction factor (taken as 0.02), L/D is the connecting pipe length to diameter ratio, and K is the minor loss coefficient, assumed equal to 1. The total flow rate between the accumulators and the primary system is then given by, 1
l
ACCUM W=nAW) (3) where n is the number of accumulators and A is the flow area of the connecting pipe, and 1/2 2(P* - P ) f W1" y CD (4)
ACCUM also calculates the derivative of the flow rate with respect to the primary system pressure for use in detemining primary system pressure ,
when one of the special cases for detemining primary system pressure exists (seePRISYS).
The variable sequence used when calling ACCUM is:
CALL ACCUM (I, n. P , P )
(
o PS ' *o , m , y , T, , V, , A,
)
L/0, 3 W P , [PS inputs outputs where I is a Boolean indicator that is true if the accumulators are blocked by the operator (see subroutine EVENTS).
l l
l l
l 1
z1 - e APPENDIX 6 Decay Heat History for Catawba Reload Cycles of 390 days for 3.8 w/o Westinghouse Optimized Fuel Assemblies.
I i
~~=.-~~
TOTAL DECAY HEAT RESULTS TIME (SEC) MW FRACTION OF FRACTION OF ENERGY ADDED BLOCK 1 PWR RATED POWER (BTU).
.0.000E+003412.339 1.0003920 1.0003910 0.0000E+00 f 0.100E+01 202. 432 0.0593468 0.0593468 0.9671E+05 0.500E+01 174.708 0.0512191 0.0512191 0.8116E+06 0.100E+02 159.045 0.0466270 0.0466270 0.1602E+07 0.300E+02 133.942 0.0392677 0.0392677 0.4379E+07
0. 600E+02 118. 487 0.0347367 0.0347367 0.7968E+07 I 0.120E+03 103.739 0.0304130 0.0304130 0.1429E+08
.0.180E+03 95.926 0.0281224 0.0281224 0.1996E+08 0.240E+03 90.792 0.0266173 0.0266173 0.2527E+08 0.300E+03 87.004 0.0255068 0.0255068 0.3033E+08 0.360E+03 83.989 0.0246230 0.0246230 0.3519E+08 0.420E+03 81.463 0.0238826 0.0238826 0.3990E+08 0.480E+03 79.273 0.0232405 0.0232405 0.4447E+08 0.540E+03 77.330 0.0226707 0.0226707 0.4892E+08 0.600E+03 75.577 0.0221569 0.0221569 0.5327E+08 0.900E+03 68.683 0.0201357 0.0201357 0.7378E+08 0.120E+04 63.661 0.0186634 0.0186634 0.9259E+08 0.150E+04 59.725 0.0175096 0.0175096 0.1101E+09 0.180E+04 56.519 0.0165697 0.0165697 0.1267E+09 0.210E+04 53.845 0.0157858 0.0157858 0.1424E+09 0.240E+04 51,577 0.0151209 0.0151209 0.1573E+09 0.270E+04 49.'629 0.0145496 0.0145496 0.1717E+09 0.300E+04 47.936 0.0140533 0.0140533 0.1856E+09 0.330E+04 46.451 0.0136180 0.0136180 0.1990E+09 -
0.360E+04 45.138 0.0132331 0.0132331 0.2120E+09 0.390E+04 43.968 0.0128902 0.0128902 0.2247E+09 0.420E+04 42.919 0.0125826 0.0125826 0.2371E+09 0.450E+04 41.973 0.0123051 0.0123051 0.2491E+09 0.480E+04 41.113 0.0120532 0.0120532 0.2609E+09 0.510E+04 40.329 0.0118234 0.0118234 0.2725E+09 0.540E+04 39.611 0.0116127 0.0116127 0.2839E+09 0.570E+04 38.950 0.0114188 0.0114188 0.2951E+09 0.600E+04 38.338 0.0112395 0.0112395 0.3060E+09 0.630E+04 37.770 0.0110731 0.0110731 0.3169E+09 l 0.660E+04 37.242 0.0109181 0.0109181 0.3275E+09 0.690E+04 36.748 0.0107732 0.0107732 0.3380E+09 0.720E+04 36.284 0.0106374 0.0106374 0.3484E+09 0.900E+04 34.000 0.0099678 0.0099678 0.4084E+09
0.108E+05 33.795 0.0099075 0.0099075 0.4662E+09 0.126E+05 32.439 0.0095102 0.0095102 0.5227E+09 0.144E+05 31.336 0.0091868 0.0091868 0.5771E+09 0.162E+05 30.398 0.0089117 0.0089117 0.6298E+09 0.180E+05 29.588 0.0086742 0.0086742 0.6810E+09 0.19BE+05 28.884 0.0084678 0.0084678 0.7308E+09 0.216E+05 28.243 0.0082799 0.0082799 0.7796E+09 0.234E+05 27.667 0.0081111 0.0081111 0.8273E+09 0.252E+05 27.146 0.0079584 0.0079584 0.3740E+09 0.270E+05 26.670 0.0078189 0.0078189 0.9199E+09 0.288E+05 26. 33 0.0076906 0.0076906 0.9650E+09
TOTAL DECAY HEAT RESULTS TIME (SEC) .MW FRACTION OF FRACTION OF ENERGY ADDED BLOCK 1 PWR RATED POWER (BTU) 0.306E+05 25.828 0.0075719 0.0075718 0.1009E+10 0.324E+05 25.451 0.0074613 0.0074613 0.1053E+10 h 0.342E+05 25.098 0.0073579 0.0073579 0.1096E+10 0.360E+05 24.767 0.0072609 0.0072609 0.1139E+10 0.432E+05 23.608 0.0069210 0.0069210 0.1304E+10 j 0.504E+05 22.649 0.0066399
' 0.0066399 0.1462E+10 O.548E+05 22.143 0.0064916 0.0064916 0.1555E+10 0.576E+05 21.847 0.0064048 0.0064048 0.1614E+10 0.720E+05 20.525 0.0060174 0.0060174 0.1903E+10 0.792E+05 19.981 0.0058577 0.0058577 0.2041E+10 0.864E+05 19.482 0.0057115 0.0057115 0.2176E+10 0.936E+05 19.031 0.0055793 0.0055793 0.2307E+10 0.101E+06 18.620 0.0054588 0.0054588 0.2435E+10 0.108E+06 19.233 0.0053452 0.0053452 0.2561E+10
{ 0.173E+06 15.717 0.0046079 0.0046079 0.3604E+10 0.259E+06 13.641 0.0039992 0.0039992 0.4806E+10 0.346E+06 12.228 0.0035847 0.0035847 0.5865E+10 l 0.432E+06 11.173 0.0032755 0.0032755 0.6823E+10 l 0.518E+06 10.348 0.0030336 0.0030336 0.7704E+10 0.605E+06 9.677 0.0028369 0.0028369 0.8524E+10 0.691E+06 9.122 0.0026742 0.0026742 0.9294E+10
, 0.778E+06 8'.653 0.0025367 0.0025367 0.1002E+11
( 0.864E+06 8.255 0.0024200 0.0024200 0.1071E+11 0.950E+06 7.911 0.0023191 0.0023191 0.1138E+11 0.104E+07 7.608 0.0022303 0.0022303 0.1201E+11 l 0.112E+07 7.338 0.0021512 0.0021512 0.1262E+11 l 0.121E+07 7.096 0.0020803 0.0020803 0.1321E+11 l 0.139E+07 6.877 0.0020162 0.0020162 0.1379E+11 0.138E+07 6.678 0.0019578 0.0019578 0.1434E+11 0.147E+07 6.495 0.0019041 0.0019041 0.1488E+11 0.156E+07 6.327 0.0018548 0.0018548 0.1541E+11 0.164E+07 6.171 0.0018091 0.0018091 0.1592E+11 0.173E+07 6.025 0.0017664 0.0017664 0.1642E+11 0.181E+07 5.889 0.0017264 0.0017264 0.1690E+11 0.190E+07 5.760 0.0016888 0.0016888 0.1738E+11 0.199E+07 5.639 0.0016532 0.0016532 0.1785E+11 0.207E+07 5.524 0.0016136 0.0016196 0.1831E+11 0.216E+07 5.416 0.0015877 0.0015877 "
0.1875E+11 0.225E+07 5.312 0.0015573 0.0015573 0.1919E+11 0.233E+07 5.213 0.0015284 0.0015284 0.1962E+11 0.242E+07 5.119 0.0015008 0.0015008 0.2005E+11 0.302E+07 4.563 0.0013376 0.0013376 0.2282E+11 0.363E+07 4.138 0.0012130 0.0012130 0.2532E+11 0.422E+07 3.808 0.0011165 0.0011165 0.2756E+11 0.504E+07 3.455 0.0010:29 0.0010129 0.544E+07 0.3037E+11 3.309 0.0009702 0.0009702 0.605E+07 0.3166E+11 3.117 0.0009139 0.0009139 0.3350E+11 0.665E+07 2.953 0.0008656 0.0008656 0.3524E+11 0.726E+07 2.807 0.0008228 0.0008228 0.3689E+11
. \
_ _ _ . J

ML20151Q166

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