ML20038C019
| ML20038C019 | |
| Person / Time | |
|---|---|
| Site: | Sequoyah  |
| Issue date: | 10/31/1981 |
| From: | Fuls G OFFSHORE POWER SYSTEMS (SUBS. OF WESTINGHOUSE ELECTRI |
| To: | |
| Shared Package | |
| ML19268A511 | List: |
| References | |
| OPS-36A31, NUDOCS 8112090425 | |
| Download: ML20038C019 (147) | |
Text
.
@ftshore PowerSystemb ArracHmEwr $.
THE CLASIX COMPUTER PROGRAM for the
- i ANALYSIS OF REACTOR PLANT CONTAINMENT RESPONSE to HYDROGEN RELEASE AND DEFLAGRATION OPS REPORT NO. 36A31 l 1
OCTOBER,1981 l
hDR DO OO 27 P PDR
PST-NE-359 .
A .[
b h.-
Offshore Power Systems do'JO Arlington Expressway 904-724-7700 Box 8000, Jacksonville, Florida 32211 Tele x: 568406 F October 27, 1981 t
Dr. L. W. Lau Tennessee Valley Authority 400 Commerce Avenue J Knoxville, Tenn. 37902 [
Dr. J. Castresana American Electric Power Service Corp. F 2 Broadway *f New York, New York 10004 d.,
Mr. A. Sudduth p Duke Power Company P. O. Box 33189 ..
422 S. Church [
Charlotte, North Carolina 28242 {
Subject:
OPS CLASIX Topical Report, No. OPS-07A35 i' (Proprietary), No. OPS-36A31 (Non-Proprietary)
V
-)
Gentlemen: :
Enclosed are proprietary and non-proprietary versions of the CLASIX Topical Report as well as other documents relevant to your use of this Topical Report and sub- i mission of it to the Nuclear Regulatory Cormiission. ,
The complete list of enclosures is tabulated at the end of this letter. The draft letter of application for withholding of proprietary infomation h'as been &
prepared and the number of copies of the Topical Report !
has been transmitted assuming that TVA will submit l the report to the Nuclear Regulatory Commission and that Duke and AEP will reference that submittal and ?
likewise request withholding on their dockets.
As per our proposal, additional modifications to CLASIX are underway. These modifications include changes to model sumps and recirculation flow, in-corporation of a variable burn fraction for propogating burns, addition of a spray heat transfer correlation, and changes to reduce the run time. These modifications will add additional realism to the program and improve l
t -Ov Page Two 7 Mr. A. L. Sudduth
( Dr. L. W. Lau Dr. J. Castresana October 27, 1981 its efficiency but are not expected to have any major impact on current results or conclusions. These mod 1-fications are discussed in Tasks 1.2.1.1, 1.2.2, 1.2.3.1, 1.2.3.2 and 1.3.1.1 of our proposal. When these modi-fications are complete, an addendum or revision to the Topical Report will be necessary. The addendum or revision will include a description of the new features as well as additional verification relative to these modifications.
Sincerely, Q C.P9 Kenneth C. Perry, Manager Safety & Systems Analysis
(~
1 /aw
Enclosures:
(1) Draft letter application for withholding of proprietary information.
(2) Letter from Westinghouse to the NRC authorizing the use of the proprietary information.
(3) Affidavit.
(4) Copies of raport OPS-07A35 (Proprietary):
TVA (for transmittal to NRC) - 5 copies TVA - 3 copies Duke- 3 copies AEP - 3 copies (5) Copies of report OPS-36A32 (Non-Proprietary):
TVA (for transmittal to NRC) - I copy TVA - I copy Dyke- I copy AEP - I copy 1
(6) Index of Responses to NRC Question 6. l
M CIASIX CDMEUTER PIOGRAM EDR E O NRLYSIS CF REAC'IOR PIANT CEtCSIl@Eff RESPONSE
. HYDROGEN RELEASE AND DEFIAGRATIQi bY Dr. G. Martin Fuls Advisory Engineer Contributors: R.M. Mariner S.L. Jones J.G. Francis P.A. Bardol Approved
- P.B. Hagy Director Power Systens Technology Offshore Power Systems 8000 Arlington Expressway Jacksonville, FL 32211 Document No. OPS-36A31 O
t -
ABSTRACT
'Ihe CIAsIX ocmputer program is based cn a multi-ocznpartment nodel of an im condenser contaiment. 'Ihe purpose of the gy,=n is to predict the tanperature
. and Iressure response of the contalment to a degraded core transient during which hydrogen is released to the omtainment and then burned. 'Ihe program has been used extensively in licensim activities by the utilities.
Extensive verification of the Irogram deronstrates that the program provides realistic, but conservative, predictions.of the temperatures and Iressures resulting frcm a hydrogen deflagraticn.
O -
l l
TMME: T G2m!NIS O Page
/
I. BACMGICUfD abo INIHXXJCIICN 1 I
II. AIRLYrICAL 10 DEL 3 III. PA7CR ASSLDJPTIONS 5 IV. Pf0 GRAM IESCRIPTION 6 V. AtRLYTICAL IEVELDPM 12 A. InterCXJmpartmental Flow Rates 17
- 1. Door Analyses 12
- 2. Flow Equations 14
- 3. Fan Flow 17 B. Passive Heat Sink Heat Transfer Rates 18
- 1. Film Coefficient of Heat Trarsfer
- 18
- 2. Radiant Heat Transfer 20
- 3. Internal Heat Transfer 21 C. Heat Transfer to the Ice 24 D. Hydrogen Igniticn and Cabustion 33 E. Cbntainnent Spray 33 F. Additicn Tables 37 G. Energy Balance 38 VI. INPtJr DESCRIPTIQI 46 VII. CUTPtJr 49 VIII. VERIFICATIOT 50 IX. CINCwSIONS 55 X. Rom m 56 XI. TABIES 58 XII. FIGURES 60 0
t TABLE OF CONTENTS Page XIII. Appendices A. Comparison of CLASIX Results with T'MD ResNits 63 B. Comparison of CLASIX Results with COC0 CLASS 9 Results 82 C. Comparison of CLASIX Results with Test-Measured Results 98' D. Evaluation of Separate Spray Time Domain and Heat 129 Transfer Assumptions E. _ Evaluation of Additions of Heat Sink, Upper Plenum, and Air Fan Head Models to CLASIX F. Evaluation of Radiation Heat Transfer Model E71313 06 O
O
I. BMNBOUND AND INIPODUCTICN v
During the incident at 'Ihree Mile Islard ('IMI) in March 1979, hydrogen, generated by the zirconium-water reaction in the degraded core, was released to the contaiment atmosphere. A spike in the contairrnent pressure m2ne hours into the transient is evidence that the hydrogen concentraticn in at least part of the containment reached ccrrbustible limits and was ignited. As an applicant for a Manufacturing License for Floating Nuclear Plants (ENP), Offshore Power Systems (OPS) was interested in the implications of the 'IMI incident cn the integrity of the ENP containment. Consequently OPS began the develognent of an analytical capability to investigate the response of the ENP contairrnent to a 'IMI type incident. The result of this developnent is the CIASIX* computer program.
A significant feature of the subject transient is the introduction of an additional gas which then results in a chenical reacticn. Thus, to ade-
~
quately analyze the transient, an inventory of the masses of the ir.dividual O constituents of the containnent atnesphere must be maintained. No existing O program for reactor plant safety analycis had such a capability. It was concluded that it would be more difficult, require more resources and, nest imp 3rtant, take nore calendar time to modify an existing program than to develop a new program specifically designed for the 'IMI type transient.
l The CLASIX cx2nputer program, in various stages of developnent, has been used to support the licensing activities of four ice condenser contaiment reactor plant designs. Analytical results produced by CASIX were instru-mental in the Tennessee Valley Authority receiving an operatire license for the Sequoyah Plant in 1980. Similar analytical results generated for the McGuire Plant of Duke Power Canpany were utilized in obtainirg a full power license in 1981. American Electric Power Service Ctmpany has used CIAS1X
- Since this type of transient would be in the category of a Class 9 accident, the Ranan nuneral IX was substituted for the Arabic 9 and shortened to CASIX for the name of the program.
O results in resolving 'IMI issues for the (bok Plants. CPS has also used CIASIX results in licensing activities relative to the Manufacturing License for the ENP.
'Ib minimize develognent time, the analytical nodel was tailored to specif-ically represent the ice condenser contairunent. Ibwever, the nodel has sufficient versatility to be applicable to a variety of contairnent configurations. 'Ibe analytical methods, of course, are general and applicable to this type transient regardless of the contairraent.
I O- .
II. ANALYrICAL MJDEL l
V The analytical model of CIASIX can represent the contairunent with up to seven cunpartments or control voltanes interconnected with a fixed set of
. flow paths. An eighth volune is included to represent a discharge volune, such as the atmosphere of another vessel, to Wiich the contairrient may be vented. A schematic of the analytical model is shown in Figure 1. Voltrae 1 in the figure generally represents the entire lower conpartment of the ice condenser containnent. However, the lower conpartment can be subdivided to include Volumes 5, 6 and 7 as shown in the figure. Voltre 5 represents the equipnent and instrument volumes off the main volune of the lower conpart-ment. Volumes 6 and 7 represent segregated voltraes associated with the pressurizer and stean generatcr enclosure volumes, respectively. The lower conpartment is vented to the ice condenser inlet plenem via the lower inlet doors which functicn the same as check valves to pennit cnly unidirectional flow. Volume 2 generally represents the ice candenser inlet plenom or the volume betwest the lower inlet doors ard the botton of the ice filled Os portion of the ice baskets. As the ice melts during the transient,
\V}
- the inlet plenun increases
- a,c in volume. Volume 3 represents the vclume between the top of the ice in the,
_ ice baskets and the top deck (bors or basically the outlet plenum. a,c 51ithin the ice filled portions of the ice baskets there is sone net free gas volume. As part of the input to the program, this volume must be specified.
a,C The typer conpartment of the containment is represented by Volume 4 and consists of the balan of the ccntairrnent net free volune. Volune 8 is the vent volume or discharge volume of the containment. 'Ihis volume is unique only because of the connectiry flow path which will be discussed below.
T J
i In a$dition to the rather conventional flow paths shown in the figure, )
i there are special flow paths that can be specified as connecting any two voltanes and for Wich the head / flow correlation may be specified. 'Ihese flow paths are utilized to represent fan flow.
I i
i a
i 4
i 4
i i _4_
1 1
I III. E7CR ASSLMETICNS G'
Discussed here are the major assumptions utilir.ied in the Irogram. Other asstrnptions are stated explicitly in the analytical develognent and sone
'are implicit in the way that the equations are written.
'Ihe only non-condensible gases asstrned to be of sufficient concentration to be considered in the Irogram are oxygen, nitrogen and hydrogen. 'Ihese gases are asstraed to be perfect gases with constant specific heats.
The water vapor Iroperties are taken frcm the A9E steam tables within the limits of the tables and may be either saturated or superheated. Above the 1500 F tpper limit of the steam tables, the steam is assumed to be a perfect gas.
In each cmpartment, or control volume, all gases are assumed to be Instan-taneously perfectly mixed.
1:xcept for the condition where hydrogen is burned as generated, the catusticn of the hydrogen is asstrned to occur at a uniform, constant rate over the period of cmbustion.
Superheated liquid entering the compartment either as breakflow or spray water is assumed to instantaner>usly vapori-a sufficie:t water to achieve thermodynanic equilibrium corres;cnding to the total Iressure of the cmpartment. The vapor and its associated energy are adds 3 to the inven-tory of the cmpartment atnesphere. Ebr the breakflow, the liquid Iortion is asstaned to fall inmediately to the f1cor to be collected by the stmps and drains. Ebr the sprays, the liquid portion nust fall through the atmosphere over sc.rne pericd of time as discussed later.
m
lv. PROGRAM DESCRIPTICN
/'
N.)T Fbliowing is a general discussion of the program, dat the Irogram is designed to cb and how it performs its functicn. Developnt of equations to arry out the rmerics is left to a later section.
As shown in Figure 1 and discussed above, the ice condenser contairraent is represented by a ruber of voltrnes interconnected with a fixed set of flow paths. Any of the voltznes may be eliminated by settirg the voltzne to zero and any of the flow paths may be eliminated by setting the flow area to zero. In each of the active voltrnes, an inventory is maintained of the masses of the constituent gases and of the total internal energy of the gases. Based cn the asstznpticn of perfect mixirg, the atmosphere of the ccrapartment will have one temperature. Frczn the assumption of perfect gases and/or the steam tables, the partial pressure of the individual gases and, consequently, the total 1ressure in the <xrtpartment mn be determined.
b)
C Each of the active ficw paths shown in Figure 1 can le represented by a flow area and a dimensionless loss coefficient. In flow paths 1, 2 and 3, the flcw areas can be centrolled by representaticn of a door which can reduce the reverse flow to zero or sane small value. In all flow paths, ,
the critical pressure ratio for transiticn to critical or choked ficw is asstraed to be a constant. 'Ihis Iressure ratio is nonitored to assure use of the appropriate flow correlaticn. Special ficw paths may also be designated for interconnection of active voltznes. Ebr these special flow paths, the head /ficw correlaticn is externally specified in tabular fonn l
and the flow paths may be restricted to operate cnly over a portion of the transient. The primary intent of these special flow paths is to represent fan forced flow. .
As indicated previously, flow path rnzuber 8 ir. a special case. 'Ihis fl.w path has a simulaticn of a rupture disc. No flow can occur until the upier ocmpartment pressure exca_ds a given value. Once the rupture di,c presstr e set point is exceeded, flow calculations fcr this ficw path an. initiated.
O.
A lea 3th, cr slug, of water aM a sutmergence depth may be specified to represent discharge mder water with the connecting pipe partially filled v
with water. This slug of water, if it exists, must be accelerated and discharged before gas flcu can be initiated. Cbnsistent with the mder-water capability, ro reverse gas flow through this flow path is permitted.
Hysirogen, nitrogen, water and heat may be added to selected ocmpartments at externally specified rates. Only the heat rates may have negative values which may be used to simulate fan coolers and r? der heat sinks. Hydrogen ard nitrogen additions must be acccrapanied by corresporxilrg tenperatures as a measure of the heat energy in the gas. Water additions nust be acccn-panied by an enthalpy. 'Ihe enthalpy of the water is ccnpared to the saturated liquid aM vapor enthalpies corresponding to the total pressure in the ccmpartment. Accordirg to a prior assunpticn, the liquid and vapr portions and their associated energy are added to the drains and atro-sphere, respectively.
Sprays may also be added to selected cunpartments by specifying the flow rate, heat transfer coefficient and tenperature as a functicn of time. The spray drop size exiting the spray rozzles and the rate of fall of the spray are assuned to be constant for a given spray. Deperxiirg upcn the instanta-neous transient conditions, scrne of the spray entering a cmment may instantaneously vaporize. The ligaid porticn falls through the atrosphere.
As the spray droplets fall, there is heat transfer between the atros,there ard the water. Deperviirg uptn the specific conditions, condensaticn, vaporization or simple temperature changes may occur during the period of tire the spray drop is fallirg.
Passive heat sinks are available in all cunpartments. 'Ihese are nodeled as one dimensional heat transfer heat sinks which may be multilayered with film coefficients of heat transfer between layers. Several film coefficient correlations fcr the internally exposed surface are available in the program or the coefficient nay be externally specified in tatular form as a functicn of either time er the tenperature difference between the heat sink surface and the cxrpartment atnesphere, n
v
- - - - _ - . ~ . - - , _. .. .. - . - . .
D e ice condenser is represented a,c (o
v
/
. 1 The ignition and rate of cx2nbustion of hydrogen are controll'ed by exter-rally specified criteria. The criteria which must be specifisi are listed in Table 1. Se first criterion is the voltrae fraction of hydrogen at #tich igniticn is asstrned to be permissible. Tests indica +e that when ignition occurs at concentrations less than about 10 voltrae percent of hydrogen, rot all of the hydrogen pres 3nt will be constned. The second parameter as listed in the table is the percent of hydrogen Iresent which is to be constrned. Experimental results also demnstrate that belcw scrne minimtrn oxygen concentration, hydrogen will rot ignite regardless of its concentra-tien. Thus, eve though the first critericn is satisfied, tha third must also te satisfied before ignition will actually take place. Se next V parameter is the oxygen concentraticn at which an existirg flame will be extinguished. Available data indicate that ocmbustion will proceed tntil all of the oxygen is exhausted. The progran monitors the oxygen content of the crrnpartment and should the oxygen be depleted belcw the stated value fcr the fourth parameter, ccr:busticn is stopped.
The deflagration of hydrogen in the Ihysical world Iroceeds as a flame front which has a velocity of a few feet per second. Based cn the di-mensions of the ccrpartrnent, the flame speed and the assumed location of the igniticn, the burn time of a ccrnpartment can be calculated. This is the fifth parameter required for crrnbustion calculations. As the flame front proceeds, it will pass through openirgs to adjoinirg ccmpartmenu. If the hydrogen concentration is sufficiently high and the regaired amount of oxygen is present, the flame will propagate into this adjoinirg compart-ment. We hydrogen concentration reqaired for Iropagation is the sixth parameter in the table arr3 the time required for the flame to propagate
frm the igniticn source to the adjoinirg ocznpartment is the propagation delay time.
During the course of the analysis, the Irogram will, qcn appropriate acenand, write an exhaustive file of al] pertinent parameters so that the transient can be restarted frm this point with nodified input. This restart feature permits the examinaticn of the results frcrn a given set of input, modification of the input and continuation the transient.
A simplified ficw diagram of the CIASIX cmputer program is shwn in Figure 2 'Ihe input to the Irogram may be a canplete set of input to initiate a new transient cr it may be a restart
- file with scrne nudified input. In either event, a cxznplete input edit is generated. Upon ctrapletion of the input edit, a finite difference integraticn loop is entered which continues until cne of the Ircgram stops is encountered. If a new transient is being initiated, an outp edit of initial conditions is generated. Othe: vise ,
the frequency at diich output is generated is controlled by the cx$nditions specified in the input.
a,c The first calculation is tne voltrwtric ntes of flow between the crra-partnents. This calculaticn includes evaluaticn of the door positicn and area of flow for those 7ths having cbors and the use of head /fics tables fcr the special flow paths. Usire the voltnetric ficw rates ard the ocmditions in the source voltrne, the rates of change of mass for each constituent ard the rate of chany: of energy in both the source and sink voltanes can be evaluated for each flow.
Heat is transferred to the surface of the passive heat sink by convective heat transfer and by radiation. As discussed triefly above, the film v
r
coefficient of heat transfer may be derived frczn cne of the built-in correlations cr fran tabular input. We radiant heat transfer rate is a ftmetion of the amtissivity of the containnent atmosphere.
Se spray ficw rate, tanperature and film ocefficient of heat transfer are linearly interpolated fran the input tables. Heat and mass transfer rates ane calculated fcr.the spray over the pericd of its fall cr until the drops evaporate.
The heat addition rate frcm the input tables are added to or subtract.ed fran the atmosphere. The hydroget ard nitrogen mass acMiticn rates must be positive and are added, with their associated enthalpies, to the atmo-
.=phere. The break flow, which alsa must be positive, is expanded against the total pressure of the atmosphere with the vapor and its associated energy being added to the atnesphere with the balance being added to the stanps and drains.
If ice exists in the ice condenser, the rate of heat transfer to the ice l will be a functicn of the ficw rate ard the constituents of the flow. As
' the steam cordenses during its passage through the ice bed, the film coefficient is adjusted ard the overall heat transfer rate to the ice evaluated.
The conditions in each ctrprtment are omnpared with the specified criteria to detemine it igniticn should occur. Each ficw path is also examined to determine if a flame frcnt has arrived fran an adjoining cxrnpartment and, if sa, if igniticn due to propagaticn should oa:ur. If igniticn occurs for either reason, the rates of remaval of oxygen and hydrogen and the rates of additicn of water vapcr ard energy are deternuned. The mass of hydrcgen to be burned is determined and the clocks for each connected flow path are initialized fcr propagaticn delay times. The propagaticn delay times are measured fran the time of igniticn. All active flow paths shcun in Figure 1 are asstraed to propagate flame whether cr not a door is present ard closed.
No propagaticn is asstrned in the fan flow paths.
O
8,C Once the time step, tenperature ard pressure have been evaluated, all other parameters can be tpdated. These parameters include such things as total pressure in each ces, the clocks for propagaticn delay tines, nass of ice in the ice condenser and all internal temperatures.
V. ANALYrICAL IEVEIDPMENT O
his secticn develops the equations utilized in the CIASIX ct:mputer program. Se develognent will generally follow the crder in duch the equations are used in the ru.:p .n as shown schematically in Figure 2.
A. Interconpartmental Flow Rates The flow paths connecting the campartments in the analytical nodel are of two classes. The first class includes those for which the ficw rate is calculated internally insed cn the differential pressure. mis class of ficw paths is further subdivided by those with doors and those without cbors. Only flow paths 1, 2 and 3 have the capability of having doors. The second class includes ficw paths for which the correspon-dence between differential pressure and flow rate is externally specified by tabular input. This class of flow paths may be restricted to operate cnly over a prtion of the transient.
O 1. Door Analyses There are three types of doors in the ice condenser contairrnent.
The icwer inlet doors in ficw path 1 of Figure 1 basically operate as check valves allows.ng flow in cnly cne direction.2e interme-diate deck doors in ficw path 2 open upward and once fully open may fail to shut. Se top deck doors in flow path 3 are basically a j flexible blankets that are asstrne$ not to close once opened even part m y.
~
a,c O
a,c (A-1)
\
(A-2)
Ebr the lower inlet doors and the intermediate deck cbors, an angle .
aM an are may be specified such that on this angle is exceeded, the flow area of the cbor will never decrease below the area e
specified. This feature nay be used to simulate failure of scrne of the intemediate deck doors to shut.
Because of the design of the top deck doors, additional features are regaired. One is a by-pass flow area to represent the cur-tainsi flow area associated with these doors. The secord is that a minimtra differential pressure is required to initiate opening because these doors are taped cbwn. Finally, because of the construction of these cbors, the flow area is asstrned never to l
! decrease regardless of the direction of flow ard/or differential pressure.
l l
I a,c l
~
I 8,C
~
1-8,C l (A-3)
The minimtri area, A', would be A for the tcp dwk doors but. :nay 1r zero or sxte other value for the other doors depending upon the history of the door ard the conditions specified for non-closure discussed above.
- 2. Flow Equations Each of the flos paths rian in Figure 1 is represented by an area ard a flos loss coefficient. In the subsonic floa region, the flee relation is represented by H =
KV /29 (A-4) where H = differential head k = loss coefficient
, V = velocity 4
gravitational constant
~
g =
In tems of a differential pressure, i
P = kV2 /2gp (A-5)
O
- _ . . . - - - . . - , _ , - . . _ _ . _ , , _ _ - _ _ _ _ . . , . . . . _ _ - _ , . _ _ , , . . . . . _ . . . . . . . , _ , _ _ , - _ , _ . . ~ . . . . , _ . _ , _ . . _ , _ , _ - - - _ - - _ , _ . ~ , _ _ . , - . . . . _ , , . , . - - . . ,
and FR = VA (A-6) where 9 = density FR = voltanetric flow rate Ccrnbinirg these three equatiom and usirg an average density FR 1
= A g(f[2(P3 1
- Pk }!I j+ k} (A~ }
L where ( )1 = - ficw path i
.= source voltrne
( )3
( )k = si.* volume The transition to sonic flow is assumed to occur at a pressure ratio of 0.5 for all flow paths regardless of the relative concen-tratiom of the constituent gases. In the sonic ficw region, the flow is a function only of the tpstream Iressure so that t'o a first approximation
\
FRg =
ks; Ej IA~O) 1 .*
,' where k sg
= sonic ficw constant Asstrning that the flow is continuous at the point of transition 1 (D [2(P.3 - Pk )/I#'3 + #k k P. = A. @ = 0.5P.
1 kg k 3 si 3 A
cr k s. = { [2(P 3 - Pk)/(93 + pk))} (A~9) 1 3 1 i
1 i
, , - - . ..my - , - .y.-...,-w__._-__-,-... .x,- ..--,v.._, . ~ . ~ , , . ~ . . .
Based an the volunetric flow rate and the assunption of perfect O mixing in end canpartment, the mass ard unergy flow rates can be determined. '1hus m = -m = -FR. (m (A-10) n3 n
k 1 "j/ V))
4 ere $t = mass flow rate m = mass th
-V. = volwne of j ccrapartment 3
n O constituent in the j O voltne
( )n.=3
( = n th constituent in the k th voline
)S The associated rate of energy transfer is b=b"-
3 k .
hn.
(A-ll) n 3 3 4ere b = energy transfer rate h = enthalpy l
As discussed above, flow path 8 in Figure 1 is unique. Although this floa path uses the same basic equations for gas flow developed abwe, same modifications are required. In this flow path, a rupture disc prevents flow until the differential pressure exceeds the rupture Iressure. In addition, this ficra path may have a slug ,
of water in the pipe at the exit and discharge under water. ,
a,c M M 4,C l
( (A-12)
! UO t
\
- t . ,
a.C (A-13) t l~
,s (A-14) ,
(A-15)
~
Once the slug has teen expelled, equations ( A-7) to (A-ll) inclo-si.e beccre valid with the substitution .
a,c (A-16)
This set of equations adegaately describes the interecrpts ental flow.
- 3. Fan Flow The fan or pmped ficw is based cn tabular input of voltraetric ficv as a functicn of the differential pressure between the cortwted cxrrpartments. During the period of operation of the fan the voltnetric flow is determined by linear interpolation of the tables. Using the fan flow rate, agaations (A-lO) and (A-ll) can be 4 f
used to determine tne mass ard energy rates.
5 &
\
t ,.
B. Passive Heat Sink Heat Transfer Rates
(
Passive heat sinks are represented by a slab cr cme dimensional, rectilinear heat transfer. Se heat sink may have multiple layers of different mterials with resistances to heat transfer between layers in 2
- the form of film coefficients of heat transfer. We surface exposed to the otznpartment nny have heat transfer by toth convection and radia-tien. We oprosite surface may be adiabatic cr transfer heat by a film coefficient'\to a constant temperature heat sink.
- 1. Film Coefficient of Heat Transfer
t g ;
where H T
= Tagami heat transfer coefficient t = time in seconds I
t = time of peak gressure frcm bicub.m in seconds P
s L 4
\
/
x
t j
g = noterial dependent coefficient having the .
dimensions Stu/hr-ft2-F I i
fi
- Hg = stagnant film coefficient f
' ' B,C
- i i .
1 a 5 s ?
E i '
s .
a,c
, ,'v (B-2) l 4
i 4
I In these equations, all constants, and conseq;ently the fil:n coefficient, have the dLmensions Btu /hr-ft2-F (B-3) 2 Thrt material dependent coefficient is given by 8,C (B-4) 4
. '/-
l l<
)
~
k h i
a e 4 }. p t r !
- 19 -
~q J e, -cn-,n,-e,._ee., ,.+ - ,,,,----,e,.,v-.e ,--,-,.,~,rs.nw-a,n . _ , ,n,,w,--..,,,-wna,--,,,,-,,.wwe,,,,m,,,re.new,n.n-s.w.v,,-enn-
S e material coefficients of interest are a,C t
(B-5) a,c 6.C (B-6)
(B-7)
- 2. Radiant heat Transfer a,c We emissivity of the water vapor is
~
a functicn of its partial pressure, the effective beam length of the radiation and the ambient tamperature. We water vapor anis-j sivity correlations are derived frat References 3, 4 and 5 ard are l
linearly interpolated in the program. Se snissivity of the wall
' surface must be specified as part of the irpat. The rate of i l
radiant heat transfer is ~
l
' l s o-8 ) .
T
) .
i
- ,, ._~.,.,----,,..-.-___.-,,_,n,,.--..,--,_
,,,n-_ - _ _ . _ .,-,n,__,~,._-_-. , - . , , - . - _ , - , - . - - . - - - - . - . -
8,C 5
C f
I t
~
- 3. Internal Heat Transfer The analytical nodel of the passive heat sinks represents 'all heat sinks as one dimensional, rectilinear heat transfer in multiple layers. Between layers, a film coefficient may be specified to represent surface effects, paint and/or gaps between ti.e surfaces.
The surface agosite the surface exposed to the compartment ambient may be adiabatic cr may have a constant triperature heat sink.
For conventional conductive heat transfer within a layer, there must be at least three temperature nodes ki the 1syer. The distance betwee.. temperature nodes, assuming a node at each surface, is Ax = 'IE/(IN-1) (B-9) where 6x = distance between teperature nodes IN = nunber of traperature nodes in the layer
'IE = thickness of the layer.
For an interral tanperature node, the rate of heat transfer into the node is Qin " CDIWJ-1 ~
J
- (- }
21 -
. _.. _.. _ .- ~. _ . ,. - _ _ . _ , _ _ . _ . _ . _ _ _ . _ . . . _ _.___ ..- _ - , _ _ _ _ - . ~
where Qin = heat transfer rate per mit area CD = ocmductivity of material W = wall nodo tanperature J = node of interest
- J-l = next nearest node toward the asnpartment te heat transfer rate out of the node is Ocut " 00(WJ - W J+1)/dx (B-ll) .
where J+1 = next nearest node away fran the canpartment Oog = heat transfer rate per unit area The heat stored in the internal node is Os = (9c)Ax(W - Wy)/Dt (B-12) where
( )N = rev 's perature Os = heat stored Pc = heat capacity of material Dt = differential time step Fran cx>nservation of mergy O in (B-13)
"Ocut + Os Canbinirg equations (B-9) to (B-13) inclusive WJ "
( e) IE (WJ_1 + JW +1 -M)+W J J (ll-14 }
'Ihis is the equation used by the Fogram to evalecte internal temperatures once a stable tine step has been determined. 'Ihe surface node of thir, type of wall representation'is associated with O
IU
anly cme half the thickness of an internal rode. 'Ihus,11 O c is the convecthe heat transfer into a surface, and 0, = (Pc)(Ax/2)( - Wg)/Dt (B-15) then using equaticn (B-13)
Oc = (Oc)( A V2)( - Wy)/M + m(Wg - W y,y)/ Ax (B-16) or h = [Oc~ CIN J~ "J+1N#-1)/E3 '
~
~
2( -1) J Wall layers with less than three tenperature nodes are special _
cases. a ,'c I
O t .
- (B-19) *a c (B-19)
L -
ac (B-20)
= .
a,c T
la,c (B-21)
J (B-22) 1 f
I (B-23) h v .
~
&,C 1
i f
, J
! C. Heat Transfer to the Ice The rtte of Mat transfer to the ice in the ice condenser is based en the film coefficient of heat transfer correlaticri developed fran the ice condenser tests at the Waltz Mill test facility (Reference 6). These correlations include the effects of the relative concen-trations of air and steam. a,c k
I
, . , _ _ , em A .a m 4 ..-ae->, Lam.. .- 4--m ,_=a#a e mA__ _.,- , .Mc4 e a_ha 2a 5&.-.L.A-, .- _,,,m.l+ ~,a sd sh*m hme--., + +-e2ew.a. - W .,w-_Len-d w 1
. 8C i
4 e
8,C (C-1) f i.
Y f 8 j (c-2) l (c-3) i ,
1 ,
! (C-4) l 1
, i 1
i 4
i J .
I l i
I i '
l i i i
(C-4 ) ,
I e
+
l t I
! (C-7) l 4
$ f
, i 1 I 4
6 4
t - >
= {
i ,
f 25 - -
i i
t
- -- g wwe m .w mww - . . ..--- - . w_ - - - -- -- -_ - - = - <-
2h___ J. --4,M*4 6.- e-A.e4 4 e+* -- --4--- m .-* eaMa-- -;.*h---ar .*e--d -ha2E--h--aE.J- E-nA=aC8 0,*- m-d- - - a -*=*- 'WJ---m
.- 3 3 J-----MLa 4
5 O >
- , 8sC
]
l
- ; 8,C
, (C-8) ;
- i. >
1 N
1
- 6 f
f r
! i
! i i
h
=
. ?
l a,C .
t !
l
- 1 l [ 8,C !
fC-9) -,
I i l i ;
t 1
i l
l i
1 ,
a i
i -
(C-10) I i-f
.i f !
l
[
i I
i e i
1 I
l (C-ll) [
l I
I l ,t i
j h
(C-12)
. l
! l 26 -
f
}
n I.-._ -_ .- - --.._._- _-__ _ , _ _ . _ _ _ _ - -- - -
I i
I i
a,c 3 (C-13)
I !
i d
(C-14) 4 4
(C-15) t L
V 1.
4 i (C-16) t 4
4 i
)
\
I I (C-17) i l (C-18)
. e is a,C l .
27 -
{
i
~~--.,-,n . , - , , , -- - - - - - - - , , - _ _._ _ _ _ , - _ _ , ~ , - . _ ww . a-.n-,,_,.--n,-_ ---.e --,
4_.A.__,. _ - e -4 _ a ..+hrA- 4 . asy4 ..r..-M.m .e&,.s6, 4 m.g_ e_'A, _ eu+._ 4_45 .5+2 S 4=2e.de e____ y. a,.A.-.4 4'M 4M4 A++dwAea-_&.A d 4%3m_4 I
h k
S,C
'1 .
I e
i i
1 S
a,c (C-19) 1 (C-20) i i ,,
f * =
{
8,C .!
l 1
I f
r I
t f f 1 !
l l E
1 8,C
}
(C-21) l i .
8,C l k i
t 1
i .
1 r
}
i m
- - 7 a,c ,
4 r
I (C-22) -
s 4 m i
. i L
l 1 '
(C-23) i s
l m 6 i
1 l i
a I
t P
28 - .
f I 4 >
- l
! L d
4
,w - wee --mw-e. -
..A sw 9 ru.s .>-sa.s .2m sam e n a -.As -k am sas--.--
- 4= ma , xn aa.r uas- - - - - - >r1 - *x-. -ame ne n. - - .u o....e--,ue-a-e. -- - - .m-.-+-
- i i
t I
i - 8,C 1
1 (c-24) *a,c s
5 I 4 .
d
- 1 8,C i,
T
}
c e
i
! +
b l 1 t t
i
- t 1
a,c .
(C-25) .
h a
= ,
J 8,C 1
i 1
y 1
5 j r t
il 0 j 1 (C-2C) *a.C.
e I
i .
l a.c :
I
! 5 l
t l r
i 1 1
E
~M 3,C (C-27) a b I
29 -
4 M
8,C O
(C-28)
E W
~
8,C
~
8,C (C-29) l l
e
~
8,C D
8,C (C-33)
M a,C 1
l l
30 -
D. Hydrogen Igniticn and Ccmbustion O(3 Hydrogen entering the containment fran an input table may be introduced as a non-condensible added to the ambient atmosphere or it may be burned as it is introduced. We latter is a special case that has two
. assmptions that must be carefully considered in utilizing this option.
The first assumption is that there is always adequate oxygen for conplete conbusticn of the hydrogen. The second is that there is no hydrogen initially gesent cr flowing in fran another cmpartment.
Attenpting to use this opticn whm these assunptions are not valid will provide invalid results.
If the cption to add the hydrogen to the conpartment atmosphere is selected, the criteria for igniticn in each ccmpartment are examined at each time step of the finite integration. Ebr ignition to occur, loth the required volume fracticn of hydrogm ard the requiral volune fraction of oxygen nust be satisfied. Based cn the perfect gas law, the ratio of the partial pressure to the total pressure is the same as the p volume fraction. We partial pressure fraction is used in the program.
As discussed previously, at the time of igniticn in a ccripartment, internal timers are started for each connected and active flow path shown in Figure 1. It is assumed that propagaticn will proceed whether doors are gesent or rot. No propagation is permitted through fan flow paths. If che propagaticn delay time has expired in a flow path, the conditions in the connected cmpartment are examined to determine if igniticn occurs. Both the volume fracticn of oxygen for igniticn and the volume fracticn of hydrogen for propagation must be satisfied.
In each conpartment where igniticn occurs, the pounds of hydrogen to be burned is determined
. a.C 8,C(D-1) k, l
l v
4 m
8,C m
- *8,C F
(D-2 )
a.C i
e 8,C (D-3)
W BG 2,C W
e 32 -
a,C (D-4) 3 (V
~ "
E. Oontaiment Siray It is asstrned that the spray ficw enters the acrnpartment with a tnifom
~
drtp diameter and that the individual dress fall at a constant unifom ve3ocity over the specified fall time. The spray flow rate, tmperature and film coefficient of heat trat sfer are linearly inter-polated fran input tables Weh are a function of tima. .
In a conventional finite difference integraticn treatment of the spray, the mass of spray etering the acrnpartment during a given time step must be tracked throughout its fall time. Rr each incrernent of spray ficw, its mass, tmperature and, because of a variable time step, the length of time since generaticn must be maintained. Trn order of magnitude of the runber of time steps to conplete the fall is 10 -
Thus, for each spray, several thousard memory locations ard many ca? -'lations would be required. 'Io simplify the trectment of the spray, a,C L .
a,c (E-1) f 8,C
~ 8,C (E-2)
O ,
33 -
3 -
.as4 .-2-e A- -- 4 wh- g & s 4,---4 a,.m.--a+44- ue _.a~A - ,A a 4 ,o A s---- .A . --4 ,,asL a.W-- - -, _ n,, , _1 -1m_-
1
. W 8sC f
.t i
4 d
(E-3) 1 1
i 4
I (E-4)
I g - ,
B,C i
.l m
a,C ,
(E-5) 1
- l D e c
a,C 1 -
l
- f l
l 8,C i
t i
(E-6) \
I (E-7) 1 (E-8) ;
_ _ ._ . _ _ p b W B,C (E-9) ;
(E-10) \
l (E-11)
O t,C
- a p
8,C (E-12)
(E-13)
(E-14)
(E-15)
ImD I
35 -
a,C (E-16)
'this equation is valid fcr heat transfer in either direction pecnided that there is ro vaporization during its period of application.
If vaporizaticn is occurring, a,C a,e (E-17) a,C a,C (E-18)
O (E-19)
< (E-20)
" a,C b,C (E-21) t
~
1 .
In the spray analysis any increase in drop diarreter due to condensa-tien is rot cutsidered. 'Ihis would reqaire Irior knowledge of dat the effects of heat renoval frcrn the atmosphere would have. If the
J conditions in the atmosphere were near or at saturated conditions, x probably nost, but not necessarily all, of the heat rem:nal would result in omdensation. At high superheat conditions, probably only a small fraction, if any, would result in :cndensation. In the region of interest in the p e au, sprays may be heate$ fran 80F to saturaticn at 50 psia cr 200F for a change of 200F. If all of this heat were used to condense steam, the diameter of the drop would increase about 6 percer.t and the area about 16 percent. Even these limiting conditions of change would not have a significant effect cn the analytical results.
Denoting the conditions of the spray entering the cmpartment with the subscript zero, the net spray ficw cmpletirg the fall to the flcer of the cmpartment is a,c (E-22)
The net energy removed frcm the conpartment atnesphere by the spray is 8,C (E-23) ard the mass rate of a&!itim to the atmosphere is E,C (E-24)
These equations in various combinations ecnpletely describe the spray /at:nosphere interaction.
The implications of the assumption that the spray heat transfer occurs I
in a different time danain than the other equations is discussed in Section VIII and Appendix D. 'Ihe assumption is shcwn to provide l
conservatively high temperatures and pressures in the contalment.
l F. Addition Tables l
Heat, hydrogen, nitrogen and water may be added to the cmpartment l
l g atnesphere. All tables are entered as functions of time ard are l (
, , , - - - , , - , , , , - , , - . - , , , - - - ae, ., --. ,-,-r-, - - , -
linearly interpolatal. Only the heat addition may have negative values
) to simulate heat renoval.
The hydrogen and nitrogen tables nust include tamperature ao that the associata$ enthalpf may be calculatci and added to the conpartment energy inventory.
Rather than tanparature, the water addition tables nust include the energy additicn rate corresponding to the enthalpy of the water. The specific enthalpy of the water is acrnpared to the saturation enthalpies correspondirg to the total pressure in the conpartment. If the specific enthalpy of the flow is greater than the saturated vapor ethalpy, the entire mass ard energy are added to the atnesphere inventories. If the specific enthalpy is less than the saturated liquid enthalpy, the entire mass and energy are relegated to the sunps ard drains with no effect cn the atnesphere. If the specific enthalpy is between the saturaticn enthalpies, the flow is treated the same as the spray but with a zero fall time.
- A r s 6.
U G. Enegy Balance Based cn the preceding discussion, the rates of change of masses and energy in each ccmpartment can be determine 3. Concurrent with these calculations, the rount of change in temperature or pressure which would reverse the process can also be calculated. Ebr example, in l
l calculating the flow between two compartments, a differential pressure is determined. If the upstream pressure were to decrease by nera than this differential, the direction of flow would reverse. Similarly, an increase in the <bwnstreern pressure by nere than the differential vould l
also' cause flow reversal. 'Ihe minimun magnitudes for toth i# creases and i
decreases in pressure which would cause flow reversal for each ccrtpart-ment are retained in nunnory and used in evaluating a stabic time step.
O G .
- 3e -
'Ihe =i==n time step is specified as input. 'Ihe initial value for the tine step to be used in the calculation is determined frun _
a.c (G-1)
Using this initial value of the time c.ep and the rates of change previously calculated, the total masses of each co .atituent and the total internal energy in each a:rnpartment can be evaluated. Based on these totals a unique pressure ard tanperature can be detentined. There are tesically three regions of interest. Saturated, superheated or above the steam tables. The conditions of pressure and tanperature at p the beginning of the time step are used as the first guess of the corditions at the end of the time step.
m 8,C (G-2)
(G-3)
(G-4) l i i i
,__ __.~ . _ _ . . _ _ _ . _ _ _ . - _ . - - - - , _ _ _ , . _ , ._ . _ _
~
O .
4 a ,C (G-5)
O (~
(G-7)
_I a
] a,C
{ -
8,C i
(G-8) l (G-9) p
{
}aC 7
a,C (G-lO)
~
O
_ 4o _
, _ -- , -- -- -e ,,- - - - -
---,,,,--.,-,-,,--,,,,-.,,,,.,.,,_,,,,,.---,,--,--._,,--,,,-,-,-,,,.-,-n--,, - .n-.,
p a,C O
'g 4 8,C (G-ll) b e
8,C
. r m
- 8,C (G-12) b
~
S iC 9 -
~
O
- 41 -
4 4 _ AMmm u Am- 2 .m._ __.442
- mm+ 1- 1 a 4 **es +N 44 4JJ--h.*+W-*---4m4 ehha_- Ld u"" .N S&W - phahM e- +4--M-d.-6A-a. 5 L-h---a _.-_m _.-g.__am J N
l J
6 r ,
't t M
D 8,C i
i 1
'l i
- l
.i e
I f
E l t i 4 4
1 4
1 M
' = . !
i 8,C i
I B,C f .
W j p I. a3C t
i l
l (G-13) 1 e
O m 42 -
___ . ~ . _- - . - . _ ---.-.. - - - . . - - - , - , . - -
sa , . , . -a 4 - mu, ham.w 4 a ,.+m- 4--64 m as--'ee- mmn'Jh-h-.W
- s m hh"'4h--- &** ---4*4A.4 A-4 a LA h h 1-
- -- M4#-E- A----hhhwh-wW4Ah_WA-a..Aas4=-AhwAa f
l f
ii I
s j
I 8.C l 4
t i
a i
i i
I I
- i. .
l 1 I t
! l i
I i
d 5 f 6 e
h
, (
n t e
- [
! 8,C -
I (G-14)
, c i
1 a
i 1
e e
l l
4 I
t (G-15) i 4
i i
2 (G-16) 4 4
(G-17)
=
I 6 1
43 -
a,c O
- *
- a,c (G-18)
.r .,
a,c 7
~
- g,c (G-19)
~1n well behaved transients the reduction in time step will not te activated for nonotcnically increasing cr decreasing portions of the transient. At a chvge in sign in the first derivative of pressure with respect to time, there muld be a brief reduction in the time step. In regions of instability where a steady state or divergirg oscillation would occur, the mininun time step is used continuously. In the regions of interest where instabilities occured, the
- maxinun pressure
- g,c oscillation experienced as to the crder of psi peak to peak and
- a,c the correspondirg tenperature oscillaticn was F using the minirun l -
_ 44 _
1 l
- , . - . ~ . - - . _ . _ _ _ _ _ - .
4 time step give by equaticn (G-19) . Note that the externally specified - . _
p time step may be less than the minimtzn value given by equation (G-19). ;
V In this event, the externally specifial. time step will always be used. '
After the pressure and temperature evaluations have been ocunpleted, a
T nunber cf parameters must k updated. - ~"
Anong thesenis the mass of; hydrogen yet to be Nrned in a compartment diere deflagration'is taking '
place. g
. . . a ', c s
J a,c s
(G-20)
~
^
Itwever, if the voltane fraction of oxygen drops below the voltane - '
fraction of oxygen required to support aanbustion, the burn rate and
^
mass of hydrogen to be burned' are cet to zero to simulate extinguishing the burn.
Since the time step is known, the clocks' measuring the pecpagation delay time can be updated. Also, the ra*.e of heat transfer in the ice -
condenser can be converted to a mass of ice melted and a change in heat transfer area. Finally, the internal heat transfer equations in the passive heat sinks are used to tpdate the nodal temperatures. '
s With the updated values, the calculations can,proceal to the next time step and iterate to the acanpletien of the ' transient.
4 Y s
- , s t
% 4
%3
~
\
\
D J b- y
,.s .
t 4
'~%g
- 4%; g
i tt- ,
VI. INR7f IESCRIPPION N(
( Contrary, to general usage, this section is not intended to be an input manual but,'as the title indicates, a description of the necessary input.
pd ,s^
'the ' primary purposes of t*, tis discussicm are to indicate the level of detail of the input and the degree of flexibility of the Irogram, and to atphasize
}). some of the asstunptions inherent in the develognent of the program.
'7ne program has the capability of continuing a transient fran an inter-mediate time in the transient, prcnided the restart file has been written and saved fran a Irevious execution of the Irogram. If the present execu-a
..tien is a restart, any input parameter can be charged that is not a funcEion of the history of the geceding calculations. Ebr example, the area cf a Nm rath is affected by the door positicn ard cannot be changed but the ficw loss coefficient can be altered. Changing initial conditions i cr tabute input for times precedire the restart time will have no effect.
s Ibwever, changing values in the table at subsequent times will have an D yeffect. ,
s
% ether or rot the ges2nt execution is a restart, restart files may be
- written at future specified times ard just prior to a given co,puter execution elapsed time.
s The heat of c&bustion and the perfect gas constants are provided with
- default values vhich may be overwritten by input. The perfect gas con-s+ ants include the specific heats at constant voltane and constant pressure,
, ard the gas ocnscant fcr the perfect gas law.
s , w '
s
'1he maximtn time step may be specified as a function of the transient time.
- s. .
s
'ihe rate at which output is generated may also be controlled as a function t
of the transient tune. '1he output is discussed later.
. s . , ,
s a m N s
,, - , . ~ . . - -. . . - . - -- - -
I Ebr each act{ve empartment, the initial conditions mst be specified and hv are not neceSsarily steady state corditions. 'Ihe net free voltane, tmpera-ture, the contents by ocustituent and burn control parameters for each ocznpartment must be specified. The burn control parameters include voltrne fraction of hydrogen and voltane fraction ef oxygen for ignition, the voltane fracticn of hydrogm fcr propagaticn, the voltrae fracticn of oxygen below which the flame is extinguished and the fraction of the hydrogen to be burned.
Ibr each 'of 'the flow paths numbered 1 to 10 inclusive in Figure 1, the ficw area, flow loss coefficient ard the propagaticn delay tinu are required.
Areas must be zero for flow paths connecting two inactive carpartraents or l an active ccmpartment to an inactive one. A door may be represented in any )
or all flow pths designated 1, 2 and 3 in Figure 1. Ebr each door, the l max 22msn angle of openirg, the differential pressure required to achiwe j this opening and the correspanding flow area are regaired. Ebr flow pt.ths 1 and 2, a special angle ard openirg may be specified so that if this angle is cnce achieved, the flow area will never be less than the area specified regardless of flow conditions. In flow path 3, a bypass ficw area and a mininun differential pressure to initiate opening may be specified. In ficw path ntraber 8, an initial length of a slug of water, depth of subnergence, exit loss coefficient, disc rupture pressure and the density of the water j, may be specified.
/ Tne ice condenser is fully represented by specifying a mass of ice with its correspondire area of heat transfer, density, heat of fusicn, flow loss
~~
/
3
' coefficient and net free voltrae.
,i s Y i
Fans a$e represented by designating a suction node and a discharge node, I
i time of act -icn, time of deactivaticn, a fan flow multiplier an3 a fan J
head / flow table number. 'Ihe fan head / flow table is simply a list of differential heads with .correspondirg voltrnetric flow rates to represent the head / flow curve. The fan flow multiplier is simply a mitiplication factcr cn the flow derived fran the table ard can be used to represent multiple parallel fans or a flow ' split between crrnpartments.
( l V
1 /
i
_ _ _ , . ,, , _ _ _ . , , ._ , _ _ m _.,__m, _ , . _ , , ,. _,-
Based cn asstmpticns in the developnent, a single fall time and a single drop size are usa! fx each spray. '1he input tables of ficw rate, tmpera-v ture and film coefficient as functions of time, supply all the reaining necessary informaticn fcr the spray.
Heat, nitrogen, hydrogen and water addition tables are discussed in the developnent of analytical equaticos. Each aMiticn table is a functicn of time with tmperature also supplied for the nitrogen and hydrogen tables arri enthalpy supplied with the water tables.
Each wall or passive heat sink is specified by a ccznpartment rnrnber, surface area, initial uniform tmperature, exterior heat sink taperature and the heat transfer correlation to be used. If the Tagami correlation is selecta3, the time of peak pressure an$ total energy as well as a multiply-ing coefficient nust be specified. If radiant heat transfer is desired, a surface snissivity and effective beam lergth are required. If an externally specified film coefficient is to be used, the film coefficient as a functicn of time cr differential temperature must also be specified. Each passive heat sink may have up to 7 layers of material. Ebr each layer, the V nurber of tenperature nodes, thickness, ccnductivity, heat capacity and exit film coefficient of heat transfer must be specified.
Regardless of whether the transient is newly started or started from a restart, a cx2nplete input edit of all input parameters is written to the out p .
- v .
_ 48 _
VII. OUTPUT O
In addition to the input edit discussed above, the program generates output at frequencies controlled by the input. The short-form output is a single line of output listing the temperature and gessure in each ocznpartment. At the sane time as the short-form is written, the time and all conditions of tauperature, partial pressures and cx:nstituent masses in each m,partment are written to a tape which can be saved ard used to generate plots of the transient. Because of the sharp peaks in Iressure experienced during a burn, the pressure is scanned durirg each burn ard the maximur pressure in the burn conpartment and the time it occured are retained in r;sory. This informaticn is written to a separate tape every time plct information is written.
At the specified interval for long form output, two separate tapes are J writtes. On one tape the detailed conditions in each voltrae and ficw path are written. Also included is infomation about doors, ficw paths, the ice condenser ard the surface tanperature ard heat rate to each wall. Each 5
icng form. output to this tape consists of a single page. 'Ib the second tape are written all of the & tails of the passive heat sinks, including the temperature at every node in every wall. This output may consist of numerous pages each time it is written ard depends cn the number of passive heat sinks and the number of redes in each heat sink.
t i The final form of output is the restart file which is also controlled by l
the input.
i l
l
_ 49 _
VIII. VERIFIC.5& ICE O .
Verification of a caputer program can be performed in a rurrber of ways.
'1he four methods of verificaticn most frequently used are 1) ocupariscn of omiculated results with the calculated results of other accepted caputer sw s, 2) ccuparisen of calculated results with test measured results,
- 3) comparison c,f cniculated results with the results of external calcula-tions performed usirg the given prwimu methodology, and 4) sensitivity studies involving various parameters used in the Irogram. Each of these methods has been employed in the verificaticn of the CIASIX ccmputer program.
For the first part of the verification analyses, CIASIX calculated results have been ecmpared with the calculated results of the Transient Mass Distribution ('IMD) , Reference 6, md CDCDCLASS9, Beference 7, cm puter programs. Both of these swims are design s wims developed by' Westing-house Electric (brioration. 'IMD has been accepted by the htclear Regula-tory Ccr.Tnissicn (NBC). Results of 00COCIASS9 analyses have been presented to the NRC Staff in support of dry contairrnent plant licensing and CCXD, Reference 8, the base program frcm which COCOCIASS9 was developed, has bee" accepted by the PRC.
Tne 'IMD program as developed for analyses of ice condenser containment response durirg the initial few secords followirg a design basis loss of coolant accident (IDCA) . Because this period is characterized by rapid pressure transients, a detailed spatial analysis is necessary and 'IMD contains a multi-crnpartment analytical nodel. Ebrthermore, since contain-ment safeguards cb not functicn durirg this period, neither the contairraent sprays nor the air return fans are included in the 'IMD analyticel model.
Far similar reasons neither nitrogen, hydrogen, nor fissicn prcduct energy additicn is included in the Inodel. Finally, since to significant heat transfer c.o the contailr.ent walls is expected to occur durirg this brief period, passive heat sinks are rot included in the 'IMD analytical nodel.
Therefore ccupariscn of CIASIX calculated results to 'IMD calculated results l is limited to nulti-ccmpartment tressure and temperature responses to high enthalpy water mass and mergy addition. 'Ihis omparison provides verifi-caticn of CIASIX pressure ard tenperature response calculations, ficw path (m} omiculations, and aspects of the O.ASIX ice condenser nodel.
Calculated results frm the CIASIX r%ima were cmpared to 'D4D calculated results for a series of cases as described in 7ppendix A. 'Ihese omparisons show very cpcd agreanent between CIASIX and 'D1D calculations with CIASIX calculated values being generally conservative relative to 'IMD calculated values.
The 00C0 program was developed for analyses of dry containment response to a design basis IDCA. Since the program was developed to analyze the entire design basis Iost IDCA transient, the CDCO analytical nodel has the capability to simulate contairrnent safeguards operaticn and heat transfer to passive heat sinks as well as high enthalpy water mass and energy additicn. Because a dry contairrnent consists primarily of a large open region surrounding the reactor coolant system, the CD00 analytical nodel provides only a single voltrne representaticn of the contairrient.
O# The 00CDCLASS9 program is an extension of the CDCD program. CIXDCIASS9 has all the features of CJCD ard also has the capability to simulate events related to degraded core accidents such as hydrogen burn Itencrnena.
Although ccmparisons of CIASIX calculated results to 0000CIASS9 calculated results are limited to single ocmpartment Iressure and tenperature resIonse to hicjh enthalpy water and/cr hydrcgen mass and energy additions, they can include simulation of hydrogen burns, heat transfer to containment sprays and/or heat transfer to passive heat sinks. Hcuever, since the CD00CIASS9 spray nodel cbes not allow evaporation and the CIASIX spray nodel does, the two spray models cannot in canpared effectively. The ccrtparisons of CLASIX calculated results to CDCOCIASS9 calculated resulta provide veri-l ficaticn of the CIASIX pressure ard tenperature response to mass and energy additions, burn nodel and nodel for heat transfer to passive heat sinks.
l l
l Calculated results fran the CIASIX g@&ou were ccrnpared to CDCOCIASS9 results for a series cases as described in Appendix B. 'Ihese cases provided f
conparisons of single ccmpartment pressure ard tarperature response to high
[G'l l
1 l
l 1
enthalpf water ard hydrogen mass and energy additions ard included hydrogen f burn simulation. These omnparisons show excellent agreenent between CLASIX j b and C000CIASS9 calculated results. l l
Pbr the second part of the verification analyses, CIASIX calculated results l have been conpared with test measured results fran receat hydrogen burn tes_ts performed at ,toth the Ebnwal test facility, References 9 and 10, and at the Lawrence Livernere National Laboratory, Reference 11. 'Ihe tests, designed to study the capabilities of diesel glow plug ignitors, Irovide data for verification of the CIASIX burn model, the CIASIX models for hydrogen and high mthalpy water mass and energy addition to the contain-ment, and sane aspects of the CIASIX models for heat trarsfer to passive heat sinks and sprays. Details of the canparisons of CIASIX calculated results with test measured results are given in Appendix C. The results of these acmparisons indicate C1ASIX ccnservatively cuerpredicts the pressure and ternperature response to a burn ever a wide range of conditions. A large portion of the conservatism has been shcun to be the result of using constant values for constituent gas specific heats in the CIASIX analytical rml model.
LJ In a3dition to the ccraparisons with other programs and with test measure-ments, CIASIX calculated results have been ccmpared with the results of external calculations using the CIASIX methodology. 'Ihese aanparisons, performs 3 throughout tN developnent of the program, test various aspects of the CIASIX conp.itations including conservation of mass and energy, heat removal by sprays, operatien of fans, heat transfer to passive heat sinks, and interpolation and integration of tabular input data. All externally calculatal results agreed with CIASIX printed output within calculated roundoff error. Samples of these a2nparison results are given in Table 2.
l Finally, ntrnerous sensitivity studies were performed . during the CIASIX developnent. Early CIASIX analyses for ice condenser contairrnents, Pefer-ence 12, includs3 sensitivity studies for all spray parameters, for the air return fan ficw rate, for the ice condenser initial ice mass and drain urnperature, ard for hydrogen burn parameters. Recently a number of p sensitivity studies were perfonned as part of the comparison to test
measured results given in Appendix C. 'Ihese studies include evaluation of the sensitivity of calculated results to various parameters associated with the passive heat sinks, to the contairrnent atnesphere constituent gas specific heats, ard to the calculational time step. The results of all sensitivity studies debnstrate that there is no musual dependence on any tested parameter.
In sunmary, four methods were used in the verification of the CLASIX computer program. Each methcd provides a level of confidence in one or nore aspects of the CIASIX calculations. Chaparisons of CIASIX calculated results wi'h 'IMD calculated results provide confidence in the CIASIX calculation of nulti-ccrnpartmmt pressure and temperature response to mass and energy additicn, flow path calculations ard ice condenser model.
Ccznparisons of CIASIX calculated results with CD00 CLASS 9 calculated results provide additional confidence in the CIASIX calculaticn of pressure and teuperature response to mass and energy addition. 'Ihese camparisons also provide confidence in the CLASIX models for hydrogen burn calculations and heat trcnsfer to passive heat sinks. Chnparisons of C[ASIX calculated
'~%
(O). results to test measured results demonstrate conservatism in the CIASIX burn nodel and provide confidence in the CLASIX models for heat transfer to passive heat sinks ard containment sprays. Sensitivity studies and ccraparisons of CIASIX calculatM results with the results of external calculations usirg the CIASIX uethodology provide added confidence in all aspects of the CIASIX calculational nodel.
The only significant aspect of the program which has not been examined in
' detail is the analytical nodel of flow path 8. Ibwever, this flow path is not germain to tM design analysis of the hydrogen mitigaticn systens for ice condenser plants.
In aldition to the verification of analytical techniques, two assumptions were alm intensively investigated. The first of these assumptions was that the heat transfer coefficient correlation was applicable to the *a,c high tenperature gases generated by a burn in the lower conpartment. As discussed in the Analytical Developnent section of this report, the r-correlations provide film coefficient values n -*
- a,c depending cn specific conditions. 'Ib ' evaluate the impact of the corre'laticn cn the nnalytical results, a typical transient for the Sequoyah plant was selected. In the region investigated, burns occurred in both the lower conpartment ard the ice condenser outlet plentrn. a,c These results indicate that there is no najor effect cn the analytical results or con-clusions fran using the ice condenser heat transfer correlations fran the Waltz Mills tests.
The second assumption that was investigated was the assumption that the v) spray heat transfer could operate in a separate time donain. A canparison of the CASIX representation with a conventional finite difference approach is presented in Appendix D. The asstrapticn of a separate time donain for the spray is shown to be conservative by predicting slightly higher tanperatures and pressures in the containment.
Basad cn the preceding discussion, it is concluded that the CASIX program, exclusive of the model of fl w path 8, is adequately verified and qualified for the type of chsign anelysis for which it is intended and, particularly, within the rangc of validity of the assumptions utilized in its develop-ment. Ebr these analyses, CASIX produces conservatively high predictions of tenpe'ratures and pressures within the containment. Containments designed to withstand the gessures and temperatures predicted by QASIX will be adequate to withstard the pressures ard tenperatures produced by actual transients.
%.s .
IX. CCtCIDSION O
V Based en the above, CIASIX is shown to be a viable tool for the evaluation of the pressure and tanperature reeponse of an ice condenser containnent to a hydrogen deflagration. Extensive use of the program for a rasnber of plants and extensive sensitivity studies have shown no ancmalies in the results. Cbnparisons with test data and other methods of analysis provide
, unple assurance that the tanperatures and pressures predicted by CIASIX are conservatively high and that a containnent designed to withstand the conditions predicted by CIASIX will have a significant margin of safety.
X. REFERENCES b
v
- 1. Tapmi, T., " Interim Report on Safety Assessments and Facilities Establishment Project in Japan for period ending June 1965 (No.1)",
1965.
- 2. Kreith, F., " Principles of Heat Transfer", International Textbook Co., )
1965, pp. 307-310. l l
S. Kreith, F., " Principles of Heat Transfer", 1973, Figure 5-35, -38.
- 4. Ekert and Drake, " Heat and Mass Transfer",1959, Table 13-3.
, 5. McAdams, " Heat Transmission", 1954, Figure 4-22.
- 6. " Ice Condenser Containment Pressure Transient Analysis Methods",
4 WCAP-8077 (Proprietary Class 2), March 1973, WCAP-8078 (Proprietary Class 3), March 1973.
- 7. " Zion Probabilistic Safety Study", Module 4, Section 4, 1981 (NRC Docket Nos. 50-295 and 50-304).
~
- 9. Appendix V of the Tennessee Valley Authority Sequoyah Nuclear Plant
- Core Degradation Program, Volume 2, " Report on the Safety Evaluation of the Interim Distributed Ignition System", December 15,1980 (NRL Docket No. 50-327).
i
50-327).
O
- 11. Iowry, William, " Preliminary Results of 'Iher:e1 Igniter Experiments in H -Air-Steam Envircunmts", from "Pr%%s of the Wrkshop crt the 3
Impact of Hydrogen cri Water Reactcr Safety", edited by Marshall Berman, Sandia Laboratories, August 1981 (NURED/CR-2017).
- 12. Appendix U of the Tennessee Valley Authority Sequoyah Nuclear Flant Core Degradation Program, Volune 2, " Report en the Safety Evaluation of the Interim Distributed Ignition Systern", December 15, 1930 (NRC Docket No. 50-327).
[
l
TAR E 1 l
i RJRN CINTRL PARATIERS
- I i
1
- 1. /0 H2 I 4ITICN
- 2. 4H CIU8UMED 2 i Y
- 3. /O O2IGNITICE ~
Y
- 4. /O O SUPPORT COMBWTICE 2
- 5. BU1N TIME:
- 6. Y
/O g PROPAGATICE
- 7. PIOPAGATICN DEIAY TIME i
i s
l
\
I l
t I
t i
f i
- l 58 -
TABLE 2 O CLASIX vs External Calculations Typical Ctrnparisons Externally CLASIX Calculated Calculated Parameter Value Value Hydrogen Addition Rate (lbn/sec) a,c interpolated fran input table values Tenperature of Hydrogen Gas (F) added interpolated fran input table values Total Hydrogen added (lba)
Fan ficw rate (cfs)
Spray heat reseval rate no evaporation
~
(Btu /sec)
Spray heat rernoval rate with evaporation (Btu /sec)
Ice Cbndenser Iower Plentzn Voltrae (ft )
I Melt (lbn)
All differences in results are within roundoff error.
l l
l 8
! I VENT VOLUME 4
/
/*
=
4 UPPE R COMPARTMENT
~
n 3
UPPER OUTLET PLENUM @ h
@! ICE BED O @ 2 LOWER INLET PLENUM
- a 1
LOWER COMPARTMENT
! I a
)
7 @ @
7 5 6 STEAM DEAD l PRESSURIZER GENERATOR ENDED VOLUME VOLUME VOLUME Figure 1 CLASIX MODEL OF THE ICE CONDENSER CONTAINMENT O .
60 -
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Fesure 2 FLOW DI AGR AM O
- 61 -
4 -
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musD Figure 2 (CONTINUED) 62 -
. - . . ~ _ _ _ . _ _ _ _ . _ . - _ _ _ . - . _ , _ _ . _ _ _ _ __._-- . _ _ _ _ _ _ . _ _ __ _ _ _ _ __._ _- _ . _ _ ___ _ _ . _ _ _ _ _ . _ _ . _ _ _ . _ _ . _ _ _ - - . _
l 1
l l
APPL!NDIX A l Otsupariscm of CIASIX Results with 'DO Results f
(~]
a l
INTRODUCTICN l
'Ihe Transient , Mass Distribution (IMD) Irogram, Reference A-1, was developed to analyze the short term phase of the transient fran a loss of coolant accident (IOCA) in an ice condenser contairraent and has been accepted by the NBC as a design tool, Reference A-2. A canparison of CIASIX calculated results to 'IMD calculated results is jxesented in this Appendix.
PODELIEi The 'IMD program was developed for analyses of ice condenser contairrnent response durirg the initial few seconds following a design basis IDCA.
Because this period is characterized by rapid pressure transients, a p detailed spatial analysis is necessary and 'IMD contains a multiccripartment V analytical nodel. Furthermore, since contairrnent safeguards do not function durirg this period, neither the contairrnent sprays nor the air return fans are included in the 'IMD analytical nodel. Ebr similar reasons neither nitrogen, hydrcgea, nor fissicn prcxluct t.nergy addition is included in the model. Finally, since to significant Nat transfer to the contairrnent walls is expected to occur durire this brief pericx1, passive heat sinks are not included in the 'IMD analytical nodel. Therefore cx2nparison of CLASIX cal-culated rcsults to 'IMD calculated results is limited to nulti-ccripartment l pressure and tanperature responses to high ethalpy water ness and energy l additicn. This canpariscn prcuides verificaticn of CIMIX pressure and l
l tenperature response cah:ulations, flow path calculations, and aspects of 1
- the CLASIX ice condenser model.
( 'Ibe 'IMD and CIASIX analytical nodels were selected to be as similar as
( possible. Both containment models include a lower canpartment, ice con-denser tpper cxxnpartment and dead ended voltrne. Schanatic diagrams of
' these nodels are give in Figures A-1 and A-2 l
l l
I I
l l -- -.. -- - _ . _ . _ _ _ _ . . . . _ _ _ _ ._ ____ _ _ _
'Ihe CIASIX ice condenser is divided into two parts, the lower and upper i
plenms. 'Ibe ice condenser nodel in 'D(D is divided into five sections ucept in the case with a saturated blowdcun and ice present in the ice ocndenstr. Ebr this transient a three cx2npartment ice condenser nodel with ice present in cnly cme ccmpartment was utilized. Although the ice con-denser was ncx3eled. for all cases, scme crrnparisons were performed by not including ice in the ice condenser.
Three sets of cbors are nodeled. These are the lower inlet doors which are located betwest the lower ccmpartment ard the inlet plentrn, the intermediate deck cbors diich are located between the ice baskets and the upper plentrn, and the top deck doors (blankets) which are located between the upper plentra and upper ccznpartment.
The hI ysical parameters used in this verification analysis are typical of an i condenser contai:Tnent. Tables A-1 and A-2 contain the 'IMD input and flow path parameters. A surinary of the CASIX input is given in Tables A-3 ard A-4.
s RESULTS Ebur crrtpariuon runs were made covering the anticipated range of the blowcbwn energy frcrn saturaticn to superheat conditions. Direct ccrpari-sons were nede between the tertperatures and pressures resulting frcm the l
'IMD and CLASIX calculations. Indirectly, these ccnparisons provide
! verification of CASIX ficw path calculations.
l The first case investigated had a saturated blowdcwn in a contaiment without ice in the ice condenser. 'Ihe lower acrpartment and upper crrnpart-ment pressures are shown in Figures A-3 arx3 A-4. 'Ihe correspcoding temperatures are given in Figure A-5. As shown in these plots, the CASIX calculated values for both temperature and pressure are generally conser-vative by being higher relative to the 'IMD calculated values over nest of the transient. CIASIX is expected to be conservative relative to 'IMD
because of the difference in the treatmer.t of the flashing cf the breakflow as it eters the contailmmt. a,c The secord case is very similar to the first case but has a superheated ,
blowdown. Figure A-6 shows the 'IMD and CLASIX calculated pressurds in the upper conparment. In this case, 1cwer conpartnent pressures are nearly identical to the tpper carpartment gessures and therefore are not in-O-
x cluded. The tanperat.tre plots for this case are give.n in Figure A-7. Close agreement exists between 'IMD and CLASIX calculated results.
The next phase of the verificaticn duplicates the first two cases and includes ice in the ice con 3enser section. Figures A-8, and A-9 are the plots fcr the saturated bicwcbwn case. The plots for the superheated blowdown case are given in Figures A-10, and ,A-1,1. Ebr both cases CLASIX psi. In additicn. the *a.c and 'IMD calculated pressures agree within calculated tenperatures agree closely with Ci.ASiX values being slightly nere ccuservative in the Icwer conpartment bu+. slightly non-conservative in the typer canpartment.
An oscillation can be observed in the CIASIX temperature plot for the lower ccmpartment in the saturated bicudcwn case with ice present (Figure A-9). Similar results were seen in an earlier ca,parison analysis in Reference A-3, and are known to be caused by convergence criteria and G at the interface between saturated and superheated conditions. 'Ihe current u)
_ ss _
version of CLASIX has a tighter convergence than the previous version so
, that most of the current plots are smoother than those found in Reference A-3. However, as can be observed from these results, there is no cumulative error leading to divergence of results. Other studies with tighter con-vergence criteria reduced the magnitude of the o;-illation but had no effect on the general rer.ul ts and conclusions. For reasonable computer time, however, the convergence criteria in CLASIX were not modified.
CONCLUSION The comparison of CLASIX calculated results to TMD calculated results has shown that the two programs are in excellent agreement with CLASIX being generally conservative over a range of conditions. The few differ-ences that occur are explained by the differences in the analytical assumptions associated with the two programs. Therefore, a high level of confidence can be placed on the CLASIX analytical predictions for multi-compartment pressure and temperature response calculations, flow path calculations and ice condenser calculations.
REFERENCES A-1 " Ice Condenser Containment Pressure Transient Analysis Methods",
WCAP-8077 (Proprietary Class 2), March 1973, WCAP-8078 (Proprietary Class 3), March 1973.
A-2 NRC letter from D.B. Yassalo, NRC Chief Engineer, Light Water Reactor P roj ect Branch to Westinghouse Nuclear Safety Manager, Ramano Salvatori, December 18, 1973.
A-3 Appendix V of the Tennessee Valley Authority Sequoyah Nuclear Plant Core Degradation Program, Volume 2, " Report on the Safety Evaluation of the Interim Distributed Ignition System", December 15,1980 (NRC Docket No. 50-327) .
66 -
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CLASIX MODE L OF THE ICE CONDENSER CONT AINMENT 71 -
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CLAS'X TMD COMPARISON 10,000 LBM/SEC BLONDOWN 500 BTU /LBM-
- NO ICE FIG'URE A-5 a
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FIGURE A-6 1
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! FIGURE A-7 i e- ,
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- - 10,000 LBM/SEC BLONDOWN '
i 500 BTU /LBM i
WITH ICE
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FIGURE A-9 4
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! 10,000 LBM/SEC BLOND 0HN 1205 BTU /LBM l WITH ICE l i
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APPENDIX B 0:nparistm of GASIX Results with rr.inerASS9 Results 00CD (Reference B-1), the base program for QXDCIASS9 (Reference B-2),
was developed by Westirshouse Electric Corporaticn fog the analyses of entire design basis pst loss of coolant accident (1DCA) transients in dry coptairnents. CXD, has been accepted by the Nuclear Regulatory Ccmnission (NIC) as a design program for this purpose. We erme_rASS9 Program is an extensicn of the 00CD progrm. 0000CIIGS9 has all the features of OXD and also has the capability to simulate events related to degraded oore accidents. Results frcm C000CIASS9 have been presented to the NRC in support of dry contairment plant licensing.
The CLASIX and 0000CIASS9 analytical models have the capability to simulate high enthalpy water addition, hydrogen mass and energy additions, hydrcgen burnirg and heat transfer to passive heat sirt.s and containnent sprays. However, the two spray nodels cannot be cmpared effectively because the 0000 CLASS 9 spray model does not allcw evaporaticn and the CLASIX spray model does. In addition, since CD00 was developed for analyses
% of dry contr.irry_nts, its analytical mccel prcntides only a sirgle voltne representation of the containment. Therefore, comparisons of CIASIX calculated results to 00COCIASS9 calculated results am limited to single cmpartment pressure and tenperature responses.
Six conparison cases were rtr. usirg the same basic transient. Hydrogen was added at a constant rate cnter a limited portion of the transient. After the hydrogen additicn had stopped, a burn was initiated at a specified time and with a specified burn rate. Wree cases were run with a saturated blowdown during the entire transient and then all three were repeated with a superheated bicudown.
Case 1 is the basic transient with a saturated blowdown. his case does not include heat transfer to passive heat sinks. Case 2 and Case 3 are the tesic transient with a saturated blowdown and include heat transfer to passive heat sinks. In Case 2 there is convective heat transfer with a constant wall surface film acefficient and no radiant heat transfer. In O
Case 3 the Tagami heat transfer corr lation is used and radiant heat p transfer is included. Cases 4, 5 and 6 are respectively identical to Cases
\ 1, 2 and 3 except they have a super %eated blowdown. Input parameters for these cases are summarized ir. lables B-1 and B-2. The initial conditions and passive heat sink parameters are typical of ice condenser containments.
The calculated pressures and temperatures as functions of time are presented in Figures B-1 through B-12. As can be seen from these figures, CLASIX and C0C0 CLASS 9 produced almost identical analytical results for all cases considered. Neither program consistently produced lower results than the other. The calculated pressure ,and temperature differences were respectively less than percent and percent. *a,c The comparison of CLASIX and C0C0 CLASS 9 indicates negligible differ-ences between the snalytical results of the two programs. This provides a high level of confidence in the CLASIX modeling of the blowdown, hydrogen 6ddition, hydrogen burning and heat transfer to passive heat sinks. Since CLASIX and C0C0 CLASS 9 have different time step and convergence criteria, the comparison also indicates 9;at these criteria in CLASIX ara adequate.
References B-1 Bordelon, F.M., and Murphy, E.T., " Containment Pressure Analysis Code (C0CO)", WCAP-8327 (Proprietary Class 2), July 1974, WCAP-8326 (Proprietary Class 3) July,1974.
B-2 " Zion Probabilistic Safety Study', Module 4, Section 4, 1981 (NRC Docket Nos. 50-295 and 50-304).
i
~. . .- - _ - . . - _ . ._
I l
'IABIE B-1 General Input Paraneters for CLNSIX and 00CDC[ ASS 9 Caparison Cases Parameter Value voltane (ft3) 1.2 x 10 6 Initial tanperature (F) 100 Initial air pressure (psia) .28 Initial steam Iressure (psia) 14.71 H2 O mass additicn rate (lhn/sec) 200 H2 O energy addition (Btu /1hn) saturated 500 superheated 1205 H2 addition rate (lbn/sec) 10 H2 additicn tenperature (F) 1500 H 2 addition initiated (sec) 30 terminated (sec) 90 Burn initiated (sec) 100 Burn rate (lhVsec) 30 O .
4
-,_-,-._,-,-,-.--,__--,,--...-----..._.._.,_,--.----..m- -- ~ - - - - . . - . . ~ ~ _ - - . - - - , . . - - - - . . . - ,
TABIE B-2 i
Passive Heat Sink Input Parameters for CIASIX and 0000CIASS9 Ctznparison Cases mil #1 Wil #2 4
Surface area (ft2 ) 2 x 10 3 x 10 5 Initial tanperatura (F) 100 100 Bnissivity* 0.4 0.9 Radiant heat transfer beam lergth (ft)* 100 100 Layer 1 - Material Stainless Steel Faint Thickness (ft) 0.06 0.001 N.rnber of nodes 30 2
'1hermal corductivity jBtu/hr ft F) 26.0 0.08 Heat capacity (Btu /ft F) 56.4 28.4 Dcit heat t3ansfer coefficient 1 x 10 4
(Btu /hr r F) 0.0 .
Layer 2 - Material concrete Thickness (ft) 1 Number of nodes 12 Thermal conductivity jBtu/hr ft F) 0.6 Heat capacity (Btu /ft F) 28.8 Exit heat t3ansfer coefficient 1 x 10 (Etu/hr r F)
Iayer 3 - Material concrete
'Ihickness (ft) 2 Number of nodes 12
'1hermal corductivity fBtu/hr ft F) 0.8 Heat capacity (Btu /ft F) 28.8 Exit heat t3ansfer coefficient (Btu /hr r F) 0.0
- Used in Cases 3 and 6.
O
= . _ . . . - . - - . . . . . _ . . .. .. - . - .. . - .. - .- . - ..-. - - . - .. - . - .. ... . - . . - . . . - -
) - - - - -
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< CLASIX COCOCLASS9 COMPARISON
' CASE 1-i 500 BTU /LBM BLOWDOWN NO HEAT SINKS I
i FIGURE B-1 l i
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+
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1 L CLASIX COC0 CLASS 9 COMPARISON CASE 1 i
l 500 BT'J/LBM BLONDOWN l l
NO HEAT SINKS t
I FIGURE B-2 I
t
. - . , . , ~ - - ~ _ - - _ . . . _ . .nr-,,--
.. . . _ _ - . _ . . . _ _ . . . = _ _ _ _ _ . .
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j WALLS WITHOUT RADIANT HEAT TRANSFER FICURE B-3
! l 1
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- - ., ~ ~ . ___.-am-,.- .,-,,m,-
, _ . . . - . . - . - . . . = . _ . _ _ . - . .. . . _ . - - - - . . - . . - . . . - - . . _ . . . - - . . - . . . .
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CLASIX COC0 CLASS 9 COMPARISON CASE 2 4 500 BTU /LBM BLONDOWN WALLS WITHOUT RADIANT HEAT TRANSFER I i FIGURE B-4 4
i
's i [
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i CLASIX COCOCLASSS COMPARISON '
t CASE 3 ,
500 BTU /LBM BLONDOWN
! HALLS HITH RADIANT HEAT TRANEFER ;
I FIGURE B-5 ,
\
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i O CLASIX COCOCL ASS 9 COMPARISON CASE 3 500 BTU /LBM BLONDOWN HALLS HITH RADIANT HEAT TRANSFER FIGURE B-6 0 .
J J
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CLASIX COCOCLASS9 COMPARISON ,
CASE 4 i
1205 BTU /LBM BLOWDOWN
' NO HEAT SINKS i
FIGURE B-7 I f
( ,
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-1
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a w- 4 4 -.@w, .hFm*K___.aw a 4 -m.*-.44-+wa-4a_J. >a_E. - . .A.A4 m+_a a Jm
. , .-. .z, -- h h_:.-A-__-L__ -_h-h,- m._ miaEd 4 mm Au._.4e.a__$ m a. o m P
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CLASIX COC0 CLASS 9 COMPARISON CASE 4 !
1205 BTU /LBM BLONDOWN NO HEAT SINKS <
FIGURE B-8 i
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-- - -.-~.-- - , - - - - - -
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i CLASIX COCOCLASS9 COMPARISON CASE 5 1205 BTU /LBM BLONDOWN HALLS WITHOUT RADIANT HEAT TRANSFER FIGURE B-9 ,
e I
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CLASIX COC0 CLASS 9 COMPARISON CASE 5 1205 BTU /LBM BLONDOWN WALLS WITHOUT RADIANT HEAT TRANSFER FIGURE B-10 95 -
.m-,~_____._,,.
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I l CLASIX COC0 CLASS 9 COMPARISON I CASE 6 1205 BTU /LBM BLOWDOWN WALLS WITH RADIANT HEAT TRANSFER i
l FIGURE B-11 l
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.. =. = _ - . - - - ~._ - .- . ._. .. - . . . . _ . _ . . . - - . . . - _ . - . . . . . . - . - . - - . . . . .- . . . - . -. - .
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{ CASE 6 4
1205 BTU /LBM BLOWDOWN i 4
WALLS WITH RADIANT HEAT TRANSFER 4
e FIGURE B-12 l1 :
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APPDOIX C (N Ocuparison of CLASIX Results with 'mst Measured Results Introduction Ccraparisons between CIASIX calculated results and test measured results frcm two series of thermal ignitor experimental tests are presented in this appendix. We two test series were condteted by Fenwal I*. m. or-porated, Ashland, Massachusetts, References C-1 and C-2, and Lawrence Livermore National laboratory (IDE), Livermore, California, Reference C-3.
The purpose of these tests was to determine the reliability and capability of thermal ignitors to initiate deflagration tnder various envircmental conditions typical of the reactor contairrnent durirg accidents.
The varicas test conditions are divided into four divisions in this appendix: dry, steam, spray ard transient. We dry cases consist of air and hydrogen mixtures, and have to additions to the vessel after the 9 1cw A pite is activatel. Steam cases are those cases in which stean was added O initially at various concentrations . Wese steam cases also have re additions to the vessel after the gicw plug is activated. The spray cases have a steady water spray in the mssel throughout the period in which the gicw plug is active. The transient cases are those in which a constant ficw of hydrogen and steam is added to the vessel during the period in which the gicw plug is active. The dry and steam tests were performed by toth Fenwal and IDE. We remaining two divisions were conducted by Fenwal. Represen-tative tests frcra each of these four divisions were selected for use in the CIASIX verification analysis. We test results were compared to CULSIX calculated results to verify the CIASIX bum model, the CLASIX models for hydrogen and high enthalpy water nass and energy additions, and sane aspects of the CIASIX models for heat transfer to passive heat sinks and sgays.
b o
_ ge _
General CIASIX Input Pbr both the Fenwal and the IDL test cxrnparisons, the free voltrae inside tN vessel was treated as a single elenent. For this simple madel, QASIX input consists of the initial conditions, burn parameters, and passive heat sink data. All of these input parameters except the heat sink da_ta and the net free gas voltrnes are case dependent and will be discussed in the next secticn.
Passive heat sink data are sunTnarized in Table C-1 for the Fenwal vessel and Table C-2 for tM I.IZE vessel. These include the wall surface area, the initial wall ternperature, the enissivity, the radiant heat transfer beam lernth, ard individual layer data. Ebr the Fenwal vessel, the wall surface area es calculated frcn the known voltrne and vessel gecnetry.
For the IDL vessel, the wall surface area was obtained frcn IHL. The initial wall tenperature is case cependent and equal to the initial gas tanperature. Irdividual layer data input to CIASIX includes the thickness, the number of rodes, the thermal conductivity, the heat capacity, and the exit heat transfer coefficient. The layer thicknesses are deternined by the vessel specifications, the thermal conductivity and heat capacity are material dependent parameters, ard the layer exit heat transfer coeffi-cients are functions of the materia]s in adjacent layers, mere rossible, passive heat sink parameters are the standard values used in ice condenser containnent analyses. 'Ihe renaining values are based cn standerd textbook values. A schenatic of the Fenwal and IRE test vessels are shywn in Figures C-1 and C-2, respectively.
Case Specific GASIX Input The CLASIX initial conditions include the initial gas temperature, initial total pressure, ard initial partial pressure or voltrae fract.icn for the gas constituents. All of these values were obtain=d directly fecn the test reports. Oxyger and nitrgen partial pressures were calculated using the standard air fractions of 0.209 for cetjen and 0.79 for nitrogen.
u)
. 99 _
'1he burn parameters include the hydrogen voltane fracticn for ignition,
(], the hydrogs fraction burned, the mininun oxygen voltane fracticn required for ignition, the minimtzn encygen voltane fraction required to support cant >usticn, and the burn time. The hydrogen parameters are case dependent and, except for the burn fraction for the Fenwal tests, are taken directly fran the test reIx>rt. The oxygen parameters are standard values that have been used in ice condenser containment hydrogen transient analyses.
For the Fenwal tests, the burn fraction is calculated frcm the test data by taking the difference between the pre-burn and post-burn hydrogen concentrations. The pre-burn concentraticn can be detennined fran the partial pressure of hydrogen initially added to the test vessel or fran the pre-burn gas analysis. The post-burn concentraticn can be detennined fran the past-burn gas analysis or fran an evaluation of oxygen depletion. The oxygen depletion is the difference between pre-burn ard post-burn oxygen ,
concentrations. 'Ibe Ire-burn oxygen concentration can be determined fran the initial partial pressure of air in the test vessel or fran the pre-burn gas analysis. 'Ihe post-burn oxygen concentration is available crily fran
\
post-burn gas analysic. If the reported data are consistent, all methods of calculat$ng the burn fraction should give the same result.
Uncertainties of Sc,e Data In many of the Ebnwal test gas analyses, both pre-burn and post-burn, the total voltrae fractions of gas constituents did not add up to 1.0 In addition, in cases fran all phases of the tests, the pre-burn gas analysis indicated significantly different gas concentrations than expected based on the pertial pressure of gas added to the vessel.
A review of the LINL test data irdicated that the data reported in Table 2 of Reference C-3 cbes not F.wa; s illustrate the actual burntng of hydrogen as reflected in the pressure traces. A good illustration is represented in IIRL test rarnber 39.1he recorded burn time for the test is five seconds. A better representatim of the burn time, as obtained fran ;
page A6 of Reference C-3, was estimated to be 3.75 seconds. Also, Erne pressure plots provided cb not give a clear indicaticn of the nature of the
- 100 -
- q. ~6s s '% p N:
s
-[\ , N ,,
burn. Sczne plots are of a jagged nature as opposa$ to the generally smcoth x O
b and romded plots. 'Ihis might indicate localized burning instead of one '
\-
large burn, as rnodeled by CIASIX.
N ..
Additionally, there is sme mcertainty in the 11NL data reported for hydrogen burn fracticn. After the bcrn has apparently ended, a rmll . fan- %
in operated to reix the gases before a sample is taken. 'Ihis rdtixing of ' ' '
the gas m can result in additional burning tecause of the exposure of more s.
hydrogen to the still hot glow plug. A small , ' ?esure increase was noted cn several tests when the fan was activated. Also, cn one of the an:2nalous tests (Test #34), a small gessure rise of cne psi was noted when the circulaticn fan was activated. The gas analysis fran this test irdicated 30 percent of the original hydrogen was consumed although no burn was indicate 3.
x t
Dry Tests
\
'Ihere are three dry cases included in Phase I of the Fenwal testing O program. All three cases were selected for inclusicn in the CIASIX veri 2 - \
b fication analyses. One of these was a 12 percent by voltrne (v/o) hydrogen test, and the other two were 8 v/o hydrogen tests. The CIASIX initiai '
conditions and burn parameters for these cases are suninarized in Table C-3.
For the 12 v/o hydrogen case, the hydrogen burn fraction was asstraa3 to be 1.0 based cn the recorded pst-burn gas analysis data and the generally accepted very large bo3y of existirg test results which indicate ecmplete or nearly acnplete cx2nbustion for this hydrogen concentration in dry air.
The burn fractions for the two 8 v/o hydrogen cases were calculated by three methcris mentioned above. 'Ihe three methods are: 1) assume the pre-burn hydrogen concentraticm indicated by the partial pressure and the post-burn hydrogen concentration as shown by the gas analysis are correct;
- 2) assure the gas analysis is correct for both the pre and post-burn hydrogen concentrations; and 3) assume gre-burn hyJ.rogen concentration fran the partial pressure is correct and calculate the post burn hydrogen ecncentration by determining the total snount of oxygen used during the burn, ard then finding the anount of hydrogen required to cxrnpletely burn that arnount. '1he pre-burn oxygen concentraticn was obtained frcm the
- 101 -
y _ ,
5 7,
N1~ s 4,.. W .'
%y5 .
s a .
pa
, m, ;N 't,s 'rtial Npressure and the Inst burn oxygen <nneentration was obtained' fran
.t v{* ..3 ' \, tru,, gas The burn fractions calculated by each of these methods W, analysis. ,
t ;werCased in the CIASlX analyses and cunpared' to the test results.
1-s
, s
'J'+, t, -
,'.,. C U,Three dry cases were selected fran the Livermore tests for inclusion in CIASIX verification analyses. %ese mses have initial hydrogen
? concentrations rangirg fran 8.0 v/o to 15.1 v/o. The CIASIX initial con-ditions and burn pirameters for these cases are summarized in Table C-4.
The results of a conpariscn of CIASIX predicted values to the Fenwal and Livernere measured values for dry cases ,Nare suntnarized in Tables C-5 and C-6, respectively. The CIASIX calculatal tenperatures are significantly higher than the test results. 'Ihis variation is attributed to the slow s response time of the thermocouples used in the tests, ard for this reason,
.no temperature cunparisons are made.
N ~
In Case l',s the Fenwel 12 v/o hydrogen case, the CLASIX calculated peak s .3 . .,
pressure; is, psin, 'and the pressure rise durity the burn is psi *a,c
~
1 cdnparedhoi53.0 psb f$r the test. In Case 2, a Fenwal 8 v/o hydrog'en case, s i x , -
psi for eadi respective ,a c i
Q' , w
\
. i the, calculated pressufe ' rise was
+
,,, 1 .- -* -
- s .
psi and y burir fraction of and . '1he calculated pressure rise for the *a.c
- x N, , . , , i . . .
. lower than the measured test result. Canparing
(- smailerIc, urn fracticn is s y .
, this, test'to other similar tests, a burn fraction of is considered *g,c
,3 Eto 4 too 1cw underestimating the true arrount of h'ydrogen burned. The calculated pressure rise for the larger burn fraction is higher than the rheasured test result. For Case 3, the final Fenwal case of this series, the o -
s -
calculated pressure rise ranged fran to psi. All of the estimates ,a,c
'cf athe 'caupleteness of this burn resulted in a higher calculated pressure rist than the 3.0 psi recorded. fcr the test. Ebr all three Livermore test casesi. the calculatal peak pressure arvi pressure rise were higher than correspandincjfvalt;es recorded in the test.
i
in additi'nc to specific test conparisons, Figure 5 of the erratun to s
Refdrence C-3 shows a conparison between the Livernere dry cases and an adiabatic pressure rise calculated usirg the CECS code. The calculations by hG the code were made by using conditions which represent the dry 1LNL tests.
- 102 -
A similar adiabatic gressure rise was calculated for a few of the dry tests using the CIASIX ccmputer code. In all cases, CI.ASIX predicted higher x -) re'shlts than b:ch the II.NL tests and the CEs Irogram, vee Figure C-3. 'Ihe higher pressure rise calculated by CLASIX is attributed to the specific I
heat asstriptions in the CIASIX program. '1he Inint representing "Special CLASIX" will be explained later.
1 Steam Tests l
l
'Ihe Fenwal steam tests consist of 12 v/o, 10 v/o, and 8 v/o initial hydrogen concentrations, and ranged fran 9.5 to 27.0 percent steam. In Phase I of the Fenwal report, six 12 v/o, two 10 v/o, and three 8 v/o hydrogen tests are reported. Five of these hydrogen tests were chosen for CLASIX verfication analyses. Initial conditions and burn parameters for these cases are str:Tnarized in Table C-7. A burn fraction of 1.0 was assumed for the 12 v/o and 10 v/o hydrogen cases since no hydroacn was recorded in the postburn gas analysis and generally accepted resOlts frcrn other tests indicate amplete conbustion at these concentrations. Ebr the p 8 v/o hydrogen cases, as in the Fenwal 8 v/o hydgen dry cases, three methods were used to calculate the burn fraction.
Livermore test cases include envircrrnental vessel conditions of approximately 30 and 40 percent steam by voltrne. '1 hey varied in initial conditions ard ranged fran 7.1 to 14.9 percent initial hydrogen. Ebur of these cases were selected for CLASIX verification analyses. Initial conditiors an3 burn parameters for these cases are strmarized in Table C-8.
All case dependent properties were cbtained frcm Table 2 of Reference C-3.
Canparisons of CLASIX calculated results to test measured results for the Ebnwal 12 v/o and 10 v/o hydrogen test cases are similar. 'Ihe CLASIX calculated pressure rises were til considerably higher than the acutal test results. 'Ihe results of these three tests are surmarized in Table C-9. One example of the CLASIX conservatism is illustrated in Case 7 a 12 v/o hydrogen test. '1he ;ressure rise calculated by CLASIX is psi, where *a'c
~
f a'c the test pressure rise was reported to be 72 0 psi. This represents a{ _
percent conservatism factor associated vith the CLASIX results.
l
- 103 -
Omparison of QASIX results to test results for the Fenwal 8 v/o G hydroge tests are more ccmplex. With the initial input, CIASIX results were lower than the measured test results. Se two cases in this atraparison are statmarized in Table D9. Se long Mrn times in toth of these cases indicate that the deflagraticn was not representab2c by a single uniform burn as nodeled by CASIX. A review of the test pressure trace, Figure C-4, iddicates that Case 10, the first of the 8 v/o hydrogen cases represented, actually has three cistinct regico which can to identified with three sets of burn parameters. Since the :2ASIX model assimed one distinct burn, results of this cnse were not valid and the case wts rerrodeled. 'Ihe results of the CIASIX calet lations with the revised nodel are presented in Pigure - -
,a,c C-4. We pressure in the vessel increased psi during the first burn of
- a.c seconds. The second porticn of the buzn was a sicw contintous burn -
. p *a,c seconds, and resulted in a Iressure rise of j Which continued for ,
psi. The pressure then began a scooth clinb to psia after which it *a.c tapered off. During the burns, 80 percent of the hydrogen was constrned which agrees with the test report. This representation of the burn agrees very closely with the actual Iressure trace. Detailed infonation was rot
' available fcr Case 11, the other Fenwal 8 v/o hydrogen case considered.
N Itowever, since this case is sunilar in type to Case 10 above, it is likely that it cx>nsists of a non-uniforn burn over the relatively long burn time of nine seconds. As shcun for Case 10, a ron tniform turn sould rot produce results conparable to the uniforn burn modeled ir CLAStX.
The results frcm cxznparisons of CASIX calculations to measured results frcm tk Livernere steam cares were generally conservative and similar to the Irevious cxznparisons w;th test results. 'Ihe results of the
! four representative cases are simnarized in Table C-10., Cas,es 12 and 13 *a c percent. Case show CASIX to have a highar Iressure ri.s,e by as nuch as - '
- a,c 14 has a calculated pressure rise of psi ccmpared to the measured value i of 9.5 psi. As mentioned Ireviously$ titis case had a recorded burn time different than that indicated by tM pressure plot. When the new burn time, a,c of 3.75 seconds was input to CASIX, the pressure rise increased to '
Se nore pai. This result is stmmar!3ed with Case 14 cn Table C-10 accurate representation of the actual burn time results in a conservatism 4
- 1 04 -
l l
acre consistent with the previous results. Case 15 resulted in a calculated (Q, peak Iressure lower than the measured result. Ebr Ose 15, the pressure U plots provided cb not give a clear indicaticn of the nature of the burn.
mis case has a long burn time and high steam concentration, and is likely to consist of a ncn uniform burn similar to Case 10, an 8 v/o hydrogen Fenwal steam mse.
Sensitivity Study
'Ib Irovide confidence in the all parameters used in the CLASIX model ard to determine the relative importance of various CLASIX parameters, a sensitivity study ms conducLe1. 'Ihe test mse used for this study was Case 7, Fenwall test 6. Various sets of parameters were charg M to determine their overall impact cn the calculated pressure and temperature.
The followire parameters were investigated:
a) Specific haat of gas ;onstituents (Cp and Cy )
b) I: eat transfer rate G i) nr:difying coefficient ii) removirg wall (adiabatic burn) c) Dnissivity d) Beam length e) Thermal conductivity f) Heat capacity g) Exit film coefficient h) Time step Of the above parameters, cnly the adiabatic barn case and the specific heat parameters had significant effect. The adiabatic burn. wa.s achieved ,
by reno /i>J the wall frczn the CLASIX input and resulted in a psi increase *a,c in the pressure rise. The specific heat values that have 'been used in the CLASlX program are constant rocan temperature values. In reality, specific heat values are temperature dependent quantities. 'Ib determine the significance of the temperature dependence of the constituent gas specific heats, these quantities were evaluated at a tenperature midway between the
[ maxaum and minimtun '.anperatures calculated by CLASIX in :Lse 7. Ose 7 Q]./
- 105 -
, - , ,- - ,. ,- - ,-r , , . - . -- -. e, - - -w , - - . - -
was then Ierun with the new specific heat values input to CLASIX. This process was repeated fcr several other tmperatures over the rarty of tarnperatures cniculated in case 7. De results of these analyses, stenar-ized in Table C-11, irdicate the temperature dependence of the constituent gas specific buts has a significant effect on the QASIX calculated gressure rise.
Since the specific heat ' mas determined to have an important effect cn the pressure rise, a special single voltne versicn of CIASIX was created which incitxles a calculation of the specific heats at each time step. Chse 7 was rertn with this special versicn. Results of this run akw a lower value for the pressure rise than calculated earlier by CLASD;, but still higher than the measured test result. Table C-12 stmaarizes a few addi~
tional cases that have been Iresented earlier in this appendix and have been rertn with the special versicn of CLASIX. The results of these cases .
are similar to those for Case 7. %e point cn Figure C-3, labeled "Specit.1 CLASIX", was obtained by usirg this special versicn of CIASIX along with rexning the wall perameters. 'Ihis point shows a c2nparison between CLASIX
\ and the special versim or CLASIX, and also represents the conservatism
' associated with each cne.
Ferwal Spray Tests A series of tests, one transient and three static, were run to de. 'rmine the effect of sprays uptn ignitor perfor:rance. 0:n of the static tests, test #2-3-1 of Reference C-1, was chzen for the CULSIX verification anclysis.
i l CLASIX input parameters for this case are stmnarized in Table C-13.
The burn fraction was calculated by usirg the pre-burn hydrogen concen-l tration indicated by the partial pressure and the Inst-burn hydrogen concentraticn as slown by the gas analysis. The spray water tenperature and flow rate were specified in Reference C-1. 'Ihe remaining spray parameters were based cn values used in ice condenser contairment analyses.
l t
I O t
t
- 106 -
l
Ptr this test, the CIACIX calculatal peak pressure is hia,and *a,c the pressure rise during the barn is psi. We test measured pressure *a,c A
U
~
rise was reported to be 50.0 psi. Se Ci.A5IX result is higher than the test measured result indicating that the QASIX nodel for this spray case is omicuhting a conservative pressure rise due to the hydrogen burn.
Ferwal Trareient Tests A series of tests were conducted in Phase II of the Fenwal test study to determine the characteristics of the burning which occurs when hydrogen is intrcduced into a test vessel at a constant rate and wher. both hydrogen ard steem are simultaneously intrcducal irco the test vessel at a constant rate. One of the transient tests was simt$ lated using CLASIX. We pressure plct for this test was cibtained fran Reference C-1 where the test is numbered 2-2-2 ard is included here in Figure C-5. CLASIX input parameters for this case are su"marized in Table C-14.
The CLASIX simulaticn of this case was dividM into a series of ten intervals. We burn parameters were adjusted in each timerinterval until an O- approximate fit was achieved. The CLASIX pressu*e history is plotted in Figure C-5. W e CAS1X analysis was stcpped at 595 seconds (9.917 minutesJ because ro burns are apparent af.ter ,
that time. The first of eight bur.ns in the CLASIX simulation cccurs at seconds witF a pressure rise of[ , psi. *a,c A sicw burn consisting of 40 per. cent. o.f the renainirn hydrogen follcus. We *a,c
- pressure then drops rapidly to psi dere it s1culy rises due to the prassure increase resulting f h,'the inccru_rg hydrogen and steam. We.,
,a,c second major burn occurs at seconds resulting in a pressure rise of psi, aM is follcwed by arEther slos burn of, 40* percent of the remain'in5
- a,c hydrogan. '1he maxirun total Iressure of psia occurred at th. e .fi,fth
~
peak. This burn also had the highest pressure' rise witn a value of psi. *a,c percent of the ,a,c After the last burn, a sicw burn occurred resulting in available hydrogen beirg burned ard was follcwed by a ra'pid pressure drop.
Fellowing this drop, ro more burns occur and the slight pressure increase is due to the continued additicn of hydrogen ard steam.
O)
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- 107 -
'Ihe CASIX simulation of Caee 2-2-2 is in close agreement with the J test measured results. The pressure increases due to eadi burn are very v
similar. 'Ibe QASIX pressure curve is shifted slightly tpaard resulting in higher maximtm pressures. The fifth peak, fcr example, actually resulted in a traximtra measured Iressure of 26.7 psia as cmpared to the CASIX calcu-1atal value of psia. The gas sample take after the transient was *a,c
~
terminated indicated a final hydrogen concentration of 23.9 percent. Alding the mass of hydroget injected durirg the 305 s,econds that CIASLX did rot ,
model, yields a final hydrogen concentration of percent in the CEISIX *a,c
~
analysis. Since the burn parameters were not defined for each burn in the transie;.t, a direct cx2nparison cannot be made between the measured test results and the CIASIX calculated results. lbwever, the CIASIX calculated pressure results indicate that -CASIX has the ability to model a transient similar to Case 2-2-2 above.
Conclusion For all tests which were representable by a single uniform hydrogen burn, CIASIX predicted conservative values for the peak pressure. This l[mV} provides a high degree of confidence in the CASIX burn r:odel and the CIASIX models for heat transfer to passive heat sinks and sprays. A high degree of conservatism has been shown to be the re%1t of using constant roon tenperature values for constituent gas specific heats in tin CIASIX analytical nodel.
References C-1 Appendix N of the Tennessee Valley Authority, Sequoyah Nuclear Pla7t Core Degradation Program, Volune 2, " Report on the Safety Evaluation of the Interim Distributed Ignition System", Decer.foer 15, 1980 (tmC Docket No. 50-327) .
C-2 Tennessee Valley Authority, "Research Program cn Hydrogen 02nbustion ard Control Quarterly Progress Report", March 16, 1981 (tGC Docket No. 50-327) .
(3 U
- 108 -
C-3 Iowry, Willian, " Preliminary Results of 'Ihermal Igniter Experiments ,
in H -Air-Steam Envircrrnents", frcm "Proceecings of the W:>rkshop on 2
the Impact of HyCuvysi cm Water Reacter Safety", edited by Marshall Berman, Sandia Laboratories, August 1981 (NUREXi/CR-2017).
9 4
9 d
t
- 109 -
. . - . . . - - . . . - . - . . . . . ~ . - . . , . - _ . . . - . - . . - - - - - . - - . - . - . . - . . - . - - - . , . . - . - . . . ,
TABIE C-1 Pl!NWRL 'IEST OCMPARISCN CIASIX INEUT PASSIVE liFAT SINK DhTA Wall surface area (ft2 ) 126.64 Initial wall temperature (F)
- Bnissivity 0.2 Radiant heat transfer beam length (ft) 4 23 Layer 1 - Stainless Steel Thickness (ft) 0.0104 Number of nodes 6
'Ihermal ocn$uctivity (BIU/hr ft F) 9.87 Heat capacity (BIU/ft F) 59.2 Exit heat transfer coefficient (BIU/hr ft F) 10 Layer 2 - Carbcn Steel O 'Ihickness (ft) 31 0.0521 Number of nodes
'Ibermal conductivity (BIU/hr ft F) 27.3 lieat capacity (BIU/ft3 F) 59.2 2
Exit heat transfer coefficient (BIU/hr ft F) 10 Layer 3 - Insulation
'Ihickr:ess (ft) 0.25 Y
Nunber of nodes 3
'Ibermal ocnductivity (BIU/hr ft F) 0.025 Heat capacity (BIU/ft3 F) 2.0 Exit heat transfer coefficient (BIU/hr ft F) 0.0
- Case dependent parameter equal to the initial gas tenperature.
O
,- 110 -
TABLE C-2 IJVEINORE 'IEST 3:MPARISCE CLASIX 22iPL7f PASSIVE HEAT SI1E IATA W.11 curface area (ft2 ) 26.2 Initial wall tsuperature (F)
Bnissivity 0.7 Radiant heat transfer beam lergdi (ft) 1.11 Layer 1 - Carbon Steel
'Ihiekness (ft) 0.015625 Number of nodes 12
'Ihermal o:xxluctivity (BIU/hr ft F) 27.3 Heat capacity (BIU/ft3 F) 59.2 2
Exit heat transfer coefficient (BIU/hr ft F) 10.0 Layer 2 - Insulation
'ntickness (ft) O.291667 Number of nodes 3 Thermal caxiuctivity (BIU/hr ft F) 0.025 Heat capacity (BIU/ft F) 2.0 Exit heat transfer coefficient (BIU/hr ft F) 0.0 i
t
- Case dependent parametex equal to the initial gas tenperature.
l l
l lO f
, . - 111 -
TABLE C-3 FRGAL TEErr COMPARISCN CLASIX INP(TT a
m r w rs
, Case 1 Case 2 Case _3 Initial Conditions, Actual test raznber 1 1 3 Temperature ( F) 180 100 180
- 1btal Iressure (psia) 18.24 17.45 18.86 O2 Partial Pressure (psi) 3.357 3.3 57 3.628 N2 Partial Iressure (psi) 12.69 12.69 13 713 H2 partial pressure (psi) 2.191 1.3% 1.510 H2 O partial Iressure (psi) 0.0 0.0 0.0 J
'} Burn Paraneters Mogen V/F for ignition 0.12 0.08 0.08 Hydroge fracticn burned
- When multiple burn fractions are given, the fractions listed are -
estiraates of the actual burn fraction.
l
- 112 -
TABIE C-4 O IIE 'IEST COMPARISKE CIASIX INPUT IRY 'IESTS 1
Case 4 Case 5 Case 6 Initial Conditions Acttml test ruriber 17 21 24 Temperature ( F) 81 54 82 Total pressure (psia) 15.9 16.5 17.2 ;
0 Partial pressure (psi) 2.957 2.904 2.958 2
N Partial gessure (psi) 11.53 11.75 11.51 2
H2 Partial pressure (psi) 1.272 1.716 2.597 H2 O partial g essure (psi) 0.0 0.0 0.0
, O Burn Parameters i
Hydrogen V/F for ignition 0.08 0.104 0.151 Hydrogen fraction burned 0.55 1.0 1.0 Minimtra oxygen V/F for ignition 0.05 0.05 0.05 i .-
l Minimum oxygen V/F to support ccr:bustion 0.0 0.0 0.0 i
I wrn time (seconds) 5.0 0.5 0.3 I
f l
- 113 -
l 1
.- . - - - . - , - , - , - - - . - - ~ - , - . - . . . . . - . , , , . - , - - , . ~ , ~ , . - . - - - - . - - . - . - - - . . , - - , - - - - - - - - - . - - - . - . .
p TAB 2 C-5 O
- wrman CLASIX RESULTS SMERY - IRY 'IESTS i
t Case 1 Case 2* Case 3*
Actual test ruznber 1 2 3 C2.ASIX Results Peak pressure (psia) a,c Pressure rise (psi)
FD;W74 pressure rise (psi) 53.0 33.0 3.0 i
l l
- M.11tiple results are due to the multiple burn fracticn estimates and correspond to the hydrogen fraction burned in Table C-3. ;
i r
I e
i
- 114 -
4
--,- , , . ,-.-,y----,.-., ,-,,.,-,...-,_-,y.m,,....,,..___,.,....,_....,,..,.-.--._,.r.,-..e..~
. ..m. ,, , - , . , . , , ..-en.,-~,
I l
i l
TABIE C-6 l
1 ITJL '1 TSP CCNPARISON l i
l CLASIX IESULTS EMBRY - IRY 'IEStrS ,
Case 4 Case 5 Case 6 Actual test number 17 21 24 CIASIX 1%sults Peak pressure (psia) a,c Pressure rise (psi) .
IJ.NL pressure rise (psi) 3.5 45.0 87.0
/
1 1
l.
O ..
e
- 115 -
'mBIE C-7 (N
- - a m m s. Cr - x - r SIEAM M S Case 7 Case 8 _Cas=J Case 10 Case 11 Initial Conditions Actual test ranber 6 13 10 5 14
'INrnperature ( F) 176 350 146 138 350
'1btal I ressure (psia) 26.64 26.58 21.11 20.75 26.44 0 Partial pressure (psi) 2 3.592 4.590 3.402 3.419 4.563 N 2 Partial Fessure (psi) 13.578 17.349 12.858 12.926 17.246 H2 al pressure (psi) 3.199 3.193 2.108 1.661 2.116 H2 O partial pressure (psi) 6.27 1.450 2.746 2.740 2.510 O Burn Parameters Hydrogen V/F for ignition 0.12 0.12 0.10 0.08 0.0e Hy:irogen fracticn burr.ed* 1.0 1.0 1.0 a,c
- When r:ultiple burn fractions are given, the fractions listed are esti: nates of the actual burn fracticn. Only the highest and icwest values are included in this table.
l t
l l
l I - 116 -
i
TABIE C-8 ,
O IIRL 'IEST CINPARISCN CIASIX INPUT l
SIEAM T E f3 Case 12 Case 13 Ce u 14 Case 15 Initial Conditions Actual test raznber 29 35 39 37 Ternperature ( F) 190 181 198 180 Total pressure (psia) 26.5 29.7 30.2 25.7 02Partial pressure (psi) 2.957 3.763 3.098 3.184 N Partial p essure (psi) 11.18 14.22 11.71 12.04 2
H2 partial pressure (psi) 3.948 2.257 3.02 2.5%
H2 O partial pressure (psi) 8.400 9.445 12.35 7.864 Burn Parameters rfydrogen V/F for ignition 0 148 0.076 0.10 0.101 i
Hydrogen fracti'n burned 1.0 0.46 0.57 0.%
Minimin oxygen \/F for ignition 0.5 0.5 0.5 0.5 ,
Mininrxi oxygen V/F to support asrbusion 0.0 0.0 0.0 0.0 Burn time (seccnds) 1.0 4.0 5.0/3.75* 4.5 1
! *Two different burn times were chosen for this case to determine its l importance.
l
- 117 -
~..--.__--..._,.._,_.....--..__ .. _-_ __._-._ .-.~._ _
TABIE C-9 FDHW 1EFf CEPARIS21 CLASIX RESULW SUPMME - STEAM 1ESTS Case 7 Case 8 Case 9 Case 10* Case 11*
Actual test ntsnber 6 13 10 5 14 CIASIX Results I
~
Peak pressure (psia) a,c Pressure rise (psi)
FINh71 pressure rise (psi) 72.0 60.0 53.7 22.6 30.0 0
- Maltiple results are due to t.he multiple burn fracticn estimates and correspond to the hydrogen fraction burned in Table C-7.
+See text for an explanaticn of results.
4 f
6
- 118 -
- - . . . . . . . _ . . . - . _ - . _ , . ~ . - - - - . . ~ _ . . - - .
TABLE C-lO IDL 'IEETT CIMPARISCE CLASIX PESUL'IS SLPMME - SIEAM TESTS Case 12 Case 13 Case 14* Case 15 Mimi test ntsnber. 29 35 39 37 (IASIX Results Peak Fessure (psia) a.c Pressure rise (psi) . .
LINL pressure rise (psi) 50.0 2.5 9.5 22.0
- The results cn the right side of Cas 14 indicate the faster burn time of 3.75 seconds.
+See text for an explanation of results.
I l
h
- 119 -
'mBIE C-ll SENSITIVITY SIUDY EH ECT & SPECIFIC MATS ;
TfMPERATURE E WHIOi Cp ard CV CIASIX CPJfUIATED M N TED PRESSURE RISE (psi) a,c i
1
- The base case is Case 7, Penwal test #6. Initial conditions and burn l parametera are given in Table C-7. The reported pressure rise for this test is 72.0 psi.
l
- 120 -
- - - _ _ . , . _ . _ _ _ _ . . . . _ _ - - . . _ _ . . . . _ . . , _ ~ _ . , _ _ _ _ _ _ _ , . _ _ _ _ . _ . . _ . - . . . . . . _ . . . . - _ . . , _ . _ _ . . . _ _ , . . . . _ - . . _ . _ .
TABLE C-12
.... SENSITIVITY SIU7f EFFTCr T SPECIFIC HEATS - SPECIAL CLASIX*
Case 7 Case 8 Case 5+
Actual test nunter FDARL 6 FDAAL 13 IDE 21 CIASIX Results Special CIASIX peak pressure (psi) a,C CLASIX pressure rise (psi)
Special CLASIX pressure rise (psi) -
Actual test pressure rise (psi) 72.0 60.0 45.0 n *Special CIASIX is a version that calctilates specific heats of each gas
( constitutent at each time step.
+An adiabatic CULSIX result of this case is plotted cn Figure C-3 for ccrnpariscn.
L
/
1
- 121 -
4
- , . . . , - ..,,,,,,w.,,,,..,-g..,,,,.,a-,,nn-,,-a n,. ,e,., w,, ,,,.,4.,.-.,,-,.w..m,,,,. ,,-,,---n,_g,,,.- _ , ,,. , .,- - .. ,,_ ,.,..._ , , ,._,, . . , . , .
i TABIE c-13 FDARL 'IEST COMPARISON CIASIX INPUT SPRAY '! ESP 4
Case 16 Initial Conditions Actual test rarnber 2-3-1 1 Temperature (F) 82.0 Total g essure (psia) 16.31 02Partial pressure (psi) 3.07' N2 partial pressure (psi) 11.61 H2 Partial pressure (psi) 1.63 H2 O partial pressure (psi) 0.0 Burn Parameters Hydrogen V/F for ignition 0.10 Hydrogen fractia. burned 0.92 Minin.am xygen V/F fbr ignition 0.05 Mininun oxygen V/F to support cabusion 0.0 Burn time (seconds) 0.65 Spray Parameters Drop diameter (p) 700.0 Drop fall time (sec) 1.06 Turnperature (F) 50.0 Flow rate (gpn) 1.9 Drop film ocefficient (Btu /hr ft2 F) 20.0 O
' - 122 -
. _ - . _ _ _ _ . _ _ _ _ _ _ - . _ . . _ _ _ - _ _ - ~ - _ _ . . - _ _ - _ . . . - . - _ , , . . . _ , _ . . . . _ _ . _ . _ . - . _ _ - . _ _ _ - _ . . , _
'mBIE C-14 FENWL TEST CIMPARI!KN CIASIX INFA' TRANSIENT 'IEST Initial M itions Case 17 Actual test ranber, 2-2-2 Temperature (F) 160.0
'Ibtal Fessure (psia) 14.7 02Partial pressure (psi) 3.087 N2 partial g essure (psi) 11.613 H2 Partial pressure (psi) 0.0 H2 O partial pressure (psi) 0.0 Additions Hydrogen addition rate (1bn/sec) 3.487 x 10 Hydrogen tenperature (F) 68.0 i Steam addition rate (1bn/sec) 0.0005 Steam energy (Btu /lbn) 1176.0 I
I l
l i
O l - D3 -
1 i
__. ___= .______--_____. __
O O O SPRAY N0ZZLE HA1ER PUMP PUESSURE IEXTRACTED FROM HEFERCNCE C-2* MERCURY FIGURE 1,.P. 14) MANOMETER RECORDING OSCILLOGRAPH INDICATING
' , AMPERATURE
~ CONTROLLER 4 V CONTROLLER GLOW PLUG 00X f CLOW PLUG BOX NALL TEMP PFC- WALL THERMOCOUPLE ER RECORDER
! \ CLOW PLUG BOX ~ MERCURY
, VESSEL HALL ^"
THERMOCOUPLE O CLOW PLUG -
to
- ( b AIR FLOW p ; ; ,
VESSEL HALL f
- FAN gg e
TEMP REC _ _ _
U i GLOW PLUG IVACUUM GLON PLUG s' CONTROL SN VESSEL TEMP I
' THERMOCCUPLE SAMPLE CULO CHECK VALVE SAMPLC STEAM
^$ Hl IN gCOOLING/CONOENSINC SUPPLY ~*~ ' FAN CHAMBER HYDROGEN e
SUPPLY VESSEL DRAIN FLOWNETER
//////. -l-FENHAL H 2 IGNITER TEST SCHEMATIC
- - FIGURE C-1 1,
}
. , _ ~ .__ . .-_ -- . . _ .. .-. - - . ~ _
l l
o o o l
i 1
) GLON PLUG CONDUCTOR AIR SUPPLY GAS FOR VENT H, FILL BOTTLE t.133 FT.3 1
{
l CIRCULATING FAN n COMPRESSED AIR SUPPLY i
"1 i I i t-CIRCUL AT ING V FAN I
[ q
- - ~)* =
X c , )#
l s __
l H
I f STEAM i GENERATOR
) : 10.6 FT .3 j 4
PRESSURE VESSEL l o
! STEAM
'! BYPASS X - TO VACUUM PUMP CONDENSATE DRAIN IEXTRACTED FROM REFERENCE j C-3, FIGURE 1, P. 31 i
l l LLNL'Hg IGNITER TEST SCHEMATIC I FIGURE C-2 i
4 h
i i
8,C PRESSURE RISE AS A CUNCTION OF H2 CONCENTRATION 6
FIGURE C-3
- 126 -
l 4
a,c l
O l
\
4 CASE 10 COMPARISCN FIGURE C-4
-!??-
- , ~ _ _ _ . . . _ _ _ _ _ _ . . . _ - . . _ . _ _ , _ _ _ . , _ _ _ _ _ . . . . _ _ _ _ _ _ . _ _ . _ . _ _ _ _ _ _ . . _ - _ - _ _ _ _ _ _ _ ._ _ _ .
O 8,C 1
O CASE 2-2-2 TRANSIENT COMPARISON FIGURE C-5 l
~
O
- 128 -
APPENDIX D Q Evaluaticn of Separate Sgray Time Dcznain and Heat Transfer Asstmpticns V
he purpose of this appendix is to evaluate the effect of the spray operating ira a tima dcmain that is different frcm that in which all other calculations operate.
In conventional analyses, a small mass of spray enters the ecmpartment each time step of the finite difference integraticn. As the transient progresses, the number of spray masses increases and each mass reacts with the canpartment atnesphere until it ecmpletes its fall or until it ccm-pletely vapo;izes. In CLASIX, the ccr.partment ambient conditions are frozen until the small arount of spray ccmpletes its fall. As far as the spray is ccncerned, it sees a steady state anbient condition. 'Ib evaluate the differences of these two asstrapticns, a special subroutine for a single voltne r:cdel in CLASIX was gepared and the results using the tw sub-routines were ccnpared.
Since cnly the heat recoved by the spray is being cxrpared, the CLASlX x model was chosen to be relatively simple. The model contains one ccrpart-ment with a single spray systen. Initial conditions for this CUGIX rodel are given in Table D-1. The time step was kept at a constant value to allow direct cxraparisons. We spray was turned cn innediately and allowed to rtn the entire transient. The heat additicn to the systen was input as a ramp function of time increasing linearly tntil a peak value was reached. 'Ihe l heat additicn rate then decreased linearly until a zero value was again achieved. No further heat was added after this. Ntnerical values for the heat additicn are given in Table D-2.
r 1
he finite difference method divides the single canpartment spray into one thousand elenr.ts ard calculates the heat rataved by the spray at an instant in time for each elsnent. Ebr the next time step, the elements move cbwn one place with the last elenent discarded ard the first element .
1 set at the spray's initial conditions. Drep terperature, drop diameter, ard mass are recorded for each elenent.
O)
\v
- 129 -
'Ihe rate of heat renoved frcm an element can be calculated by two p -thods.
NM b = hA AT = hA(TeD-T I ID-1) mC AT =mC (Tf-TD Q =
p g p gg (>2 )
h = drop film ocefficient ,
A = total surface area of the drops in an element m = total mass of the drops in an elenent Cp = specific heat of the drops At = differential time TC = ctrpret tenperature Tg = drop tenperature Tg = updated drop tanperature after the differentud time The drop film coefficient (h), the specific heat of the drops (C P),
, and +he time step ( At) are all constants dose values are given in Table D-3. The conpartnent tenperature C(T ) is input directly to the subroutine frcun tre CIASIX program.
The surface area and mass of the drops in each element can be express-ed as functions of the drop dianeter.
^ (~
A = n4 n (-)
o
=(D) o A"Ao(D} O 3 3 3 m = npf n(h ," = (h) m=m g (h) o (D-4 )
o o l
i D Ao Mn ) 6 m
Do 3" D i
4 np 5n3
< O
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,-~....,n, - . , , , ,.,,,,,,,,,,,..,~,,...-.,,,-...-,.,..nna,., . , - . . ~~-,-,~-.,,,-,.,...,,n--,-.- ~ , , , , . , - - - - , - - < , , .
D = drop diameter n = the TR2ftler of drops in each eleraent ,
P = drop density which is a constant
( ) ,= M tial M tions Substituting (D-3) and (D-4) into (D-1) and (D-2) and setting (D-1) equal to (D-2) enables the updated drop tenperature to be calculated.
2 3 T hA( ) (TC-TD C(g_T
" "o p At I Tf= 6CP 9 ( ) (T C-TD ) + TD I I At this point a determination of Wether or not saturation conditions within the drop are met must be performed. 'Ihe conpartment pressure, which is input fran the main CIASIX program to the subroutine, is used to find a corresponding saturaticn taprature (Tg) fran the steam tables. If the updated drop temperature is lower than the saturation tamperature, satura-(s ticn conditions are not present and the heat rewed fran each element is calculated.
Q=mCp(Tg-TI D
)
When the updated drop tenperature becones higher than the saturation tenperature (Tg ), saturation conditions occur and an excess of heat (og )
far each elenent is calculated.
Og = nCp(Tf-TET) ID-7)
The mass of spray vaporized ( Am) is then calculated.
(I>-8 )
Am = Og/hfg h fg = latent heat of vaporization of the spray 4 This enables tha heat removed by each elenent to be found.
U ,
- 131 -
fg Q = - Am hf (D--9 )
%/
hf = specific enthalpy of the liquid spray the mass of each elernent and the drop diameter nust then be updated.
= m - A m (D-10) 3 ,
D' = Do ng (D-ll)
The values of heat recoved by each individual elernent are then strrned to give the total heat removed by the spray (Og) for erch time step.
1000 Og= [01 (>12 )
i O The rount of spray mass vaporized during each ti.Te step is calcu-lated similarly.
1000 mg= [ mg (D-13 )
i ine total heat removed (Og) and the total mass vaporized ( g) for euch time step must then be converted into heat and vaporization rates which are returned by the subroutine to the CLASIX program, b=Og/ A t (D-14)
[n = Q At (D-15)
The tanperature and pressure of the ccrapartments are then calculated by C ASIX.
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me integrata$ heat renxwed by the spray is calculated directly frcm a
' heat balance at any particular instant in time. Se following method of calculating the integrated spray heat removal can apply when either the spray subroutine cr the finite difference method subroutine is used with CIASIX.
= Ogg (I)-16 )
[b gdT + [bg dT - rO ogg = initial heat of the systen
[OdT=
A integrated heat added to the system Q7 = total '.wat of the system S
dT = integrated heat remsved by the spray 033, which is the initial heat of the system, is found at the start cf the V transient. Thefb dT A term is the integrata$ heat added to the systern a~.3 is calculated usiry the ramp function of heat addition. Q T is the total heat of the system at a given time fourx3 in the CIASIX results. g[ddTisthe integrated heat removed by the spray at a particular time.
RESULTS The contairrient tanperature and pressure responses calculated by CLASIX usirg the spray subroutine with a separate time dcraain and the cmventional finite difference method subroutine are given in Figures D-1 and D-2. As expected, the CLASIX results using the spray subroutine Iredict higher temperatures and Iressures because the CLASIX spray sub.-
rrutine removes less heat than the finite differenw method subroutine-Si:ce the same ramp function of heat addition was used with teth sub-routines, the shape of the contairment pressure and tenperature response plots agree closely.
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p he contairrnent tenperature respcnse, Figure D-1, shows the CIASIX res,ults, using both subroutines reaching peek value"; almost simultaneously *a,c at seccnds. De *results using the CIASIX spray subroutire sirw a peak q-taperature of ,k diile the the finite difference method sabroutine *a,C
~~
ehoWE a peak tenperature of F. As the two transients continue the *a,c tarperatures decrease and approach f _~U F *with the finite difference method *a ,c m
subroutine approaching this value sooner.
The contairnent pressure response, Figure D-2, is similar to the cmtairment temperature respcnse. We peak values are { psia for the *a c CLASIX spray subroutine and psia for the finite difference methcd *a,c sabroutine. These peak values occur at seconds after the start of the *a,c
~
transient. As, the two transients continu'e , the pressures decrease and psia with the finite difference metled subroutine approaching *a.c approach this valt$ ' sooner.
The difference between the integrated spray heat removed using the CASIX spray subroutine and the finite difference methcd subroutine is d found in Figure D-3. As anticipated, the difference is greater in the a,c regicn where there is heat additicn. The maxir:tn difference occurs at \
seconds with the finite difference method subroutine rexrving i a,c Btu nere heat with the spray than the CLASIX spray subroutine. As the transient progresses, this difference decreases and approaches a zero value.
l
\
l
' - 134 -
l 1
I l - - ~ - - - - -
i w*
CCNCWSION
'Ihe ocanparison of the results using the CASIX spray subroutine and the finite difference method subrautine show excellent agreenent with the CIASIX subroutine always predicting conservatively high containment presture and tenperature responses. This was anticipated because the CIASIX <
l subroutine rames less heat than the finite difference method subroutine.
l Therefore, the CIASIX calculations of the containment pressures and J temperatures using the spray subroutine are valid and conservative.
- 135 -
t
_ _ _._,. _ _.. _ __ ... _ __. , ~.- _ _.. _ ,__. _ _ _ . _..__,_ _., _ _. . . _ . . _ _ . _ . - _ . - , . _ _ _ . _ _ _ . . . _ . _ . _ . _ . . . _ . _ _ _ . . . . . _
3 TABLE D-1 CLASIX PARAMETERS vblime of Oznpartamt: 1,000,000 Ft Initial Tenperature of Conpartment: 100 F Iriitial Nitrogen Psrtial W%mto:: 11.61 PSIA Initial Oxygen Partial Pressure: 3.07 PSIA Initial Steam Partial Pressure: 0.30 PSII.
Time Step: 0.01 Secorris 1
l i
I i
}
~
1 j
1
. - 136 -
J 4
J
- . , - - - , - , - - - , - - - _ . - - - - - - . _ . _ _ . - _ . . - , , , - . - , . . , . - - . . , - _ . ~ . - _ _ _ . - - - - - - -
TABIE D-2 EAT ADDITION TABLE TIME: (SECEDS) NAT RATE (MU/SEE) 0.0 0.01 50.0 1,000,000 100.0 0.01 O
O
- 137 -
TABE D-3 SPRAY PARAMEM:RS Initial Sgray Flow Rate: 1000. IB/SEC Initial Spray Temperature: 100 F Initial Drop Diarreter: 0.0276 Inches Drop Fall Time: 10.0 Seconds Drop Film Coefficient: 20.0 BIU/HR-Ft - F Drcp Density: 62.4 LB/Ft Drop Specific Heat: 1.0 BIU/LB F i
1 i
h i
I l - 138 -
i t
--n---,,,, . , - - - - - - - , -,w,- - , - v.,..-,_.---,n---.-,n-,.,-r-n.a .--,-n,..-----,-~-,----an_,--,~,.- - - , - , , - -
~ ,
8,C I
l O
1 i
M' W
CLASIX SPRAY / FINITE DIFFERENCE METHOD TEMPERATURE COMPARISDN FIGURE D-1 0
- 139 -
~
a,c O
CLASIX SPRAY / FINITE DIFFERENCE METHOD PRESSURE COMPARISON FIGURE D-2 O
- 140 -
L_
- 6. .
f a,c O
(
l --
l '
! DIFFERENCE DF INTEGRATED HEAT REMOVEC E't i SPRAY USING THE CLASIX SPRAY AND FINITE DIFFERENCE METHOD l
l FIGURE D-3
- 141 -
( . - . -. .-_ -_-_-_ . . . - _ _ _ _ _ __