ML20067B937
| ML20067B937 | |
| Person / Time | |
|---|---|
| Site: | Cooper  |
| Issue date: | 01/09/1990 |
| From: | Brandon J, Holcomb E NEBRASKA PUBLIC POWER DISTRICT |
| To: | |
| Shared Package | |
| ML20067B884 | List: |
| References | |
| NPP1-SBO-007, NPP1-SBO-7, NUDOCS 9102110114 | |
| Download: ML20067B937 (525) | |
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SUBJECT CONTROL ROOM HEATUP CLIENT NPPD ORIGINATOR f, REVIEWER M & # M APPROV __' ihfe o CALCULATION NO. NPP1-SBO-007 CALCULATION NPPl='90-007 COOPER NUCLEAR STATION CONTROL ROOM HEATUP ANALYSIS
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-JOB NO. NP-110 DATE 11/30/89 PROJECT Q1L STATION BLACKOUT (SBO)
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CLIENT. NPPD ORIGINATOR _ <
REVIEWER /'[o APPROVED b CALCULATI'bN NO. NPP1-5B0-007 !
i REVIEWER'S STATEMENT 3 t
7)./1C CALdJL A*T C W %/ A I R C \/l E b ) C C ANC FhuMc TC ET Co tA ?LE rc h ub Cn G k EC IN ITc A :014 & Tion E, C hLit)L A TItINS R'EFERE NCE:, hND couCLL) Inbd! .
THE RfV/EW caWrir7ED o F;
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i f(bg 7~h E ' LJ.Sc ' o F HEA TINf.x-$ th N O " CON TEl-l P T"dsIH PUTEW CODEC FOR TMIC A NAL.Y[IC .
-- AN ExAntuATlo N c7 THE APPRoPOATENEn oF U$l% TH E , R EFG REN4G D .6cLA 2 R.A C/ A Tin N AND
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I SUBJECT CONTROL ROOM HEATUP CLIENT- NPPD . ORIGINATOR M" REVIEWER [ ~ APPROVE b -
CALCULATION NO. NPP1-SBO-007 l
- REVIEWER *S= STATEMENT (CONT'D)
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CDM PUTER lode IHPUT DECkc u)Ee e SPOT CHECX EO : Phs2 A W L)2 u Y.
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SUBJECT CONTROL ROOM HEATUP CLIENT NPPD, ORIGINATOR Mb REVIEWER (:fN APPROVED CALCULATIOdNO. N_P P 1 - S B O -007 TABLE OF CONTENTS REVIEWER'S STATEMENT 2 OBJECTIVE 7 CALCULATION OVERVIEW 7
1.0 INTRODUCTION
9
,;p 1.1 CONTROL BUILDING LAYOUT 10 1 1.1.1 CONTROL ROOM DETAIL 10 2.0 METHODOLOGY OVERVIEW 11 2.1 PROBLEM APPROACH 11 2.1.1 - COMe) UTER CODE STATUS 13 2.2 ASSUMPTIONS AND CONSERVAT!SM 13 3.0 EXTERNAL HEAT LOADS- 17 3.1 EXTERNAL AIR TEMPERATURE 17 3.2 SOLAR HEAT FLUX 17 4.0 INTEPNAL HEAT LOADS 19 a.1 ELECTRICAL EQUIPMENT HEAT LOADS 19 4.1.1 ELECTRICAL PANEL LOADS 19 4.1.2 EMERGENCY LIGHTING LOAD 20 4.1.3 COMPUTER SYSTEM LOAD 20
,4 4.1.4 ANNUNCIATOR-LOAD 20
) 4.1.5 SECURITY SYSTEM LOAD 20
f/6 2 M O*f - C B $ - oc ?
l 4.2 *ERSONNEL MEAT LOADS jfjkl j ./ 20 4.3
SUMMARY
OF LOADS 00
.n
?y 4.4 CONTROL ROOM INITIAL HEAT STRUCTURE 21 AND BULK AIR TEMPERATURES 4.5 ADJOINING ROOM TEMPERATURE 5 21 5.0 CONTROL ROOM MODELING 23 5.1 CONTROL ROOM AND ACCEES AREA VOLUMES 23 5.2 CONTROL ROOM CEILING AND CONCRETE ROOF 23 5.3 NORTH WALL 25 5.4 SOUTH WALL 26 5.5 WEST WALL 26 5.6 EAST WALL 26 5.7 FLOOR 27 5.8 HEAT SLAB AREAS 27 6.0 CONVECTIVE HEAT TRANSFER OS 6.1 CEILING AND FLOOR 28 6.1.1 HEAT EXCHANGE WITH CONTROL ROOM AIR 28 tv I 6.1.2 CE! LING AIR SPACE 32 6.2 NORTH'AND EAST WALLS 37 6.2.1 WALL AIR SPACES 37 6.2.2 NORTH WALL EXTERNAL HEAT TRANSFER COEFFICIENT 41 7.0 RADIATIVE HEAT TRANSFER 45 7.1 EXTERIOR RADIATION 45 7.2 INTERIOR RADIATION 45 8.0 AIR LEAKAGE 48 c.0 RESULTS 40 9.1 TIMESTEP CONTROL 49
10.0 CONCLUSION
S 50
11.0 REFERENCES
51
-)
4/5 f N/M .:Bf-co7 1C.0 FIGURES fy 53
N' ,
ATTACWMENTS
!. Development of HEATING-6 One-Dimensional Thermal Model of the Control Room Ceiling anc Concrete Roof Structures
- 11. HEATING-6 Coce Output Deck for the One-Dimensional HEATING-6 Thermal Mocel 111. Monthly Summary Solar Raciation Data - June 1977 IV. CNS Control Room Roof Insulation Information V. Letter EEH-09-084 from E.E. Holcomb. Enercon Services, Inc. to W. L. Swant:, NNPD, "CNS Control Room Electrical Lead Summary",
Dated 11/14/89 VI. Details of Leakage Coefficient Calculations for CONTEMPT-LT/028 Input Deck.
VII. CONTEMPT-LT/029 Input anc Output for the 4-Hour SBO Simulation t.
s
,)
SHEET E Or d8 JOB NO. No-110 DATE 11/30/89 PROJECT CNS ETATIQN BLACKOUT iSBO)
EUBJECT CONTROL ROOM HEATUP CLIENT NPPD ORIGINATOR REVIEWER 4' APPROVED CALCULATION NO. NPP1-SBO-007 OBJECTIVE The purpose of this calculation is to determine the *emperature
, of the Cooper Nuclear Station (CNS) Control Room during a costulated E station blackout (580) event lasting 4 hours4.62963e-5 days <br />0.00111 hours <br />6.613757e-6 weeks <br />1.522e-6 months <br />.
CALCULATION. OVERVIEW w
This calculation involves the following principal steost
- 1) A brief introduction is provided.
- 2) The droblem approach is discussed. Key assumptions and' conservatism are identified..
- 3) The am'bient air and solar insolation boundarv cond-itions are developed.
- 4) Internal' heat loads are Quantified. Initial condi-tions are given for the control room and heat structures.
Temperatures in the spaces adjacent to the control room are discussed.
- 5) The control room analytical model is developed.
, Individual heat structure models are detailed, and
(\g) boundary conditions for each slab are oiscussed.
2/$f
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- 6) Convective neat transfer coefficients are calculated, for those heat structures where default correlations
- are not used.
- 7) Radiative heat transfer configuration factors are provided as required.
- 9) A model for air infiltration into the control room is developed.
- 9) Results are presented for a 4-hour simulation of the control room heatup.
- 10) The necessary references and figures complete the main part of the document. Supporting documentation is included as attachments to the calculation.
t/ br NP-110 DATE 11/30/ec JOB NO.
PROJECT' CNS STATION BLACKOUT _ (SBOL qv. g SUBJECT CONTROL ROOM WEATUP Il NPPD ORIGINATOR [ M CLIENT REVIEWER / 8' ARPROVED CALCULATION NO. NAAl-SBO-007_
1.0 INTRODUCTION
and related issues are being addressed by the Station blackout Public Power District (NPPD) in response to the Station Nebraska Rule, 10 CFR 50.63, and Regulatory Guide (RG) 1.155.
Blackout
.erge NUMARC B7-00 (Reference 1) also provides guidance that is in the guidelines in part identical to RG 1.155, and adherence to 67-00 la sufficient to demonstrate compliance with the SBO NUMARC Rule.
NUMARC 07-00 requires that temperature severity be assessed in areas g
the plant containing eauipment whose function is essential to I i of the mitigation and control of an SBC event, and also in areas wnere perform manual operations. Areas operators are required to containing essential equipment and whose steady state temperature designated would be eipected to exceed 120 degrees Fahrenheit are Areas reauiring operator as 5B0 dominant areas of concern (DAC).
presence must be addressed for habitability concerns, especially if the area temperature is expected to exceed 110 degrees F.
The subj ec t of this calculation is the CNS Control Room heatup 4
during a postulated 580 event in which ventilation is lost for before offsite AC power can be restored. Four hours is the hours in Reference 2.
recuired CNS SBO coping duration, determined Control Room is affected,- SBO occurrence is Insofar as the accompanied by a loss of forced ventilation and normal lighting, Therefore.
and a loss of power to non-essential electrical panels.
offsite
- heat loads in the room are reduced because of the loss of AC power. The problem is basically to determine the magni tude of
}
l
/0/68
&,- MPf .T3W-coy the remaining loads and to ascertain the steocy state room temperature for this situation, i.e. internal room heating less than normel but without the benefit ei air conditioning. The rh metnodology applied to problem is discusseo in Section 2. 1.1 CONTROL BUILDING LAYOUT The site layout at CNS is shown in Figure 1. The Control Building is located on the north side of the reactor complex, between the Radwaste and Turbine Generator Buildings. The Control Building contains (at elevation 932' - 6") the Control '/ Room and the Computer Room, which are shown in plan view in Figure 2. These two rooms are connected Ov the double doors on the east side of the Control Room. Another set of double doors, at the southeast corner of the Control Room, leads to the Turbine Generator Building. The heatup analysis herein focuses on the thermal response ("o of the Control Room, the coundary of which is defined by Figure 2. 1.1.1 CONTROL ROOM DETAIL It is useful at this point to introduce some details of the Control Room construction, to support discussions in the sequel. Extracted from Burns & Roe ! Drawing 4526, Figures 3a and 3b show cross sections of the Control Room. These sections illustrate the interior wall and ceiling construction in relation to the concrete building enveloce. The interior ceiling, constructed of acoustic tile and gypsum ooard, covers most of the Control Room area defined in Figure 2, except for the " Access Area" regions on the south and west sides of the Control Room, exterior to the outer rows of electrical panels.
//l6 ?
M PP" - SS pf- oo 7 es/ f 2.0 METHODOLOGY OVERVIEW JP/F ' (/x'. (# . The CNS Control Poom heatup is determined computationally, using the HEATING-o (Reference 3) anc CONTEMPT-LT/028 (Reference 4) computer codes as the primary analytical tools. The Control Room is treatec as a single, well-mixed volume, and one-dimensional models are employed for heat conduction through structures. Appencix E of NUMARC G7-00 provides a simplified methodology that can be used for some room heatup calculations. In the NUMARC methodology, it is as sunied that the temperature of major heat sinks, such as the walls and ceiling, is constant. With respect to the CNS Control Hoom, two aspects of the ceiling heat transfer prevent direct application of the NUMARC methocology: i) The roof of the Control Room is suDjected to transient / solar heating, therefore, the assumption of a constant temp?rature has to be justified. Also, the roof might prove to be a heat source on a summer day instead of a heat sink,
- 11) The CNS Control Room has a suspended interior ceiling that is composeo of acoustic tile and gypsum board.
The assumption of a constant temperature for these relatively thin layers of material would be questionable. (See Figures 3a & 3b). Highlights of the problem approach and key assumptions are presen tet' in the next few subsections. 2.1 PROBL EM APPROACH The CNS Control Room heatup problem is divided into two principol parts. First, the steady periodic temperature of ceiling structures is
- 5) the solar heated roof and heat 1
1
. . _ . . . . _ - .. _ _ ~ , . . _ _ - _ . . _ _ . . _ . _ . . _ _ _ - .
. . ~ . _ _ _
~ Gf& V ' ;)
f [, , Mffl- $1 hoof determined, to establish roof initial conditions at the onset of' the 5B0. This computation is performed with the HEATING-6
?
-:fft.p.H computer code. . HEATING-6 was-chosen for.this phase of the calculations, because of tractability'in treating- the solar heat flux term and because of~ code 4eatures which facilitate
" treatment of heat = transfer ~in the air space between the i
Control Room tile' ceiling and concrete roof. Since the CNS- _ Control Room roof is constructed of concrete and is over two feet- thick, the thermal capacitance and time constant of the roof have'a bearing-on the problem. Therefore, 'the 7' > HEATING-6 simulation is performed.for about four daysL to ensure that a meaningful steady state is obtained. The HEATING-6 code input model development and the results of the steady state computations are detailed in Attachment 1. I For the -.second. . phase of the problem, the temperatures obtained-from HEATING-6 are used-to initialize-the roof = heat structure.
- for the Control Room transient heatup calculations over: the 4 :
- hour SBO-time period. .
The- transient 1 computations: are' perf ormed with - the CONTEMPT . LT/028' computer program. -The Control' Room is treated as a wel1-mixed lumped-volume,-forfreasonsito be discussed in' the- )
!sec tions ' which fol' low. Six major' heat s t ruc'tu res' (i.e. the:
walls, roof / ceiling 'and' floor) are- modelled. Minor heat. ,
' structures,; including-passive heat sinks, are note: considered.
The roof,' air . space and ceiling -transient . response. _is.
, . computed, sing simplified external boundaryJconditions which
~
~
areL based on the results:of the HEATING-6 analysis.- Control n Room internalJ heat loads consist :mainly of: . _e l ec t r i c a l:-
. equi pmen t , with a minor amount (i.e. < -1 KW) . contributed by oersonnel. The electrical' load determination is detailed-in -Sec tion . '4 and'its supporting. attachments. No ' credit is-l taken.-for -forced ventilation (e.g._-from battery-powered fans)--
4
'or' opening of. doors. The' calculation does, however, model air s
- ,, leakage from the Control Room via infiltration. Details ~ of r ) the computer code input model construction are provided in e
I l
/J/b6 y j?.h NAPf# SAb # 00 5 Sections 5 through 6. The results of the transient /
l computations with CONTEMPT-LT/028 are presented in Section C. key assumptions for the transient analysis are highlighted in h Section 2.2. 2.1.; COMPUTER CODE STATUS The computer code calculations used in this were run on mainframes at Power Computing Company in Dallas, Texas. Both codes exist in a quality assured, fully configured status and are controlled by the PCC OA program. The HEATING-6 computations were performee with OA version 0584 HEATING-e is a proven procuct which nas been in the commercial marketplace for several years. Developed at the Oak Ridge National Laboratory, it has Oeen subjected to extensive testing and assessment, as documented in Reference 3A. CONTEMPT-LT/028 was developed at the Idaho National Engineering Laboratory for analysis of containment behavior. It has generalized compartment modelling fea'tures which make it well suited to room heatuo analysis. Version JUL82, installed in the PCC CALIB and residing on the NOS2 System for the CYBER 990 computer, was utilized for the computations in calc. NPP1-SBO-007. Like HEATING-6, the code has undergone thorough testing prior to installation in PCC OALIB. 2.2 ASSUMPTIONS AND CONSERVATISM 2.2.1 The 500 is assumed to occur from 14: 00 to 18:00 hours. V The combination of highest ambient temperatures and ( ) highest roof temperatures occurs during this time
g Eg' ,
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/VW-CB&oo7 i
interval. Dased on the results in Attachmant 1. pe.1 control room includes allg L
} 2.2.2 The tot 4ree volume of the The of the encloseo volume. 'But see Item 2.2.4).
volume of electrical panels, furniture, people, etc. is not subtracted from the room volume since these are not physically modeled. This approach results in a more rapid energy deposition to the room than would actually occur, because electrical energy is immediately dissipated in the room air rather than heating the pnysical mass of the panels. Conservatively, no creoit is taken for passive heat sinks. 2.2.3 Control room and access area (Ficure 2) are lumped ? together as one volume, since both areas contain electrical panels which would be activa during SBO. 2.2.4 The air volume between the control room suspended ceiling and the concrete roof slab is not included in the control room net free volume calculation. 2.2.5 The internal energy generated in the control room is / assumed to be evenly distributed throughout the room as opposed to modeling localized sources because: 2.2.5.1 The personnel and emergency lighting loads are distributed throughout the room. 2.2.5.2 The computer system heat load results from a total of eleven items, the largest of which is rated at 600W. Terminals, CRTs. etc. are consid-ered to be distr 2buted throughout the room rather than concentrated at a single location.
/4f6 V Y y/ * ' //h*f- ZBW- 00 Y
/
2.2.5.3 The majority of electronic panels have open eacks, tv . .
, which greatly enhances panel cooling and energy districution. The active panels curing 5B0 are 3 castributed throughout the room. The largest individual panel load is aoout 2.3KW, wnich is aoout the same heat as generatec by a kittnen stove burner. Individual panel loacs are celineated in Section 4 Also see Figure 4 2.2.5.4 CNS procedures direct the control room /
operators to obtain portable sucply fans in the event of a ventilation failure that cannot be readily corrected, to car ry away heat from the control room console. (No credit for fan cooling has been taken in the analysis. Heat transfer from the room air to the major structures is modelled by natural convection). fa% 2.2.6 Stored energy within the electrical panels and lighting, ' y which were energized prior to the onset of the SBO, is neglected. This is considered to be a small amount of energy, and neglecting it should be more than offset by not taking credit for the control room interior passive heat sinks. 2.2.7 The initial equilibrium temperature of the Control Room just prior to loss of HVAC is assumed to be 23 degrees C. See also Section 4.4. 2.2.8 The areas immediately adjacent to the Control Room Y (see Figures 1 and 2) are assumed to be at a constant temperature of 90 degrees F for the 4-hour 5B0. Further discussion regarding- this assumption is provided in Section 4.3.
) i
' /d/Af
$ N </? NEP/- $B$- 00 7 2.2.9 Referring to Figure 2, there aro O doors betwrsn tha /
main portion of the control room and the " Access f'f Areas" on the west, south and east sides. there are two sets of double doors between the Control Further, Room and adjoining areas. Very conservatively, no explicit credit has been taken for opening of doors in the analysis. Implicitly, any opening of doors would further support the assumption that the room is well-mixed. / % 4- i (W .
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0.0 EXTERNAL HEAT LOADS -
$Y }l'h
- (6tt- .1 EXTERNAL AIR TEMPERATURE p The outside air temperature cata useo in this analv=.s are ASH 9AE 1% design values based on US Weather Bureau recores for Omaha. Nebraska. (Use of data from Omaha was considered appropriate for the reasons listed in Section 3.2). The cata are cresented in Table 1. page 23.10 of ASHRAE (Reference 5)." The 1% high temperature value is 94 degrees Fahrenheit, and a conservative value of 76 degrees F was assumed to be the low ' temperature. The high an low values were used to develoo a sinusoidal function of ambient temperature vs. time, which is given in Attachment 1. 3.2 SOLAR HEAT FLUX Solar energy is conservatively assumed to irradiate the entire V [Dg. surface of the control building roof for tne ent_ s solar day. y Shadows cast on the Control Building roof from other structures were ignored. (Roof elevations are indicated on Figure 1. The Turbine Building, to the east, is 58 feet higher than the Control Building. The Reactor Building, on the sou th side, is 100 feet higher). The waterproofing material on the surface was assumed to be asohalt. An absorptivity of 0.94 is used for' solar heating, based on the 0.938 solar cell value in Reference 6 and the carbon black value in Reference 7. While / Reference 8 indicates that an asphalt emissivity value of 0.93 would be a good choice, a slightly conservative value of 0.90 is assumed for reradiation from the heated asphalt surface. The solar heat flux data used in this analysis are from. -the National Oceanic and Atmospheric Administration (NOAA) recort titled " Monthly Summary Solar Radiation Data". Data from Omaha,k-Nebraska were used because of its proximity to CNS. The \
) available edited data from June of 1977 to June of 1989 were
/f/6 C l W.} t. 9 M - S B p'- o o F \
examined. (Rederence 9 Attachment III). Omaha, at 41 I degrees 22 minutes north latitude, is located sufficiently (t*! close to Brownville, at 40 degrees 21 minutes north latitude, such that the Omaha cata are considered applicable to CNS. The Omaha data are considered slightly conserva ive because of a slightly longer day length. Climates are very similar, because Brownville and Omaha are both located on the Missouri River. A typical day near the summer solstice was selected to repr esen t the CNS roof solar heat flux. The typical day was one which exhibited clear sky features and had a combination of peak mid-day total heat flux and maximum integrated heat flux. June 19, 1977 well fits these criteria, as seen in / Attachment III. The data from 6 to 7 AM are indicated to be cuestionable but were in the came range as other data for that month and thus have been retained. Data from 7 to B AM appear anomalously low, possibly indicative of a cloud cover. These b \ data have been edited by taking the maximum, non-questionable
.value for that time period during the month of June. This
" typical day" is in fact considered a representative upper bound of summer conditionn. This heat flux condition is assumed'tu persist for 4 days in the steady oeriodic solution V in Attachment I.
l Based on the development in Reference 7 the heated roof ceradiates to the sky according to (1) q" out = h*6 * (TR**4 - TSKY**4), where g' TR and TSKY are the roof and sky absolute temperatures, respectively, sigma is the Stefan-Boltzmann constant, epsilon is the roof emissivity, and q" out is the. net radiative heat L flux between the roof and the sky. l i n-l o
W4r
/W e * //ppy- a 4 - 00 =
The sky temperature is relateo to the amelent temperature. TAMB, by (2) TSKY = 0.0552 : TAMB**1.5. where both TSKY and TAMD are in cegrees Kelvin. and TAMB varies with time as discussed in Section 3.1. 4.0 INTERNAL HEAT LOADS 4.1 ELECTRICAL EQUIPMENT HEAT LOADS To determine the Control Room electrical loacs, all creakers powering Control Room equipment wnich would be active during an SBO were examined from the standpoint of determining those which would generate heat in this room. (See NPPD Calculation NEDC-89-1947 for the detailed loads breakdown)./ .w The systems of interest are the 125VDC system and the No-Break Power Panel (NBPP), i.e. uninterruptible AC circuits powered through- inverters. The electrical loads in the subsections which follow reflect loads which terminate and dissipate heat in the Control Room. Power supplies a'id other equipment located exterior to the Control Room werr- not included in the load summaries. The CNS Control Room electrical loads are summarized in
/
Attachment V and its exhibits and are as follows: 4.1.1 ELECTRICAL PANEL LOADS AC Loads No-Sreak Power Panel 4753W / j
Jy'4 0 ,
~
DC Loacs Div. I & II 2721W jf7e# (;) A.1.2 EMERGENCY LIGHTING LOAD (30 - 12W bulbs) 260W (IndicatAng Lighte) 344W / 4.1.3 COMPUTER SYSTEM LOAD (CRTs, etc.) 3960W <
-See Exhibit B of Att. V-4.1.4 ANNUCIATOR LOAD 1938W e'
-See Exhibit D of Att. V-4.1.5 SECURITY SYSTEM LOAD SAS Console 1494W /
-See Exhibit C of Att. V- i fr y The analysis results-will show that it is unnecessary to power down the security system-from the standpoint of control room heatup. The inclusion et the SAS load is conservative, because the security cubicle is outside of the control room proper.
4.2 PERSONNEL HEAT LOADS B people (3000 BTU /hr) 879W ' (Reference 10, page 47) 4.0
SUMMARY
OF LOADS The total heat' load is 16,449W . V r v) .
aAr . TW 'f /VP/Y- SBi l- ce Y 4.4 CGNTROL ROOM INITIAL HEAT STRUCTURE-AND BULK AIR TEMPERATURES The control room, initially air conditionec, is assumed to f-' have a bulk air temperature of 23 degrees C (73.4 degrees F) / at the start of t:1e GBO. At time zero the air conditioning is lost. One side of eacn heat structure is in contact with the Control Room air. The initial temperature of each heat s truc ture is cc termined via the CONTEMPT-LT/028 code, in which a steady state temperature profile is established for each slab prior to commencement of the transient computations. One comment is in order regarding the heat strutture initialization. Adjoining rooms on the south and erst and beneath the Control Room are air-conditioned spaces, es will De discussed in the next section. Since interior climate control is continuous, the walls between these spaces would be at approximately the.same temperature as the surrounding room air. at the onset of an 580, i.e. about 73 deg. F. The heat , structure initialitetion does not take credit for this. Very f%Y conservatively, the' side of the-structure not in contact with the Control Room air is assumed initially to be at the temperature of the adjoining space, which is 90F, 4.5 ADJOINING ROOM TEMPERATURES A conutant temperature of 90 degrees Fahrenheit is assumed
- for the bulk-room air temperature of the adjoining ocms.
-This bounoary temperature is held constant for the SEO duration.
- a. This assumption is based on the results of the HEATING-6 analvsis discussed in Section 7.1 and the reasoning tMatv interior walls and rooms not exposed to solar flux and having insignificant internal heat loads will be at lower temperatures, i ?
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- b. It is considered conservative. since the normal operating temperatures of the spaces surrounding the Control Room -
I ( are less than 00 degrees F. Refer to Figures 1 & 2. The Computer Room. on the ecst, is normally air conditioned and would have no significant sources of heat during an 580. (Procedures dictate that the # doors between the Control and Computer Rooms be opened in the event of loss of Control Room ventilation. although the analysis has not modelled this large flow path). On the south, the access corridor (i.e. the " Office Bldg. Controlled Corridor") is normally air conditioned and has no heat sources. 'The access corridor acts as a buffer zone between the Control and Reactor Buildings. The two are separated by massive Concrete walls. Similarly, the Cable room, immediately beneath the control room, is part of the Control Bldg. envelope and is also air conditioned. Most of the electrical equipment in this room would be inactive during the SBO. Temperatures in the Radwaste and Turbine V (~4 i Generator Buildings normally do not exceed about 85 deg. F. The assumption of a constant temperature of 90F for these pr adjoining areas is considered conservative,
- c. Using the Appendix R drawings (Reference 15) and Burns & s e Roe Drawing No. 2066, it can be seen that the Control Room-is .far away and well insulated from areas that would be heated during an 580 (e.g. the drywell, RCIC room and the DC switchgear rooms). In all cases, separation from the Control Room and heated areas is by at least two major V floors or walls. ,
1 l
- d. It was necessary to telect one temperature for all adjoining.
rooms because of code input constraints. p i l l l
.)
J 6"
/ VVfr ZD/ ~ Oo Y S.O CONTPOL ROOM MODELING
.? Y Y,
- e. Major features of the CONTEMPT-LT/028 model of the CNS Control Room f
are shown in Figure 5. The modelling approach has been discussed in previous sec tions . Modelling detail reduces basically to calculation of the room net free volume, to ced inition of the heat slae areas, thicknesses and constituent materials, to mocelling of air infiltration, specification of boundary conditions and internal energy generation, then sapplying the necessary Control cards reouireo by the input processor. Whenever possible, the LT/028 model development relies on data generated in the HEATING-6 model development in Attachment '. 5.1 CONTROL ROOM AND ACCESS AREA VOLUMES The dimensions of the Control Room envelope have been (I%Y presented in Figures 2 and 3. From sheet 24, the Control Room net free volume (NFV) is NFV = S4,018 ft**3 / The Control Room is simulated as a "Drywell" (i.e. compartment volume no. 3) in the CONTEMPT-LT/028 deck. This is done ; because of the greater modelling latitude wnen using this compartment option. 5.2 CONTROL ROOM CEILING AND CONCRETE ROOF - HS2 Based on the discussion in Se e tion IV of Attachment I and on Figures 3a & 3b, the constru-tion of the suspended ceiling and roof is illustrated in Figure 6. This figure also indicates y, the application of bou,dary conditions. At the top of the
) concrete slab, a large heat transfer coefficient (HTC) is used i,
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f/4 S' IP M M - SB d-oc~ tc impress a constant surface temocrature of 90 cegrees F on the slab. The 90 F value is bounding and based on Figure 1-7 I of Att. I. For the air space, heat exchange by natural convection and thermal ractation as allowed. Finer noding 15 usec for the air region acjacent to the thinner layers (i.e. the tile & gypsum) consistent with coce inanual recommendations for mesh spacing at material interfaces. The acoustic tale is coupled to the room air via a temperature-dependent, natural k convective HTC. Heat transfer Coefficients for this heat structure (HS) are developed in Sections 6.1.1 and c.l.2.s Material properties are taken from Sect. IV-B ef Att. 1. ' ' 5.; NORTH WALL - HS1 The north wall heat structure model is shown in Figure 7. .ne right side of the structure is connected to the control room air via the CONTEMPT-LT/028 default correlation for natural (%,t convection to vertical surfaces (Ref. 4). The left side as v exposed to the outside air temperature, discussed an Section 3.1. A constant HTC of 0.2 Dtu/hr-ft2-degf is used for the . north wall exterior, based on values obtained while initiallting the heat slabs with the code. The above HTC takes no credit for wind cooling of the north wall and is conservative with respect to heat losses. (Control Room " interior' wall natural convection heat transfer coefficients calculated with the code default correlation are aoout 0.4 to 0.5. for example). Heat transfer across the interior air space in the wall considers natural convection and thermal radiation, discussed in Sections 6.2.1 and 6.2.2. From Dwg. 4S26. Section F2 and Detail 10 (Figure 8) the interior panels are S/8" thick. The thin plastic laminate facing is neglected. The panels are assumed to be Douglas Fir plywood. From Reference S. Table 3A, p. 22.13, the (, thermal properties aret
)
_ _ _ . . _ . - ~ - i S $? am- ses - oa densaty = 34 lbm/ft*831 1 thermal conductivity = 0.067 Btu /hr*4t-degf l specific heat = 0.29 Stu/lbm-cegf. , 5.4 SOUTH WALL - H34 The south wall heat structure model is shown in Figure 9 The well is taken to be a 2-feet-t .ic k concrete slab. It is ll assumed that the wall is unfaced. Since the spaces adjacent to the wall are access areas. Both saces of the well are convectively coupled to air in the surrounding spaces via the code's default correlation, as was done for the north wall. The Office Building Controlled Corridor is considered to jr remaan at'a constant temperature of 90 F. fT WEST WALL - HS5 f 5.5 : The west wall modelling, illustrated in Figure 10, is identical to the south wall modelling, except the left and / right sides of the structure are switched. 5.6 EAST WALL - HS6 The east wall model, _ based on Dwg. No. 4526 and Detail No. 10, p/ is shown in Figure 11. This wall is assumed to be feced on both sides, with the facing Lonstruction the same as discussed in Section 5.3. Natural convection to the adjacent rooms Y. again uses the code default correlation. Natural convection and thermal radiation are modelled in the al'. interior air spaces via an equivalent conductance, see Section 6.2.1. E
- .~_
J i
)
2 ?/dl AT/'t- f2t-oc~l 5.7 FLOOR - H53 N &
,ff
] The floor heat structure as simulateo as an 9-inch-thick The bottom of this slab concrete slab. as shown in, Figure 12.
15 convectively coucleo to the caOle room aar by a temperature-depencent natural convectiv? HTC which as entered 45 tabular input in the LT2B ceck. This tabic is cevelopec in V Section 6.1. The approach for the bottom side of this slab is the same as used for the Control Room ceiling. For the top surface of the slab, a constant value of 0.21 is used for the heat transfer Coefficiente as Dxplained in Item vi) of Section 6.6.1. 5.8 HEAT SLAB AREA 5 determined, Using Figures 2 & 3. the heat s truc ture areas are as listed belows (L% HS1 - NORTH WALL - AREA = 64.0833'
- 11.3333'
- 726.3 ft2
+ 15.5*
- 11' H52 - CEILING - AREA = 56.75'
- 54'
= 3.235 ft2 /
(See also sheet 24).
/
H53 - FLOOR - AREA = 69.5'
- 64.0833' = 4.454 ft2 V H54 - SOUTH WALL -
AREA = 64.0833'
- 14.25' = 913.2 ft2 v l
HSS - WEST WALL - AREA = 69.5'
- 14.25' = 490.4 ft2 #
H56 - EAST WALL - AREA = 69.5*
- 11.3333' = 787.7 ft2 V
..]
~ . . . ,
Efllli A//ff" $3 f 09 Y~ 6.0 CONVECT!VE WEAT TRANSFER ** Eg W/,p + (1'?h t.1 CE! LING AND FLOOR [ o.l.1 MEAT EXCHANGE WITH CONTROL ROOM AIR For the floor and ceiling. the characteristic lengths are cuite large. Approramate heat transfer f coefficients are chosen based on the following approacht
- 1) The surface temperature is assumed to be approximately eoual to 90 deg. F for purposes of /
HTC calculations.
- 12) To calculate h'. the +ollowing correlation from Ref. 5 for turbulent natural convection is used for the ceiling:
Nu = 0.13 * (Gr Pr)*80.33 . 7g This equation has the advantage that the heat transfer coefficient is independent of the characteristic length (L). The equation is valid for GrPr up to 1.0E+12. < iii) to take into account the range of validity, the Rayleigh numove is set to the above value, then the allowable values of the characteristic lengths are determined, as shown on sheet 00."- It is seen that the allowable value of 'L' depends on the temperature difference. From Dwg. No. 4526, the largest characteristic length is about 33 to 37 feet on the main control room floor, in reasonably good agreement with the maximum allowable values of "L' for temperature ,
, differences (i.e. Tf - Ts) of 20F or less. Using"
( 4 J the cube root of the air space volume between I r- - -, - . -,.
2Y/0 C sY Y ,%p)Y ffp'~cc j the suscenced ceiling and the luminous grid, a value of 'L' of about 20 feet results, withy resultant values of GrePr indicated to be althin the range of valicity of the correlation (column E). Av) It does not matter wnat value of 'L' is enosen for the heat transfer coefficient calculations, as 'h' depends primarily on delta 'T'. Scoping calculations with the 'LT28' model , indicated that a surface temperature of 90F and celta 'T' values of 5 to 10F are reasonable assumptions. v) The values of 'h NC' inoicated on sheet 00 were entered into the input deck as a temperature dependent function for the ceiling. For small values of delta 'T*, an average value of h a
)
m.4785 at Tf = 43F is used based on sheet 30.
.z vi) For the floor, p. 2.13 of Ref. 5 indicates that a value somewhat less than-1/2 the ceiling velue in appropriate. Using a reduction ratio of 12/27,p based on the ratios of coefficients in the laminar flow equations in Table S, p. 2.12, eno e an assumed delta 'T' of 10F, a heat transfer coefficient of about 0.21 results. This is applied to the floor as a constant value using a tabular function et time in the LT28 input deck.
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$URFACE 1[MP (F) 90 1.0i+0B(BR6FR(1.0l+12 setteseste I hATUFAL CONVitfl0W 16 hoy-89 NAIURAL CONV[CilDb FILMILMP GASTERP L tR*N SPIPR NVNl h h*
t vist to 11 (f t) HOR SURF HDR $UDF HUR $URF HOR $($F kiu/hrftt (It2/pl PR (F) (F) k U.C4 Hi,C4 H4.C4 N U.(4 d4.t4 0.01466 0.56t5 0.712 60 30 20.00 9.0032E+11 9.0032f+11 12:!.0E; 0.9201 0.01491 0.50815 f.7105 70 50 24.601.0M0!+12 !.37t4f *11 10!7."! ?. 'f R 0.01516 0.6070 0.709 80 70 32.11 1. M00E+12 2.4170i+11 909.7t! 0.t!!B - 0.01529 0.6179 0.7083 85 80 41.17 1.0M0t+12 1.1465E+11 631.545 c.4629 0.01541 0.628 0.7075 % 90 ERR 1. M00E+12 0.00Mt+00 0.0% 0.0M0 e 42.60 1. M00f+12 1.0345(+11 0.4742 rg 0.01554 0.6381 0.7069 95 100 610.261 f 0.01566 0.6462 0.706 100 110 34.39 1.0000!+12 1.9675(+11 756.110 0.5920 5 0.01570 0.6585 0.70525 tot 120 30.54 1.0000!*12 2.P074E+11'" B51.205 0.6716 0.01615 0.68t5 0.703 120 150 25.45 1.0000t+12 4.E537t+11 1021.648 0.B2% 0.01664 0.7316 0.7 140 190 22.84 1.0M0t*l2 6.7141t+11 1136.344 0.9471 O.01712 0.7747 0.698 160 230 21.661.0M0E*12 7.8)42E+11 1200.456 1.0276 0.01759 0.6187 0.696 190 270 21.08 1.0000E+12 f.5416!+11 1233.550 1.0649 0.01806 0.9636 0.694 200 310 00.21 1.000M+12 f.f 713t+11 1249.12 1.12K C.0ltt) 0.9095 0.693 220 250 20.74 1.0000E+12 f.97:Pl+11 1:53.971 : 16 0.01999 0.9561 0.691 240 390 20.791.0M0(+12 6.90lil+11 12 0.5!! 1.1974 0.01945 1.0034 0.689 260 00 20.93 1.0000E+12 9.72:St+11 1242.117 1.0%0 . 0.0199 1.0517 0.626 290 470 21.131.0000E+12 B.4BMt+11 1230.492 1. 243 0.02034 1.1009 0.687 300 510 21.28 1.0000t+12 9.1869t+11 1216.236 1.2369
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e.2 NORTH AND EAST WALLS vg y ; -l-6.2.1 WALL AIR SPACES The procecure used for the wall air spaces is 51 malar to the procedure defined in Section t.l.2 except that & different convective heat transfer correlation 15 used to account for the vertical orientation of the walls. A constant, slightly conservative value of the heat transfer coefficient is calculated anc used to determine an effective thermal conductivity for the air spaces. As mentioned, this method simplifies the model by reducing the number of heat structures recuired. The procecure 1% detailed on the next 4ew pages. I i r l i l t *!
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W/bf NPPf- SZp'-oo y 7.0 RADIATIVE HEAT TRANSFER , 7% a,/4 7.1 EXTERIOR RADIATION Solar raciation was previously discussed in Section 3.2. Also see Section V.B.2 of Attachment 1. Because direct application of a heat flux boundary condition to a structure is not possible using tne CONTEMPT-LT/028 computer code, the steady periodic temperatures of the ceiling and roof heat structures were first determined using the HEATING-6 conduction code, which does allow heat flux boundary conditions. For tne CONTEMPT analysis. the temperature at the top of the roof was then entered as constant boundary temperature and applied to the structure surface using a large heat transfer coefficient, effectively forcing the roof surface temperature to the bounding value determined in the HEAT' '
,-6 calculation. k' Attachments I and 11 are the HEATING-6 code thermal model development calculation and printed code output, respectively.
Section 3.2 above and the Atta chments detail the methodology used in applying the solar heat flux. Attachment I shows the resultant calculated t em pe ra tuv e's (Figure 1-7) that were used as the basis for the initial conditions for the CONTEMPT-V LT/020 analysis. 7.2 INTERIOR RADIATION To evaluate the radiant heat transfer coefficient in the wal: and ceiling' internal spaces, the assumed geometry is parallel surfaces of infinite extent. The overall configuration factor then depends only on the emissivities of the opposing L surfaces, as indicated on the next two pages. This information is used as input to Sections 6.1.2 and 6.2.1 for calculation of the linearized radiative heat transfer l ,,,,, coefficient. l
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WMt M/Y- sag-c o 7 0.0 AIR LEAKAGE [M,[") Because of the temperature difference between the Control Room and adjoining areas, some air flow will occur, mainly through the doors to the Computer Room and the doors leading to the Turbir,e Building. The following assumptiono are made in order to calculate the air exchanget I
- a. All doors to the Control Room are assumed to be closed, and only .
one set of doors is considered to leak. Since AP 2.4.0.4.8 requires that the doors to the Control Room and the Ccmputer Room be opened in the event of loss of ventilation, this approach is conservative.
- b. The door crack width is assumed to be 0.1 inch on the sides and V top, and 1/2 inch on the bottom.
4
- c. The air exchange rate (0) is determined via Figure 7 on p. 21.7 ef ASHRAE. "O" is then equated to the flow rate which would be calculated by "LT28", and loss coefficients are determined as a function of differential pressure for input to the code.
9
- d. The leakage rate from the contro) room is always less than 0.35 ,
s AX/HR during the 4 nour 580, whic h is a very '" tight" room; thus indicating that the methodology is conservative. (See Figure 13.)
- e. Calculations of leakace coefficients are provided in Attachment VI to support tt.e values used in the input deck.
.. s s
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df l l /VM- SRW~ 00 7 9.0 RESULTS Results of the analysis using the CONTEMPT-LT/028 computer code are plotted in Figure 14 The Control Room heats up Quickly to about 92 degrees F in the first 30 minutes after loss of HVAC. The < heatup rate slows, with a gradual increasD toward equilibrium noted thereafter. The calculated maximum a*.r temperature after A nours is 100.3 degrees F. The heatup rate between hours 3 and 4 is 1.05 / degrees Fahrenheit per hour. Digital temperature data are listed on the code output provided in Attachment VII. 9.1 TIMESTEP CONTROL A timentep of 0.1 seconds was used for entire 4-hour simulation. The results would not be expected to be sensitive to timestep reductions below this value, say to 0.01 second, because of the relatively slow nature of the room heatup / process. f\ Adequate choice of timestep is indicated by the convergence ratio 'DE/E' listed on the 'LT28' output in Attachment VII. This ratio is of the order of 1.E-06 for the entire transient. Per Reference 4, timestep reductions are warranted when this rat'io exceeds about 1.E-03. The Control Room air temperature was printed every 10 seconds for the first minute of the transient, every minute for tha next 39 minutes, and every five minutes thereafter. Heat structure print frequency was somewhat less, to reduce the size of the output listing.
)
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10.0 CONCLUSION
S ZM' (*% the bapts of Reference 1, the discussion in Sectkon 1.0 and On the computed r ? s u l ',5 , it is concluded that the Control Room at Cooper Nuclear Station would not be a dominant area of concern p curing a postulated 4-hnur station blackout event, since the calculated room temoerature is significantly less than 120 degrees Fahrenheit. Since the calculated maximum room temperature is less than 110 degrees Faheenheit, with margin, it is concluded that there would be no habitabi '.i ty concerns pilth respect to performance of operator / actions in the Control Room during the 4-hour period. The computed results have been arrivec a'c using a conservative approach and several, significantly conservative assumptions. There is, therefore, good confidence that the results would bound the actual room temperature for the postulated 500 scenario. teh
M O $ N /') Y - $ 3 / ~ e 0 5
11.0 REFERENCES
44/ $# TW jf/ r:h,
" Guidelines and Technical Baset for NUMARC Initiatives
- 1. NUMARC 07-00 Address 2ng Ftation Blackout at Light Water Reactors".
Survices. Inc., " Station Blackout Coping Assessment for
- 2. Enercon Cooper Nuclear Station", Report No. NPP!-PR-O!, Rev. O, March 30, 1989.
- 3. Elrod, D. C., G. E. Giles and W. D. Turner, " HEATING-6: A Multidimensional Heat Conduction Analysis with the Finite Difference Formulation", NUREG/CR-0200, Volume 2. Section F10, ORNL/NUREG/CSD-2/V2, October 1981.
3A. Bryan, C.B. et. al. " HEATING-6 Verification", Martin Marietta ! Energy Systems, Inc. Report No. K/CSD/TM-61, December 1986.
/** *} 4 Hargroves, Don W. and L.J. Metcalfe, " CONTEMPT-LT/028 - A Computer Program for Predicting Containment Pressure-Temperature Response to a Loss-of-Co71 ant Accident", NUREG/CR-0255, E.G.&G. Idaho,Inc. TREE-1279, March 1979.
Handbook & Product Directory 1977 Fundan en ta l s" , S. "ASHRAE American Society of Heating, Ref rigerating and Air-Cor ditioning Engineers, Inc., New York, 1977., The Macmillan Co.,
- 6. Chapman, Alan J., " Heat Transfer, 2nd Edition",
London, 1967. , A. and William A. Beckman, " Solar Energy- Thcemal
- 7. Duffie, John Processes", John Wiley & Sons, New York, 1974 Omega Engineering, Inc., " Temperature Measurement Handbook and O.
Encyclopedia". Section 'T', Stamford, Ct., 1985.
)
- J22 l89' i
N
/V M - f 8 (l - O O Y-9 Oceanic and Atmospheric Administration (NOAA), " Monthly National
, _ fs} Summary Solar Radiation Data" (for Omaha, Nebraska) June 1977, Volume 1 Number 6, Environmental Data and Information Service, National Climatic Center Ashville, N.C., April 1979.
- 10. Holman, J. P., " Thermodynamics", McGraw-Hill Book Company, New York, 1969.
- 11. Burns & Roe Drawing 4526, DCN Rev. No. 1, W.C. 2520, " Control &
Computer Rooms Plan, Sections & Details", 11/10/69.
- 12. Burns & Roe Drawing 4176 Rev. No. 14, W.O. 2520,
- Structural Control Building Roof Plan & Sections", 9/1/68.
- 13. Baumeister, T., editor., " Marks' Standard Handbook for Mechanical Engineers", 8th ed., McGr.w-Hill Book Co., New York.
- 14. Parker, arald D., et. al., " Introduction to Fluid Mechanics and Heat Transfer", Addison-Wesley Publishing Co., Heading, Ma., 1974.
- 15. " Cooper Nuclear Station Safe Shutdown Component Lecst.ons & Emergency Route Lighting", NPPD Drawings CNS-EE-175 through 589, May 19, 1987.
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\ PROJECT CNS STATION BLACKOUT (SBO)
SUBJECT CONTROL ROOM HEATUP CLIENT NPPD ORIGINATOR / , " REVIEWER [- d.# /. APPROVED CALCULATION NO. NPP!-SBO-007 AT1ACHoENT 1 OF NPPI-SBO-007 DEVELOPMENT OF HEATING-6 (*% -( ONE DIMENSIONAL THERMAL MODEL OF THE COOPER NUCLEAR STATION CONTROL ROOM OEILING AND. CONCRETE ROOF
SHEET 2"'E OF #3 JOB NO. NP-110 DATE 11/30/e9 l PROJECT CNS STATION BLACKOUT ($80) SUBJECT CONTROL POOM HEATUP CLIENT NPPD ORIGINATOR 8 M-REVIEWER [0 APPROVED CALCULATION NO. NPP1-SBO-007
- 1. PURPOSE The purpose of this attachment is to develop a one-dimensional geometric representation of the control room ceiling and concrete roof structures for implementation into the HEATING-6 computer code, iri order to determine the steady state temperature of the ceiling and . roof structures. A ' constant control room air temnerature, consistent with an air conditioned space, it-assumed in addition to a conservative
( ) periodic ~ exterior temperature and solar heat f l ux .- The resultant-temperatures will be used as initial structure temperatures in the SBO control room heat-up analysis in order to increase modeling accuracy and-eliminate excess computer time.
.11. METHODOLOGY The HEATING-6 computer code is a multidimensional heat conduction code using the finite difference formulation (Reference 3). It can be used to Jsolve steady-state'and/or transient problems-of one to three dimensions
, in . various coordinate' systems. HEATING-6 code input models can- be basically categorized into 3 sections -
geometric input, boundary
-conditions, and code options. Geometric input-is concerned with- the physical configuration. dimensions of the- system and constituent materials. . Boundary conditions are used to apply radiative and convect < ,, :i ve heat transfer and define temperature conditions, all of which can k) ' vary with time, temperature or position- .
in
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y.??g' :- 3l23I W/P/ CSgd - o o 5 Code cotions are mainiv related to input and output reovirements. Geometric input is discussec in Section IV, boundary conditions in
. y((* '
Section V, anc code options in Section VI. The HEATING-6 code output is included as Attachment 11 and incluces a printout of the input deck. Input values listed here have been converted to units of BTUS, hours, feet and degrees Fahrenheit in the input deck. Ill. ASSUMPTIONS Referring to Fig. 1-1, 1-2a and 1-2b, the following modelling approach (nd key assumptions were employed when developing the HEATING-6 thermal models A. The thermal model represents the following structurest
- 1. Interior control room ceiling materials
- 2. Concrete slab roof and insulation
- 3. Air space between the control room ceiling and roof slab
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, 4 The luminous ceiling units, in the control room proper, are not ,Jdeled because tJey do not greatly impede vertical movement of air in the control room volume.
- 5. The wire hangers and carrier channels which support
~
the suspended control room ceiling will not be modeled for simplicity. B.= Inherent in the one-dimensional geometry for the HEATING-6 thermal model, it is assumed that there is no horizontal heat transfer in any of the materials or air spaces. Neglecting end effects is a reasonable assumption considering the size of the building roof ar,ea covering the control room (see Fig. I-1, extracted frem Reference ll) C. The control room is air coldititned and is assumed to have a normal operating, constant bulk air temperature of 23 degrees C (73.4 degrees F). (' ) i
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D. Convective heat transfer in the air space above the acoustic e tile room ceiling to the concrete roof is not included, which
'I 1 is conservative. This is implemented to ensure that roof structure temperatures are conservative. (Natural convection can be re4Sonably expected to occur in this zone and is included in the CONTEMPT-LT/028 model of the air space).
E. Heat .is transferred across the air space between the control room ceiling and the concrete slab roof by radiative exchange. G. The extb"ior temperature is sinusoidal and based on ASHRAE 1 */. design temperature values for Omaha, Nebraska. H. Solar heat flux is from NOAA's Monthly Summary Solar Radiation l Data for Omaha, Nebraska on June 19, 1977. No credit is taken-i for shading of the Control Bldg. roof by adjacent structures. The Reactor Bldg., adjoining and immediately to the south, is-190 feet higher,-for example.
'4%
k', I. The roof response was. computed for a four-cay duration prior to SBO occurrence in order to obtain a steady periodic solution. IV. HEATING-6 THERNAL MODEL GEOMETRIC INPL. Cross sectional drawings of the areas of interest are presented in P!gures 1-2a and 26.. These figures (extracted from Reference 11) list the 1,a t e r i o r structural dimensions and materials. Figure 1-3 (extracted from. Reference 12) details the concr~.e slab thickness. Details of the roof slab'inculation and waterproofing are from Attachments IV and V. A. MATERIAL DIMENSIONS (1 Accurtic Ceilino Tile
, The thermal model represents a one-dimensional slice beginning k, at the bottom of the acoustic ceiling tile which is in contact L
x-c/as l$ r WPPf- CBf / -co? With the control room air volume. Because no dimensions are given for the tile thickness, a thickness of 3/4 inch will be i assumed from scaling of the original drawing. This dimension is consistent with actual measurements of samples of acoustic tile. Gypsum Board Above and in direct contact with the tile is a 1/2 inch thick gypsum board. It will be assumed for simplicity that the tile and board are in perfect contact and that there is no paper covering on the gypsum board. Dev Air Between the gyptum board and the concrete roof slab is an air space of 2 feet 9 and 3/4 inches. Concrete sw As presented in Figure I-3a, the concrete roof slab has a minimum thickness of 2 feet and a maximum thickness of 2 feet 4 and 1/2 inchen. An average thic kt ess of 2 feet 2 and 1/4 inches is used in-the model. Firestone 150 91 Roof insulation l ll 2 and The Firestone ISO 95 roof insulation has a thickness of 5/8 inches per Attachment IV. Asphalt Wateroroofino The insulation is covered by a waterproofing material of asphalt. The asphalt is assumed to be 3/8 inch thick. The concrete roof slab, insulation and waterproofing are assumed to be in perf ec t contac t with each other.
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I
) The upper surf.cr of the waterproofing is the upper boundary of
, $*h A3 s ts/ # am- ag-oa the mocel and is in contact with the atmospheric temperature and solar raciation.
-B. MATERIAL THERMAL PROPERTIES Acoustic Ceilina Tile The tile is assumed to be mineral fiberboard, wet molded acoustical tile. Thermal physical properties ares (Reference 5,
' Table 3A p. 22.15 0 75 degF) i Density = 23 lb/cu ft Thermal Concuctivity = 0.42 BTU-in/hr-sq ft-degF
. Specific Heat = 0.14 BTU /lb-degF Gypsum Board Thermal properties are-for gypsum board I
i Density = 51 lb/cu ft 9 (at 99 degF Reference 13, Table 3 p. 4-63) Thermal Conductivity = 0.062-BTU /hr-sq ft-degF/ft (at ", degF-Reference 13, Table 3 p. 4-63) Mean Specific Heat = 0.259 BTU /lb-degF (Gypsum) (between 32 and 212 degF Reference 13, Table 17 p. 4-9) Dry Air The-thermal properties of dry air at one atmosphere are from Reference 6, Table A.7 p.565. Since the -density-and thermal conductivity of air vary with temperature to a greater degree 1;) than the other materials, values or temperatures from 60 to 180 l
Z- ?l ? 3 cegrees Fahrenheit are given. t,% Z
) Density (1bm/cu ft) =
0.07633 (60 degF) 0.06614 (140 degF) 0.07 50 (80 cegF) 0.06401 (160 degF) 0.07087 (100 cegF) 0.06201 (180 degF) 0.06843 (120 degF) Thermal Conductivity (BTU /hr-ft-F) = 0.01466 (60 degF) 0.01664 (140 degF) 0.01516 (80 degF) 0.01712 (160 degF) 0.01566 (100 degF) 0.01759 (180 degF) 0.01615 (120 degF) Specific Heat Cp = 0.24 BTU /lb-F (60 to 180 degF) Ninematic Viscosity (sq ft/hr) = 0.5685 (60 degF) 0.7316 (140 degF) 0.6078 (6? degF.) 0.7747 (160 degF) fr 0.0187 (180 degF) (% ! 0.6482 (100 degF) 0.6895 ( 120 r egF ) Prandtl Number = 0.712 (60'degF) 0.700 ('140 deqF) 0.709 (80 degF) 0.698 (160 degF) 0.706 (100 degF) 0.696 (180 degF) 0.703 (120 degF) Concrete Thermal properties are for sand and' gravel concrete Density = 142 lb/cu ft (at 75 degF Reference 13, Table 3 p. 4-63) Thermal Conductivity = 1.05 BTU /hr-sq ft-degF/ft ( ). (at 75 degF Reference 13, Table 3 p. 4-63) l l,_-_-_ - - - - - - - - - - - _ - - - - - - - - _ - - _ - - --- _ - - - _ _ - _ _ _ _ - _ _ - _ _ _
Z- Of.23 4d , ' / ._ CW V e A///1 - 3Bgt - o o v-Mean Specific Heat = 0.156 BTU /lb-degF (Concrete) j (between 32 and 212 degF Reference 13. Table 17 p. 4-9) cirestone I SO 9_ji Rooi 'nsulation Firestone ISO 95 consists of a polvisocyanate (urethane) foam matrix containing Freon R-11 gas (Attachment IV) Thermal properties are Density = 1.9 lb/cu ft (Attachment IV) Thermal Conductivity = 0.131 BTU-in/hr-sq f t-deqF (Attachment IV) Mean Specific Heat = 0.38 STU/lb-degF for Expanded Polyurethane (R-11 exp.) for aged stock (Reference 5, Table 3A p. 22.14 @ 75 degF) Asphalt Waterproofino The waterproofing material is assumed to be 0.375 inch built-up roofing isphalt (Attachment IV). The thermal physical properties are (Reference 5, Table 3A p. 22.16 @ 75 degF) Density = 70 lb/cu ft Thermal Conductance (C) = 3.00 BTU /hr-sq ft-degF Specific Heat = 0.35 BTU /lb-degr (s l
~._.
- ~ - f j .? 3 4Wf- sa 9'- 00 7 V. HEATING-6 THERMAL MODEL BOUNDARY CONDITIONS f yY ;.h
'{ er3}. A. INITIAL CONDITIONS The analysis is started just before sunrise on the first day (time
- 4.56 hrs) and temoeratures for the various structures were initially assumed to range from 73.4 to 100 degrees F.
These initial temperature estimates need only be the approximate temperatures that the structures would have in order to initialize the HEATING-6 run e r.d to reduce the computational time required to reach a steady periodic solution. B. BOVNDARY COND'. TION #1 l l This boundary condition represents the atmospneric conditions 1 to which the outer surface of the control building is exposed. It consists of a 24 hour periodic change in air terperature, j varying solar radiation, and' convective air currents. In the-HEATING-6 thermal model, this boundary condition is applied to h\ the top surface of the waterproofing as a surface to boundary condition.
- 1. AIR TEMPERATURE Air t'emperature is based on data from " Table 1 -
Climatic Londitions for the United States" of Chapter 23 of ASHRAE (Reference 5) and is' discussed in more detail in the main body-of the calculation, Section 3.1. Values fcr the outside air temperature are entered into 'the HEATING-6 input de:k as a function of time in Table 3 of the deck (Attachment II). A temperature value for each hour starting at midnight (time =0) and ending after 4 days was calculated using a cinusoidal equation with a maximum temperature of 94 drgrees F and minimum temperature of 76 degrees F; the minimum is assumed to occur at time =5 hrs, just after sunrise. (.,., .
)
f- /Ojh 3 A'l'E ( " $ E f G 0 Y" l' T = B5. + 9. x sin (P!/12. x (t - 11.)) jppfg where: T = Temperature (cegrees F) t = Time (hours, based on 24-hr cycle) PI z 3.14159
- 2. SOLAR RADIATION Solar radiative heat flux data from NOAA's " Monthly Summary Solar Radiation Data" for Omaha, Nebraska (Reference 9, Attachment Ill) are entered into the HEATING-6 deck (Attachment !!) as a functicn of time via the subroutine "BNFLUX". The digitization procedure results in a value approximately 10*/. conservative on the integrated daily heat flux. Added discussion for using NOAA data is also provided in Section 3.2 ot the main body of this calculation. See that section regarding choices of roof absorptivity, emissivity and the treatment of heat losses to the sky.
- 3. CONVECTIVE HEAT TRANSFER 3
h1 Heat transfer from the upper surface of the control building roof to the atmosphere by convection was estimated using Table 11 p. 22.26 of ASHRAE (Reference 5). For a flat horizontal surface of 4 sq. ft. or more facing upward and a 50 degree temperature differential with the air, the heat transfer coefficient (h) is equal to: h = 2.03 BTU /hr-sq ft-degF Although the temperature difference can be greater than 50 degrees for much of the time, a smaller, entimated value of
'h' will be used for conservatism:
h= 1.00 BTU /hr~sq ft-degF and- entered into the input deck as a forced convection heat transfer coefficient. Although input using the code's forced
, 2 ,,
k convection option, no credit is actually taken for the
}
, 17'YYf23 od r
t W /,Y,> W/'?Y-s!'f-oo;}:- cooling effect of winds on the roof. The value of 'h' used l should result in an uncerestimate of convective heat losses
- r~ is, t h e_' surface, thus introducing '( from conservatism into the calculated roof temperatures.
C. BOUNDARY CONDITION #2 This boundary condition represents the heat transferred between the top surface of the gypsum board and the bottom surface of the concrete roof slab by radiation. In the HEATING-6 thermal model, this boundary condition is applied as a surface-to-surface boundary condition. For conservatism, no convective heat transfer was assumed to occur. Again, this contributes to an-overcalculation of the roof-temperatures in the initialization procedure.
- 1. RADIATIVE HEAT TRANSFER For two parallel infinite slabs, the shape factor (SF) for
?.b '
i radiation from surface 1 to surface 2 15: 1
" ~~~~~~~~~~~~~~~~~
SF1 -2 1/e g + 1/e 2
~
I i wheret eg = emissivity of concrete ,
= 0.94 (Reference 8) e7 = emissivity of gypsum board
!, = 0.90
- SF -2 1
= 0.85
- This value was estimated since-the details of the gypsum board covering is uncertain; it was assumed to be paper.
1
J- /2. /4 3
/W$J e - a f-007 The radiative heat transfer coefficient hg entered into HEATING-6 input deck is the product of the shape factor and b) the Stefan-Bolt: man constantt
= (0.85) (0.1714E-08 BTU /hr-sq ft-degR**4) nR yielding:
hR = 1.45BBE-09 BTU /hr-sq ft-degR**4 . D. BOUNDARY CONDITION M3 This boundery condition represents the interface of the bottom of the acoustit ceiling tile and the constant temperature control room air. Th;s is modeled as a surface to boundary condition and
-is applied to the bottom surface of the acoustic tile. No radiative heat transfer was modeled. The boundary condition consists only of a constant 73.4 degree F bouncary temperature t I and a constant, estimated heat transfer coefficient of 1.0 Btu /hr-ft**2-degf. Considering that natural convective correlations yield values of 'h* of approximately 0.5 for the large horizontal surfaces in the control room, a vclue of
~
'1.0 in the presence of a forced air system appears reasonable.
h VI. HEATING-6 THERMAL MODEL-CODE OPTIONS Code input and output options are described in detail in Reference 3. A few of the code options are presented here in order to clarify the
-analysis. The HEATING-6 code output deck is presented in Attachment II.
The calculated results were written to the output file- at every timestep, per the third entry on the third card in the input deck, and per Section F10.5.5.3 of Reference 3. a
Z-/3f23 [N($ WPPf- Sff - po 7 TRANSIENT PARAMETERS - The problem was solved with the transient calculation option _using the Crank-Nicolson implicit solution scheme per the " TRANSIENT PARAMETERS" card (s>: _
- initial time step = 0.5 sec.
- ft . S.. multiplier factor = 1.1
- minimum time step = 0.01 sec.
The above selections are explained on page F10.5.35 of Reference 3. The automatic time step features of the code have also beer, invoked. A 1 maximum change of 1% is allowed in the temperature at any given node before time step size is cecreased. The code default options have been used for convergence criteria. PRINTOUT TIMES - hardcopy output was provided for selected intervals in order to facilitate comparisons of calculated temperatures to the l l individual nodes. l l l NODES MONITORED - the nodes monitored, indicated in Att. II, determine which areas of .he thermal model are selected for temperature monitoring.- Figure 1-4 is a " MAP OF THE NODE NUMBERS", depicting all the nodes in the model along with their coordinates. The " NODES MONITORED" ; were limited-to eleven to simplify data processing, but this parameter allowed for sufficient temperature monitoring.- 5.0 -ANALYSIS RESULTS-Results of the 96 hour thermal response analysis are plotted in Figure I-5. It--is apparent that the maximum temperatures for the ceiling
- and.
roof structures:have been reached and that a periodic steady state has been achieved. The roof surface temperature is characterized by _ periodic heatup in response to the daily solar load, accompanied by cooldown at night as a result of_ radiative cooling to the sky. The black asphalt surface gets very hot, perhaps moreso than would be expected. This is due to conservatism in the model. Inner layers of k} the roof are heated substantially less due to the_ thermal mass of the
/
f-///ci?
$'I fr ~
A/R'f~ JEl ~ 00 r-concrete and the protection afforded by the ISO-95 insulation. The results of this analysis provide the basis for the roof boundary conditions in the control room volume analysis using the CONTEMPT-LT/028 code. Figure I-6 is a page from the HEATING-6 output deck whic- istrates the node temperatures for Time = 84 hours (4th day at Noon) . Figure I-7, plotted on an expanded scale, illustrates the roof response for the last 36 hours.of the simulation. Steady state is indicated. A value of 90 degrees '# is considered a bounding value for the surface temperature at the top of the concrete layer and one which accounts for variations in the solar insolation and ambient temperature. r . i
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a - m - G3 dl 2, - CNS CONTROL ROOM ROOF TEMPERATURE 1-0 NST. C.R. TEMP 73F - ACT'l SQL O v v v V y V 94 - V 7 V V y V 92 - V y V a v y V 2 7 7 I~ 7 g 88 -
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[ A8Efe-AID WAS UPGRADtD TO RELEASE 5.4 WHICH ttJCtODES MAJOR EtatANCEteENTS TO ABtNO DI AGNOST ICS. 'MANLJALS MAY BE ORDE Rf D F Rose
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/ STOP 89320.2057 CPU OMIN Ot.57 SRB OMIN OO.46SEC VIRT 288K SvS 280K EMT SK SYS BRG8K IEF3741 STEP e.....e.e.... ..e....ee........e..............e.e......e..SEC
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kOMAND DATA ACQUISITION STSffd ~ _ _ STEP NAME LkED START TIMEj 0,57.Q9.89 VIRT_Sy$ _U$ED 280K__,PAGE INS _ 3 _5TEP..iC8 ___,OO.QO.Ot:57
- PGM NAME IEWL SiOP IIME 20.57.43.67 ,v!RT CORE USED 288K PAGE 0015 O JOB IC8 00.00.01.7T *
- DISPATCH PRTY 105 ELAP. TIME 00.00.33.78 SWAPS /PAGES O/ O SRB TIME 00,00.00.46 CONDIllDN CODE 0000 *
- PERF. GROUP t SRU 21.83 TRANS ACT TIME 00.00.39.49 OCCUPANCY 00.00.00.00 *
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- EXCF STATISTICS ,
ExCP COUNT
- UNIT EXCP COUNT UNjf EXCP COUNT UNIT _ EXCP COUNT UNIT EXCP COUNT. UNIT EXCP COUNI UNIT
- 288 153 ore 246 288 O C42 0 893 376 C54 3ns *
- 891 2 28B 267 EXCP TOIAL 1.430 VIO PAGE INS O VIO PAGE OUTS O~ PAGES SWAPPED IN O ;
IEF2361 ALLOC. FOR V9xNPit0 GO IEF2371 C54 ALLOCATED TO PGM=*.OD g IEF23?I JES2 ALLOCATED TO FTO5FOOf IEF237I JES2 ALLOCATED TO FTO6 FOOT _]{[3371_JES2 ALLOCATED TO FTO7 FOOT IEF2371 893 ALLOCATED 10 F TO4 FOOL IEF237I JES2 ALLOCATFD TO FTO6 TOOL IEF1421 W9xNPt10 GO - STEP WAS EXECUTED - COND CODE 0000 I _{E[265I }Y$89320.T2057Q6.RAOOO.W9XNPitO.GOSET KEPT IEF2851 VOL SER NOS= W80003. l IEF2851 JES2. JOB 06723.SIOOO103 SYSIN IEF2851 JES2. JOB 06723.SOOOOtOS SYSDUT ! . I E E285 L._vtS2. JOs9672hsQQQQ t O9 Sv500T IEF285I SYS89320.Y205706.RAOOO.W9XNP110.ROOOOOO4 DELETED l VOL SER NOS= WORK 32. IEF2851 IEF2851 JES2. JOB 06723.SOOOOtto SYSOUT _![F373[_$1E ]PCO / } TART 89320.2057 280K EX1 JK SYS 8852K IEF3741 89320.2058 CPU OMIN 84 OO.4tSEC VIRT 896K Sv5
..... /.GO......../..STOP...............................
........ STEP 85SEC SP8.............OMIN
. KOMANO DATA ACQUI$1 TION }YSTEM _ _ _ _ _ _ . _ _ _ ___ __ ?*
- STEP NAME GO START TIME 20.57.43.84 VIRT SYS USED 280K PAGE INS O STEP ICR 00 00.14.85 *
- PCM NAME PCM**.DO STOP TIME 20 58.36.08 VIRT CORE USED 896K PAGE OUTS O JOB TCR 00.00.96 62 *
- DISPATCH PRTY 105 ELAP. TIME 00.00.52.24 SWAPS /PAGES O[ O SRB TIME 00.00.00.49 CONOIIION CDOE 0000 *
- PERF. GROUP 1 SRU 122.37 TRANS ACT TIME 00.00.58.25 OCCUPANCY 00.00.00.00 *
.-+ *
..s........e.....................e..................................................................................................
.** EMCP STATISTICS
- EXCP COUNT UNIT EXCP COUNT *
- UNIT ExCP COUNT UNIT EXCP COUNT UNIT EXCP COUNT UNIT ERCP COUNT UNIT (3
- C54 58 693 434 Os l Gk A '
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. e .e 3 . . e
- 4 <
a
- EXCP TOTAL ~492 ~ VIO PAGE. INS O VIO PAGE OUIS O PAGES SWAPPED IN O. '*
e .. . e... .eee....e. ....... .ee ....e....... .... .....e..e...ee e......... 4 .........e....... .... . ...o....ee.e........e...ee.. es.e IEF2371 898' -ALLOCATED TO'SYSOOOOt
.1[F2851 _ 5V589320.Y205836.RAOOO.W9XNPttQ3RQQQOQQt- MEPT IEF285I ' VOt. SER NOS= worm 31.
IEF2851 SY S89320. T 205706. R AOOO , W9 xNP 1 tO IL D ADSE F DELETED.. IEF2851 VOL SER NDS= tWORK31. I(F2M[ CS4 ' ALLOCATED TO $Y$0QQO3;. _ _,, .. . _2__,__ SYS89320.T205836.2A000.w9mNPtto.ROOOOOO3:_,_ _ _ MEPT --, IEF285I IEF2851- 'VOL.SER NOS= W80003. IEF28SI SYS89320.7205706.RAOOO.W9XNPt10.GOSET DELETED-JEF285I - VOL_$ER NO5= id8000h: _.,m_a ;_ _ _ ' , . - r IEF375! JOB /W9XNP1107 START 89320.2057-. IEF3761 DOS /W9xNPitOf STOP' 89320,2058 CPU OMIN 16.62SEC SRB OMIN CO.895EC
.eeeeeee.eeeeeeeeeee..eeeees.seeeeeeeeeeeeee.eeeeeeeeeeeeeeeeee...e..eeeee .e.e ee..........e.ee..e......e ..ee.seee.e...see......ee
~ ^ ~~~~' ' ~ ^^ ~ ~ '
~TOsiB ND DIYAN CQUI55'i!65 SYSl(M'
.00.00.16.62
- JOB LOG NUMBER - W9xNPt10 89320 20 57.00.95 TCB TIME . SRB TIME 00e00.00.89
~
- PROF 5ASIMER [NERCON INIT DA'TE 11/i6/89 89.320" ~ ~INiTIAliON TIME' '20.57.06ftG
- e ACCTG DATA ttE66VieJK TERM DATE' 1t/tG/89 89:320 TERMINATION IIME 20 58 36.63, *
~ ~
- OS-VS2 REL 03m8 i6i/ SERVICE ~~1/ 146.ti E UFSiD TIME" ~ ^ ~ O Ot 30Ts7 ~ =
o .e
- SYSTEM ID PCC4- CLASS Z COMPLETION STAitJS COOOO' *
- e. e e . e e e e e . e . e e . o e. e e e.e e s.o.e e e.o e. s e e e e e e e e o.e. e e e.s e e e e e e e e. .e e e e e e e.e e e e e e e . . . .e s... .e.o ...e. e. e e e . o o . e e e e e e e e .. . e s. . . e . . . . e.
- TOTAL MAINFRAME UNITS
- e .
__}Y$ TEM RESOURCE tfNIT$ ($RtJ) . 146.14.
- e
- APPt.ICATION RESOURCE UNI TS I ARU) *
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_ _ _ IBM
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- SOURCE EBCDIC LIST NODECK OBJECT NOMAP.NOf0RMAT COSTMI NOXREF AtC .
C**"*"* C'?**"* __; , ._. . _ _, _ . . _ _ _ . _ _ ,. C"*"'t
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I$N 0002. SUBROUTINE BNFLUX (RVALDE.R.1H.2. TIM.TSN.VALUE.NUMBfR,N) C'********************************************************************- C . C EJ E. HOLCOMB- ~.tO/25/89 C C4""*"""""""*"""'*'"""*""*****""'**"" C. .. C "" SUBROUTINE TO CALCUL ATE NET HE AT EOAD C ON CNS CONTROt.' ROOM ROOF. C . _ . _ _ _ . . . , _ _ . _ , . _ _ C ISN 0003 REAL*8 RVALUE.R.TH.Z. TIM.TSN.VALUE - ISN 0004- COMMON /100 NIT / IBIN.! ECHO.IERROR.IMATLB.IN.IO. Z IPLOf.!PLO!O.[RIC W ITPl% ITgOUT __ _ _ . _ _ _ , , ___, _ _ _ __,_. C . ISN 0005 DIMENSION IIME(20).OS(20) ISN 0006 DATA TIME /O. 4.56EO. 4.78 5.5. 6.5. 7.5. 8.5. 9.5 10.5.'t1.5 I 12:5,,_,!3 1 %,_j!,},fj%:$,,!@;g _ It7.5, 19,22 18 %19_5 57,p2 4t 19:44F 21 / _ ISN 0007 DATA 0570.. O. 3,87 f).67.72997..298.95,j263.11, t35 96 e9
,Z 268.2 284.6 7 7 219.70.j160.70.j >
Z 99.24 43.15.p. 299 f. O.. O / 10.74 C ~ ~ - ~ ' ~~ ~~~ ISN 0008 DATA EPS. SIGMA. ALPHA /O.90. O.1714E-06. O.94/ ISN 0009 DATA C1.C2.C3.C4/11.EO.12,EO.85.EO.9.EO/ C C 1) HEATING-6 INPUT TIME UNITS MUST BE HuuRS "* C 2) *0S' IS MEASUwED SOLA2 LOAD AT OMAHA. NEORASKA C NEAR SUMMER SOLSTICE JUNE l19 '1977 EDITED DATA. C -3) AMBIENT TEMPERATURE IS'ASSUMfD TO' FOLLOW A SINUSOID. C BA_$ED ON 11_DE}IGN VALUIj$ FOR OMAHA NEB. C ISN 0010 NPTS = 20' ; ISN 0011 FLUXIN = 0. . . ISN 0012 PJ = 4.*AJAN W O_E_0_j' ISN 0013 ITMP
- NPTS - t C
ISN 0014 OTIME
- TIM /24 ISN_ pots REFTIM = (DT IME '- INT (DTIs4E ))*24.
ISN 0016 ARGt = Pl*(IIM-Ct)/C2i C ISN 0097 TAMS = C3 + C4* SIN (ARGt) I$N _018 0 TAMBR = TAMB + 459J 9 ISM 0089 TAMBE = TAMBR/t.8 ISN 0020 TSKYK = 0.0552
- T AMBK" 1.5
! ISN 0021 TSKYR = 1 8*TSKYK ISN 0022 TSNR = TSN + 45_9 _.69 _ ISN 0023. DO 10 !=1.ITMP .. r ISN 0024 IF (REFTIM .GE.' TIME (I+1)) GO TO 10 ISM 0026 -TIME .i ~' -
'l RAT'=
FLUAIN(REFTIM-TIME
- ALPHA *( 5(I) +(I))[(TIME 5AU (D$(I(I+t)U )26(S())))
i ' ( ISN 0027 I) I 4 4
- .d! A-
_ _ __ ._ _ ._ _ . _ _ _ _ _ _ _o
N ~... wt ' ( DAIE 89.320/20.5F.08 PAGE 2 LEVEL 2.3 (FRO 7) BNFLUX 05/360 FORTRAN H EXTENDED ISN 0028 GO 10 100 ., 3 ISN 0029 10 CONTINUE C ISN 0030 100 OOUT = EPS
- SICMA * (~5NR**4 - TSKvR***)
C ISN 0031 QNET = FluxlN - QOUT C ISN 0032 RVAtUE = QNET ISN 0033 RETURN _ _ ISN 0034 {ND _ _ _ _. _ _ , _ . __ _ 000000 47 TO F OOC ENT Lbt ' BC 15.12(0.15) 000004 07 DC xtt'07' DC CL 7
- BNF L UN ~ ~ ~~~~~ ~ ~ ~ ~
000005 C205C6D3E4E740 14.12.12 631 ~ OOOOOC 90 EC D OOC STM 000010 18 40 tR 4.93 000012 98 CD F O20 LM 12.13.32(15)
. _ __ S T ._ _ _ f . ! ( 0, f 3 ),_, _._ ____
000016 SQ.30.D 004____ _. ST 13.8(0.4) OOOOIA 50 00 4 008 BCR 15.12 0000 IE 07 FC 7 E s4POR AR Y FOR FlxfFLOAT DC XL4*00000000' 000088 00000000 DC Xt4 00000000* OOOO8C 00000000 DC xL4*4E000000' 000090 4E000000 000094 00000000 ,_ _ D_C XL4'QOOOOOOO*_. ._. ._ _ CONSTANTS DC XL4'4FC80000* 000098 4F080000 DC NL4'00000000' OOOO9C 00000000 XL4'4EOOOOOO OOOOAO 4EOOOOOO DC OOOOA4 80000000 DC XL4 80000000* OOOOA8 42180000 DC XL4'42tSOOOO' DC XL4"uGOOOOOO' OOOOAC 00000000 NL4*431CEBOA* 000000 43tCBBOA OC 000084 0000000C DC 2L4*00000000 000088 00000000 DC X L 4 *60v0sxx6' OOOOBC 00000001 00 xL4*0000000i* OOOOCO 00000004 DC xL4 00000004-OOOOC4 000000t4 DC xL4*00000084* OOOOC8 3FE21965 DC XL4*3FE21965* OOOOCC 41100000 DC XL4*41t00000' 000000 41180000 DC XL4'41180000' 000004 411CCCCD DC ut4'48tCCCCD' 000008 41400000 DC NL4'41400000 OOOODC 42f80000- DC XL4'42tBOOOO' OOOOEO 43tCBBOA DC NL4'43tCBBOA* OOOOE4 00000000 DC xL4'00000000 OOOOE8 00000000 OC XL4'OOOOOOOO' ADCONS TOR VARIABLES AND CONSTANTS ADCONS FOR COMMON OC Kt4'OOOOOOOO* 000238 00000000 ADCONS FOR EXTERNAL REFERENCES De ut4'OOOOOOOO SIN OOO23C 00000000 ATAN 00024O 00000000 .sc xL4*00000000 DC XL4'OOOOOOOO' FRxrRe 000244 00000000 DATA CONSTANTS DC XL4'4tCOOOOO' Ct OOOOF4 41800000 C2 OOOOF8 41COOOOO DC xL4*41COOOOO' DC xL4*42550000' C3 OOOOF C 42550000 4 ta
l' LEVEL 2.3 (Fx07) BNFlux 05/360 FORTRAN tt EXTENDED DATE 89.320/20.57.09 PACE 3 OC *L4*41900000* C4 000100 41900000 EP5_, OOOfQS 40E66665 DC kt4'40E66666* , XL4'40FOA307' DC A L TH A DOOt2C 40FOA3D7 StGMA 000134 3975C902 DC XL4'3975C902' DC XL4'00000000* OS 000190 00000000 000894 00000000 DC XL4"00000000 QS . . _ _ _ _ _ . DC XL4'423 DEB 85' OS 000198 4130EB85 05 OOO19C 4212AB85 DC XL4'4212A885' ( . 0001A0 4248E8F6 DC XL4'4248E8F6* 05 0001A4 4287F5C3 DC xL4*4287F5C3' _05 __ _ . _ _ _ . _ _ . . _ _ ' 000148 42C39tEC DC XL4*42C39fEC' 05 DC XL4'42FtE307' 05 l OOOfAC 42FtE307 05 000980 43 TOC 385 DC XL4'4310C385* 000184 4318CBOA DC XL4*439tCBOA" QS DC XL4'431289tF* OS 000188 431289tF 05 OOOtBC 4312AF33 DC XL4*4312AF33' DC XL4*43tO7tC3* OS 0001C0 43tO7tC3 05 0001C4 42088333 DC xt4*420BB333' ^' ~~~ ~' ~ ~ ~ ~ 0001C8 42A08333 DC XL4'42AOB333' 05 ~~ DC XL4'4263307t' OS OOO1CC 42633071 05 0001D0 42282666 DC XL4'42282666' 0001D4 41ABD704 DC XL4'41ABD704' OS DC XL4'OOOOOOOO' 05 000108 00000000 05 0001DC 00000000 DC XL4'00000000' DC xL4*00000000 i1ME 000tEO 00000000 TIME OOOtE4 4148FSC3 DC XL4'4148F5C3' DC XL4'414C7AEt' TIME . 0001E8 414C7AEt TIME l OOO t E C 41580000 DC XL4'4tS80000* ' DC XL4'4tG80000* TIME i OOO t F O 49680000 TIME l OOOtF4 41780000 DC XL4'41780000" DC XL4'4tB80000' TIME OOOtF8 41880000 TIME l OOO1F C 41980000 DC XL4'41980000' I DC XL4'4tA80000' TIME 000200 41A80000 TIME 0002O4 41880000 DC kt4'41880000' DC XL4'4tC80000' TINE ' 000208 4tC80000 TIME OOO20C 41080000 DC XL4'4tD80000' l DC XL4'4tE80000' IIME 000210 4tEBOOOO ItME 000214 4tF80000 7C XL4'41F80000' DC XL4'42tOBOOO' TIME 000218 42108000 TIME DOO2fC 42118000 f tC Xt4'4211800C'
?C XL4*42128000* T I Mt 000220 42128000 itME 000224 42133852 DC XL4'42133852' DC XL4'421370A4' TIME 000228 421370A4 itMr OOO22C 42180000 DC XL4'42tBOOOO' t
000250 58 AO D 094 100001 t 10 148( O.13) L ? _152(,0,13) 4 000254 58 70 D Q98 _ 19 l 000258 58 60 D 224 L E. 548( O.13) O OOO25C 78 00 0 090 (E O. 144( O.137 STE O. 292( O.13) FtUx!M 000260 70 00 D 124 l 000264 58 FO O 218 9. 15,_536LO,13l__ A T AN __. _ _ _____ _ 000268 49 10 D 04C la t. 76( O.137 OOO26C 05 E F BALR 14.15 OOO26E 47 00 O OOC BC 0, 12( O. Of 000272 78 20 D 080 LE 176( O 41400000 e MER 2,~ 2 ~6- ~ ~ ~ ' ,13 ) 000276 3C 20 TIM i 000278 68 40 D 148 LD 4 328( O.13) i ' OOO27C 60 40 D ORO DD 4 128( O.t3) 4218000000000000 i 000280 28 00 SDR O uO ~~ 000282 38 04 LER O. 4 4 4
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