ML17157A804
| ML17157A804 | |
| Person / Time | |
|---|---|
| Site: | Susquehanna  |
| Issue date: | 11/05/1990 |
| From: | Chaiko M, Murphy M PENNSYLVANIA POWER & LIGHT CO. |
| To: | |
| Shared Package | |
| ML17157A805 | List: |
| References | |
| NUDOCS 9108260165 | |
| Download: ML17157A804 (142) | |
Text
COTTAP-2, REV. 1 THEORY AND INPUT DESCRIPTION MANUAL Prepared by.
N. A. Chaiko and H. J. Murphy
'5 (<
NOVEMBER 5, 1990 9103260165 910319 PDR ADOCK 05000337 P PDR
PAL Form 2454 i10/83)
Cat, s973401
$ E -B- N A -04 6 R- .0 1'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY - ER No.
Date It- I> 19 ~~ CALCULATION SHEET Designed by PROJECT Approved by CONTENTS 1 ~ INTRODUCTION
- 2. METHODOLOGY 2.1 Model Description 2.1.1 Mass and Energy Balance Equations 2.1.1.1 Balance Equations without Mass Transfer Between Compartments 2.1.1.2 Balance Equations with Mass Transfer Between Compartments 2.1.2 Slab Heat Transfer Equations 12 2.1.2.1 Conduction Equation and Boundary Conditions 13 2.1.2.2 Film Coefficients 17 2.1.2.3 Initial Temperature Profiles 23 2.1.3 Spdcial Purpose Models 2.1.3.1 Pipe Break Model 24 2.1.3.2 Compartment Leakage Model 25 2.1.3.3 Condensation Model 28 2.1.3.4 Rainout Model 33 2.1.3.5 Room Cooler Model 34 2.1.3.6 Hot Piping Model 35 2.1.3.7 Component Cool-Down Model 39 2.1.3.8 Natural Circulation Model 41 2.1.3.9 Time-Dependent Compartment Model 43 2.1.3.10 Thin Slab Model 43 2.2 Numerical Solution Methods
- 3. DESCRIPTION OF CODE INPUTS 53 3.1 Problem Description Data (Card 1 of 3) 54 3.2 Problem Description Data (Card 2 of 3) 55 3.3 Problem Description Data (Card 3 of 3) 59 3.4 Problem Run-Time and Trip-Tolerance Data 60
rrPE 1. Form 2lSl (rar831 Ckr, l973401
$ E -B- N A-0 4 6 Rev.0 l
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY .ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~Lof Approved by 3.5 Error Tolerance for Compartment Ventilation-Flow Mass Balance 61 3.6 Edit Control Data 61 3.7 Edit Dimension Data 62 3.8 Selection of Room Edits 63 3.9 Selection of Thick-Slab Edits 63 3.10 Selection of Thin-Slab Edits 64 3.11 Reference Temperature and Pressure for Ventilation Flows 64 3.12 Standard Room Data 65 3.13 Ventilation Flow Data 66 3.14 Leakage Flow Data 67 3.15 Circulation Flow Data 68 3.16 Air-Flow Trip Data 69 3.17 Heat. Load Data 70 3.18 Hot Piping Data 71
- 3. 19 Heat-Load Trip Data 73 3.20 Pipe Break Data 74 3.21 Thick Slab Data (Card 1 of 3) 75 3.22 Thick Slab Data (Card 2 of 3) 78 3.23 Thick Slab Data (Card 3 of 3) 79 3.24 Thin Slab Data (Card 1 of 2) 80 3.25 Thin Slab Data (Card 2 of 2) 81 3.26 Time-Dependent Room Data (Card 1 of 2) 82 3.27 Time-Dependent Room Data (Card 2 of 2) 84
- 4. SAMPLE PROBLEMS 85 4.1 Comparison of COTTAP Results with Analytical Solution 85 for Conduction through a Thick Slab (Sample Problem 1) 4.2 Comparison of COTTAP Results with Analytical Solution for Compartment Heat-Up due to Tripped Heat Loads (Sample Problem 2) 96 4.3 COTTAP Results for Compartment Cooling by Natural Circulation (Sample Problem 3) 98 4 4 COTTAP Results for Compartment Heat-Up Resulting from a High-Energy Pipe Break (Sample Problem 4) 103 4.5 COTTAP Results for Compartment Heat-Up from a Hot-Pipe Heat Load (Sample Problem 5) 112 4.6 Comparison of COTTAP Results with Analytical Solution for Compartment Depressurization due to Leakage (Sample Problem 6) 117
- ~
PPLL Form 2l54 l1$ S3)
C4t. e9Q401 F -B- N A.-04 6 Rev.0 1'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of
~ ~ ~
- 5. REFERENCES 122 APPENDZX A THERMODYNAMZC AND TRANSPORT PROPERTZES OF AZR AND WATER 126
l PPKL Form 2I54 (1083)
Cat. t9%401
$ F -B- N A =04 6 Rev.ap Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date DesIgned by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of
- 1. INTRODUCTION COTTAP (Compartment Transient Temperature Analysis Program) is a computer code designed to predict individual compartment environmental conditions in buildings where compartments are separated by walls of uniform material composition. User input data includes initial temperature, pressure, and relative humidity of each compartment. In addition, ventilation flow, leakage and circulation path data, steam break and time dependent heat load data as well as physical and geometric data to define each compartment must be supplied as necessary.
The code solves transient heat and mass balance equations to determine temperature, pressure, and relative humidity in each compartment. A finite difference solution of the one-dimensional heat conduction equation is carried out for each thick slab to compute heat flows between compartments and slabs. The coupled, equations governing the compartment and slab temperatures are solved using a variable-time-step O.D.E.
(Ordinary Differential Equation) solver with automatic error control.
COTTAP was primarily developed to simulate the transient temperature response of compartments within the SSES Unit 1 and Unit 2 secondary containments during post-accident conditions. Compartment temperatures are needed to verify equipment qualification (EQ) and to determine whether a need exists for supplemental cooling.
PPdL Form 2i54 (10/83)
Cat. S9D401 (F B fq A-Q4 5 Rev. Q Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
CALCULATION SHEET Date Designed by 19 PROJECT Sht. No. ~of Approved by The scale of this problem is rather large in that I
a model of the Unit 1 and Unit 2 secondary containments consists of approximately 120 S
compartments and 800 slabs. In addition to the large size of the problem, the temperature behavior is to be simulated over a long period of time, typically one hundred days. Zt is therefore necessary to develop a code that can not only handle a large volume of data, but can also perform the required calculations with a reasonable amount of computer time.
Zn addition to large scale problems COTTAP is capable of modeling room heatup due to breaks in hot piping and cooldown due to condensation and rainout. It also contains a natural circulation model to simulate inter-compartment flow.
The purpose of this calculation is to demonstrate the validity of this computer code with regard to the types of analyses described above. This validation process is carried out in support of the computer code documentation package PCC-SE-006.
pphL Form 2454 lror83r Car, e97&or S< -B- N A-0 4 6 gee O ~.
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. 8 of Approved by
- 2. METHODOLOGY 2.1 Model Descri tion The compartment mass and energy balance equations, slab heat condition equations, and the COTTAP special purpose models are discussed in this section. An outline of the numerical solution procedure used to solve the modeling equations is then given.
2.1.1 Mass and Ener Balance E ations Two methods are available in COTTAP for calculating transient compartment conditions. The desired method is selected through specification of the 1
mass-tracking parameter MASSTR (see problem description data cards in section 3.2).
2.1.1.1 Balance E ations without Mass Transfer between Com artments If MASSTR 0, the compartment mass balance equations are neglected and the total mass in each compartment is held constant'throughout the calculation. This option can be used if there is no air flow between compartments or if air flow is due to ventilation flow only '(i.e., there are no leakage or circulation flow paths) . In COTTAP, ventilation flow
PPhl. Fofrft 2454 1fof83)
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Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. fff of Approved by rates are held constant at their initial values> thus, if the net flow out of each compartment is zero initially, then there is no need for a compartment mass balance because the mass of air in each compartment remains constant.
Zn this mode of calculation, the moisture content of the air (as specified by the value of compartment relative humidity on the room data cards, see section 3.12 ) is only used to calculate the film heat transfer coefficients for thick slabs; the effect of moisture content on the heat capacity and density of air is neglected. The compartment energy balance used in COTTAP for the case of MASSTR=O is P
a C
va VdT dt r
=Q light +0Qpanel +0motor +Q cooler Qwall misc piping N
+ P W vj. (T vj. +a)o C pa (T .)
vj (2-1) j=1 where ~ compartment (room) temperature 0 T
Z ( F),
t ~ time (hr),
p a
density of air within compartment (ibm/ft3 ),
C va constant-volume specific heat of air (Btu/ibm 0F),
V ~ compartment volume (ft3 ),
Qli light h compart ent lighting heat lead (Btu/hr).
panel
= compartment electrical panel heat load (Btu/hr),
Q otor
= compartment. motor heat load (Btu/hr),
PP9t. Form 2454 t>583)
Cat, e913%1 SE -B- N A-046 Rev0g:
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY. ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~ of Approved by cooler compartment cooler load (Btu/hr),
heat load due to hot piping (Btu/hr),
piping wall rate of heat transfer from walls to compartment ai r (Btu/hr),
misc miscellaneous compartment heat loads (Btu/hr),
N v number of ventilation flow paths connected to the compartment, W
Vj ventilation flow rate for path j (ibm/hr),
T V j
~ air temperature for ventilation path j ( 0 F),
C pa (T .)
vj specific heat of air evaluated at T . (Btu/ibm 0 F),
v3 a = 459.67 F.
0 Ventilation flow rates are positive for flow into the compartment and negative for flow out of the compartment.
Compartment lighting, panel, motor and miscellaneous loads, which are input to the code, remain at initial values throughout the transient unless acted on by a trip. Heat loads may be tripped on, off, or exponentially decayed at any time during the transient. Use of the heat load trip is discussed in Section 3.19, and the exponential decay approximation is discussed in Section 2.1.3.7.
The compartment room cooler load is a heat sink and is input as a negative value. The code automatically adjusts this load for changes in room
ppd,L Form 2454 n0/831 Cat. <<97340I SE -~- N A -0 4 6 Rev.Q P Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. 4 of Approved by I
temperature. Coolant temperature is input for each cooler and remains constant throughout the transient. See section 2.1.3.5 for a detailed description of this calculation.
The initial compartment piping heat loads and overall heat transfer coefficients are calculated by COTTAP based on piping and compartment input data. Overall heat transfer coefficients for hot piping are held constant throughout the transient and heat loads are calculated based on temperature differences between pipes and surrounding air. No credit is taken for compartment heat rejection to a pipe when compartment temperature exceeds pipe temperature. When this situation occurs, the piping heat load is set to zero and remains there unless compartment temperature decreases below pipe temperature. If this should occur a positive piping heat load would be computed in the usual'anner. Piping heat loads as well as room cooler loads may be tripped on, off, or exponentially decayed. See Section 2.1.3.6 for a detailed description of the piping heat load calculation.
The rate of heat transfer from walls to compartment air is calculated from N
w h.A.(Tsurfj. - T),
r (2-2) wall .
E j j '~1 where N ~
w the number of'walls (slabs) surrounding the room,
- h. =
j film heat transfer coefficient (Btu/hr ft2 0 F),
PP5L Form 2L54 (la(83)
Cat. %7340l SE N A -0 4 6 Rev.Q y'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19
'ROJECT CALCULATION SHEET Sht. No. ~ of A. = surface area of wall (ft2 ),
and
= wall surface temperature 0 T
surf j. ( F).
Use of MASSTR=O is only valid for the case where compartment temperatures undergo small or moderate variations. For these situations, maintaining constant mass inventory in each compartment is a fairly good approximation since density changes are small. If large temperature changes occur, compartment mass inventories will undergo significant fluctuations in order to maintain constant pressure. In this situation a model which accounts for mass exchange between compartments is recpxired. Use of MASSTR=.O, where applicable, is highly desirable especially for problems with many compartments and slabs because large savings in computation time can be realized. The more general case of MASSTR=1 is described below.
2.1.1.2 Balance E ations with Mass Transfer Between Com artments When the mass-tracking option of COTTAP is selected (MASSTR~1), special purpose models are available for describing air and water-vapor leakage between compartments, circulation flows between compartments, and the effect of pipe breaks upon compartment temperature and relative humidity.
ppat. Form P<<5<<<1$ 83t C<<t. <<973<<01 S~ -B" N A -G 4 6 Rev.Q ]
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of A. ~ surface area j of wall (ft2 ),
and 0
T surfj.
~ wall surface temperature ( F).
Use of MASSTR~O is only valid for the case where compartment temperatures undergo small or moderate variations. For these situations, maintaining constant mass inventory in each compartment i.s a fairly good approximation since density changes are small. If large temperature changes occur, compartment mass inventories will undergo significant fluctuations in order to maintain constant pressure. In this situation a model which accounts for mass exchange between compartments is required. Use of MASSTR=O, where applicable, is. highly desirable especially for problems with many compartments and slabs because large savings, in computation time can be realised. The more general case of MASSTR~1 is described below.
2.1.1.2 Balance E ations with Mass Transfer Between Com artments When the mass-tracking option of COTTAP is selected (MASSTR~1), special purpose models are available for describing ai.r and water-vapor leakage between compartments, circulation flows between compartments, and the effect of pipe breaks upon compartment, temperature and relative humidity.
pplLL Form 2<<si n0183)
C<<t. <<913401 SE -B- N A-046 RevQp Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of The air and vapor mass balance erpxations that are solved by COTTAP for the case of MASSTR~1 are N
VdP a ~P W.Y dt j~l vj vj Nl
+ E W . Y 3<<<<1 3 3 N
+ Z jul (W
cj,in Ycj,in - Wcj,out Ycj,out l<<
~ ~ ~ ~ ~ (2-3)
N VdP ~ P W . (1 Y .)
dt j~l Nl
+ g W . (1-Y .)
13 13 N
.. .. )
ro'2-4)
+ Z c
(1-Y - (1-Y
[W cj,in cj,in W cj,out cj,out
+W bs
-Wcond -W where p a
~ compartment air density (ibm/ft3 ),
p v compartment water vapor density (ibm/ft3 ),
N v number of ventillation flow paths connected to the compartment,
ppct. Form 2454 nOI83i Col, I873401 x
I SE -B- N A -0 4 6 Rev,p g>
Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~O of Approved by N
1
~ number of leakage paths connected to the compartment, N
c
~ number of circulation paths connected to the compartment, W
lj ~. total mass flow through leakage path j (ibm/hr),
W cj,in. . = total inlet mass flow through circulation path j (ibm/hr),
W cj,out
. = total outlet mass flow through circulation path j (ibm/hr),
l Y
vj . ~ air mass fraction for ventilation path j, Y
lj ~
. air mass fraction for leakage path j, Y .
cj,in . ~ air mass fraction of inlet flow for circulation path j, Y
cj,out
. = air mass fraction of outlet flow for circulation path j, Wbbs steam flow rate from pipe break (ibm/hr),
W = water vapor condensation rate (ibm/hr),
cond W
ro
~ water vapor rainout rate (ibm/hr).
The compartment energy balance for MASSTR 1 is Vf(Tr+a o )p a~a dC r
(T r) + p a
C pa (T
r) + p v~r dh (T r)
PP<<L Form 2<<54 nOr83)
C<<r. <<9'<<Oi SE -B- N A -0 4 6 Rev.0 1'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of vv -
p R p a
R ] dT a
dt r r o pa r
~ -V(T + a )C (T )dp dt a
- Vh (T )dp + (T+a o )(R dP + R dP )V v dv Zp a ddt
+Q.+Q+0+Q light panel Qmotor cooler + Q piping
+ 0 + 0 + Q mall misc .
break + W bs h
v, break
- W h (T ) W h (T )
N W .[Y .(T .+a )C vj.)h v (Tvj.)]
+ (T .) + (1-Y j=l vj vj rj o pa vj E
N j=l lj lj lj o pa 1 j
+QW1[Y1(T1+a)C(T1)+(1Y1)h(T1) lj v lj I N
+Z W .. [Ycj,in cj,in .. (Tcj,in .. +a o )Cpa (Tcj,in.. )
j 1
+ (1-Y .. )hv (Tcj,in) ]
cj,in .
N c
j<<<<1 W
cj,out
. [Y cj,out (T+a)C r o pa (T) r
+(1Ycj,out . )h v (T)],
r (2-5) where h saturated water vapor enthalpy (Btu/ibm),
h v,break
= enthalpy of steam exiting break (Btu/ibm) h (P v r) if pipe contains liquid, h (P v p
) if pipe contains steam, P ~ compartment pressure (psia),
r P
P
= pressure of fluid within pipe (psia),
ppB,L Foim 2i54 n(v83)
Cat. e973401 SE -B- N A -0 4 6 Rev.P y'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY - ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. I~ of Approved by R
v
~ ideal gas constant for steam (0.1104 Btu/ibm R)
R ~ ideal gas constant for air (0.0690 Btu/ibm 0 R),
Q break heat transferred to air and water vapor from liquid exiting break as it cools to compartment temperature C
(Btu/hr),
W bs steam flow rate exiting pipe break (ibm/hr),
h f~ saturation enthalpy of liquid water (Btu/ibm).
All other variables in (2-5) are as previously defined. The basic assumption used in deriving (2-5) is that the air and water vapor behave as ideal gases. This is a reasonable assumption as long as compartment pressures are close to atmospheric pressure which should nearly always be the case.
2.1.2 Slab Heat Transfer B ations The slab model in COTTAP describes the transient behavior of relatively thick slabs which have a significant thermal capacitance. Eor each thick slab, the one-dimensional unsteady heat conduction equation is solved to , ~
PP41, Form 2454 (10/831 Col. 4973401 SE -B- N A -0 4 6 Rey 0 >
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY. ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of obtain the slab temperature profile from which the rate of heat transfer between the slab and adjacent rooms is computed. All thick slabs must be composed of a single material: composite walls cannot be modeled with COTTAP .
A special model is also included in COTTAP for describing heat flow through thin walls which have little thermal capacitance. The thin slab model is discussed in section 2.1.3.10.
2.1.2.1 Conduction E ation and Bounda Conditions The temperature distribution within the slab is determined by solution of the one-dimensional unsteady heat conduction equation, aT s
pat - < a 2
T s
tax 2 (2-6) subject to the following boundary and initial conditions:
-h [T (t) - (o,t)], (2-7) 3T Bx k 1 rl T s
X~
BT -h 2 [Ts (Lt) - T z2 (t)J, (2-8) 3x X~L k T
s (x,o) ax+ b, (2-9) where 0
T s
(x,t) = slab I temperature ( F),
t ~ time (hr),
PP&L Form 245'0r&3)
Col, 0970401 SE -B- N A -0 4 6 R~v 0 1'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of x ~ spatial coordinate (ft),
~ thermal diffusivity of slab m k/(p s Cps ) (ft2 /hr),
~ thermal conductivity (Btu/hr ft F),
p ~ slab density (ibm/ft3 ),
C ps m specific heat of slab material (Btu/ibm F) 1 h ~
1 film coefficient for heat transfer between thy slab and the room on side 1 of the slab (Btu/hr ft F),
h 2
= film coefficient for heat transfer between thy slab and the room on side 2 of the slab (Btu/hr ft F),
T rl1(t) Temperature of room on side 1 of slab ( F),
T r22(t)
= Temperature of room on side 2 of slab ( F).
The slab and room arrangement described by these equations is shown in Figure 2.1. Note that the spatial coordinate is zero on side 1 of the slab and is equal to L on side 2, where L is the thickness of the slab.
Values of thermal conductivity, density, and specific heat are supplied for each slab and held constant throughout the calculation.
The rate of heat flow from the slab to the room on side 1 of the slab is given by q (t) h A[T (o,t) <<T (t) ], (2-10)
PP&L Form 2<<&d (l0(83)
Cat. <<913<<Of SE -B- N A -0 4 6 Rev () y Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~8 of Approved by al (t) ~ SS(t) on side 1 of slab Slab Room Temp <<
Room on side 2 of slab at temperature T.l(t) r'1 T (x,t) at temperature T (t) s r2 Side l of slab ~Side 2 of slab Film coefficient hl Fil coefficient. h2 Heat Transfer Area, A Heat Transfer Area, A X=O X=L Figure 2.1 Thick slab and adjacent rooms
PPtLL Forrtt 2454 (10I83)
C91, 991340t N A-046 Rev.0g:
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~&of Approved by and the rate of heat transfer from the slab to the room on side 2 is obtained from q (t) ~ h A[T (L,t) - T (t)J, (2-11) where A is the surface area of one side of the slab.
A slab can also be in contact with outside ground. Calculation of the heat loss from a slab to outside ground would involve modeling of multi<<dimensional unsteady conduction which would greatly complicate the analysis. As a simplifying approximation, heat transfer from below grade slabs to the outside ground is neglected by setting the film coefficient equal to zero at the outer surface of every slab in contact with the outside ground. This is a conservative approximation in the sense that the heat loss from the building will be underpredicted giving rise to slightly higher than actual room temperatures. The governing equations for a below grade slab with side 2 in contact with ground are (2-6) through (2-9) but with h 2 set equal to zero. If side 1 of the slab is in contact with ground then hl is set to zero.
ppAL Form 245'$ 83)
C4t. l873i01 N A 0 4 6 Rey Q )
Dept. PENNSYLVANIAPOWER 5 LIGHT COMPANY- ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~7of Approved by 2.1 2.2
~ Film Coefficients Film coefficients for slabs can be supplied as input data or values can be calculated by the code (see section 3.21 for a discussion of how to select the desired option) .
Zf the film coefficients are supplied as input data, two sets of coefficients are required for slabs which are floors and ceilings (a slab is defined as a floor or a ceiling depending upon its orientation with respect to the room on side 1 of the slab). A value from the first set is used if heat flow between the slab and the adjacent room is in the upward direction; a value from the second set is used if the direction of heat flow is downward. Only one set of film coefficients is required for vertical slabs because in this case the coefficients do not depend upon the direction of heat flow. User-supplied coefficients are held constant throughout the entire calculation. Natural-convection film coefficients are, however, temperature dependent, and values representative of the average conditions during the transient should be used.
Suggested values of natural convection film coefficients for interior walls and forced convection coefficients for walls in contact with outside air are given in ref. 11, p. 23.3; note that the radiative heat transfer I l
component is already included in these coefficients. l
PPEL Form 2454 noI83)
CSt. 4973S01 SE -B- N A-04 6 Rev.a y'ept.
.PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of Correlations are also available in COTTAP for calculation of natural convection film coefficients. Coefficients for vertical slabs are calculated from (ref. 8 p.442) h = k 0.825 + 0.387 Ra cl C (2-12)
[1+(0 492/P )9/16)8/27 wher e h cl1 = natural convection film. coefficient for vertical slab (Btu/hr ft2 0F),
k ~ thermal conductivity of air (Btu/hr ft F),
C ~ characteristic length of slab (slab height in ft) .
The Rayleigh and Prantl numbers are given by 2 3 Ra ~ g8(3600) (T surf -T )C /@(x) r L P (2-13)
Pr ~ AC P
/k, (2-14) where g ~ acceleration due to gravity (32.2 ft/sec 2 ),
coefficient of thermal expansion for air 0 -1 g ( R ),
g ~ kinematic viscosity of air (ft2 /hr),
PPiLL FOrm 2i54 tttt183t Cat. tt913401 SE N A-046 RevQP Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of a = thermal diffusivity of air (ft2 /hr),
"viscosity of air (ibm/hr-ft).
Air properties are evaluated at the thermal boundary layer temperature which is taken as the average of the slab surface temperature and the bulk air temperature of the compartment. The moisture content of the, air is also accounted for in calculating the properties (see Appendix A for calculation of air properties).
For horizontal slabs, the natural convection coefficient for the case of downward heat, flow is calculated from (ref. 17) h ~ 0.58 k 1/5 c2 Ra (2-15)
L and for the case of upward heat, flow the correlations are (ref. 8, p.445) h c3 ~ 0.54 k 1/4 7 Ra (Ra<10 ) (2-16)
L h 0.15 k 1/3 7 c3 Ra (Ra>10 ) (2-17)
C The characteristic length for horizontal slabs is the slab heat transfer area divided by the perimeter of the slab (ref. 18) .
PPdL Form 2l54 nOI831 J.
CaL l973401 SE -B- N A -0 4 6 R ".0 y'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. 40 of Approved by The effect of radiative heat transfer between slabs and compartment air is also included in the COTTAP-calculated film coefficients. For the applications of interest, temperature differences between a slab surface and the surrounding gas mixture are relatively small (typically < 10 F) .
Therefore the following approximate relation proposed by Hottel (ref. 19 pp. 209-301) for small temperature differences 'is used to compute the radiation coefficient:
h ~ n<a (6 +1) (4+a+b-c) e QT 3
w,av av (2-18) 2 where o Stetan-Boltzman constant (0.1712x10 -8 Btu/hr ft R ),
T 4
[ [(T +a ) +(T 4 1/4 o av r o surf +a o) ]/2) ( R)
T ~ compartment Z air temperature ( F),
T ~ slab surface temperature 0 surf ( F),
s
~ slab emissivity C
w,av ~ water vapor emissivity evaluated at T av a ~ 459.67 F.
0 Only the water vapor contribution to the air emissivity is included in equation (2-18) because gases such as N and 0 2'.are transparent to thermal 2
I I
I
PP&L Form 2454 n0r&3)
Col. @910401 SE N A -0 4 6 Rev 0
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PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of radiation (ref. 11, p.3.11), and the effect due to CO is negligible 2
because of its small concentration (0.03% by volume, ref. 12, p.F-206) .
The emissivity of water vapor is a function of the partial pressure of water vapor, the mean beam length, the gas temperature, and the total pressure (ref. 13, pp.10-57, 10-58) .
The Cess-Lian equations (ref. 21), which give an analytical approximation to the emissivity charts of Hottel and Egbert (ref. 22), are used to compute the water vapor emissivity. These euqations are given by 6
w (TP,P,P a w'wm L ) =A [1 exp(AX1/2 )] (2-19) o 1 X(T,P a
iP,P L m
) ~ P L w m I 300 t L T 3 P +
a [5(300/T)
(101325)
+ 0.5] P w
(2-20) where T ~ gas temperature (K),
P ~ air partial pressure (Pa),
P ~ water vapor partial pressure (Pa), and L ~ average mean beam length m (m) .
The coefficients A and A are functions of the gas temperature, and for purposes of this work, they are represented by the following polynomial expressions:
pp&L Form 245<< (lorLr'r Car. <<sncor Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. 22 of Approved by A (T) ~ 0.6918 2.898x10 T
-5 -9 2 0 1.133x10 T (2-21) and A (T) = 1.0914 + 1.432x10 T + 3.964x10 T (2-22) where 273K < T < 600K. Tabular values of A and A over the wider o 1 temperature range 300K < T < 1500K are available (ref. 21). Zn equation (2-18), 8 has the value 0.45, and a and C are defined by a
I)in[a w (TP <<P Bln(PwL m
<<P
)
L m
) ] (2-23) and 3ln[e w (T,P,P,P L ) ] (2-24) m r)ln (T)
Values of n,a and b are obtained through differentiation of the Cess-Lian equations. The average mean beam length Lm for a compartment is calculated from L
m R 3.5V/A (2-25)
Which is suggested for gas volumes of arbitrary shape (ref. 19) . Zn (2-25) V is the compartment volume and A is the bounding surface area.
PP&1. Form 245l n0r831 Cat. e973401 SE. -B- N A -0 4 6 Rev.0 y Dept. .PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~~ of Approved by 2.1.2.3 Initial Tem erature Profiles The initial temperature distribution within a thick slab is obtained by solving the corresponding steady-state problem, 2
d T s
(x,O)/dx 2== 0, (2-26) dT (x,O) dx 0
-h kl
[T rl (0) - T'0,0) s
] g (2-27)
The dT dx (x,o) solution is x=L
-h-2 [T (LrO) s '2 - T (0) ]. (2-28)
T s
(xO) =ax+b, (2-29) where h [T (0) T (0) ] (2-30) k+hL+kh/h b ~ T (0) + k h [T (0) - T (0) l ~ (2-31) h 1
[k + h L + k h 2 2
/h 1 ]
Equation (2-29) is an implicit relation for the temperature profile because of the temperature dependence of the film coefficients. An iterative solution of eq. (2-29) is carried out in COTTAP.
ppBL Form 2454 n$ 83)
Ca<. s9rm>
SE -B- N A -0 4 6 Rev.0 y'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~+of Approved by 2.1.3 S ecial Pu ose Models 2.1.3.1 Pi e Break Model Pipe breaks can be modeled in any COTTAP standard compartment. Lines may contain steam or saturated water as indicated by the Fluid State flag, ZBFLG, on the Pipe Break input data cards (see Section 3.20) . Zf the pipe contains water, the following energy balance is solved simultaneously with the continuity equation to determine the flowrate of steam exiting the break:
W bth f (P p ) ~Wbs h (P v r) + [W -W bs ]h (P r ),
f (2-32) where W total mass flow existing the break (ibm/sec.),
Wbbs steam flow exiting break (ibm/sec.),
h f~ enthalpy of saturated liquid (Btu/ibm),
hv ~ enthalpy of saturated vapor (Btu/ibm),
P P
~ fluid pressure within pipe (psia),
P r ~ compartment pressure (psia).
As a conservative approximation, the liquid exiting the break is cooled to I room temperature and the sensible heat given off is deposited in the
ppd 1. Form 2l54 nord3l Cat, t973l01 SF -B- N A -0 4 6 Rev.0 1'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET DesIgned by PROJECT Sht. No. 4~ of Approved by compartment air space. This heat source is represented by the term, Q
break-, in eq. (2-5) and is calculated from Q = lW -Wb] [h (P)-h (T)] (2-33) where T r is the compartment temperature.
The total mass flow out the break and the pipe fluid pressure are specified as input to the code.
Zn the case where the pipe contains high-pressure steam, all of the mass and energy exiting the break is deposited directly into the air space of the compartment. This is a reasonable approximation for steam line pressures of interest in boiling water reactors.
2.1.3.2 Com artment Leakage Model Znter-compartment leakage paths such as doorways and ventilation ducts can be modeled using the leakage path model in COTTAP. Leakage paths are specified on leakage path data cards (Section 3.14) by inputting the leakage path ZD number, flow area, pressure loss coefficient, ZD numbers of rooms connected by the leakage path, and the allowed directions for
PP&t. Form 2c54 ttor&3)
Cat, rr97340t SE -B" N A -0 4 6 Rev.0 >
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATIONSHEET Sht. No. ~ of leakage flow. Zf a leakage path loss coefficient is set to a negative value, then leakage flow is calculated from the simple proportional control model:
W l m C pl (A l/Amax 'P
) (2-34) where W = leakage flow rate (ibm/hr),
pl proportionality constant (ibm-in2 /hr-lbf),
A l leakage path flow area (ft2 ),
A = max flow area for all leakage paths (ft2 ),
rIIP pressure differential between compartments (psia) .
The constant C is specified on the input data cards (Section 3.2). The model given by (2-34) is used primarily to maintain constant pressure in compartments by allowing mass to "leak" from one compartment to another.
For example, a compartment containing heat loads can be connected, by way of a leakage path, to a large compartment which represents atmospheric conditions. The compartment will then be maintained at atmospheric pressure even though significant air density changes occur due to compartment heat up.
PP&L Form 2c54 nor83i Col. @973401 SE -B- N A -0 4 6 Rev.Q g'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~4 of Approved by A leakage model suitable for calculation of compartment pressure transients can be selected by setting the associated loss coefficient equal to a positive quantity. Zn this case the leakage rate is computed by balancing the intercompartment pressure differential with an irreversible pressure loss:
1 li li (3600) ~ hP (2-35) 2 2g P 1A1 (144) where K = loss coefficient for leakage path (based on Al),
A 1
= leakage area (ft2 ),
W 1
= leakage flow rate (ibm/hr),
p 1
= density within compartment which is the source of the leakage flow (ibm/ft3 ),
BP = pressure difference between compartments associated with leakage path (psia) .
A maximum leakage flow rate for each path is calculated from Wl 1 tmax p min (V1'iV ) C p2'2-36)
PP4l Form 2454 (10/83)
C4t. rr973401 SE -B- N A -Q 4 6 Rev.Q g'ept.
. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~4of Approved by where Vl and V are the vo 1 umes ( ft 3 ) of the compartments connected by the leakage path, p (ibm/ft3 ) is the average of the gas density for the -1 two compartments, and C p22 (hr ) is a user specified constant.
2.1.3.3 Condensation Model COTTAP is- capable of modeling water vapor condensation within compartments and also allows moisture rainout in compartments where the relative humidity reaches 100%.
Condensation is initiated on any slab if the surface temperature is at or below the dew point temperature of the air/vapor mixture in the compartment. This condition is satisfied when T
surf (Tsat (P )
v (2-37) where T sat, (P v )
is the saturation temperature of water evaluated at the partial pressure of vapor within the compartment. T surff is the slab surface temperature.
pp&L Form 2l54 n0/83)
Cat. e973401 SE -B- N A-0 4 6 Rev,0 f Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of Zn order to avoid numerical instabilities caused by rapid fluctuation between natural convection and condensation heat transfer modes, the condensation coefficient is linearly increased to its full value over a 2 minute period. Similarly, the condensation coefficient is decreased over a 2 minute period if condensation is switched off. Modulating the transitions between the two heat transfer modes allows use of much larger time steps than would otherwise be possible. The condensation heat transfer coefficient is calculated from the experimentally determined Uchida correlation which includes the diffusional resistance effect of non-condensible gases on the steam condensation rate (ref. 16 p. 65, ref.
- 20) .
Values of the Uchida heat transfer coefficient, as a function of the compartment air/steam mass ratio, are given in Table 2.3. COTTAP uses linear interpolation to obtain the condensation coefficient at the desired conditions.
'1 PPa 1. Form tfa5l (10/831 ffgrm1 Cat.
SE -B- N A -0 4 6 Rev,0 1 Dept. PENNSYLVANIAPOWER & LIGHT COMPANY Date 19 CALCULATION SHEET ER No.
aloof Designed by PROJECT Sht, No.
Approved by Table 2.3 Uchida Heat Tranfer Coefficient*
Mass Ratio Heat Transfer Coefficient (Btu/hr-ft -
(Air/Steam) P)
(0.10 280.25 0.50 140.13 0.80 98.18 1.30 63;10 1.80 46.00 2.30 37.01 3.00 29.08 4.00 23.97 5.00 20.97 7.00 17.01 10.00 14.01 14.00 10.01 18.00 9.01 20.00 8.00
>50.00 2.01
- Values from ref. 16, p. 65
PP&L Form 2I54 (>0183)
Cat. %13401 SE -B- N A -0 4 6 Rev.0
>'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET DesIgned by PROJECT Sht. No. ~I of Approved by The compartment gas mixture contains a large percentage of air even under conditions where condesnation occurs. Under these conditions, natural convection heat transfer between air and walls is still significant. Zn addition, radiation heat transfer between the vapor and walls also occurs during condensation. Under conditions where condensation occurs, the rate of heat transfer to a wall is calculated from a =-h A (T T (2-38) u w r surf where q = rate of heat transfer to the wall (Btu/hr),
h u = Uchida heat transfer coefficient (Btu/hr>>ft2 0 F),
A =
w wall surface area (ft2 ),
o T
r ~ compartment air temperature ( F),
~ wall surface temperature 0 T
surf ( F).
PPAL Form 2454 I>0/80) ~ )
Cat. 40%401 SE N A -0 4 6 Rev.Q gl Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of The corresponding condensation rate at the wall surface is calculated from
-h)Aw r - T surf W = (hu (T (2-39) cond h
where h = natural convection/radiation heat transfer coefficient, h + h ,
c r (Btu/hr-ft - 0F),
2 h
c
= natural convection coefficient (Btu/hr-ft2 -0F),
and h = thermal radiation coefficient (Btu/hr-ft 0 r F).
Equation (2-39) accounts for the fact that during condensation a significant fraction of the total heat transfer rate to the slab surface is in the form of sensible heat. In computing the sensible heat fraction, it is assumed that the condensate temperature is approximately equal to the slab surface temperature, i.e., the major resistance to condensation
'I heat transfer is associated with the diffusion layer rather than the condensate film.
PP6L Form 2l54 nOI83l Col. @913403 SE -B- N A -0 4 6 Rev.0
>'ept.
.PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~~ of Approved by 2.1.3.4 Rain Out Model Rain out phenomena is important in compartments containing pipe breaks.
The model used in COTTAP is a simple proportional control model that maintains compartment relative humidity at or below 100%. Zt is activated when the relative humidity reaches 99%. The rain out of vapor is calculated from W
ro
= (200.0 RH 198.0) max(W .,
vap,in'lC ) (RH > 0.99), (2-40) and W
ro
~ 0.0 (RH < 0.99), (2-41) where W
ro
~ rate of vapor rainout (ibm/hr),
C rl user specified constant (see section 3.2),
W vap,in . net vapor mass flow into the compartment (ibm/hr),
RH = relative humidity.
PPAL. Form 2454 n0/83l Cjt, 097340l
'SE -B- N A -0 4 6 R-v.o y:
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY 'ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~~ of Approved by 2.1.3.5 Room Cooler Model The room cooler load is assumed to be proportional to the difference between compartment ambient temperature and the average coolant temperature. Zt is calculated as follows:
cool =C(T-T),
c,avg r (2-42) where Q cool
~ cooler load (Btu/hr),
C Qcool initial c,avg initial Tr
- initial),Btu/hr 0
F,
= 0 T
c, avg average coolant temperature ( F),
(T c,in
. + T c,out )/2 and o
T r = compartment temperature ( F).
The inlet cooling water temperature, T i, is supplied as input, and the is calculated c,in'utlet cooling water temperature, T cgout , from the cooling water energy balance, Q
cool =C(Tc,avg
- T)r ~W cool Cpw (Tc,in
- T c,out ), (2-43) where W
cool
~ cooling water flow rate (ibm/hr),
pphL Form 2454 nar83) car. rr973401 S~ N A-046 Rev.0>
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of C
pw
= specific heat of water (1 Btu/ibm 0 F).
The code checks to ensure that the following condition is maintained throughout the calculation:
cool Wcool C pw (Tr
- T (2-44)
! c,in
. )
2.1.3.6 Hot Pi ing Model In COTTAP, the entire piping heat load is deposited directly into the surrounding air. This is a conservative modeling approach because in reality a substantial amount of the heat given off by the piping is transferred directly to the walls of the compartment by radiative means.
If film coefficients accounting for radiative heat transfer between compartment air and walls are used in compartments containing large piping heat loads some of this conservatism may be removed.
The piping heat load term in Equations (2-1) and (2-5) is calculated from Q ..
piping
= VIED (T f T '2-45) r )i
PPlkL Form 2c54 tlor83>
CaL tr013401 SF- "B- N A "0 4 6 Rev.O lt Dept. PENNSYLVANIAPOWER & LIGHT COMPANY- ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~4 of Approved by where U = Overall heat transfer coefficient (Btu/hr-ft2 -0F),
D ~ outside diameter of pipe or insulation (ft),
L ~ pipe length (ft),
0 T ~ Pipe fluid temperature ( F),
~ Compartment 0 T
r temperature ( F) .
COTTAP calculates U based on initial conditions and holds the value constant throughout the transient. Calculation of U for insulated and uninsulated pipes is considered separately. In both cases, however, the thermal resistance of the fluid and the metal is neglected. For insulate'd pipes, the overall heat transfer coefficient is calculated from U ~ D. ln(D /D ) + 1 (2-46) 2k H +H c r where D i ~ Insulation outside diameter (ft),
D P
~ Pipe outside diameter (ft),
k ~ Insulation thermal conductivity (Btu/hr ft 0F),
H c
~ Convective heat transfer coefficient (Btu/hr ft2 0 F),
H r ~ Radiation heat transfer coefficient (Btu/hr ft2 0 F).
pp2L Form 2454 n0/821 Cht. rr973401 SE "B- N A -0 4 6 Rev.Q y'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER, No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~3of Approved by For uninsulated pipes, U~Hc +Hr (2-47)
The convective heat transfer coefficient, H , is calculated from the c
~
correlation for a horizontal cylinder (ref. 8, p. 447):
'ollowing H
c
= (k.
air /D)o 0.60 + 0.387 Ra (2-48) 9/16 8/27
[1+(0.559/Pr) )
where kair
. = thermal conductivity of air (Btu/hr-ft-0 F),
D 0
= pipe outside diameter for uninsulated pipes (ft),
~ Insulation outside diameter for insulated pipes (ft),
Ra ~ Rayleigh number, and Pr ~ Prandtl number.
In (2>>48), the air thermal conductivity, Rayleigh member, and Prandtl number are all evaluated at the film temperature which is the average of the surface temperature and the bulk air temperature (ref. 8, p. 441) .
H r is calculated from (ref. 10, pp. 77-78)
~ CG(T 4 T 4 -T H
r r surf )/(Tr s ) I (2-49) where e ~ pipe surface emissivity,
PP41. Form 2454 110I831 Ca1. rr9 73401 SE N A-046 Rcv.Qy Dept. .PENNSYLVANIAPOWER & LIGHT COMPAN f ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~S of Approved by a m Stephan Boltzman constant (0.1712xl0
-8 Btu/hr-ft2o4
- R ),
~ compartment 0 T
r ambient temperature ( R),
0 T
surf
= pipe surface temperature ( R) for uninsulated pipes insulation surface temperature ( 0 R) for insulated pipes.
The Rayleigh number is given by:
~ (3600) 2 g (T 3 R
a surf -T )Do r (2-50) where g ~ 32.2 ft/sec 2 g ~ volumetric thermal expansion coefficient (1/ 0 R),
v ~ kinematic viscosity (ft2 /hr),
a ~ thermal diffusivity (ft2 /hr),
0 T
surf
~ pipe surface temperature ( F) for uninsulated pipe,
~ insulation surface temperature ( 0F) for insulated pipe, 0
T r ~ compartment ambient temperature ( F),
D 0
~ pipe outside diameter (ft) for uninsulated pipe,
~ insulation outside diameter (ft) for insulated pipe.
The Prandtl number is calculated from Pr ~ C I1/k, (2-51)
P
PPAL Form 2954 (10/83)
Cat, rt923401 SE -B- N A -0 4 6 Re..0 >
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~9 of Approved by where C = specific heat (Btu/ibm 0 F),
P I2 = viscosity (ibm/ft hr),
k = thermal conductivity (Btu/hr ft 0F) .
2.1.3a7 Com onent Cool-Down Model Zn COTTAP, the cooling down process of a component such as a pipe filled with hot stagnant fluid or a piece of metal equipment that is no longer operating is simulated through use of a lumped-parameter heat transfer model. The equation governing the cool-down process is pC V dT = -UA[T(t) - Tr (t) ], (2-52) p dt with T(t) 0 m T 0
(2-53) where T is the component temperature, p, C,P and V are the density, specific heat and volume of the component. U is the overall heat transfer coefficient, A is the heat transfer area, Tr is the ambient room temperature, and t0 is the time at which the component starts to cool down.
PPd L Form 2<<5<< (10)83) ca~. <<9yuoi SE N A -0 4 6 Rev.0 1'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~> of Approved by Since most of the rooms in the secondary containment are rather large, it is reasonable to assume that the component temperature changes much faster than the room temperature> that is, Tr (t) is fairly constant during the cooldown process of the component. With this assumption, T (t) can be r
replaced with T r (to ) in equation (2-52) to obtain VPC UA d UA[T-T dt r (t0 ) I = -UA[T(t)-Tr (t 0,) I. (2-54)
Rewriting (2-45) in terms of the heat loss from the component, Q, gives
+d
= -Q(t), (2-55)
Ydt where Y is the thermal time constant of the component and is given by Y ~ pC V/UA. (2-56)
P The solution to (2-46) is Q(t) ~ Q(t0 ) exp[-(t-t0 )/Y]. (2-57)
The approximation given by (2-48) is used in COTTAP when a heat load is tripped off with an exponential decay at time, t0 .
The time constant, Y, for a component can be specified on the heat load trip cards (see section 3.19), or in the case of hot piping, the time filled with liquid, constant may he calculated hy the code. Pot pipes the
~
~
PPI,(. Form 2454 (l0/83I C4(. 4973401 SE -B- N A "0 4 6 Rev.Q P Dept. PENNSYLVANIAPOWER & LIGHT COMPANY. ER No.
Date 19 CALCULATIONSHEET Designed by Approved by PROJECT Sht. No. ~of volume average density and the mass average specific heat of the licgxid and metal are used in the calculation of Y. For pipes initially filled with steam, the volume average density is used, and the average specific heat is calculated from C
p
= ([U (T f fo )
U (T f ro )]/(Tfo ro )
-T + M C mpm
)/(M+M f m ),'2-58) where U f = total internal energy of the fluid (Btu),
T fo the initial fluid temperature "( F),
T = the initial room temperature ( 0 F),
zo M
m
= mass of metal (ibm),
M f mass of fluid (ibm),
C = specific heat of the metal (Btu/ibm 0 pm F) .
2.1.3.8 Natural Circulation Model The natural circulation model in COTTAP can be used to described mixing of air between two compartments which are connected by flow paths at different elevations. The rate of air circulation between compartments is calculated by balancing the pressure differential, due to the difference in air density between compartments, against local pressure losses within the circulation path;
pphL Form 2a5a rr0'83t Cat, rr9734m N A "0 4 6 Rev.Q y'.
Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
19 CALCULATION SHEET Date Designed by PROJECT Sht. No. ~of Approved by W
c
= 3600 2g(P a2 -P al ) (E u -E 1 ) (2-59) where W c
= circulation flow rate (ibm/hr),
p,p al a2
= air densities in compartments connected by circulation path (p > p ), ibm/ft3 ,
E,E u ~ elevations of lower and upper flow paths respectively (ft),
a K,Ku m pressure-loss coefficients for lower and upper flow paths respectively, A1',A ~ flow areas of lower and upper flow paths respectively (ft )a g m acceleration due to gravity (32.2 ft/sec ) .
A leakage path (see Section 2.1.3.2) is included in the circulation path model in order to maintain the same pressure in both compartments. Thus, the flow rate calculated from eq. (2-59) is adjusted to account for this leakage.
rrrr6r. Form 2r54 l10r86)
Carrr97>0>
SE -B- N A -0 4 6 Rev.0 y'ept.
.PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Shr. No. ~80f Approved by 2.1.3.9 Time-De endent Com artment Model As many as fifty time-dependent compartments can be modeled with COTTAP.
Zn this model, transient environmental conditions are supplied as input data. The data is supplied in tabular form by entering up to 500 data points for each time-dependent room, with each data point consisting of a value of time, room temperature, relative humidity, and pressure.
A method is also available in COTTAP to describe periodic tsinusoidal) temperature variations within a room. In using this option, the amplitude and frequency of the temperature oscillation and the initial room temperature are supplied in place of a data table.
2.1.3.10 Thin Slab Model Zt is not necessary to use the detailed slab model discussed in section 2.1.2 to describe heat flow through thin slabs with little thermal I
capacitance. Slabs of this type have nearly linear temperature profiles, I
and thus, the heat flow through the slab can be calculated by using an I
overall heat transfer coefficient. The rate of heat transfer through a thin slab is obtained from
PP8,1. Form 2a541101821 C91. rr9 13401 SE -B- N A -0 4 6 Rev.P g:
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY. ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. 9+ of Approved by q =UA[T (t) - T (t)J, (2<<60) where q = rate of heat transfer from the room on side 1 of the slab to the room on side 2 (Btu/hr),
U = overall heat transfer coefficient'for the thin slab (Btu/hr ft20 F),
A = heat transfer area of one side of the thin slab (ft2 ) .
Overall heat transfer coefficient data is input to COTTAP for each of the 1
thin slabs and the values are. held constant throughout the calculation.
For thin slabs that model floors or ceilings, two values of U must be supplied; one for upward heat flow and the other for downward heat flow.
For thin slabs that are vertical walls only one value of U can be supplied. Up to 1200 thin slabs can be modeled with COTTAP.
2.2 Numerical Solution Methods The governing equations to be solved consist of 3N sr + N tdr ordinary differential equations and N s
partial differential equations, where N sr is I the number of standard rooms, N tdr is the number of time-dependent rooms,
ppht. aorn 2a5a ttor83t Cat. e973401 S~ IN A -0 4 6 Rev.0 gI Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by e
PROJECT Sht. No. ~~ of Approved by and N s
is the number of thick slabs. An energy balance and two mass balances are solved for each of the standard rooms to determine air temperature, air mass, and vapor mass. In addition, the one-dimensional heat conduction equation is solved for each of the thick slabs. Ordinary differential equations are also generated for the time-dependent rooms; these equations are used only for time step control and will be discussed later in this section.
The initial value ordinary differential equation solver, LSODES (Livermore Solver for Ordinary Differential Equations with General Sparse Jacobian Matrices), developed by A.C. Hindmarsh and A.H. Sherman is used within COTTAP to solve the differential equations which describe the problem.
LSODES is a variable-time-step solver with automatic error control. This solver is contained within the DSS/2 software package which was purchased from Lehigh University (refe 2).
Before LSODES can be applied to the solution of the governing equations in COTTAP, the N s
partial differential equations describing heat flow through I I
thick slabs must be replaced with a set of ordinary differential I I
I equations. This is accomplished through application of the Numerical Method of Lines (NMOL) (ref. 3). In the NMOL, a finite difference approximation is applied only to the spatial derivative in equation (2-6),
PP8 t. Form 2454 rror83>
Car, rr9 7340 I SE -B- At A-04 6 "; .01 Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of thus approximating the partial differential equation with N coupled ordinary differential equations of the form dT
~3. . = T sxxi., i~1,2,...rN, (2-61) where N is the number of equally spaced grid points within the slab, T S3.
is the temperature at grid point i, and T SXX1
. is the finite-difference approximation to the second-order spatial derivative at grid point i.
Fourth-order finite difference formulas are used within COTTAP to calculate the T SXX3.
.. These formulas are contained within subroutine DSS044 which was written by W.E. Schiesser. This subroutine is also contained within the DSS/2 software package. For the interior grid points a fourth-order central difference formula is used to compute T SXXi T .
SXX3.
~ [-1 126 2
T Si-2
. + 16 T Si. 1 30 T .
S3.
+ 16 T .
si+1
- T .
si+2 ]
+O(~ )i (2-62) where i = 3,4,...,N-2, and f5 is the spacing between grid points. A six-point slopping difference formula is used to approximate T SXX1
. at i equal to 2 and N-lr
PPSt, Form 2954 l10/831 Cat. 9973aot SE -B- -0 4 N A 6 Rev.o ]
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of T ~
1 [10 T - 15 T - 4 T + 14 T 6 T + T sxx2 2 s1 s2 s3 s4 s5 s6 ]
+ 0(~ )a (2-63) and T
sxxN-1 126 1
2
[10 T sN
- 15 T sN-1
- 4 T sN-2
+ 14 T sN-3 6 T sN-4
+ T sN-5 ]
+ O(6 ). (2-64)
The finite difference approximations at the end points are formulated in terms of the spatial derivative of the slab temperature at the boundaries rather than the temperature, in order to incorporate the convective boundary conditions (2-7) and (2-8) . The formulas are T
sxxl
=
~
126 1
2
[-415 T + 96 T 6
sl s2 36 T s3 s4
+ 32 T 3
-3 T 506T ] + 0(h 4 ), (2-65) 2 and T
sxxN
~
126 1
2
[-415 T 6
sN
+ 96 T sN-1
- 36 T sN-2
+ 32 T
- 3. sN-3
-3T +506T ] +O(b ), (2-66) 2 where T sxl and T sxN are given by T
1 h [T (t) T (t) ] (2-67) k
PP3,r Form 2<<54 (19r83)
Cat. <<973401 SE -B- N A -0 4 6 Rev.p i'ept.
PENNSYLVANIAPOWER 8 LIGHT COMPANY .ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~of Approved by and T = -h2 tT (t) T (t) ]. (2-68) k The total number of ordinary differential equations, <<q<< to N, be solved is now given by N
N =3N sr +Ntdr +
.~
N (2<<69) eq gj'~1 where N , is the number of grid points for slab j. Note that at least six grid points must be specified for each slab.
Zt was previously mentioned that equations are generated for each time-dependent room and are used for purposes of influencing the automatic time step control of LSODES. The equation generated for each time dependent room is dT ~ g(t), (2-70) where T tdr is the time-dependent room temperature and g(t) is the time derivative of the room temperature at time t. For rooms where temperature versus time tables are supplied, g(t) is estimated by using a three-point LaGrange interpolation polynomial. For rooms with sinusoidal temperature
pp&L Form 2a&a (10r&31 Cat, e913401 SE -B- N A-04 6 novo 1 Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of variations, calculation of g(t) is straightforward. These equations are input to LSODES so that the time step size can be reduced if very rapid temperature variations occur within a time-dependent room. A sufficient number of calls will then be made to the temperature-versus-time tables and the room temperatures will be accurately represented.
COTTAP can access five different solution options of LSODES. The desired option is selected through specification of the solution method flag, MF (see section 3.2) . The allowed values of MF are 10, 13, 20, 23, and 222.
The finite-difference formulas used in LSODES are linear multi-step methods of the form k
Y =E a.y 3.-hE2 B.F 3 ~ 3 3 (2-71) 0 where h is the step size, and the constants j' a., and 8 . are given in ref. 1, pp.113 and 217. The system of differential equations being solved are of the form d y = F(y,t), (2-72) dt with y(0) - yo ~ (2-73)
pp6L Form 9<<5<< n0'83)
Cat, <<973<<0i SE N A-046 Rev,Q Dept. PENNSYLVANIAPOWER & LIGHT COMPANY. ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. $0 of Approved by Equation (2-71) describes two basic solution techniques, Adam's method and Gears method (ref. 5 and 6), depending upon the values of k 1 and k .
2 If k 1 ~1, eq. (2-62) corresponds to Adam's method, and if k =0 it reduces 2
to Gear's method. In both cases, the constant 8 is non-zero.
0 Since 8 0
go, the finite-difference equations comprise an implicit algebraic system for the solution.y . In LSODES, the difference equations are n
solved by either functional iteration or by a variation of Newton's method. If the functional iteration procedure is chosen, an explicit method is used to estimate a value of y; the predicted value is then into the right-hand-side of eq. (2-71) and a new value of n'ubstituted yn is obtained. Successive values of yn are calculated from eq. (2-71), by iteration, until convergence is attained. MP~10 corresponds to Adam' method with functional iteration, and MP=20 corresponds to Gear's method with functional iteration.
Unfortunately, the functional iteration scheme generally requires small time steps in order to converge. The method can, however, be useful for rapid transients of short duration.
The time step limitations associated with the functional iteration procedure can be overcome, at least to some degree, by using Newton's
PPAL Form 2954 t tarot)
Cat. 9913lol SE N A-046 Rev.P~
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~S of Approved by method to solve the implicit difference equations. For ease of discussion, solution of eq. (2-71) with Newton's method will be described for Gear's equations (k2 =0) only; the procedure is similar when applied to the Adam's method equations.
The conventional form of Newton's iteration scheme applied to Gear's difference equations is described by 7
[s+1] ~ [s] '
[s] -1 ~ [s]
37 k
[s] ))
n-i "hBo F(t n'n 1
i=1 i Za. y" ~
y (2-74) where I is the identity matrix, [BF/By] is the Jacobian matrix, and the superscript s is the iteration step. In (2-74) the Jacobian is evaluated at every iteration step along with the inversion of the matrix
[I-hB0BF/By]. For large systems of equations this procedure is very time consuming.
In LSODES, the Jacobian is evaluated and the subsequent inversion of
[I-h 80 BF/By] is carried out only when convergence of the finite difference I
equations becomes slow. This technique is called chord iteration (ref. 5)
PP8,L Eorm 24' >0>83>
Ca<e9uco>
SE -B- N A -0 4 6 Re..0 g'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of and is much more efficient than the conventional Newton's iteration scheme. Also, for very large systems of equations that result in the NMOL solution of partial differential equations, most of the elements of the Jacobian are zero. If MF 222, LSODES determines the sparsity structure of the Jacobian and uses special matrix inversion techniques designed for sparse systems.
If MF=13 or 23 a diagonal approximation to the Jacobian is used, that is, only the diagonal elements of the Jacobian are evaluated, all other entries are taken as zero. (MF=13 corresponds to Adam's method and MF=23 corresponds to Gear's method).
Pp<<L FOrm 2<<A <1583)
Gal, <<91340l SF- -B- N A -0 4 6 Rev.Q g Dept. PENNSYLVANIAPOWER 5 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of
- 3. DESCRIPTION OF CODE INPUTS This section gives instructions for preparing an input data set for COTTAP. The data cards that are described must be supplied in the order that they are shown. Comment lines may be inserted in the data set by putting an asterisk in the first column of the line. However, comment lines should not be inserted within blocks of data: they should only be used between the various types of input data cards. For example, comment cards can be supplied after the last room data card and before the first ventillation flow data card but not within the room data cards and not within the ventillation flow data cards.
The first line in the input data set is the title card. This card is printed at the beginning of the COTTAP output. A listing of all the input data cards following the title card is given below. The words that must appear on each card are listed in order: Wl is word 1, W2 is word 2, etc.
The letters I and R indicate whether the item is to be entered in integer or real format.
ppaL Form 2a5a nor83)
Cara9rwo>
~E N A -0 4 6 Rev 0
)'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY - ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~G of Approved by 3.1 Problem Descri tion Data (Card 1 of 3)
Wl-I NROOM = Number of rooms (compartments) contained in the model (maximum value is 300) . NROOM does not include time-dependent rooms.
W2-I NSLB1 = Number of thick slabs (maximum value is 1200). These are slabs for which the one-dimensional, time-dependent heat conduction equation is solved.
W3-I NSLB2 = Number of thin slabs (maximum value is 1200) . These are slabs which have negligible thermal capacitance.
W4-I NFLOW = Number of ventilation flow paths (maximum value is 500) .
W5-I NHEAT = Number of heat loads (maximum value is 750) .
W6-I NTDR ~ Number of time-dependent rooms (max value is 50) .
W7-I NTRIP ~ Number of heat load trips (maximum value is 500).
ppsL Form 2454 nsall Ca4 N97340l SE -B- N A-046 P "0~
Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT C
Sht. No. ~of W8-I NPIPE ~ Number of hot pipes (maximum value is 750).
W9-I NBRK ~ Number of pipe breaks (maximum is 20) .
W10-I NLEAK = Number of leakage paths (maximum is 500) .
Wll-I NCIRC ~ Number of circulation paths (maximum value is 500) .
W12-I NEC = Number of edit control cards. (At least one card must be supplied, and a maximum of 10 cards may be supplied).
3.2 Problem Descri tion Data (Card 2 of 3)
Wl-I NFTRIP ~ Number of flow trips (maximum value is 300) . Flow trips can act on ventilation flows, leakage flows, and circulation flows.
W2-I MASSTR ~ Mass-tracking flag.
0~> Mass tracking is off. In this case, compartment mass balances are not solvedr the total mass in each compartment is held constant. In cases where this option can be used, it results in large savings in
ppLL Form 245'01s3)
Cat, <<973401 SE -B- N A -0 4 6 Rev.0 Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~~ of Approved by computer time. In order to use this option, the following input variables must be specified as:
NBRK=NLEAK=NCIRC=NFTRIP=O
=1=> Mass tracking is on; mass balances are solved for each compartment.
W3-I MF Numerical solution flag. MF=222 should only be used if MASSTR~O. If MASSTR~1, the recommended methods are MF=13 and MF 23. MF=10 and MF 20 use functional iteration methods to solve the finite difference equations and generally require smaller time steps and larger computation times than MF~13 and MF=23.
~10~> Implicit Adam's method. Difference equations solved by functional iteration (predictor-corrector scheme) .
~13~> Implicit Adam's method. Difference equations solved by Newton's method with chord iteration. An I
I
PP4L Form 245'or83l Car. <<973401 SE -B- N A -0 4 6 Rev.Q $
'ept.
PENNSYLVANIAPOWER 8r LIGHT COMPANY ER No.
CALCULATIONSHEET Designed by PROJECT Sht. No. ~Sof Approved by internally generated diagonal approximation to the Jacobian matrix is used.
=20~> Zmplicit method based on backward differentiation formulas (Gear's method) . Difference equations are solved by functional iteration; Jacobian matrix is not used.
=23=> Zmplicit method based on backward differentiation formulas. Difference equations are solved by Newton's method with chord iteration. An internally-generated diagonal approximation to the Jacobian matrix is used.
~222~> Zmplicit method based on backward differentiation formulas. Difference equations are solved by Newton's method with chord iteration. An internally-generated sparse Jacobian matrix is used. The sparsity-structure of the Jacobian is determined by the code.
ppdL Form 2<<5<<n0I83) '
Cw, <<973401 8E -B- N A-0 4 6 Rev.Q ]
Dept. .PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~~of Approved by W4-R CP1 Parameter used in calculation of leakage flows.
Xncreasing CP1 increases the leakage flow rate for a given pressure difference. The recommended value of CPl is lx10 4 . Larger values of CPl can be used if compartment pressures increase above atmospheric pressure during rapid temperature transients.
W5-R CP2 ~ Parameter used in calculating maximum allowed values for leakage flows. The recommended value of CP2 is 150.
Increasing CP2 increases the maximum leakage flow rates.
W6-R CR1 Parameter used in rain out calculation. Increasing this parameter increases the rain out rate when rain out is initiated. The recommended value of CR1 is 10.
W7-I XNPUTF ~ Flag controlling the printing of input data.
~0~> Summary of input data will not be printed.
=1<<<<> Summary of input data will be printed.
pphL Form 2454 n0/83)
Cat. 4973401 SE N A -0 4 6 Rev.O y'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY- ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~Eof Approved by W8-I IFPRT = Ventilation-flow edit flag.
=0=> Ventilation-flow edits will not be printed.
=1=> Ventilation-flow edits will be printed.
W9-R RTOL = Error control parameter. RTOL is the maximum relative error in the solution. The recommended value of RTOL is lxlo 3.3 Problem Descri tion Data (Card 3 of 3)
W1-I NSH = Number of time steps between re-evaluation of slab heat transfer coefficients. If a pipe break is being modelled, this parameter must be set to zero. If there are no pipe breaks included in the model, NSH may have a value as large as 10 without introducing significant errors into the solution. For problems involving a large number of slabs (but no pipe breaks), a value of 10 is recommended.
PPAt. Form 2454 t1$ 83)
Cat, 197340I SE, -B- N A "0 4 6 Rev.0 y'ept.
PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. 4O of Approved by W2-R TFC = mass fraction threshold value. If the mass fraction of air or water vapor drops below the value specified for TFC, that component is essentially neglected during the calculation. A recommended value for TFC is 10
-5
-5 Specifying TFC much smaller than 10 should be avoided because it can sometimes lead to negative mass of the small component.
3.4 Problem Run-Time and Tri -Tolerance Data Wl-R T = Problem start time (hr).
W2-R TEND = Problem end time (hr) .
W3<<R TRPTOL Trip tolerance (hr). All trips are executed at the trip set point plus or minus TRPTOL.
W4-R TRPEND ~ The maximum time step size is limited to TRPTOL until the problem time exceeds TRPEND (hr). Note that a large value of TRPEND and a small value of TRPTOL will lead to excessively large computation times.
PPCL Form 2454 n0'83)
Col. 4973401 SE -B- N A -0 4 6 I'".. 0 y Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~4of Approved by 3.5 Error Tolerance for Com artment Ventilation-Flow Mass Balance Omit this card if NFLOW 0.
Wl-R DELFLO m The maximum allowable compartment ventilation flow imbalance (cfm), i.e., the following condition must be satisfied for each" compartments Net Ventilation Flow (cfm) into Compartment < DELFLO.
The recommended value of DELFLO is lx10 -5 . It is particularly important to ensure that there are no ventilation flow imbalances when the mass-tracking option is not used (MASSTRm0) because in this case the code assumes that the mass inventory in each compartment remains constant throughout the transient.
3.6 Edit Control Data NEC edit control data cards must be supplied2 on each card the following three items must be specified.
PP0(. Form 245'0t03) S Cht. N972l0(
SF- N A -0 4 6 Rev.O
>'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No.. CW of Approved by W1-I IDEC ~ ID number of the edit control parameter set. The ID numbers must start with 1 and they must be sequential, i.e., IDEC 1,2,3,...,NEC.
W2-R TLAST ~ Time (hr) up to which the edit parameters apply. When time exceeds TLAST, the next set of edit control parameters will control printout of the calculation results.
W3-R TPRNT Print interval for calculation results (hr), i.e.,
results will be printed every TPRNT hours.
3.7 Edit Dimension Data Wl-I NRED ~ Total number of rooms for which the calculation results will be printed. This includes both, standard rooms and time-dependent rooms.
W2-I NS1ED ~ Number of thick slabs which will be edited. Associated heat transfer coefficients are edited along with the slab temperature profiles.
PPE,L FOcm 2454 IIO/83)
Cat, s97340I SE -B- N A -0 4 6 Rev.0 1I Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~~ of Approved by W3-I NS2ED = Numbers of thin slabs which will be edited.
3.8 Selection of Room Edits On this card(s) enter the ID numbers of the rooms to be edited. Include both, standard rooms and time-dependent rooms (note that time-dependent rooms have negative ID numbers). Enter the ID numbers across the line with at least one space between each item. The data can be entered on as many lines as necessary. Room edits will be printed in the order that they are specified here. For each room specified, calculation results such as temperature, pressure, relative humidity, and mass and energy inventories will be printed along with the various heat loads contained within the room. Omit this card if NRED~O.
3.9 Selection of Thick Slab Edits Enter the ID numbers of the thick slabs to be edited. Each ID number should be separated by at least one space. If the ID numbers cannot fit on one line, additional lines may be used as necessary. The temperature profile that is printed for each thick slab consists of seven temperatures at equally spaced points throughout the slab. In general, these temperatures are determined by quadratic interpolation since in most cases
ppLL Form 2454 (10/83)
Cal. N973401 SE -~- N A -0 4 6 Rev.Q
>'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date t9 CALCULATION SHEET Designed by PROJECT Sht. No. ~~of Approved by the locations do not correspond to grid points. Omit this card if NS1EDmO.
3.10 Selection of Thin Slab Edits Specify the ID numbers of the thin slabs to be edited. Enter the items across each line and use as many lines as necessary. Thin slab edits will be printed in the order that they are listed here. For each thin slab specified, the heat flow through the slab and the direction of heat flow will be printed. Omit this card if NS2ED=O.
3.11 Reference Tem erature and Pressure for Ventilation Flows Omit this card if NFLOWmO.
Wl-R = Temperature 0 TREF ( F) used by code to calculate a reference air density. The reference density is used by the code to convert ventilation flows from CFM to ibm/hr.
W2-R PREP Pressure (psia) used to calculate the reference density
ppht. Form 2a54 n0i83>
C4I. N913l01 SE -B- N A -0 4 6 R..V.O 1'ept.
PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. 4~ of Approved by 3.12 Standard Room Data Wl-I IDROOM = Room ID number. The ID numbers must start with 1 and must be sequential.
W2-R VOL = Room volume (ft3 ) . In order to maintain constant properties in a compartment throughout the calculation, enter a large value for VOL (e.g. 1xlO 15 ) .
W3>>R PRES = Initial room pressure (psia).
W4-R TR = Initial room temperature (
0 F).
W5-R RHUM = Initial relative humidity (decimal fraction) . For the case of MASSTR~O, this parameter is only used in calculating heat transfer coefficients for thick slabs.
W6-R RMHT = Room height (ft) . This parameter is used in the calculation of condensation coefficients for thick slabs.
pphL Form 2454 nOI83l Cat. %13401
~ -B- N A-04 6 Rev.Q p Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of 3.13 Ventilation Flow Data Omit this card(s) if NFLOW 0.
Wl-I ZDFLOW = ZD number of the ventilation flow path. Values must start with 1 and be sequential.
W2>>I IFROM ID number of room that supplies ventilation flow. This can be a standard room or a time-dependent. room.
W3-Z ZTO = ID number of room that receives flow. This can be a standard room or a time-dependent room.
W4>>R VFLOW = Ventilation flow rate (ft3 /min). This volumetric flow is converted to a mass flow rate using TREF and PREF supplied above. The mass flow rate is held constant throughout the calculation unless the flow is acted upon by a trip.
PP4L Form 2ISl n0r83)
Cat. 99%401 Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~7of Approved by 3.14 Leaka e Flow Data Omit this card(s) if NLEAK=O.
W l- I IDLEAK = ID number of the leakage path. Values must start with 1 and must be sequential.
W2-R ARLEAK = Area of leakage path (ft ).
W3-R AKLEAK = pressure loss coefficient for leakage path based on flow area ARLEAK. Specify a -1 for AKLEAK if the simple, proportional control model is desired, see Section 2. 1.3.2.
W4-I LRM1 ID number of room to which leakage path is connected.
This can be a standard room or a time-dependent room.
W5- I LRM2 - ID number of the other room to which the leakage path is connected. This can be a standard room or a time-dependent room.
e W6-I LDIRN Allowed direction for leakage flow.
PPtLt. Form 2c5c n0/83)
Cat. tr073401 SE "B" N A-046 Rev.O>:
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~4of Approved by 1 => leakage from compartment LRM1 to compartment, LRM2 only.
2 => leakage can be in both directions: from LRM1 to LRM2 and from LRM2 to LRM1 3.15 Circulation Flow Data Omit this card(s) if NCZRC~O.
Wl-I ZDCIRC ID number of circulation flow path. Values must start with 1 and must be sequential.
W2-I KRM1 ~ ID number of room to which circulation path is connected.
This can be a standard room or a time-dependent room.
W3-I KRM2 ~ ZD number of other room to which the circulation path is connected. This can be a standard room "or a time-dependent room.
W4-R ELVL ~ Elevation of the lower flow path (ft).
a WS-R ELVU ~ Elevation of the upper flow path (ft) .
pp6L Form 296a nar831 Cal. 9976401 SE -B- N A -0 4 6 Rev.0 Dept. PENNSYLVANIAPOWER & LIGHT COMPANY'R No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~4of Approved by W6-R ARL ~ Flow area of the lower flow path (ft2 ) .
W7-R ARU = Flow area of the upper flow path (ft2 ).
WB-R AKL = Loss coefficient for lower flow path referenced to ARL.
W9>>R AKU = Loss coefficient for the upper flow path referenced to ARU.
3.16 Air-Flow Tri Data Omit this card(s) if NFTRIP=O.
Wl-I IDFTRP Trip ID number. The 1D numbers must start with 1 and must be sec(uential.
W2-I KFTYP1 Type of flow path.
~ 1 ~> Ventilation 2 > Leakage 3 > -Circulation
PP<<,L Farm 2<<5<<{10/831 It Cat. <<913<<01 SE -B- N A -0 4 6 Rev.Q P Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. ~Oof Approved by W3-I KFTYP2 = Type of trip.
1 > trip off
~ 2 => trip on Note that all air flows are initially on unless tripped off.
W4-R FTSET ~ Time of trip actuation (hr).
W5-I IDFP ID number of flow path upon which the trip is acting.
3.17 Heat Load Data Omit this card(s) if NHEAT=O.
Wl-I IDHEAT ~ Heat load ID number. ID numbers must start with 1 and must be secpxential.
W2-I NUMR ~ ID number of room containing heat load.
W3-I ITYP Type of heat load.
~ 1 ~> Lighting
~ 2 => Electrical panel a
PPdL Fontt 2954 n$ 83)
Cat. e91340l Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~l of Approved by
= 3 => Motor
= 4 => Room Cooler
= 5 => Hot piping I
~ ~
= 8 => Miscellaneous t W4-R QDOT = Magnitude of heat load (Btu/hr). If this is a piping heat load ( ITYP=5) enter 0.0 for this parameter; the value of QDOT will be calculated by the code. If ITYP=4, QDOT should be negative.
W5-R TC = Temperature ( F) of cooling water entering cooler if ITYP-4. If ITYP is not equal to 4 enter a value of -1".
W6-R WC - Cooling water flow rate (ibm/hr) if ITYP=4. If ITYP is not equal to 4 enter a value of 0.
- 3. 18 Hot Pi in Data Omit this card(s) if NPIPE=O.
Wl- I IDPIPE - ID number of pipe. The ID numbers must start with 1 and must be sequential'
PPdL Form 24M ttiatt Cat, tt973lO I N A-046 RevP):
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATIONSHEET Sht. No. ~ of W2-I ZPREF ID number of associated heat load.
W3-R POD ~ Outside diameter of pipe (in).
W4-R PZD ~ Inside diameter of pipe (in).
W5-R AZNOD ~ Outside diameter of pipe insulation (in) . If the pipe is not insulated set AZNOD equal to POD.
W6-R PLEN Length of pipe (ft).
W7-R PEM Emissivity of pipe surface.
I W8-R AINK ~ Thermal conductivity of pipe insulation (Btu/hr ft F).
Zf the pipe is not insulated set AZNK~O.O.
0 W9-R PTEMP ~ Temperature ( F) of fluid contained in pipe.
W10-I ZPHASE ~ 1 if pipe is filled with steam.
2 if pipe is filled with liquid.
pp&L Form 24M nSN>
Cht. 4973401 SE -B- N A-0 4 6 Rev.0 ]l Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by Approved by PROJECT Sht. No. ~of 3.19 Heat Load Tri Data Omit this card(s) if NTRZP 0.
Wl-I ZDTRIP = Trip ZD number. ZDTRIP must start with 1 and all values must be sequential.
W2<<Z ZHREF = ZD number of heat load that is to be tripped.
W3-I ITMD ~ Type of trip.
~1~> Heat load is initially on and will be tripped off.
m2~> Heat load is initially off and will be tripped on.
W3-R TSET ~ Time (hr) at which trip is activated.
W4-R TCON ~ Time constant for heat load trip. The following options are available if ITMD~1:
~ Zf TCON~O.O, the entire heat load is tripped off at
a ppKL Form 2c54 nOI831 Cat. 4973401 SE -S- N A -0 4 6., Rev.Q g Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of
~ Zf the heat load is a piping heat load (ITYP~5), TCON can be set to -1 and a time constant will be calculated by the code. This time constant will then be used to exponentially decay the heat load when it is tripped off.
~ A time constant can be supplied by setting TCON equal to the desired time constant (hr).'hen the heat load is tripped off, it will exponentially decay with the user-supplied time constant. This option can be used with any heat loads it is not restricted to just piping heat loads.
0.0 if ITMD~2.
3.20 Pi e Break Data Omit this card(s) if NBRK~O.
Wl-I , ZDBK ~ ID number of break. ZDBK must start with 1 and all values must be sequential.
PPSL Form 2454 (1SN)
C4l. N973l01 SE -B- N A-046 Rev.0$
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~S of Approved by W2-I ZBRM = ID number of room in which pipe break occurs.
W3-R BFLPR = Fluid pressure within pipe (psia).
W4-I ZBFLG Fluid State flag.
= 1 ~> fluid in pipe is steam
= 2 => fluid in pipe is licpxid water W5-R BDOT = Total mass flow exiting the break (1bm/hr) .
W6-R TRZPON Time at which break occurs (hr).
W7-R TRZPOF = Time at which break flow is turned off (hr).
W8-R RAMP ~ Time period (hr) over which the break develops. The total mass exiting the break increases linearly from a value of zero at tMRZPON to a value of BDOT at t-ZRIPON+RAMP.
3.21 Thick Slab Data (card 1 of 3)
Omit this card(s) if NSLB1 0.
PPAt. Fotm 2454 (tDt83)
Cat. tt97340 I SE N A -0 4 6 Rev.0 >t Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of W1-I IDSLBl = Slab ZD number. IDSLB1 must start with 1 and all values must be sequential.
W2-I ZRM1 = ZD number of room on side 1 of slab. A standard room or a time-dependent room can be specified. If side 1 of the slab is in contact with ground enter a value of zero.
W3-I ZRM2 ID number of room on side 2 of slab. A standard room or a" time-dependent zoom can be specified. Zf side 2 of the slab is in contact with ground enter a value of zero.
W4-I ZTYPE ~ Type of slab.
= 1 if slab is a vertical wall
= 2 if slab is a floor with respect to room ZRM1.
= 3 if slab is a ceiling with respect to room ZRM1.
W5-I NGRIDF = Number of grid points per foot used in the finite-difference solution of the unsteady heat conduction equation. A minimum of 6 grid points per slab is used by the code, and the maximum number of grid points used per slab is 100.
NGRZDF causes the total number Zf the specified value of of grid points for the tI
ppdL Form 2454 n$ 83)
Ca1, t973401 I
Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. 17 of Approved by slab to be outside of these limits, the appropriate limit will be used by the code.
W6- I IHFLAG = Heat transfer coefficient calculation flag. Heat transfer coefficient data must be supplied for any slab side that is in contact with a time dependent room.
0 if no heat transfer coefficient data will be supplied for the slab. The code will calculate natural-convection and radiation heat transfer coefficients for both sides of the slab.
- 1 if heat transfer coefficient data will be supplied for side 1 of the slab. The code will calculate natural-convection and radiation heat transfer coefficient for side 2.
2 if heat transfer coefficient data will be supplied for side 2 of the slab. The code will calculate natural-convection and radiation heat transfer coefficients for side 1.
- 12 if heat transfer coefficient data will be supplied for both, side 1 and side 2 of the slab.
pp&L Form 2454 no/Mr C4t. I@13401 SE -B- N A-0 4 6 Rev.a PENNSYLVANIAPOWER & LIGHT COMPANY 'R No.
>'ept.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of Allow the code to calculate film coefficients for slab surfaces in contact with ground.
W7-R CHARL m characteristic length of the slab (ft) .
= height of the slab if ITYPEml.
= the heat transfer area divided by the perimeter if ITYPEm2 or 3.
If the value of CHARL is set to 0.0, the code will calculate a value for the characteristic length. In this e case, the code assumes that the slab is in the shape of a sguare.
3.22 Thick Slab Data (Card 2 of 3)
Omit this card(s) if NSLB1=0.
Wl-I IDSLB1 = Slab ID number.
W2-R ALS ~ Thickness of slab (ft) .
pp<< t. Form 2<<5<<n0/83)
C<<l, <<97340't I SE -B- N A -0 4 6 Rev.o g Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ oi W3-R AREAS1 = Slab heat, transfer area (ft2 ) . This is the surface area of one side of the slab.
W4-R AKS = Thermal conductivity of slab (Btu/hr ft0F).
W5-R ROS = Density of slab (ibm/ft3 ) .
W6-R , CPS = Slab specific heat (Btu/ibm-0 F) .
W7-R EMZSS = Slab emissivity 3.23 Thick Slab Data (Card 3 of 3)
Zf ZHFLAG=O for a slab, then do not supply a card in this section for that particular slab. If IHFLAG 1 or 2, only supply the required data; leave the other entries blank. Zf ZHFLAG=12, supply all the heat transfer coefficient data for that slab. Omit this card(s) if NSLB1 0.
Wl-I ZDSLB1 = Slab ID number.
W2-R HTC1(1) Heat transfer coefficient for side 1 of slab if ITYPE=1 (Btu/hr-ft2 0F).
pphL Form 2<<5a n0/80)
Cat. <<973<<01 SE -B- N A-046 Rev,Pg'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by PROJECT Sht. No. ~O of Approved by
= Heat transfer coefficient for upward flow of heat between slab and room IRM1 if ITYPE~2 or 3 (Btu/hr-ft2 0 F).
W3-R HTC2(1) ~ Heat transfer coefficient for side 2 of slab if ITYPE=1 (Btu/hr-ft2 0 F).
= Heat transfer coefficient for upward flow of heat between slab and room IRH2 .if ITYPE~2 or 3 (Btu/hr-ft2 -o F) .
W4-R HTCl(2) ~ Heat transfer coefficient for downward flow of heat between slab and room IRM1 if ITYPE~2 or 3 (Btu/hr-ft2 -0 F). Do not supply a value if ITYPE=1.
W5-R HTC2(2) ' Heat transfer coefficient for downward flow of heat between slab and room IRH2 if ITYPE~2 or 3 (Btu/hr-ft2 -0 F). Do not supply a value if ITYPE=1.
3.24 Thin Slab Data (Card 1 of 2)
Omit this card(s) if NSLB2~0.
ppaL Fotttt 2454 nDt83t Cat. tt97340t SE -B- N -A -0 4 6 Rev.p g'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by t9 PROJECT CALCULATION SHEET Sht. No. ~ of Wl-I ZDSLB2 = Slab ZD number. ZDSLB2 must start with 1 and all values must be sequential.
W2-I JRM1 = ZD number of room on side 1 of slab. A standard room or a time-dependent room can be specified. A thin slab cannot be in contact with g'round, i.e., do not specify JRM1 or JRM2 equal to zero.
W3-I JRM2 = ID number of room on side 2 of slab. A standard room or a time-dependent room can b'e specified.
W4-I JTYPE = 1 if slab is a vertical wall.
= 2 if slab is a floor with respect to room JRM1.
= 3 if slab is a ceiling with respect to "room JRM1.
W5-R AREAS2 ~ Slab heat transfer area (ft2 ) . This is the surface area of one side of the slab.
3.25 Thin Slab Data (Card 2 of 2)
Omit this card(s) if NSLB2~0.
pprLL Form 2<<5<<norN) \
C<<r. <<973401 SE -B- N A -0 4 6 Rev.O Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by Approved by PROJECT Sht. No. ~of Wl-I IDSLB2 Slab ID number.
W2-R UHT(1) Overall heat transfer coefficient for slab is JTYPE=1 (Btu/hr>>ft2 -0 F) .
~ Overall heat transfer coefficient for upward flow of heat
'I through slab if JTYPEm2 or 3 (Btu/hr-ft -0 F).
2 W3-R UHT(2) = Overall heat transfer coefficient for downward flow of heat through slab if JTYPEm2 or 3 (Btu/hr-ft2 -0F). Do not supply a value of JTYPEml.
3,.26 Time-De endent Room Data (Card 1 of 2)
Omit this card(s) if NTDR~O.
Wl-I IDTDR ID number of time-dependent room. IDTDR must start with
-1 and proceed secgxentially (i.e.,
IDTDR~ 1 <<2 <<3 << ~ ~ ~ <<NTDR)
W2-I IRMFLG ~ 1 if temperature, pressure, and relative humidity data will be supplied.
pplL Form 2454 n0rajj Cat. l97340I SE, -B- N A-046 Rev.Qy Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of
= 2 if a sinusoidal temperature variation will be used for this room. Zf this option is chosen there cannot be any flow to or from this room.
W3-I NPTS ~ Number of data points that will be supplied if ZRMFLG=1.
Each data point consists of a value of time, temperature, pressure, and relative humidity. NPTS must be less than or equal to 500. Since output is determined by interpolation, time-dependent-room data must be supplied at least one time step beyond the problem end time.
~ 0 if ZRMFLG~2.
W4-R TDRTO ~ Initial room temperature (
0 F) if IRMFLG=2.
~ 0.0 if ZRMFLG~1 W5-R AMPLTD Amplitude ( 0 F) of temperature oscillation if IRMFLG=2.
~ 0.0 if ZRMFLG=1.
W6-R FREQ ~ Frequency (rad/hr) of temperature oscillation if ZRMFLG 2.
~ 0.0 if ZRMFLGm1.
PPKL Form 2<<5<<n0IMI C<<t, <<91340l SE -B- N A -0 4 6 Rev.0 y'ept.
PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of 3.27 Time-De endent Room Data (Card 2 of 2)
Supply the following data for each time-dependent room that has a value of ZRMFLG=l. Omit this card(s) if NTDR=O.
Wl-Z ZDTDR ZD number of time-dependent room W2-R TTZME ~ Time (hr).
~ 0 W3-R TTEMP Temperature ( F) .
W4-R TRHUM ~ Relative humidity (decimal fraction) .
WS>>R TPRES ~ Pressure (psia).
Repeat words 2 through 5 until NPTS data points are supplied. Then start a new card for the next time-dependent room.
t~
pp&L Form 2i54 nOIN)
Cat. l973401 SE -B- N,A=04 6 Rev.O.O Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. S~ of Approved by
- 4. SAMPLE PROBLEMS 4.1 Com arison of COTTAP Results with Anal tical Solution for Conduction throu h a Thick Slab (Sam le Problem 1)
A description of this problem is shown in Figure 4.1. A standard room is on side 1 of the slab and a time-dependent room is in contact with side 2.
The temperature in the time-dependent room oscillates with amplitude A 0
and frequency Q. There are no heat loads or coolers within the standard roomy heat is only transferred to or from the room by'onduction through the slab.
The equations describing this problem are aT s /at
= a8 2 T s /ax,2 (4-1)
- -1 3T 3x s
x=0 h
k
[T rl (t) - Ts (Opt)]g (4-2)
-h-2 [T (L,t) - T A sin(W) ], (4-3) k s r2 (0) 0 T (x 0) s ax+ b, (4-4)
P 1C 1 Vl dT Ah [T (0 g t) T (t) ] (4-5) dt
PPSL Form 24'10r83)
Cat. rr973c0>
-B- -0 4 SE N A 6 Rev 0 I!
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
19 CALCULATION SHEET Date Designed by PROJECT Sht. No. +6 of Approved by Room 1 Room 2 Standard Room Time-Dependent Room Room temp, T rl (t) "'Room temp, Volume, Vl T r22(t) -Tr22(0)+A0 sin(00t)
Air density, p Film coefficient, h Slab Specific heat, C vl1 ~ TelllP r Initial pressure, P T s
(x,t)
Film coefficient, hl Side 1 of slab Side 2 of slab X=O X=L e
Figure 4.1 Description of Sample Problem 1
ppct. Form 2l5i n183)
Cst. l973l01
$ f N A -04 6 Rev.00 Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATIONSHEET Sht. No. ~ of where a and b are given by equations (2-30) and (2-31) ~ It is assumed that both rooms have been at their initial temperatures long enough for the slab to attain an initial steady-state temperature profile.
The general solution to this problem is rather complicated, but the solution takes a much simplier form for large values of t.
This problem was also solved with COTTAP. Values for the input parameters used in the calculation are given in Table 4.1 and a copy of the COTTAP input data file is given in Table 4.2.
The slab temperature profiles at 900 and 2000 hours, calculated with COTTAP, are compared with the asymptotic form of the analytical solution in Figures 4.2 and 4.3. The results show good agreement. The COTTAP results for the temperature in room 1 are compared with the analytical solution in Figure 4.4r again, the results show good agreement.
PPdL Form 24$ 4 {10/N)
Cat. NQ 73401 SE -B- A A -04 6 Rev.pg Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of Table 4.1 Values of Parameters used in Sample Problem 1 Parameters Value T
rl0) 80 F T (0) 200 F A 100 F 0
0.5 rad/hr h 1.46 Btu/hr ft F h 6.00 Btu/hr ft2 0 F
0.0325 ft2 /hr 1.0 Btu/hr ft F V 800 ft A 300 ft 2 ft 10 14.7 psia
TSO FOREGROUND HARDCOPY 0 ~ ~ ~ PRINTED 89284.1100 JSNAME=EAMAC.COTTAP.SAMPLI.DATA MOL=DSK533 COTTAP SAMPLE PROBLEM I -" RUN I t1 ~ ~ 1 ~ 1 ~ ~ 0 ~ ~ ~ ~ 10 ~ ~ ~ ~ ~ ~ 011 ~ ~ 00 ~ 11 ~ ~ ~ 0040000000 0 0 4 0 0 0 4 0 0 4 1 4 1 4 1 1 0 4 0 4 1 0 0 4 0 ~ ~
PROBLEM DESCRIPTION DATA ( CARD I OF 3 )
NROOM NSLAB'I NSLAB2 NFLOW NHEAT NTDR NTRIP NP I PE NBRK NLEAK NC I RC NEC I I 0 0 0 I 0 0 0 0 0 I
~ 1 ~ 1 ~ 0 ~ 0 0 400~ 000 ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ 0 0 ~ 0 ~ ~ ~ 00 ~0 00~ 000 0 0 0 4 0 1 4 ~4 4 4 4 0 1 0 4 4 4 4 1 0 ~ 1 1 ~ 0 4 0 0
~ PROBLEM DESCRIPTION DATA ( CARD 2 OF 3 )
NFTRIP MASSTR MF CPI CP2 CRI I NPUTF I F PRT RTOL
~
0 0 222 41 ~ ~ 10 ~ ~ ~ ~ 4 ~ ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ ~
- 2. D4 2. 0 1 ~ ~ ~ ~ ~ ~ ~~ ~ ~
10.
00 ~ 00 ~
I I I.D-5
~ '1 0 ~ ~ 1 0 0 ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ 0 0 ~ ~ 0 ~ ~ ~ ~ ~
PROBLEM DESCRIPTION DATA ( CARD 3 OF 4
~ NSH TFC 0 1.0-5 4 ~ 0 ~ ~ 0 ~ ~ ~ ~ ~ ~ 0 ~ ~ 11 ~ ~ ~ 1 ~ 1 ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 000 ~ ~ 1 ~ 010 ~ ~ ~ 0100 ~ 1 ~ ~ ~ 4 ~ ~ ~ 1 PROBLEM TIME AND TR IP TOLERANCE DATA T TEND TRPTOL TRPEND
+41
.0 2000.0 10.00 0.00
~ 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 0 1 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 0 0 0 0 0 0 0 ~ ~ 0 0 0 ~ ~ ~ 0 ~ ~ ~ ~ ~ 4 0 ~ 0 0 ~ 0 ~ 0 ~ 0 0 ~ 1 ~ 44110 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE
( OMIT THIS CARD IF NFLOW = 0 )
DELFLO I.D-5
~ 0 ~ ~ 1 ~ 4 4 4 ~ ~ ~ 1 ~ 0 4 ~ ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ 0 ~ 0 0 ~ 0 0 ~ 0 ~ 0 0 ~ ~ 0 0 1 0 0 ~ ~ ~ 1 ~ 0 0 ~ 0 1 0 0 ~ 0 1 ~ ~ 0 0 ~ 0 EDIT CONTROL DATA CARDS IOEC TLAST TPRNT I 2000. 100.
4 ~ 0 4 1 0 ~ 1 1 4 4 ~ 0 ~ ~ ~ ~ ~ 1 ~ 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 0 ~ 0 10 ~ 0 0 0 0 ~ ~ 0 ~ 1 ~ 1 0 ~ 0 ~ 0 4 0 0 1 1 4 ~ ~ 0 0 0 1 ~ 0 EDIT DIMENSION CARD NREO NS LEO NS2ED 2 I 0 1 44 1 4 ~ ~ ~ ~ ~ 0 ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 I ~ ~ ~ ~ ~ 0 ~ 1 1 ~ ~ 0 1 1 ~ 1 ~ 1 I I ~ 1 1 1 0 0 4 1 4 4 ~ 1 1 1 4 ~ ~ 0 I ~ 4 4 ~
ROOM EDIT DATA CARO(S)
I -I 0010 440444040440440004444404000000444
~ 44444440 ~ 1 ~ ~ ~ 1000 ~ ~ 0 ~ 01 ~ ~ ~ ~ 00 ~ ~ I
~ 0 ~
EDIT CARD(S) FOR THICK SLABS 444444440 ~ 0 4 0 1 ~ 1 ~ ~ 1 0 ~ ~ 0 1 ~ ~ ~ ~ ~ ~ 0 ~ 0 ~ ~ ~ ~ ~ 0 ~ 4 ~ ~ 0 0 ~ 1 4 0 0 ~ ~ 0 1 4 1 1 1 ~4 0 4 1 4 1 1 1 ~ 0 1 ~ 1 EOI T CARDS FOR THIN SLABS 4 4 44044444 1 ~ 1 ~ 000 ~ 40 ~ ~ 1 ~ 0 ~ 10 ~ 0 ~ ~ ~ ~ ~ 00 ~ ~ ~ ~ 1 ~ 1 ~ 0 0 1 1 0 1 4 1 1 4 4 4 4 4 0 4 4 1 0 1 4 4 0 1 1 4 1
'REFERENCE PRESSURE FOR AIR F LOWS (OMIT THIS CARD IF NFLOW=O TREF PREF 100. 14. 7
~ 1 ~ ~ 1 1 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ 1 ~ 1 ~ 14 ~ 111 ~ ~ 01 1 ~ 0 0 0 1 1 ~ 1 ~ 0 1 4 1 4 1 1 1 ~ 1 4 ~ 1 ~ 4 ~ 1 ROOM DATA CARDS (DO NOT INCLUDE TIME-DEPENDENT ROO MS)
~ IUROOM VOL PRES TR RELHUM RM HT I 800. 14.7 80.0 0.5
~ ~ ~ 10 ~ ~ 4' 10.0 410 0001 1414
~ 444 444444 1 ~ 11 ~ ~ 1 ~ 111 ~ ~ ~ ~ ~ 411 ~ 1 ~ ~ ~ ~ 11 ~ 1 ~ ~ 141 ~ ~ ~ 11 ~ 11 AIR FLOW DATA CARDS
( OMIT THIS CARO IF NFLOW = 0 )
I IIF I AW I FROM I TO VFLOW
s 4 4 ~ 4 ~ 0 ~ 0 ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ 0 0 ~ ~ ~ ~ ~ ~ ~ 4 0 ~ ~ 4 4 ~ 0 0 ~ ~ 0 4 ~ ~ ~ 4 4 4 0 ~ 4 4 ~ 4 4 4 \440000 LEAKAGE PATH DATA
( OMIT THIS CARD IF NLEAK = 0 )
IDLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN
~ ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ ~ ~ 4 ~ 0 0 0 ~ 4 ~ ~ ~ ~ ~ 0 0 0 ~0 0 ~ 0 ~ ~ 0 ~ ~ 4 4 4 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ 4 ~ ~ 0 0 4 4 4 4 4 ~ 4 AIR FLOW TRIP DATA IDFTRP KFTYPI KFTYP2 FTSET IDFP
~ 444 ~ 0 ~ ~ ~ 00 ~ ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ 00 ~ ~ ~ ~ 0 ~ ~ 0 ~ ~ 00 ~ 0 ~ ~ ~ ~ ~ ~ 4~~ 00 ~ 0 ~ 00 ~ ~ 0 ~ ~ ~ 00 ~ 0 ~ ~ 044 HEAT LOAD DATA CARDS
~ IDHEAT NUMR ITYP QOOT TC WCOOL
~ 4 4 0 0 ~ 0 0 ~~0 ~0 ~ ~4 ~~ 0 ~ 0 0 ~~ ~ 0 ~ ~ ~ 0 00 0~ 00~ ~0 ~ ~ 0 0 ~ ~ ~~ ~ ~0 ~ ~ ~ ~ 0 ~ ~ 0 ~ 4 4 4 4 4 4 4 4 4 4 4 ~~
PIPING DATA CARDS r
~ IDPIPE IPREF POO PID AIODN PLEN PEM AINK PTEMP IPHASE 4444 ~ 4400 ~ ~ 4 ~ ~ 4 ~ ~ 4 ~ ~ ~ ~ 4 ~ ~ 4 ~ ~ ~ 0000 ~ ~ 04 ~ 00000 ~ ~ 0 ~ 000 ~ 4 ~ 04 ~ ~ 404 F 4'4444 HEAT LOAD TRIP CARDS IOTRIP IHREF ITMO TSET TCON
~ ~ ~ 4 4 ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ 4 ~ ~ ~ ~ 0 4 0 ~ ~ ~ 0 ~ 0 0 0 ~ 0 0 ~ 0 ~ 0 ~ 0 0 0 0 ~ 0 ~ ~ 0 ~ 0 0 ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ ~ 4 ~ 4 4 0 ~ ~ 404 STEAM LINE BREAK DATA CARDS 4
~ IDBRK IBRM BFLPR IBFLG BOOT TRIPDN TRIPOF RAMP 4
~ 4 4 4 ~ 4 4 ~ 4 ~ ~ 4 0 4 4 ~ ~ 4 4 ~ ~ 0 ~ ~ 4 ~ 0 4 0 0 0 ~ 0 0 ~ 0 0 ~ 0 0 0 0 0 0 0 0 ~ 0 0 0 0 ~ 0 ~ 0 ~ 0 0 0 0 0 ~ 4 4 4 4 4 ~ 0 044 THICK SLAB DATA CARO (CARD I OF 3) 4 ID SLB I I RM I I RLI2 I TYPE NGR I0 IHFLAG CHARL
~
I I 4 4 4 ~ 4 ~ 0 ~ 4 ~ 4 ~ ~ 4 ~ 0 ~ 4 ~ 4 4 0 0 0 0
-I 4000 I 'I 5 12 10.
~ 0 0 0 0 ~ 0 ~ 4~ ~ 0 04 4 0 ~ ~ ~ ~ ~ ~ ~ 4 4 4 0 ~ ~ 0 0 ~ 4 4 0 0 4 4 4 044 THICK SLAB DATA CARD (CARO 2 OF 3) 0 I OSLB I ALS AREAS I AKS ROS CPS EMIS I 2.0 300. I . 00 140. 0.22 0.8
~ 4 ~ 4 ~ ~ ~ 404 ~ 4 ~ ~ ~ 0004 ~ ~ ~ ~ ~ 000 ~ 40040 ~ 0000 ~ 00 ~ 00004 ~ 4 ~ ~ ~ ~ ~ 00 ~ 044 ~ ~ 000 ~ 0 ~ 4 THICK SLAB DATA CARD (CARD 3 OF 3)
~ IDSLBI HTCI(1) HTC2(l) HTCI(2) HTC2(2)
I 1.46 6.00 044444
~ 4 4 4 4 4 ~ 0 ~ 4 ~ 0 ~ ~ 440 ~ 0 ~ ~ ~ 0 ~ ~ 00 ~ ~ ~ ~ 00000444 ~ 0 ~ ~ ~ 04444 ~ ~ 44 ~ ~ ~ 4 ~ ~ 440 ~ 0 ~ 0 THIN SLAB DATA CARO (CARD I OF 2) 4 IDSLB2 JRMI JRM2 JTYPE AREAS2 4
~ 4 ~ 0 4 0 4 0 0 0 0 0 0 0 0 0 ~ 0~ 0 ~00~0~0~400004 00~ 4004000000 0~ 0 040 44 044000 4404040 0 040 THIN SLAB DATA CARO (CARO 2 OF 2) 4 IDSL82 UHT(l) UHT(2) 4 44 ~ 044 ~ ~ ~ 04 ~ ~ ~ ~ ~ 040 ~ 00 ~ ~ ~ ~ ~ 0 ~ 00 ~ ~ 0 ~ ~ 04004 ~ 4 ~ 004 ~ 000440 F 4'4404444440 44 ~
4 TIME-DEPENDENT ROOM DATA IDTOR IRMFLG NPTS TDRTO AMPLTO FREQ
-I 2
~ 44 ~ 44 ~ ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ 44 ~ ~ ~
0 200.0 100.0
~ ~ 4 ~ ~ 04 ~ 440 ~ ~ 4 ~ ~ 4 ~ ~ 0 ~ 4 ~ ~ ~ ~ 004 0.50
~ 4 ~ ~ 44 ~ 4440 ~ 44 ~ 444 TIME VERSUS TEMPERATURE DATA
~ I l)TDR TTCME TTEMP TT IME TTEMP TTIME TTEMP
~ t ~ 4 ~ 4 4 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ ~ 4 4 ~ ~ 4 4 ~ ~ ~ 4 4 4 4 4 4 ~ ~ 4 4 ~ 4 4 ~ 4 4 ~ ~ ~ 4 ~ 4 ~ ~ ~ 4 4 4 ~ 4 0 ~ 4 4 4 4 4 4 4 444
~ ~ 4 4 ~ ~ ~ ~ ~ ~ 4 4 ~ ~ ~ ~ ~ ~ ~ 4 4 ~ 4 4 ~ 4 ~ ~ ~ 4 4 4 4 4 4 ~ 4 4 0 4 ~ 4 ~ ~ 4 ~ 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 ~ ~ 4 4 ~ ~ 444
TSO FOREGROUND HAROCOPY ~ ~ ~ 0 PRINTED 89284.1045 SNAME=EAMAC.COTTAP.SAMPLI.DATA DL=DSK533
( OTTAP SAMPLE PROBLEM I -- RUN 2 o 0 0 0 0 0 ~ ~ ~ 0 ~ 1 0 0 0 0 0 ~ 0 ~ 1 ~ ~ ~ ~ ~ ~ 0 0 ~ ~ ~ 0 0 ~ 0 0 ~ 0 ~ 0 ~ 0 ~ ~ ~ 1 0 0 0 0 0 0 1 0 1 ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ 0 1 0 ~
PROBLEM DESCRIPTION DATA ( CARD I OF 3 )
NROOM NSLAB'I NSLA82 NFLOW NHEAT NTOR NTR I P NPIPE NBRK NLEAK NCIRC NEC I I 0 0 0 I 0 0 0 0 0 2
~ 0 1 ~ 0 ~ 0 0 0 0 0 0 0 0 ~ 0 0 ~ 0 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 1 0 ~0 0 1 0 0 0 0 0 ~ ~ ~ 1 1 ~ ~ 0 0 ~ ~ ~ ~ 0 ~ ~ 0 0 ~ ~ 0 0 0 ~ 0 ~ 0 PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )
NFTRIP MASSTR MF CP I CP2 CRI INPUTF IFPRT RTOL 0 0 222 2.04 2.0 10. I I I .D-5
~ 0 1 0 ~ ~ ~ ~ 0 ~ 0 0 ~ 0 0 0 ~ ~ ~ 0 0 ~ ~ 0 ~ 0 0 0 ~ 0 ~ ~ ~ ~ ~ 1~ ~0000 10 ~ ~ 0 ~ ~ 0 ~ 1 ~ 0 0 ~ 0 1 0 0 0 0 0 ~0 1 ~ 0 0 ~ 0 PROBLEM DESCRIPTION DATA ( CARD 3 OF 3 )
NSH TFC 0 I . D-5
~ 1 0 1 ~ 0 ~ I ~ 0 ~ 0 ~ 0 I ~ ~ ~ 0 ~ ~ ~ ~ 0 ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ 0 0 0 0 0 0 0 0 0 1 0 0 0 ~ 0 0 0 ~0 ~ 1 0 0 1 ~ 0 ~ 0 0 0 1 1 0 0 0 0 1 0 ~
PROBLEM TIME AND TRIP TOLERANCE DATA T TEND TRPTOL TRPENO 0.0 1520.0 IO.DO 0.00 1 ~ ~ 0 ~ 0 ~ ~ 1 ~ 11 ~ ~ ~ 00 ~ ~ ~ 0 ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ ~ ~ 01 ~ ~ 1 ~ ~ ~ 0 ~ ~ ~ 00000 ~ 0 ~ ~ 00011 0 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BA LANCE
( OMIT THIS CARD IF NFLOW = 0 )
DELFLO 1.0-5
~ 00100 ~ 0 ~ 1 ~ ~ 10 ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ 0 ~ ~ ~ 00 ~ 0 ~ ~ 0 ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ 1 ~ ~ ~ 1 ~ ~ ~ ~ 00001 EDIT CONTROL DATA CARDS IDEC TLAST TPRNT I 1500. 1500.
t ~ ~ 110 ~ 00 1520.
0 ~ ~ ~ ~ ~ ~ 00 I.
~ ~ 1 ~ 0 ~ ~ ~ ~ ~ ~ 11 ~ 00000 ~ 0000 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ 0 1 ~ ~ ~ ~ 1 ~
EOI T DIMENSION CARD NREO NS I ED NS2ED 2 I 0
~ a0 ~ 10 ~ 011 ~ ~ ~ ~ 00 ~ 0 ~ 10 ~ 0 0 0 0 0 ~ 0 0 ~0 0 0 0 0 0 0 00 0 1 0 ~0 0 ~ 0 ~ 0 0 ~ ~ ~ 1 ~ 1 ~ 0 ~ 0 0 ~ ~ 0 0 0 0 0 0 1 1 ROOM EDIT DATA CARD(S) 000 ~ 00
-I
~ ~ ~ 1 ~ 00111 ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ 0 ~ 0 0 0 0 0 ~ ~ ~ ~ ~ 1 ~ 0 1 0 0 ~ ~ ~ ~ 0 ~ ~ 0 1 ~ ~ 0 0 ~ ~ 0 0 0 0 0 0 00 0 0 EDIT CARO(S) FOR THICK SLABS
~ 0 ~ ~ 0 ~ 0 ~ 000000 ~ 1 ~ ~ 0 0 ~ ~ ~ ~ ~ 0 1 ~ 1 ~ 0 ~ 1 0 0 1 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 ~ ~ 1 0 0 0 1 0 0 1 0 0 ~ 0 1 0 1 1 1 1 EDIT CARDS FOR THIN SLABS
~ 1 ~ 10000 ~ 0 ~ ~ 11 1 ~ ~ ~ ~ 1 0 ~ 1 ~ 0 ~ ~ ~ 0 0 0 ~ 0 0 0 0 0 0 1 0 0 ~ ~ 0 ~ 0 ~ 1 0 1 0 ~ ~ ~ ~ 1 0 0 ~ ~ 0 0 0 0 0 0 ~ 0 0 0 0 ~
REFERENCE PRESSURE FOR AIR FLOWS (OMIT THIS CARD IF NFLOW=O)
TREF PREF 1(10. 14. 7
~ 00101000 ~ ~ ~ ~ 10 ~ 0001 ~ ~ ~ ~ ~ ~ 1 ~ 0 0 ~ 0 ~ 0 ~ 0 ~ 0 0 0 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ 0 1 ~ ~ ~ 0 1 1 1 1 0 0 1 1 0 R OOM DATA CARDS (00 NOT I NCL UDE TIME-DEPENDENT ROOMS)
I (>ROOM VOL PRES TR RELHUM RM HT I 800. 14.7 80.0 0.5 10.0 11001
~ ~ 0 \ 0 01 10 1 110 ~ 0 ~ 110 ~ ~ 0 ~ ~ ~ ~ 0 ~ ~ 1 ~ ~ ~ 0 ~ 1001 ~ 01 ~ 10 ~ ~ 0 ~ 0 ~ ~ 00 ~ ~ ~ ~ 10 ~ 1 ~ ~ ~ 1 ~
AIR FLOW DATA CARDS OMIT THIS CARD IF NFLOW = 0 )
e ~ I I ~ ~ ~ ~ ~ ~ 0011
~ ~ ~ I ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ I ~ 11 ~ ~ I ~ ~ ~ 010011 ~ I ~ ~ ~ ~ ~ ~ I ~ 01111111100 ~ I ~ ~ ~ I LEAKAGE PATH DATA
( OMIT THIS CARO IF NLEAK -" 0 )
IOLEAK ARLEAK AKLEAK LRM1 LRM2 LOI RN
~ I I I I ~ ~ I ~ ~ I ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I I I ~ ~ I I I I I I ~ I ~ I I I I I I I ~ I ~ ~ I ~ 010000000001 ~ ~ ~ ~ ~ I~
AIR FLOW TRIP DATA
~ IDFTRP KFTYP1 KFTYP2 FTSET IOFP
~ ~ I ~ ~ ~ ~ I ~ I ~ I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 10 ~ 00 ~ 10 ~ ~ ~ ~ ~ ~ III~ I ~ 0000 ~ I ~ ~ ~ 0000 ~ 00 ~ ~ 00100 ~ I ~
HEAT LOAD DATA CARDS
~
IDHEAT NUMR ITYP QOOT TC WCOOL
~ t ~ 11 ~ I ~ ~ 01 ~ ~ ~ ~ ~ ~ I ~ ~ I ~ I ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ I~ ~ I ~ ~ ~ I~ ~ ~ I ~ I ~ I ~ ~ ~ ~ ~ ~ ~ ~ I I ~ I ~ ~ ~ ~ I ~ ~ ~ I ~
PIPING DATA CARDS
~ IDPIPE IPREF POD PIO AIOON PLEN PEM A INK PTEMP I PHASE t I I I I ~ ~ I ~ I I ~ ~ ~ ~ ~ I I I ~ ~ I I I ~ I ~ I ~ ~ ~ I ~ ~ ~ I ~ I I ~ I I I II I I I II I IIII I IIIII I I I I I ~ ~ I I I I HEAT LOAD TRIP CARDS IOTRIP IHREF ITMD TSET TCON t ~ ~ ~ ~ ~ 010 ~ ~ ~ I ~ I ~ 00 ~ ~ ~ ~ I ~ ~ ~ ~ I ~ ~ I ~ ~ 00 ~ ~ ~ 01 ~ I ~ 0000 ~ ~ ~ ~ ~ I ~ 1110 ~ 1001 ~ 01 ~ I ~ 111 t STEAM LINE BREAK DATA CARDS
~ IDBRK IBRM BFLPR IBFLG F RAMP
~ ~ I II ~ I I~ ~ I ~ ~ ~ ~ II~ ~ ~ ~ 0 ~ ~ ~ 0 ~ IIII~ IIII ~ ~ ~ ~ I II I I I
~ ~ 0 ~ I I ~ 01 ~ ~ I ~ I ~ ~ 0101 ~ 10 ~ I~
THICK SLAB DATA CARO (CARO 1 OF 3)
IDSJ Bl IRMl I RM2 I TYPE NGRID IHFLAG CHARL
-1 15 12 10.
~ I~ ttI
~ ~ ~ 11 ~ ~
1 I ~ I ~ ~ ~ ~ ~ ~ ~ ~ 01 ~ ~ 10011 ~ ~ I ~ ~ ~ II ~ 000 ~ ~ ~ ~ 00 ~ ~ 00 ~ ~ I ~ ~ I ~ I ~ I ~ ~ I ~ 100 ~ I THICK SLAB DATA CARD (CARO 2 OF 3)
I DSLB 1 ALS AREAS) AKS ROS CPS EMI S 2.0 300. 1.00 140. 0.22 0.8 I ~ 01 ~ ~ ~ ~ ~ ~ ~ I ~ 1001 I ~ ~ ~ ~ ~ ~ 10 ~ 10 ~ ~ ~ ~ ~ ~ ~ ~ 100 ~ 01 ~ ~ ~ ~ ~ ~ ~ ~ 11101 ~ I ~ ~ I ~ ~ ~
1
~ t~ ~ ~ ~
THICK SLAB DATA CARO (CARO 3 OF 3 )
t IIJSL81 HTC1(1) HTC2(1) HTC 1 (2) HTC2 (2) 1.46 6.00 I ~ ~ I ~ 1111 ~ 100 I~ ~ I~
~ t 1
~ ~ ~ ~ ~ ~ ~ t ~ ~ ~ I I ~ ~ ~ ~ ~ ~ I ~ ~ ~ I ~ ~ 00 ~ ~ ~ ~ ~ ~ ~ I ~ ~ 10100
~ ~ ~ ~ ~ ~ ~ ~ ~
t THIN SLAB DATA CARD (CARO 1 OF 2) t
~ I OSL82 JRM1 JRM2 JTYPE AREAS2 t
~ I I I ~ ~ ~ ~ I I I I ~ I ~ I I I ~ ~ ~ I ~ ~ I I I I I ~ ~ ~ I I I ~ ~ ~ I ~ ~ ~ I I ~ I I I I I I ~ I ~ I ~ 111111 ~ 01 ~ 00 ~ 100 THIN SLAB DATA CARO (CARO 2 OF 2) t
~ IDSL82 UHT( 1 ) UHT(2)
~ ~ t t ~ IIII I ~ ~ ~ ~ ~ 00 ~ ~ ~ ~ ~ ~
TIME-DEPENDENT I ~ ~ ~ I ~ ~ 001 ~ ~
ROOM DATA I ~ I ~ 011111000 ~ I ~ I I I I I I I I I I I ~ ~ I I I ~ ~ ~ I I 1010R IRMFLG NPTS TORTO AMPLTD FREQ
-1 - 200.0 100.0 0.50
~ ~ ~ 11 ~ I ~ ~ ttt ~ I ~ ~ ~ ~ I ~ ~
I ~ ~ ~ tt ~ ~ ~ ~ ~ ~ ~ ~ I ~ 11 2 0
~ ~ tt ~ ~ I~ ~ ~ ~ ~ ~ ~ ~ I~I~ I~ ~ ~ ~ ~ 11 ~ I ~ 111 TIME VERSUS TEMPERATURE DATA
~ IDTDR TTIME TTEMP TTIME TTEMP TTIME TTEMP t
~ 1tt ~ ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ 01 ~ ~ ~ I I
~ ~ 101 ~ I~ ~ ~ I ~ I ~ 1101 ~ 11 ~ ~ ~ ~ ~ 10 ~ 1101 ~ 11 ~ I ~ I I ~ I ~ ~ I ~
~ t~ 11 ~ ~ I~ ~ ~ ~ ~ ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ ~ 1111 ~ 11 ~ ~ ~ I ~ ~ I ~ 000 ~ ~ 111 I ~ ~ 11 ~ ~ ~ I ~ ~ ~ 11t ~ ~ I g I
RGURE 4.2 COMPARISON OF COTTAP CALCULATED TEMPERATURE PROFILE WITH ANALYTICALSOLUTION (t=900 hr)
FOR SAMPLE PROBLEM t 220 210 Ql Q) 200 I~
Legend 190 ANALYIICAL 4 COTTAP 180 170 0.5 1.5 x (tt) o (C
C)
FIGURE 4.3 COMPARISON OF COTTAP CALCULATED TEMPERATURE PROFILE WITH ANALYTICALSOLUllON (t 2000 hr)
FOR SAMPLE PROBLEM 1 250 240 Legend Q) ~WALVTlCAL 230
~ COTTAP 220 l~
50- 210 200 190 180
' I 0.5 1.5 O Cg x (tt) CD
FIGURE 4.4 COMPARISON OF COTlAP CALCULATED TEMPERATURE OSCILLATION WITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 1 200.6 I 200A Legend ANALYTICAL M
4 ~ COTTAP O 200.2 LJ CI M
K 200 O
O O
199.8 O
4J CL I- 199.6
!L 4J I
199A 150 1505 1510 1515 1520 TIME (hr) c C)
PP8 L Form 24S4 (!N83)
Cat. l973401 V
SE -B- N A -04 6 Rev.ag Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~9of Approved by 4.2 Com arison of COTTAP Results with Anal tical Solution for Com artment Heat U due to Tri ed Heat Loads (Sam le Problem 2)
This problem consists of two compartments separated by a thin wall. One of the compartments is maintained at a constant temperature (COTTAP time dependent room) g the temperature in the other compartment is calculated by the code. The compartment for which the temperature is calculated contains 4 heat loads and 5 associated heat load trips. The timing of these trips matches the plot in figure 4.5.
The analytical solution for the room temperature is T
r (t) =Tr (0)e +Tcon (1-e )
-tB/a t yB/a
~ ( ) (4-6) 0 a where the constants a and B are defined in Appendix B, Tcon is the compartment temperature on the opposite side of the thin wall, and Q is the function shown in Figure 4.5.
kW <
0 0 0 III Ol A~
'0
'D X7 Q @r
( IO 2 yo 03 a a AI O O Q>o o 'C P m
0 X X
m CO C
O I n~
~ 30QQ i~L rZ o>
C0 O~
>a~> L a x Ti:p o~ I 0
~m HPC,+ l I0ag L Tb P O~ Om Z gy S
TiI)P O~~
III x r
~aOoo O gpu+ J ~aQ Q. m~
-l~A m
O Hca k Lo~d t3 Tv p =0 g ~~/ L<c.d g &p DCCC D
~
'X
+ /Oo&
CA m 37 Z Z 0
0
'I CD
/o /g 20 0 T>~g (Hrs) C CD
L PPKL Form 2iSl (1$ N)
Cat. t970401
$F 9 lq A.-04 6 Rev Qi Dept. PENNSYLVANIAPOWER 8c LIGHT COMPANY ER No.
CALCULATION SHEET Date 19 Designed by Approved by PROJECT Sht. No. ~of Because of the complexity of this function, a FORTRAN program was written to perform the necessary numerical integration and to evaluate the analytical solutions The COTTAP input deck is given in Table 4.3. Comparison of the COTTAP results with the analytical solution is shown in figure 4.6. As can be seen, the COTTAP results agree with the analytical solution.
4.3 COTTAP Results for Com artment Coolin b Natural Circulation (Sam le Problem 3) 5 In this problem, a compartment containing a heat source of 10 Btu/hr is initially cooled by forced ventilation flow drawn from outside air (outside conditions are represented by time>>dependent compartment, -1).
Ventilation flow is tripped off at t~ 1 hr. Since the'compartment is not airtight, air leakage between the compartment and the environment occurs which maintains the compartment at atmospheric pressure. This air transfer process is modeled by means of a leakage path. No air flow to the compartment occurs from t~ 1 hr to t~ 2 hr (except for leakage flow)r at t~ 2 hr, two vents at different elevations are opened allowing natural circulation flow through the compartment. In order to simulate this, a natural circulation flow path is tripped on at t= 2 hr, and at the same time, the leakage flow is tripped off because the circulation flow model already allows for air leakage.
~ ~ 4 TSO FOREGROUND HAROCOPY 111 ~ PRINTED 89284. 14 12 SNAME=EAMAC.COTTAP~ SAMPL2.DATA ~
OL=OSK534 COTTAP SAMPLE PROBLEM 2 41 ~ ~ 1 ~ ~ 4444141I11 ~ 4 ~ ~ 4 ~ ~ ~ I~ ~ 4 ~ ~ 4 ~ ~ 4 ~ ~ ~ 1 ~ 1 ~ 44I4 ~ ~ ~ 44I ~ ~ 4411 ~ ~ ~ 4 ~ ~ ~ ~ 1 ~ 44 1 ~ 44 ~
PROBLEM DESCRIPTION DATA ( CARD 1 OF 3 )
NROOM NSLA81 NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBR K NLEAK NC I RC NEC 1 0 1 0 4 1 5 0 0 0 0 1 1 4 4 ~ 1 14 4 ~ ~ 4 ~ ~ I4 ~ 4 ~ ~ ~ 4 ~ 4 ~ ~ ~ ~ ~ ~ I
~ 1 4 4 4 4 ~ 1 4 ~ ~ 4 I4 4 ~ 4 1 4 4 4 I ~ ~ ~ ~ 4 4 ~ ~ ~ 14 ~ 4 ~ 4 ~ 44444 ~ ~
PROBLEM DESCRIPTION DATA ( CARD 2 OF 3 )
NFTRIP MASSTR MF CP1 CP2 CR1 INPUTF IFPRT RTOL 0 0 222 2.04 2.0 10. I 1 1. 0-5 1 4 ~ ~ 4 ~ ~ ~ ~ 4 4 4 4 ~ 4 4 ~ ~ 1 ~~ ~ ~ ~ ~ ~ ~ ~ ~ 4 ~ 4~ 44 ~ ~ ~ ~ 4 1 4 4 4 4 ~ 4 4 1 ~ ~ 4 4 1 ~4 ~ ~ ~ 1 ~ ~ ~ 4 4 4 1 4 4 ~ ~
PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )
NSH TFC 0 'I
. 0-5 41 1 ~ 14 ~ ~ ~ 444 ~ ~ 1 ~ ~ ~ 14 ~ ~ 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ 444 ~ 4 1 ~ 4144444 ~ 44 ~ 4444 ~ ~ ~ ~ ~ 44 ~ 4 ~ ~ 4 ~ ~ 444 PROBLEM TIME ANO TRIP TOLERANCE DATA T TEND TRPTOL TRPEND 0.0 40.0 0.005 40.0 41414
~ 4 ~ 4 ~ 44414444 ~ 44444 ~ ~ ~ ~ ~ ~ 44 ~ ~ ~ ~ 4 ~4 ~ ~ I4 ~ 4I~ ~ ~ 4 ~ ~ 4 ~ 41 ~ ~ ~ ~ 4 I ~ 4 ~ ~ 4 ~ ~ 44441 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANC
( OMIT THIS CARO IF NFLOW = 0 )
DELFLO
~ ~ 4 ~ 1 ~ ~ ~ 4 4 1 4 ~ 4 ~ ~ 4 4 ~ ~ 4 ~ ~ ~ ~ 4 ~ 1 4 ~ 4 4 4 ~ ~ 4 4 4 4 1 4 4 ~ 4 4 4 4 4 4 4 1 4 ~ ~ 4 4 ~ ~ ~ ~ ~ 4 ~ ~ ~ ~ 4 1 4 4 1 EDIT CONTROL DATA CARDS IDEC TLAST TPRNT 1 60. 2.0
~ 4 ~ ~ 44444414 ~ 44 ~ ~ 44 ~ ~ ~ ~ ~ ~ ~ 4 ~ 4 ~ ~ ~ 41 ~ 44414 ~ 414 ~ 4444444144 ~ ~ ~ 4 ~ 41 ~ 44 ~ 4 ~ 11 ~
EO I T DIMENSION CARO NRED NS1ED NS2ED 2 0 1 441444414 ~ 1 ~ ~ ~ ~ 4 4 ~ ~ 4 1 ~ ~ ~ 4 4 ~ ~ 1 ~ 4 ~ 4 ~ 1 1 4 1 1 4 4 4 ~ 4 4 4 4 4 ~ 4 ~ ~ ~ ~ ~ 4 4 4 4 ~ ~ ~ ~ ~ ~ 4 4 ~ ~ 4 4 ROOM EDIT DATA CARO( 5)
-1
~ 4 4 4444444 ~ 4 4 4 ~ 4 ~ 4 4 4 4 4 4 ~ ~ 4 ~ 4 ~ ~ 4 4 ~ 4 ~ ~4 ~ ~ 1 ~ 1 ~ 4 1 ~ 4 1 ~ ~ ~4 4 4 4 ~ ~ 4 ~ 4 ~ 4 4 ~ 1 4 ~ 4 1 4 ~ 4 EDIT CARO(S) FOR THICK SLABS
~ 444444444 ~ 1 4 4 4 4 ~ ~ ~ 1 4 4 4 ~ ~ ~ ~ 4 4 4 ~ ~ 1 ~ ~ ~ ~ 4 4 4 4 1 4 4 1 4 4 4 4 4 4 ~4 ~ ~ ~ ~ 4 ~ ~ 1 ~ 1 ~ ~ ~ ~ 4 4 \41 EDIT CARDS FOR THIN SLABS
~ ~ 1 ~ ~ ~ ~ 1 ~ 4 4 1 4 4 4 ~ 4 4 4 4 4 4 ~ ~ ~ ~ ~ 4 4 4 4 1 4 ~ 4 4 4 4 4 4 4 4 ~ 4 4 4 4 ~ 4 ~ 4414 ~ 414 ~ 41 ~ ~ 44 ~ 4 ~ 4444 REFERENCE PRESSURE FOR AIR FLOW (OMIT THIS CARD IF NFLOW=O)
TREF PREF f 4414 ~ 4441 4 4 4 4 4 ~ ~ 4 4 4 ~ ~ ~ 1 ~ ~ ~ 4 4 4 ~ ~ 1 ~ 4 1 4 4 4 4 ~ 1 4 ~ 1 ~ 4 4 1 4 4 ~ 4 4 1 ~ ~ 4 4 1 1 ~ ~ ~ 4 1 1 4 4 4 4 1 ROOM DATA CARDS (DO NOT INCLUDE TIME-DEPENDENT ROOMS)
~ I DROOM VOL PRES TR RELHUM RM HT 10 000. 14.7 100.0 0.5 10.0 4411
~ ~ 1114 ~ 444 4 1 ~ 4 4 ~ 1 ~ ~ 4 4 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ 4 4 4 ~ 4 1 4 4 4 1 ~ 1 4 ~ 4 4 4 ~ ~ ~ ~ 444 ~ ~ 1 ~ 41 ~ 14144 AIR FLOW DATA CARDS
( OMIT THIS CARO IF NFLOW = 0 )
1nri nw IFROM ITO VFLOW
1 ~ ~ ~ 0 0 0 ~ 1 0 ~ ~ ~ 0 ~ ~ ~ 0 ~ 1 ~ 1 ~ ~ ~ ~ 0 ~ 0 ~ 1 0 ~ 1 ~ 1 ~ ~ ~ 1 1 1 1 1 ~ 1 1 ~ 1 1 1 1 ~ ~ 1 ~ ~ ~ 1 1 1 ~ 0 ~ 1 0 ~ ~ ~ ~ ~
LEAKAGE PATH DATA
( OMIT THIS CARO IF NLEAK = 0 )
IOLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN
~ ~ ~ 0 ~ ~ ~ ~ ~ ~ 0 1 0 1 0 ~ ~ 0 00~ 0 ~ ~ 0 ~ ~ 1 ~ ~ 0 0 0 0 ~ 0 0 0 0 0 0 ~ 0 0 0 ~ 0 ~ 0 0 1 1 1 0 0 1 ~ 0 1 1 0 ~ 1 1 0 0 ~ ~ ~ ~ 0 AIR FLOW TRIP DATA IDFTRP KFTYPI KFTYP2 FTSET IDFP 1 ~ ~ ~ ~ 00000 ~ ~ 00 ~ 0 ~ 0 ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ 0 ~ 0 ~ 00 ~ 0 ~ 0 ~ 0 ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
HEAT LOAD DATA CARDS IDHEAT NUMR ITYP QDOT TC WCOOL I I 2 'I 000. -1. 0.
2 I 3 'I 000. I . 0.
3 I 3 3000. -1. 0.
4 I 8 2000. I . 0.
- ~ ~ 1 ~ ~ 000 ~ 0 ~ I ~ ~ Ol ~ ~ 0 ~ 0 ~ 0 ~ 0 ~ ~ ~ ~ ~ 00 ~ 0000 ~ 00 ~ 0 ~ 00 ~ eeel ~ ~ 00 ~ ~ ~ ~ 10000 ~ ~ ~ ~ ~ 000 ~ 0 ~
PIPING DATA CARDS IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE 1 ~ 1 0 0 0 ~ ~ ~ ~ 0 1 ~ 1 0 ~ ~ ~ ~ ~ ~ 0 0 1 1 ~ 0 ~ ~ ~ ~ ~ ~ ~ 0 0 0 0 0~~000001 0~ ~~ 0 1 ~ 1 1 ~ 1 ~ 0 ~ 0 ~ ~ ~ ~ 1 0 ~ ~ 1 HEAT LOAD TRIP CARDS I DTR IP IHREF ITMD TSET TCON I 'I 2 1.0 0. 0 TRIP ON 2 I I 5.0 0. 0 TRIP OFF 3 2 I 10.0 0. 0 TRIP OFF 4 3 2 15.0 0. 0 TRIP ON 5 4 I 20.0 5. 0 EXPON DECAY s \ 00000000 ~ ~ ~ ~ ~ ~ 011 ~ 0 ~ 0 ~ ~ ~ 0 ~ ~ ~ 010 ~ ~ ~ ~ 10 ~ ~ 110 ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ ~ 00000000 ~ ~ 0 ~ 1 ~ ~ ~ ~
STEAM LINE BREAK DATA CARDS
~
IOBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP I
1000000000 ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 ~ 00 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ 000 ~ ~ ~ 00 ~ 00 ~ ~ 1 ~ ~ ~ 111 ~ 1 ~ ~ 0 ~ 0 ~ ~ ~1 THICK SLAB DATA CARD (CARO I OF 3)
I I OSLB I IRMI IRM2 ITYPE NGRIO IHFLAG CHARL oeooooo ~ 00 0 ~ ~ ~ ~ 0 ~ 0 ~ ~ 11 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0000 ~ 0 ~ ~ 0 ~ ~ ~ ~ 0 ~ 00 ~ ~ 1 ~ ~ 0 ~ ~ 0 ~ 1 ~ 0 ~ 010 ~ ~ ~ ~ 0 THICK SLAB DATA CARD (CARD 2 OF 3)
IDSLB I ALS AREASI AKS ROS CPS EMI S t ~ ~ ~ ~ ~ 0000 0000 ~ ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ 0 ~ 00000 ~ ~ 0 ~ 00 ~ 1 ~ 1 ~ 0 00001 ~ ~ ~ 000 ~ 1 ~ 0010 ~
THI C K SLAB DATA CARD (CARO 3 OF 3 o
~ I OSLB I HTCI ( I) HTC2( I) HTCI(2) HTC2(2) 1 ~ ~ 1 ~ 100 ~ 0 0 ~ 0 ~ ~ ~ ~ ~ 0 ~ ~ 1 1 1 ~ 0 0 0 0 1 ~ 1 1 1 ~ 1 0 0 ~ ~ 0 0 1 0 ~ 0 ~ 0 0 0 0 0 0 ~ 1 ~ 0 ~ ~ 1 0 ~ ~ ~ 1 0 1 ~ 0 0 0 ~
THIN SLAB DATA CARO (CARO I OF 2)
IDSL82 JRM I JRM2 JTYPE AREAS2 I I -I
~ 1 ~ ~ 1 ~ ~ ~ ~ ~ 1 ~ 11 ~ 01 ~ ~ ~
I 500.
111 111 1111
~ 11111111 ~ ~ oo ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ 0 ~ 0 ~ ~ ~ 1 ~ ~ 1 ~ 1 ~ ~ ~ ~ ~
THIN SLAB DATA CARD (CARO 2 OF. 2)
IOS LB2 UHI( I ) UHT(2)
I 0.33 111111 111 t11111 ~ ~ ~ 111 ~ 1 ~ ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ 1 ~ 1 ~ 11 ~ ~ ~ 1 ~ 1 ~ ~ ~ 111 ~ ~ ~ ~ ~ 1 ~ 111 ~ ~ 1 ~ 11 ~ ~ ~ ~
TIME-DEPENDENT ROOM DATA I DTDR IRMFLG NPTS TORTO AMPLTD FRED
-I 01111111 I 3 0.0 ~
0.0 ooooooe ~
0.00 ooeoeooooeoo ~ ~ ~ 1 ~ 1 ooooo~o ~ ~ ~ oooo ~ ~ 1 ~ ~ ~ ~ 1111 ~ ooooeo
~IMF <ERSIIS TEMPFRATURE DATA nnF (
-1 0.00 100.0 0.50 14.70 50.00 100.0 0.50 14. 70 100.00
~ ~ ~ ~ ~ ~ ~ ~ Ij4 4 ~
100.0 0.50 14. 70 I1 ~ 0 ~ ~ ~ 0 4 4 0 I~ ~ 0 ~ ~ 0 ~ 0 ~ ~ 1 4 I0 ~ 0 ~ ~ ~ ~ ~ 1 0 ~ 0 0 ~ 0 ~ I4 4 4 4 4 0 ~ 0 0 i4 4 ~ i0 0 4 1 J 4 4 ~ 4 0 ~ ~ ~ 0 ~ 0 4 0 4 4 ~ 0 ~ 0 t 4 ~ 1 0 0 ~ ~ ~ 4 l~ ~ i1 ~ 0 ~ ~ ~ 0 ~ 0 ~ ~ ~ ~ 0 0 ~ ~ l~ 4 0 4 4 ~ 4 4 4 ~ ~ 0 ~ ~ ~ 0 ~
~ I ~
~
FIGURE 4.6 COMPARISON OF COTTAP CALCULATEO COMPARTMENT TEMPERATURE WITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 2 135 130 125 120 O
O 115 O Legend LLI 110 ANALYTICAL
~ COTTAP LJJ 105
,0 100 0 10 20 30 40 TIME (hr)
PP8,L Form 24'10/N)
Ca). t973401 SE . N A =04 6 Rev.0g Dept. PENNSYLVANIAPOWER 8c LIGHT COMPANY ER No.
CALCULATIONSHEET Date 19 Designed by Approved by PROJECT Sht. No. ~of The walls of the compartment consist of 3 slabs: a vertical wall (slab l), a ceiling (slab 2), and a floor (slab 3) which is in contact with the outside ground. The temperature, relative humidity, and pressure within the time-dependent compartment are held constant throughout the transient. The COTTAP input data file for this problem is shown in Table 4.4. The COTTAP results for this problem are given in Figure 4.7.
4.4 COTTAP Results for Com artment Heat-U Resultin from a Hi h Ener Pi e Break (Sam le Problem 4)
A high energy pipe break is modeled using a standard COTTAP compartment that is connected via a leakage path to a time dependent volume. The pipe break is initiated in the standard compartment at time 0.5 hr and is terminated at time 2.5 hr. The time dependent volume is maintained at 0
95 F and 14.7 psia. The leakage path maintains constant pressure in the standard compartment by allowing flow between it and the time dependent compartment.
The COTTAP input file is shown in Table 4.5 and results of the COTTAP run are given in Figure 4.8 ~
TSO FOREGROUND HARDCOPY ~ ~ 10 PRINTED 89304.0951 OSNAME=EAMAC.COTTAP.SAMPL3.DATA VOL=OSK533 COTTAP SAMPLE PROBLEM 3 01101000000000 ~ 0000000 ~ 0 ~1 0 0 0 0 0 0 0 0 0 ~0 0 0 0 1 00 0 0 1 0 0 ~ 0 0 0 0 0 0 0 0 0 0 ~ 0 ~ 0 1 0 1 ~0 ~00 0
~ PROBLEM OESC RIPTION DATA ( CARD I OF 3 )
0 NROOM,NSLABI NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NCIRC NEC I 3 0 2 'I I 'I 0 0 I I 8
~ ~ ~ ~ 1 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 0 0 0 0 ~ 1 ~ 0 0 0 1 1 1 0 1 0 0 0 ~ 0 ~ ~ 0 ~ ~ ~ 0 0 0 0 ~ ~ 0 1 0 ~ ~ 0 ~ ~ 0 ~ ~ 0 1 1 ~ 1 1 ~ 0 ~ 1 1 011 PROBLEM OESC RIPTION DATA ( CARD 2 OF 3 )
NFTRIP MASSTR MF CPI CP2 CR'I INPUTF IFPRT RTOL
~ ~ 0 0 ~
I 10 2.04 001 ~ 00 0 1 0 ~ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ ~ 0 ~ ~ 0 0 0 5.
5 150. I I I . D-5
~~~~ 0 0 0 ~ 0 0 1 0 0 ~1 0 ~ ~0 0 0 ~~ ~0 10 0 ~ 0 1 PR OBLEM 0 ESCRIPTION DATA ( CARO 3 OF 3 )
1 0 NSH TFC 10 1. 0-5 01100 ~ 0 ~ 0 0 0 0 0 0~00 0 0 1 0100000 0000000000001~0~000000000000010000~ ~1 ~ 1 ~ ~ ~ ~ 1 1 1 PROBLEM TIME AND TRIP TOLERANCE DATA 0
0 TEND TRPTOL TRPENO 11111101 0.0 3.0 0.005 3.0
~ ~ ~
I 1 1 0 1 0 0 ~ ~ ~ ~ ~ 1 1 ~ ~0 ~ 0 ~ ~ 1 0 ~ ~ 1 ~~ I ~ ~ 1 ~ 0 0 1 ~ ~ ~ ~ ~ ~ ~ ~ I ~ ~ ~ 1 1 1 1 1 1 1 1 ~ 1 ~ ~ lI 1 ~ ~
1 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE 1 ( OMIT THIS CARD IF NFLOW = 0 )
1 1 DELFLO I.D-5
~ 111 1111010 1 ~ 1 ~ ~ ~ 1 1 1 ~ ~ 0 ~ 1 ~ 1 1 1 1 ~ 1 1 1 1 1 1 1 ~ ~ 1 ~ ~ 0 1 0 1 ~ 1 1 ~ 1 0 1 1 ~ ~ 1 1 ~ 1 1 ~ 1 1 ~ ~ 0 ~ ~ 1 1 EDIT CONTROL DATA CARDS 1
1 [ OEC TLAST TPRNT I 0.1 0.01 2 1.0 0. 10 3 1.1 0.01
- 2. 0. 10 5 2.2 0.01 6 10.0 0. 10 7 24.0 0.20 8 500.0 5.00 0111 100010 ~ 0 ~ 000101 1 1 0 1 1 ~ 0 1 1 0 1 0 1 ~1 1 1 1 1 1 ~ ~ 00 ~ ~1 ~ 0 ~ 1 1 ~ 0 1 0 0 0 1 1 ~ 1 1 ~ ~ ~ 1 ~ ~ 1 1 1 1 0 EO I T 0 IMENS I ON CARO 1
1 NRED NSIEO NS2ED 2 2 0 1 1 ~ 1 1 0 ~ 0 0 ~ ~ 0 0 0 ~ ~ 0 0 ~ ~ 1 1 ~ ~ 1 0 ~ 0 0 0 1 0 0 0 1 1 1 1 ~ 1 1 1 ~ ~ ~ 1 ~ 1 ~ 1 ~ ~ 1 ~ 0 0 ~ 0 0 1 1 0 1 1 1 ~ 0 ~ ~ 0 1 1 0 ROOM EDIT DATA CARO(S) 0 I
1 1 ~ ~ 1
-I 1 ~ ~ 1 1 0 1 1 1 ~ 1 ~ 0 ~ ~ 1 ~ 1 ~ 1 ~ ~ 1 0 1 ~ ~ 1 ~ ~ 1 ~ 1 ~ 1 ~ 1 ~ 0 1 1 1 1 ~ ~ 1 1 1 ~ 1 ~ ~ ~ 1 1 ~ 1 ~ 1 ~ ~ 1 1 ~ 1 1 1 0 EDIT CARD(S) FOR THICK SLABS I 2 111 1 1 1 1 ~ 0 ~ ~ ~ 1 ~ ~ ~ ~ 0 1 1 ~ 1 1 1 1 0 0 ~ 0 0 1 ~ ~ 1 1 ~ ~ ~ ~ ~ 1 1 1 1 1 ~ 0 ~ 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 ~ 1 1 ~ 1 ~ 1 ~ 1 1 1 EDI T CARDS FOR THIN SLABS 1
1
~ 1 1 1 ~ 1 1 1 1 1 ~ 1 ~ ~ ~ ~ 1 1 1 1 1 ~ 1 ~ 1 1 ~ 1 1 ~ 1 1 1 1 ~ 1 ~ ~ 1 ~ 1 ~ 1 1 1 ~ ~ 1 1 ~ ~ ~ ~ ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ ~
1 1 1 REFERENCE PRESSURE FOR AIR FLOWS 1 (OMIT THIS CARO IF NFLOW=O) 1 TREF PREF 100. 14. 7 0 ~ 0 0 ~ 1 ~ 0 1 ~ 1 ~ 1 1 1 ~ ~ ~ 1 ~ 1 1 1 1 ~ 1 0 1 1 1 1 0 0 1 ~ ~ 1 ~ ~ ~ 1 1 ~ 1 1 1 1 0 ~ ~ ~ 1 ~ 1 1 ~ 1 1 1 1 1 1 1 1 1 ~ 1 ~ 0 ~ ~ 0 ROOM DATA CARDS NOT INCLUDE TIME-DEPENDENl'OOMS) 1 i issci)IIM vwc S iw l(t I HIIM IIM HT
30000. 14.7 80.0 0.5 27.5 111 1 1 1 0 1 1001 0 ~ ~ ~ 0 1 ~ ~1 1 1 0 1 ~1 1 1 01 1 1 0 ~1 ~ 1 1 0 0 00 ~ ~ 1 1 ~ 0 ~ ~0 0 0 ~ ~ 0 ~ 0 1 0 0 1 1 ~ 1 1 1 0 1 1 0 1 AIR FLOW DATA CARDS 1 ( OMIT THIS CARO IF NFLOW = 0 )
1 IDFLOW IFROM ITO VFLOW I -I I 'I.D4 FAN 2
111 11011 111 ~ 11 I
~ 1 ~ 000 ~ 1
-I I . D4 100100000000000001 0
~
FAN 00000 0 ~ ~ ~ ~ 000 ~ 00 ~ 0 ~ 0 ~ ~ 1 ~ 0001001 0 LEAKAGE PATH DATA 0 ( OMIT THIS CARD IF NLEAK = 0 )
0 IDLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN I 1.0 -1.0 I - 'I 2 111 0 0 0 0 0 0 1 0 1 0 0 00 0 00 0 ~0 0 0 0 0 0 0 0 0 0 0 1000000100 10 01 00 0 0 0 001 0 ~ 0 0 ~0 0 0 1 1 1 0 0 0 0 0 0 0 0 CIRCULATION PATH DATA 0
1 IDCIRC KRMI KRM2 ELEVI ELEV2 ARIN AROUT AKIN AKOUT 001 I
~ 0000000101010 I
~
-I 10001'00 3.
~ 0 ~ ~ ~ 0 ~ 0 12.
~
- 50. 50. 5.
0000 ~ 011 ~ 0 ~ ~ 0 ~ 000 ~ 001 ~ 000011111100 5.
0 AIR FLOW TRIP DATA 0 IDFTRP KFTYPI KFTYP2 FTSET IDFP I 3 I 0. 0 I 0 TRIP CIRC FLOW OFF .AT START 2 I I 1.0 I 0 TRIP FAN OFF 3 I I 1.0 2 0 TRIP FAN OFF 4 2 I 2.0 I 0 TRIP LEAKAGE PATH OFF 5 3 2 2.0 I 0 START NATURAL CIRC
~ 1 1 1 ~ 1 1 0 1 ~ 1 1 0 ~ 1 0 0 1 0 1 1 1 ~ 1 ~ 1 1 0 ~ 0 ~ 0 ~ ~ 0 0 ~ 0 0 ~ 0 0 100 00000 0~0 0 000 0 0 0 0 0 0 1 1 1 1 01100 1 HEAT LOAD DATA CARDS 1
IDHEAT NUMR I TYP OOOT TC WCOOL I I 3 100000. -1. 0.
~ 1 1 1 1 1 1 ~ ~ 1 1 0 ~ 0 1 ~ 0 1 1 ~ 0 1 ~ 0 ~ 1 1 0 ~ ~ ~ 1 ~ 1 ~ 0 ~ 0 0 0 0 0 ~ ~ ~ 0 ~ 0 1 0 ~ 0 1 1 1 1 1 0 ~ 1 1 ~ ~ 1 ~ 1 ~ 01111 1 PIPING DATA CARDS 1
IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHA SE 1 1 0 0 0 0 1 0 0 0 ~ 1 0 0 1 0 ~ 0 00 ~ 1 0 0 0 ~ 0 1 1 ~ 0 0 ~ 0 0 1 0 0 0 ~ ~ ~ 1 ~ 0 000 ~ 0 0 0 0 0 1 0 1 0 0 ~ ~ 0 0 0 ~ 00 HEAT LOAD TRIP CARDS IDTRIP IHREF I TMD TSET TCON I I I 10. 0 0.
00111100000 1 1 0 1 0 0 0 0 0 0 1 ~ 0 ~ ~ 0 1 ~ ~ ~ ~ 1 0 0 0 0 1 1 0 1 ~ 1 ~ 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 00011 0 STEAM LINE BREAK DATA CARDS 0
IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP 0
~ 1 0 0 0 0 0 1 1 0 1 ~ ~ 0 0 0 1 1 ~ 1 1 1 ~ ~ 1 ~ ~ 1 0 1 0 0 0 0 1 1 0 0 0 0 0 ~ ~ 0 ~ ~ 1 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ 0 0 1 ~ 0 0 1 ~ 0 0 0 1 1 0 1 THICK SLAB DATA CARD (CARD I OF 3)
IDSLBI IRM I I RM2 I TYPE NGR ID IHFLAG CHARL I I -I I 10 2 30.
2 I -I 3 10 2 30.
3 I 0 2 'I 0 0 30.
10010101111 ~ 1 ~ ~ 1 1 1 0 ~ 1 1 ~ 1 ~ ~ ~ ~ ~ ~ ~ 1 1 ~ ~ ~ ~ 1 ~ ~ ~ 1 1 ~ ~ ~ ~ 0 ~ ~ ~ ~1 1 1 ~ ~~ ~ 1 1 1 0 ~ 1 0 1 11111 0 THICK SLAB DATA CARD (CARO 2 OF 3) 1 IDSLB I ALS AREASI AKS ROS CPS EMI S I 3.0 3800. 'I . 0 140. 0.22 0.80 2 2.0 960. 1.0 140. 0.22 0.80 3 4.0 960. 1.0 140. 0.22 0.80 1 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ 1 1 1 ~ 1 ~ 1 1 1 1 1 0 1 ~ 1 1 ~ 1 1 ~ ~ 1 1 1 ~ 1 ~ 1 1 ~ 1 0 0 0 1 1 ~ 1 1 1 1 ~ ~ 0 0 ~ 1111111111110 1 THICK SLAB DATA CARO (CARD 3 OF 3)
IDSLBI HTCI ( I ) HTC2(1) HTCI(2) HTC2(2)
I 3.7 2 3.7 3.7 1 ~ 1 ~ 1 ~ 11111 1 1 1 1 1 ~ 1 1 II 1 1 1 ~ 1 ~ ~ ~ 0 1 ~ ~ ~ 1 1 ~ 1 ~ 1 0 ~ ~ ~ ~ I ~ 0 ~ 1 0 0 0 ~ 0 0 1 1 ~ ~ 1 ~ 1111 ~ 110 ~ ~ 00 THIN SLAB DATA CARD (CARO I OF 2) lRM l IRM'7 ITVPF ARFaS'P
1
~ 1111 ~ 1 0 ~ 1 1 0 1 ~ ~ 0 0 0 1 ~ 1 0 0 1 ~ ~ ~ ~ 0 1 ~ 1 0 ~ 1 1 ~ 0 0 ~ 0 0 0 ~ 1 0 0 ~ 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 THIN SLAB DATA CARD (CARD 2 OF 2) 0 0 IDSLB2 UHT(1) UHT(2) 01000 0 ~ 0 ~ 0 1 1 0 0 1 0 ~ 0 ~ 0 0 ~ 0 ~ 1 ~ ~ ~ ~ 0 0 0 ~ 0 0 0 1 ~ 0 0 0 0 0 ~ 00 ~ 0 ~ 00 0 01000110 ~ 0111 1 ~ 0 0 ~ ~ 0 0 TIME-DEPENDENT ROOM DATA IOT OR IRMFLG NPTS TDRTO AMPLTO FREQ
-1 'I 4 80. 0 0.0 0.00 0 OUTSIDE AIR
~ ~ 0 0 ~ 11010111 ~ ~ ~ ~ ~ ~ I I~ ~ 0 ~ ~ ~ ~
I I I 1 I ~ 0 1 ~ ~ ~ 0 ~~ ~0 ~ ~ 1 0 ~ 0 ~ ~ 0 0 ~ ~ ~ 1 0 0 0 0 0 1 0 1 ~ 0 0 ~ 0 ~ 0 ~ ~ 1 ~ 1 I I TIME VERSUS TEMPERATURE DATA
~ I OT DR TT I ME TTEMP RHUM PR ES
-I 0 .00 80.0 0.50 14. 70 1 .00 80.0 0.50 14. 70 2 .00 80.0 0.50 14. 70 5 .00 80.0 0.50 14. 70 00 ~ 01 0010111 ~ 0 ~ 0 ~ 0 ~ ~ 0 ~ 0000 000~ ~ ~ 00000 ~ 0 ~ 0 ~ 000 0 ~ 00 00 ~ 100001 ~ 1 ~ ~ 01011 ~ 11 ~ ~
010 ~ ~ 000 ~ 0010 ~ 0 ~ 110 ~ 0 ~ ~ ~ ~ ~ ~ 000 ~ ~ ~ 00 ~~ 00 ~ ~ ~ 000 ~ 0 ~ 0 ~ 0 ~ 00 ~ ~ ~ 00 ~ ~ ~ 00 ~ ~ ~ 11 ~ ~ ~
figure 4.7 COTTAP TEMPERATURE PROFlLE FOR SAMPLE PROBLEM 3 100 CD I 95 I
CL O 90 O
O Ck' 85 CL LIJ CL I
80 0 0.5 1.5 2.5 TIME (hr)
TSO FOREGROUND HAROCOPY 1 ~ ~ 0 PRINTED 89285. 1301 OSNAME=FAMAC.CQTTAP.SAMPL4.DATA VOL=DSK540 COTTAP SAMPLE PROBLEM 4
~ ~ ~ ~ 1 ~ ~ ~ I ~ ~ 00 ~ ~ ~ 0000 ~ 00 ~ ~ ~ ~ ~ 0 ~ 001 ~ 1 ~ 0 ~ ~ ~ 000I ~ 00110I ~ 10 ~ 1101 ~ 11010 ~ 0 ~ 1 ~ ~ ~ 000 PROBLEM DESCRIPTION DATA ( CARO 1 QF 3 )
NROOM NSLAB'I NSLA82 NFLOW NHEAT NTOR NTRIP NPIPE NBRK NLEAK NCIRC NEC 1 3 0 0 0 1 0 0 'I I 0 6
~ 1 ~1 ~ ~~ ~ ~ ~ 0 0 ~ 1 ~ ~ 10 ~ ~ ~ ~ 0 ~ ~ '
~0~ ~ ~ ~ ~ ~ ~ 0~~ ~ 1 ~ ~ 0 1 0 0 0 0 ~ ~ 1 ~ ~~ 0 11 1 1 1 0 ~ 00 0 1 1 ~ 10 0 ~
PROBLEM DESCRIPTION DATA ( CARD 2 OF 3 )
0
~ NFTRIP MASSTR MF 0 1 13
'PI S.D4 CP2 150.
CRI 50.
INPUTF IFPRT I 'I RTOL I.D-5
~ 1 ~ ~ 0 ~ 000000 ~ 00 ~ ~ 00 ~ 0 ~ 00 ~ 0 ~ 00 ~ 0 ~ 0 ~ 000 ~ 00 ~ 0 ~ 00000000000 ~ ~ 0 F 00 ~ ~ 1000 ~ 10100 PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )
NSH TFC 0 I . 0-5 0010I ~ 000 ~ 0 ~ ~ 0000000001000000 ~ ~ 0 ~ ~ 00 ~ ~ 0 ~ 00 ~ ~ 00 ~ 000000 ~ 0101000 ~ 011 ~ 00000 ~ 0 0 PROBLEM TIME ANO TRIP TOLERANCE DATA T TEND TRPTOL TRPEND 0.0000 6.0 0.005 6.0 10 ~ 0 ~ ~ 00 ~ ~ ~ 1 0 ~ 000000010 ~ 001001 ~ 00001000 ~ ~ 00000 111000000000
~ 1 ~ ~ ~ 1 ~ ~ 00 ~
0 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE
( OMI T THIS CARD IF NFLOW = 0 )
1 OELFLO 1.0-5
~ ~ 10 ~ 0~ ~ 0011 ~ 110 ~ ~ 0 F 01 0 ~ 0 0 1 0 0 ~ ~ ~ 1 0 0 1 0 1 ~ ~ ~ ~ 0 0 0 0 0 1 1 0 0 ~ ~ ~ ~ ~ 0 ~ 0 1 ~ ~ 1 ~ 0 ~ 0 1 0 1 1 1 0 EDI T CONTROL DATA CARDS 0
0 OEC TLAST TPRNT I 0.5 0. 10 2 0.6 0.005 3 2.5 0. 10 4 2.6 0.005 5 6.0 0.20 6 25.0 ~ 0.50 00 ~ 0 0000000 0001 ~ 00 00 ~ 001000 ~ ~ 0001 ~ ~ 00100000000000 ~ 1000 ~ 000 ~ I ~ ~ 1 F 1 '00000 0 EDIT DIMENSION CARO 0 NREO NS1ED NS2ED 2 3 0 0000 ~ ~ ~ 0 ~ ~ ~ ~ ~ ~ 0 0 0 0 0 0 0 1 0 0 ~ 0 0 ~ 0 0 ~ 0 0 ~ 0 ~ 0 0 ~ 0 0 ~ 0 0 0 0 0 0 ~ ~ ~ 0 001 1~ 0~000~ 1 0~ 000010 0 ROOM EDIT DATA CARD(S)
I 010 ~ 0 0
-I0 ~ 0 ~ 0 0 0 0 1 0 0 0 1 ~ 0 1 1 1 1 0 ~ 0 ~ 0 ~ 0 0 0 ~0 0 0 0 0 ~ 0 0 1 0 0 1 ~ 00 ~ 00011000 ~ 0 ~ ~ 0 ~ ~ 0000 ~ ~
1 EDIT CARD(S) FOR THICK SLABS 0
I 2 3
~ 01 ~ 0 1 0 ~ ~ ~ 0 ~ 1 0 1 0 0 0 1 0 ~ 0 1 1 ~ 0 ~ ~ 1 1 0 0 0 0 0 0 0 0 ~ ~ ~ 0 0 ~ 0 0 0 1 ~ ~ 0 1 1 0 1 0 0 0 ~ 0 1 ~ 1 1 1 0 0~0100 EO I T CARDS FOR THIN SLABS 0
0 011 ~ ~ ~ ~ I ~ ~ 1 1 1 1 1 1 ~ ~ 1 1 1 1 ~I ~ 0 1 1 1 ~ 1 0 0 I
~ ~ ~ 1 ~ ~ ~ 1 ~ 0 1 ~ 0 1 1 1 ~ ~ ~ 0 I ~ 1 I
~ ~ ~ ~ 11 ~ 1 ~0 0 0 0 0 0 0 0 I ~ 0 1 REFERENCE PRESSURE FOR AIR FLOWS 0 (OMIT THIS CARD IF NFLOW=O)
TREF PREF 100. 14. 7
~ 111 ~ ~ ~ 0 1 Ol ~ ~ ~ ~ 1 ~ 0 1 I ~ I~ ~ 0 0 I
~ 0 ~ ~ 1 1 0 ~ I ~ ~ ~ 1 0 1 ~ ~ 0 0 ~ ~ 1 ~
I I ~ 1 ~ ~ ~ 1 ~ 10 ~ ~ 111 ~ ~ ~ ~ ~ 11 ~ ~ 1 ~ 1 ~
1 ROOM DATA CARDS (00
~ NOT INCLUDE TIME-DEPENDENT ROOMS 1
0 IDROOM PRES TR RELHUM I
11 ~
105~ 11 14.7'1 ~ 0 95.0 a ~ ~ 1 1.0 111 ~ ~ 11, ~ 11
t AIR FLOW DATA CARDS t ( OMIT THIS CARO IF NFLOW = 0 )
t t IDFLOW t
IFROM ITO'FLOW ttt t
ttttt~~ttttttttttttttttttt LEAKAGE PATH DATA ttttttttttttttttttttttttttttttttttttttttttt t ( OMIT THIS CARD IF NLEAK = 0 )
t t IDLEAK ARLEAK AKLEAK LRM1 LRM2 LDIRN 1.0 -1.0 I -1 2
~ t t t ~ t t t ~ ~ t t t ~ t t t t t t t t t t t ~ t t t t t t t ~ t ~ ~ ~ t t ~ t t t t t t t ~ t t t t t t t t t t ~ t 't ~ ~ t ~ t ~ t t t ~
t CIRCULATION PATH DATA t
IDCIRC KRM1 KRM2
- ELEV1 ELEV2 ARIN AROUT AKIN AKOUT t
tttttttttttttttttttttttttttt t AIR FLOW TRIP DATA
~ t ~ ~ ttt ~ ttt ~ tttt ~ t~t~ ttttttt ttttt ~ ~ ~ ~ t ~ ttttt IOFTRP KFTYP1 KFTYP2 FTSET IDFP ttttt~t~ ttt~tttttttttt~ttttt~tt~tttttt~~tt~~tttttt~t~ttt~ ~ ~~ ~ ~ t~ t~ tttttt t HEAT LOAD DATA CARDS IOHEAT NUMR ITYP QDOT TC WCOOL t t 't t ~ t t t t t t ~ t ~ t t t ~ t t t t ~ t t t t t ~ t t t t ~ t t t ~ t t ~ t t t t t t t t t t t t t t t t t t t t t t t t t t ~ ~ t ~ t t PIPING DATA CARDS t
IOPIPE IPREF POD PID AIOON PLEN PEM AINK PTEMP IPHASE
~ ~ ~ ~ ~ tt~ ~ ~ ~ ttt~~ ttt~tttt~~ttttt~tttt~~ttttt~ttttttttt~ttttttttttttt~ tt~ t t HEAT LOAD TRIP CARDS t
IDTRIP IHREF I TMD TSET TCON t
tttt~ ~ tt~ ttt~ ~~tttttttttttttttt~~tt~~ttt~ttttttttttttttt~ ~ ~ ttttt~ ~ttt~t~
t STEAM LINE BREAK DATA CARDS t
IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP 1000. 2 1800. 0.5 2.5 0.5 tttt ~ tt ~ ttt ~ ttttttttttttt ~ ttttttt ~ t ~ ~ tt ~ t ~ t ~ ~ t ~ ttttttttttttt 1 1
~ ttt ~ ~ ttt ~ t ~
THICK SLAB DATA CARD (CARO 1 OF 3)
I DSLB I I RM1 IRM2 ITYPE NGRID IHFLAG CHARL 1 1 -1 1 15 2 0.
2 1 0 2 'I 5 0 0.
3 -1 3 15 2 0.
t~ tt~ ~tt~ t~ tttttttt~tttttt~ttttttt~t~ ~ ttt~t~ tt~t~tttttttttttt~ t~ tttttttt 1
THICK SLAB DATA CARD (CARD 2 OF 3) t IDSL81 ALS AREAS1 AKS ROS CPS EMI S 1 2.75 1000. '1.00 140. 0.22 0.80 2 4.00 800. 1. 00 140. 0.22 0.80 3 2.75 800. 1 . 00 140. 0.22 0.80
~)
0
00 00000 0 0100000 0 tt ~ 1000 1000 ~ 01 ~ 10 ~ 00 0 ~ 010 ~ 10000 ~ 00 t10101000 tf 0 ~ 101 ~ 00 0 THICK SLAB DATA CARD (CARD 3 OF 3)
IDSLB I HTCI(i) HTC2(i) HTCI(2) HTC2(2)
I 0.6 3 0.9 0 .4 11110 010 ~ 00 ~ 00 0010 1 ~ 1 f 10 0100 ~ 0 00 0 110000 0 ~ 11 0 ~ ~ 0 0 ~ 1101 ~ 1 0 0 t0001000111 0 THIN SLAB DATA CARD (CARD I OF 2) 0 IDSLB2 JRMI JRM2 JTYPE AREAS2 1
00000000 0 1 ~ 00 00 000000000 0 00 00 ~ 0 000 0 0 0 0 00 ~ 0 ~ 0 ~ 0 0 0 10 000 ~ 100010 t00000011010 0 THIN SLAB DATA CARD (CARD 2 OF 2)
IOSL82 UHT(1) UHT(2) 01010000 1 0
tttftf TIME-DEPENDENT 0 0 0000 ~ 001010 1000 0 ~ 000 ROOM DATA 0~ 01000 ~ 010 1 ~ ~ 0110 11110000110011100 0
IDTDR IRMFLG NPTS TORTO AMPLTD FREQ
-I 00101000 I
0 0 00 00 0 0 ~ tf 3 000000000~0000000~000 0.0 f 0 0 0 0.0 0.00 0 OUTSIDE AIR 000000000~000000100000010000 1 TIME VERSUS TEMPERATURE DATA 0
0 IDTDR TTIME TTEMP RHUM PRES
-I 0.00 95.0 0.60 '14. 7 10.00 95.0 0.60 14.7 50.00 95.0 0.60 14. 7 tf tf 11010101 1010 0 11 0 00000 0 0 0 0 t 0 ~ 0 t t 0 0 0 0 0 0 t 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 00001 ~ 0 0000 ~ 10 0 1000000 100 0 0 0 0 0 0 0000 000 00 0 000 00 0 ~ 0 00 0 0 0 0 0 0 f 0 00 00 0 00 000 0 00010001f 0 000 0
FIGURE 4.8 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 4 180 CA 160 I
Z:
IJJ 140 O
O Z'- 120 I
100 LxJ CL I
o 7c QCl 80 CD 3
TIME (hrs) n O
ppdL Form 2<<5<<nar83) c<<r. <<073<<0r SE -B- N A-0 4 6 Rev. 01 Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATIONSHEET Sht. No. ~ of 4.5 COTTAP Results for Com artment Heat-u from a Hot Pi e Load (Sam le Problem 5)
This test problem consists of a standard COTTAP compartment that contains a large hot pipe and a room cooler. A COTTAP leakage path, which allows flow between connected rooms when a pressure differential exists, links the standard compartment to an infinitely large compartment. The large compartment maintains steady pressure in the connected compartment.
The hot pipe being modeled contains steam at a constant temperature of 0
550 F. It is a 20 inch diameter insulated pipe having a wall thickness of one half inch and an insulation thickness 'of 2 inches. The piping heat load is tripped off at 1 hour. At this time the heat load exponentially decays. The thermal time constant associated with the decay is calculated by the code.
The unit cooler is rated at 20,000 Btu/hr with a cooling water inlet temperature of 75 0 F.
The input file for this run is listed in Table 4.6 and results are shown in figure 4.9.
TSO FOREGROUND HARDCOPY 0000 PRINTED 89285. 1403 OSNAME=EAMAC.COTTAP.SAMPLS.DATA VOL=DSK536 COTTAP SAMPLE PROBLEM 5 14 ~ ~ 0 ~ 4000000 ~ 000000 ~ 011 ~ 00 ~ 11 ~ ~ 0 ~ 004000000100000 ~ 0104 ~ 400014 440100000 PROBLEM DESCRIPTION DATA ( CARO I OF 3 )
0=
NROOM NSLABI NSLAB2 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NC IRC NEC 2 0 0 0 2 0 I 0 I 0 I t 0 0 ~ 0 0 ~ 0 0 ~ 0 1 0 ~ 0 0 ~ 0 ~ 0. ~ 1 ~ ~ ~ 0 ~ 0 ~ ~ 0 0 0 0 00 0 0000000000 1
0 0 1 0 0 0 0 0 0 0 ~ 0 0 ~ 0 ~ 0 0 ~ ~ 0 0 ~ 0 0 PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )
NFTRIP 0
MASSTR 1
MF 23
'P 5.D4 I CP2 150.
CRI 10.
INPUTF I
IFPRT I I RTOL
.0-5 410000100000100000400001100 ~ 00000010400 ~ ~ 00000 ~ ~ ~ ~ 004t40400 ~ ~ 1 000044000t PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )
0 NSH TFC 0 1.0-5 0 1 140411 0 0 0 4 1 1 0 ~ 0 0 0 1 0 1 ~ ~0 4 0 1 ~ 0 ~ 1 0 04000 00 0 0 ~ ~ 4 ~ ~4 4~ 1 0 ~ ~4 ~4 ~ 1 1 1 4 4 1 4 4 0 1 40 ~ ~
0 PROBLEM TIME ANO TRIP TOLERANCE DATA T TEND TRPTOL TRPEND 0.0 001400t10111000000ttt 4.0 0.05 4.0
~ 00 ~ 0010010 ~ ~ Ottttt ~ 0 ~ 01 ~ 0 ~ 0 ~ 0 ~ 0000000 ~ ~ 0000100000 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE 1 ( OMIT THIS CARD IF NFLOW = 0 )
0
~ DELFLO I.D-S
~ 44 ~ 40000440 ~ 1 ~ Ot ~ 0 ~ 00 ~ 1 1 1 ~ t~ 11111~0040t0~~~0~4~~00~410111110~~01011040~
0 EDI T CONTROL DATA CARDS IDEC TLAST TPRNT 25.0'0 0. 10
~
I 411141014444 ~ 040 0 1 04 tt 1 '1 100~1 1 ~1 0 01 1 001 00 0 0 011 0 ~1 ~ 1 ~0 0 1 1 0 4 0 0 1 1 0 4 ~ 1 4 4 0 1 4 EDIT DIMENSION CARD 0
NRED NS IED NS2ED 2 0 0 0 1 1 4 1 110040 0 1 1 0 1 11 1 0 4 0 1 104 ~0 ~4 01 1 0 1 ~11 0 0 ~0 0 0 0 ~4 0 0 ~~ 1 1 1 ~ ~0 ~ 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 ROOM EDIT DATA CARD(S) 1 I 2 0 1 4 0 4 0 4 4 4 0 0 1 4 0 0 0 0 0 0 ~ 0 0 0 4 0 0 ~ 0 4 0 ~ ~ ~ 0 4 4 0 t04 t04 0000004 ~0 0~~4~4401101104 41000 EDIT CARD(S) FOR THICK SLABS 0~ 0410 ~ ~ ~ 000 ~ 0 ~ 0 1 ~ ~ 0 0 0 0 0 010 ~ 0 0 0 0 ~000 ~ 10 0 00 0 ~ 0 0 ~ ~ ~ ~ ~ 0 0 1 1 1 ~0 ~ ~1 0 0 1 0 ~ ~ ~ ~ 10 0 0 EDIT CARDS FOR THIN SLABS 1
0~ 0410 ~ 000 ~ 04 40 0 0 0 ~ ~ 0 ~4 04 ~ ~ 04 04 ~ 0 1 ~010 t101t11~101~11~400~0~4441$11111110 0 REFERENCE PRESSURE FOR AIR FLOWS 0 (OMIT THIS CARO IF NFLOW=O)
TREF PREF 100. 14. 7 1 1 1 1 1 1 0 4 1 1 1 1 1 1 4 1 ~ 1 1 1 ~ ~ ~ 1 ~ 4 t ~ ~ ~ 1 1 0 1 0 4 ~ 1 ~ 1 ~ ~ 4 1 1 1 4 ~ 1 ~ 4 ~ 1 1 ~ 1 1 4 1 1 1 1 1 ~ 1 ~ ~ 4004 1 4 ROOM DATA CARDS 0 NOT INCLUDE TIME-DEPENDENT ROOMS)
IDROOM VO L PRES TR RELHUM RM HT I 10000 14.7 100.0 0.5 10.0 2 I .D15 14.7 100.0 0.5 4 4 1 0 0 010.0 4 4 1 1 4 1 4 4 4 4 0 4 4 0 4 ~ 1 1 1 0 ~ 4 ~ 0 1 0 0 0 1 0 1 0 1 1 0 0 ~ 4 0 0 1 0 ~ 0 1 ~ 1 1 0 1 1 0 0 1 1 ~ 0 1 0 0 10 ~ 44 t A IR FLOW DATA CARDS 1 ( OMIT THIS CARD IF NFLOW = 0 )
4
~ 1 nc ~ nial $ cnnao vvn
0 IDSLB2 JRMI JRM2 JTYPE AREAS2 4
000 Ol ~ ~ 44 ~ ~ ~ 4044000 ~ 0 ~ ~ ~ 00 ~ 4004 ~ 00 ~ 0401 ~ 44 ~ ~ 004 ~ 400 ~ ~ ~ ~ 0 ~ OOOP 0 1 ~ J4 0 ~ I If 0 0 THIN SLAB DATA CARD (CARD 2 OF 2)
IDSLB2 UHT(1) UHT(2) 0
~ OO 0
OOOIOt4004 ~ 4000 ~ ~ OJ4410040004041 ~ OIOl ~ ~ I ~ ~ 4000 ~ ~ ~ 04 ~ 0000000 ~ 044 ~ 404 ~ 0 TIME-DEPENDENT ROOM DATA I DTDR IRMFLG NPTS TDRTO AMPLTD FREQ 044 ~ ~ ~ 0 0 4 ~ 0 4 ~ ~ 0 ~ 0 0 0 0 ~ 0 ~ 0 0 0 4 ~ ~ 0 ~ ~ 0 1 ~ 1 ~ 0 0 1 4 ~ ~ ~ 4 4 ~ 4 ~ ~ ~ ~ ~ ~ ~ 0 0 4 ~ 0 4 0 ~ 4 0 4 4 4 0 ~ 0 0 TIME VERSUS TEMPERATURE DATA 4
I DTDR TTIME TTEMP RHUM PRES 0
OOO 4000 ~ lO ~ 400000000000 ~ 000 ~ 0 ~ 0010000I ~ Oi0000100104000000004J ~ OOJJOOOOOJOO 004 ~ 1 ~ ~ 0 ~ ~ ~ 0 ~ 01440 ~ 0 ~ ~ 00400 ~ ~ ~ ~ 0 ~ 0 ~ 0 ~ 001004 ~ ~ ~ 00ii004 ~ 000 ~ ~ 00414 ~ ~ 0044 ~ 0
0 000000000 ~ ~ ~ ~ 0 0 ~ 000~0000~00~ 00~ 0~ ~ ~ 0 0 ~ 0 0 0 0 0 0 0 0 0 ~ 0 ~~ ~00 0 00 ~0 0 ~0 ~ 0 0 0 0 ~0 ~ 0 0 0 LEAKAGE PATH DATA 0 ( OMIT THIS CARD IF NLEAK = 0 )
IOLEAK ARLEAK AKLEAK I.RMl LRM2 LO!RN I 'I
.0 -1.0 I 2 'I
~ ~ ~ ~ ~ ~ 0 ~ 0 ~ 00 0 0 0 0000 0 00 00 ~ ~ ~ ~ 0 0 0 0 ~ 0 ~ ~~ 0 0 ~ 0 ~ 0 ~ 0 ~ ~ ~ 0 00 ~ 0 0 0 0 000 00 ~ 0 0 0000~00~
CIRCULATION PATH DATA 0
IDCIRC KRMI KRM2 ELEVI ELEV2 ARIN AROUT AKIN AKOUT 0000000000 0000' 0 0 ~ 00000000000000000 ~ 00 ~ 000 ~ 0 0 0 0 t 0000 ~ 0 ~ 0 ~ ~ ~ ~ 00 ~ 0 0 0 00 0 0 0 0 A IR FLOW TRIP DATA 0
IDFTR P KFTYPI KFTYP2 FTSET IDFP 0000000000 000000000000000000000000000000000 '00 F 000000000000t00000000ttt H EAT LOAD DATA CARDS 0
IOHEAT NUMR ITYP QDOT TC WCOOL I I 4 -20000. 75. 2000.
2 0000 00000 ~ 00 5 O.DO 00000 0 0 ~ ~ 00000000000000
-1. 0.
00000 0000 ~ ~ ~ ~ ~ ~ 00000 0 0000000 0 000 0 0 0 0 ~
0 PIPING DATA CARDS 0
I DPI PE IPREF POD PID AIODN PLEN PEM A INK PTEMP IPHA SE 00 I
~ 0 ~ ~ 000 ~ 000 2
' 20. I9.
000000000000000tttttt00000 24. 50.
F
.85 .05 0000000000t00000000000000 550. I 00 00
~
0 HEAT LOAD TRIP CARDS IDTRIP IHREF ITMD TSET TCON
~ ~ 0~ ~ 0 ~
I 000 2
0 0 0 ~ 0 ~ 0 0 ~ 0 ~ 0 0 0 0 I l. -1.
t0 0~ ~0 ~~ ~~~~ ~ 00~00 0 ~000 ~00000~ ~ ~ 00 00000 00 ~ 00 0 ~
STEAM LINE BREAK DATA CARDS I OBRK I BRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP 0000 ~ ~ 0000 ~ 0 0 0 0 0 0 0 t 0 ~ t 0 t 0 ~ 0 0 0 ~ ~ 0 0 ~ 0 0 0 0 0 0 0 ~ 0 0 ~ ~ 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 t 0 0 0 0 0 0 0 0 THICK SLAB DATA CARD (CARD I OF 3)
IOSLB I IRM'I IRM2 ITYPE NGRID IHFLAG CHARL 0
0000 '0 ' ' 0000000I ~ ~ ~ ~ ttt ~ ~ 0000 THICK SLAB DATA CARD
~ ~ ~ 0000000000I ~ ~ 0 ~ ~
(CARD 2 OF 00 ~ ~ 00 3)
~ 000 ~ 000 ~ tl~ 00 ~ 0000 IDSLBI ALS AREASI AKS ROS CPS EMIS
~ ~ ~ ~ 00 ~ 00 ~ 0000 ~ 00 ~ 0 ~ t ~ 00 ~ 000000000 ~ ~ 0 ~ 0 ~ ~ ~ ~ 00 00 ~ ~ ~ 0 ~ ~ 000 0 ~ 0 ~ ~ 00 ~ 00 ~ 0 ~ ~
0 THICK SLAB DATA CARD (CARO 3 OF 3) 0 IDSLB I HTCI ( I) HTC2(1) HTCI (2) HTC2(2) 0 OOOO ~ ~ 00 ~ ~ 00000 ~ 000 ~ ~ ~ 00 t ~ tt 0 0 ~ ~ ~ 0 ~ 0 0 0 t ~ 000 ~ 00 ~ ~ 00000000000000000t 0 00\00 0 THIN SLAB DATA CARD (CARD I OF 2)
FIGURE 4.9 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 5 120 115 U)
CL 110 I
LID CL I
105 100 2
TIME (hr)
PPdl. Form 2cSl n0/83j Cat, r973401
~E N A:-0 4 6 R(,,0 )
Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. JL7 of Approved by 4.6 Com arison of COTTAP Results with Anal tical Solution for Com artment De ressurization due to Leaka e (Sam le Problem 6)
A compartment is initially at a pressure of 14.7 psia and a temperature 0
of 150 F. The initial relative humidity is set to 0.001 so that the compartment contains essentially pure air. This compartment (compartment 1 in the COTTAP model) is connected to a time-dependent compartment by means of. a leakage path. The pressure in the time-dependent compartment
-5 is fixed at 10 psia. The leakage flow area is 0.01 ft 2 and the associated form-loss coefficient has a value of 4.0. Leakage is initiated at t=0. Table 4.7 shows the COTTAP data file for this case, and the COTTAP output is contained in Section F.6.
Figure 4.10 shows a comparison of the COTTAP results with the corresponding analytical solution ~
TSO FOREGROUND HARDCOPY +i+i PRINTED 89286. 1008 DSNAME=EAMAC.COTTAP.SAMPL6.DATA VOL=OSK532 COTTAP SAMPLE PROBLEM 6
~ ~ 4 ~ 400440 ~ ~ 0004 ~ 00004004 ~ 4 ~ 1 ~ ~ 0I4 ~ ~ ~ ~ 000 ~ ~ 0444400 ~ 00 ~ 40000 ~ 04 440 ~ ~ 0 ~ 404 PROBLEM DESCRIPTION DATA ( CARD I OF 3 )
NROOM NSLABI NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NCIRC NEC I 0 0 0 0 0 4400 ~ 0 ~ ~ 0 ~ 000 ~ 04 ~ ~ ~ 40004444 0~ 4 ~ ~ tO0 ~ 0 ~ ~ 4 ~I ~ 0 ~ ~ 0 0~ ~ ~ ~ ~ 34 ~ ~
I
~ ~ 0 ~ ~ 0 ~ ~ ~ ~ 0 ~ ~ ~ OO ~ 0 J ~
PROBLEM DESCRIPTION DATA ( CARO 2 OF 3 )
~ NFTRIP MASSTR MF CPI CP2 CRI INPUTF IFPRT RTOL 0 I 23 5.04 150. 10. I I I .D-5
~ 4 0 ~ 0 0 0 ~ 0 ~ ~ 0 0 1 0 ~ ~ 0 0 0 0 ~ 0 ~ ~ 40~000 ~ 0 1 0~ ~ ~ 0 4 0~0 0 0 ~ 0 0 4 0 0 4 ~4 0 4 4 04 ~ 0 0 4400444400 PROBLEM DESCRIPTION DATA ( CARO 3 OF 3 )
4 NSH TFC 0 I . 0-5
~ ~ 0 1 4 ~ 0 ~ ~ ~ ~ 4 4 t ~ i i 0 ~ 0 0 4 ~ ~ ~ ~ ~ ~ 4 0 0 0 ~ ~ 0 0 4 t ~ ~ ~ 0 ~ ~ ~ 0 0 ~ ~ ~ 4 4 1 0 ~ ~ 0 0 ~ l ~ ~ 44144 ~ 400 ~
PROBLEM TIME ANO TRIP TOLERANCE DATA 0
T TEND TRPTOL TRPEND 0.0 0.2 0.005 4.0
~ ~ 04 ~ ~ 040 ~ ~ ~ ~ ~ J0 ~ ~ 4 ~ ~ ~ ~ ~ 00 ~ ~ ~ ~ i4t0 ~ ~ 0000 ~ 040 ~ ~ 40 ~ Oi 0 ~ 0 ~ 4440 ~ 04 i ~ 40 ~ 44 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE
( OMIT THIS CARD IF NFLOW = 0 )
DELFLO
'I 0-5 I ~ 4 4 I ~. 4 4 0 ~ ~ ~ ~ 0 0 4 0 4 0 4 ~ ~ 0 4 4 4 0 0 4 4 4 4 ~ ~ 0 ~ 0 ~ ~ ~ 1 ~ 0 4 ~ 4 ~ 0 0 ~ '
0 4 ~ ~ ~ 4 0 ~ ~ ~ ~ ~ 0 ~ ~ 4 0 ~ 4 ~ ~
EDIT CONTROL DATA CARDS IDEC TLAST TPRNT I 0.5 0.01 2 0.6 0.01 3 5.0 0. 10 0 4 ~ 0 ~ ~ 4 4 ~ 4 0 ~ I4 4 0 4 0 0 ~~ ~ i ~ 0 ~ ~ 4 ~ 0 ~ ~ ~ ~ 0 ~ 0 l ~ ~ 4 0 0 0 4 4 444~4~4440 ~ ~ ~ 4 4 4 0 I0 4 ~ 0 4 4 0 4 0 EDIT DIMENSION CARD NREO NS I ED NS2ED 2 0 0
~ ~ 4 4 0 0 ~ 0 0 ~4 4 0 ~4 ~4 ~ 1 ~ 0 ~ ~ ~ 0 0 0 ~ ~ ~ ~ ~4 0 4 1 0 ~ 0 ~ ~~ 4 4 ~0 ~ ~ ~ 0 0 4 ~0 0 0 ~ 4 ~ ~0 ~0 4 4 4 4 1 ~
0 ROOM EDIT DATA CARD(S)
I -I
~ 0 ~ 0 4 ~ 1 0 4 4 ~ ~ 4 ~ ~ 0 0 ~ ~ ~ ~ ~ ~ ~ 0 ~ 4 0 ~ 4 0 4 4 0 4 4 ~ ~ ~ ~ 0 ~ 4 ~ 4 0 ~ 4 ~ 0 ~ 4 I4 4 4 4 ~ 4 4 4 ~ 4 ~ 4 4 4 ~ ~ ~ 4 ~
4 EDIT CARO(S) FOR THICK SLABS 4
4 044 ~ ~ ~ 4 0 4~ ~ ~ ~ 4 0 ~ 0 0 04 ~ 0 ~4 4 4 0 4 1 4 0 0 0 0 0 0 ~~ I4 ~ 4 ~ ~ ~ 4 0 4 ~ ~ 4 4 4 4 I 0 4 4 4 0 4 4 1 4 I0 ~ i 0 iiy EO I T CARDS FOR THIN SLABS 144 4 4 4 0 4 i4 0 4 4 IO 4 0 ~ ~ I ~ 4 ~ 0 4 0 4 ~ i1 1 4 ~ 0 ~ 4 ~ ~ 4 0 0 ~ II 0 ~ 0 4 0 ~ 4 l ~ ~ 04 ~ 10 ~ 4 ~ ~ 0 ~ 440 ~ 4 ~ ~ ~ 44 REFERENCE PRESSURE FOR AIR FLOW (OMIT THIS CARO IF NFLOW=O)
IReF PREF 0 100. 14. 7
~ 4 4 ~ 4 ~ ~ 1 ~ ~ 4 ~ 4 ~ 4 ~ Oi ~ ~ ~ ~ 4 ~ 0 ~ i04 ~ f4440 ~ 4 ~ ~ 4044 ~ 4l l4 ~ ~ 0 1 4 1 4 4 4 ~ ~ 0 ~ 4 4 4 ~ 4 0 1 0 4 4 t ROOM DATA CARDS (00 NOT INCLUDE TIME-DEPENDENT ROOMS)
DROOM VOL PRES TR RELHUM RM HT I 10000. 14.7 150.0 0.001 10.0 t ~ 40 ~ 40
('H
~ ~ ~ ~ ~ ~ ~ ~ 4 ~ ~ 4444I44t ~ 4000 ~ 4 ~ 0440 ~ 0 ~ ~
AIR FLOW DATA CARDS ARO NFLI 0 444 4 ~ 4441444 ~ ~ 444 4 4 ~44 4 4 4 0 P
IDFLOW IFROM ITO VFLOW 1
10101000 ~ 1 1 ~1 0 1 0 0 ~ 0 \1~10~0~1~01000011101111~1~01111101~11011111~10101000 0 LEAKAGE PATH DATA 0 ( OMIT THIS CARO IF NLEAK = 0 )
IDLEAK ARLEAK AKLEAK LRMI LRM2 LOIRN I 0. 01 4.0 I -I I 01000011 1 0 ~ 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 ~ 0 1 0 0 ~ 0 0 1 1 ~ 0 0 0 0 ~ 1 1 1 0 1 1 1 0 1 0 ~ 0 0 0 0 0 0 0 0 CIRCULATION PATH DATA 0
IDCIRC KRMI KRM2 ELEV1 ELEV2 ARIN AROUT AKIN AKOUT 0
11 ~ ~ 1000 0 0 1 0 0 0 0 0 0 ~ 0 1 ~ 0 1 ~ ~ ~ 0 0 ~ ~ 0 ~ 0 0 0 0 0 ~ 0 0 0 0 0 1 ~ 1 0 0 0 0 0 ~ ~ ~ ~ ~ ~ 0 1 1 0 ~ 0 0 ~ 0 ~ 0 0 1 ~ 0 1 AIR FLOW TRIP DATA
~ IDFTRP KFTYPI KFTYP2 FTSET I OFP 0
00000000 000100000100011001 ~ 0 ~ 0000 ~ 000000001011000 ~ ~ 1 ~ 1000100100 ~ 00010 ~ ~ 0 HEAT LOAD DATA CARDS 1
IDHEAT NUMR ITYP QOOT TC WCOOL 1
~ 1111101 ~ 1 1 1 ~ 0 001 1 ~ ~1111100 ~00000000000000001 ~~10101 ~ 0 ~ 0 00 10 111 111 ~ ~ 0 1 ~ 0 PIPING DATA CARDS IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE 10100001 1 ~ 0 ~ 1 1 0 ~ 0 1 0 0 ~ 1 ~ ~ ~ 0 1 0 0 0 ~ 0 ~ 0 ~ ~ ~ 0 ~ ~ 0 0 0 0 0 ~ ~ 1 ~ 0 ~ 0 ~ 0 0 ~ ~ 0 ~ ~ 0 ~ 0 0 0 0 0 0 1 1 1 0 HEAT LOAD TRIP CARDS
~ IDTRIP IHREF I TMO TSET TCON 01101010 1 1 ~ ~ 1 ~ ~ ~ 0 0 ~ 0 0 1 1 ~ 0 0 ~ 1 0 ~ 0 ~ ~ 0 0 ~ ~ 0 1 0 0 1 ~ ~ ~ ~ ~ 0 0 ~ ~ ~ 0 ~ 0 0 1 ~ ~ 0 ~ 0 ~ ~ 0 1 0 0 0 0 ~ 1 STEAM LINE BREAK DATA CARDS IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP
~ 1010011 0 ~ 1 1 0 0 0 ~ 0 ~ 0 ~ ~ 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 ~ 0 0 0 0 0 0 0 0 ~ 0 0 0 0 ~ 0 0 0 0 0 0 1 0 0 1 THICK SLAB DATA CARO (CARD I OF 3)
IDSLB I IRMI IRM2 ITYPE NGRID IHFLAG CHARL
~ 1 1 1 1 1 ~ 1 1 1 ~ 1 ~ 1 ~ ~ 1 0 0 ~ 0 ~~ 0 ~ ~ ~ ~ ~ 0 1 1 0 0 0 0 ~ ~0 0 ~ ~1 1 1 1 ~ ~ ~ ~ ~ ~ ~ ~ ~ 00 ~ 1 ~ 11 ~ ~ ~ 00 ~ 0 ~ 11 1 THICK SLAB DATA CARD (CARD 2 OF 3) 0 IDSLB I ALS AREASI AKS ROS CPS EMI S CA
~ 1 ~ 1 0 1 0 1 1 1 1 ~ 1 0 0 ~ ~ 0 ~ 1 0 0 0 0 ~ ~ ~ 0 ~ 0 0 ~ 0 ~ ~ 0 ~ ~ 1 0 ~ 0 ~ ~ 1 0 1 0 1 ~ 1 1 ~ 0 0 ~ ~ 0 1 ~ ~ ~ 1 0 ~ 1 0111 I THICK SLAB DATA CARD (CARD 3 OF 3) CD 1
IDSLBI HTCI ( I) HTC2( I) HTCI (2) HTC2(2) 10010111 1 1 1 1 ~ 0 0 ~ ~ 0 ~ ~ ~ ~ 1 1 0 1 ~ ~ ~ ~ 0 ~ ~ 1 ~ 1 1 1 0 0 0 ~ 0 0 0 1 1 ~ ~ 0 ~ 0 0 ~ 1 ~ 1 ~ 1 1 1 I~ ~ I1 ~ 1 1 1 1 ~
THIN SLAB DATA CARD (CARD I OF 2) "I CQ O
CD
(
O
4 IDSL8 2 JRMI JRM2 JTYPE AREAS2 01014000 0 0 0 4 0 0 0 4 ~ ~ 0 0 0 0 0 4 4 1 0 4 0 ~ ~ ~ 0 0 ~ 0 0 0 0 0 ~ ~ 0 0 4 ~ ~ ~ 0 ~ ~ ~ ~ 10 ~ 4440 ~ 0 ~ 004404 ~ ~ ~
THIN SLA8 DATA CARD (CARO 2 OF 2) 0 IOS L82 UH1 ( I ) UHT(2) 0 01000000 00 ~ 000 ~ 0 ~ 01000 ~ ~ ~ 0I~ ~ ~ 4 ~ 00 ~ 0000 ~ ~ ~ I ~ 1 ~ 4 ~ ~ 4001 ~ ~ 0 ~ 04 ~ ~ ~ ~ ~ 4114 ~ 10440 0 TIME-DEPENDENT ROOM DATA 0
I DTDR RMFLG NPTS TDRTO AMPLT0 FREQ
-I I 00004004 0040400 4000010040000000 3
~~
0.0 00 ~ ~ 04044 ~ 040 0.0
~ ~ 000 0.0
~ ~ ~ 0 ~ 0440 ~ 00 ~ ~ 400 ~ 004 0 TIME VERSUS TEMPERATURE DATA 0
IDTDR TTIME TTEMP RHUM PRES
-I 0.0 150. 0.01 I . D-5 10.0 150. 0. 01 1. D-5 20.0 1 150. 0.01 1. 0-5 1 1 1 1 1 1 4 0 4 0 ~ 0 4 1 0 4 0 4 0 0 0 4 0 0 0 0 4 1 0 0 0 0 4 0 ~ ~ 0 0 0 0 0 4 0 1 0 0 000404411 ~ ~ 00 ~ ~ ~ 1 ~ ~ ~ ~ 1 ~ ~ 0 40 00~0 00 00 4 0 0 0 0 0000 ~ 000000040 ~ 04000000400010040 ~ ~ 0 0 04 04 1 ~ ~ ~ 04 4 ~ ~ ~ 4 0 4 04 ~ 0
FIGURE 4.10 COMPARISON OF COTTAP CALCULATED COMPARTMENT AIR MASS WITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 6 700 650 CO Legend ANALYTICAL I 600 0 COTTAP I 550 CL C) 500 z
V)
V) 450 0
400 350 0.00 0.05 0.10 0.15 0.20 TIME (HR)
PPd L Form 2ddd (15831 Cdl. 9973401 SE -B- N A.-O 4 6 R~v.0 ],
Dept. PENNSYLVANIAPOWER II1 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of
- 5. REFERENCES
- 1. Gear, C.W., Numerical Initial Values Problem in Ordinar Differential
~Zations, Prentice-Hall, Englewood Cliffs, Hs, 1971, Ch. 11.
- 2. Pirkle, J.C. Jr., Schiesser, W.E., "DSS/2: A Transportable FORTRAN 77 Code for Systems of Ordinary and One, Two and Three-Dimensional Partial Differential Equations," 1987 Summer Computer Simulation Conference, Montreal, July, 1987.
- 3. Schiesser, W.E., "An Introduction to the Numerical Method of Lines Integration of Partial Differential Equations," Lehigh University, Bethlehem, PA, 1977.
- 4. Lambert, J.D., Com utational Methods in Ordina Differential
~E ations, 1973., Chapter B.
- 5. Hindmarsh, A.C., "GEAR: Ordinary Differential Equation System Solver," Lawrence Livermore Laboratory report UCID-30001, Rev.l, August, 1972.
PPAL Form 245l (10I83)
Car, l9D40'r SF. -B-. >> a.-04 b Rev.aq Dept. PENNSYLVANIAPOWER & LIGHT COMPAN f ER No.
Date 19 CALCULATIONSHEET Designed by Approved by PROJECT Sht. No. ~of
- 6. Hindmarsh, A.C., "Construction of Mathematical Software Part III: The Control of Error in the Gear Package for Ordinary Differential Equations," Lawrence Livermore Laboratory report UCID-30050, Part 3, August 1972.
- 7. Hougen, O.A., Watson, K.M., and Ragatz, R.A., Chemical Process
- 8. Incropera, F.P., and DeWitt, D.P., Fundamentals of Heat Transfer, Wiley, New York, 1981.
- 9. "RETRAN-02 A Program for Transient Thermal-Hydraulic Analysis of Complex Fluid Flow Systems, Volume 1: Theory and Numerics,"
Revision 2, NP-1850-CCM, Electric Power Research Institute, Palo Alto Calf., 1984.
- 10. Kern, D.Q., Process Heat Transfer, McGraw-Hill, New York, 1950.
- 11. ASHRAE Handbook 1985 Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA.
e ppCL Form itese n0r83)
Cat, e973l01 SE -B- N A.=O 4 6 Rev.0 1 Dept. . PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date Designed by Approved by 19 PROJECT CALCULATION SHEET Sht. No. ~ of
- 12. CRC Handbook of Chemistr and Ph sics, 56th Edition, R.C. Weast,
,editor, CRC Press, Cleveland, Ohio, 1975.
- 13. Chemical En ineer's Handbook, 5th Edition, R. H. Perry and C. H.
Chilton, editors, McGraw-Hill, New York, 1973.
- 14. ASME Steam Tables, 5th Edition, The American Society of Mechanical Engineers, United Engineering Center, New York, N.Y., 1983.
- 15. McCabe, W. L., Smith, J. C., Unit 0 erations of Chemical Engineering, 3rd Edition, McGraw>>Hill, New York, 1976.
- 16. Lin, C. C., Economos, C., Lehner, J. R., Maise, L. G., and Ng, K. K.,
CONTEMPT4/MOD4 A Multicompartment Containment System Analysis Program, NUREG/CR-3716, U.S. Nuclear Regulatory Commission, Washington, D.C., 1984.
- 17. Fujii, T., and Zmura, H., "Natural convection Heat Transfer from a Plate with Arbitrary Inclination," Znt. J. Heat Mass Transfer, 15, 755 (1972) .
PP&'L foram 2454 n$ 83)
Cat. s91340t Dept. PENNSYLVANIAPOWER 5 LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. /25 of Approved by
- 18. Goldstein, R. J., Sparrow, E. M., and Jones, D. C., "Natural Convection Mass Transfer Adjacent to Horizontal Plates," Int. J. Heat Mass Transfer, 16, 1025 (1973).
- 19. Hottel, H. C. and Sarofim, A. F., Radiative Transfer, McGraw-, Hill, New York (1967).
- 20. Uchida, H., Oyama, A., and Togo, Y., "Evaluation of Post-Incident Cooling Systems of Light-Water Power Reactors," Proceedings of the Third International Conference on the Peaceful Uses of Atomic Energy, Geneva, Switzerland, Vol. 13, p. 93 (1964).
- 21. Cess, R. D., and Lian, M. S., "A Simple Parameterization for the Water Vapor Emissivity", Transactions, ASME Journal of Heat Transfer, 98, 676, 1976.
- 22. Hottel, H. C., and Egbert, R. B., "Radiant Heat Transmission from Water Vapor," Trans. Am. Inst. Chem. Eng. 38, 531, 1942.
ppdL Form 2I54 n0td3)
Cd). t973C01
$ P -g N A.-04 6 Rev 02.
Dept. PENNSYLVANIAPOWER 8 LIGHT CQINPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. lg6 of Approved by APPENDIX A THERMODYNAMIC AND TRANSPORT PROPERTIES OF AIR AND WATER The methods used within COTTAP to calculate the required thermodynamic and transport properties of air and water are discussed in this section.
A.l Pressure of Air/Water-Va or Mixture The partial pressure'f air within each compartment is calculated from the ideal gas equation of state, P = p 10. 731 (T + 459. 67) /M (A-1) a a r P
a
= partial pressure of air (psia), a'here p
a
= density of air (ibm/ft3 ),
compartment temperature 0 T ( F),
and M
a
= molecular weight of air = 28.8 ibm/lb mole.
The partial pressure of water vapor, P v, is also calculated from the ideal gas equation of state. The total pressure with in the compartment, P , is then obtained from r'=P+P (A-2) r a v
0 )
pp&L Form 2lS4 (10rN)
Clt. t973401
$ f -B- N A.-04 6 Rev 01 Dept. pENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by Approved by PROJECT Sht. No. ~of A.'2 S ecific Heat of Air/Water-Va or Mixture The constant-volume specific heat of air Cva is given by C
va
=C -R/Ma (A-3) pa C
pa
= constant-pressure specific heat of air (Btu/ibm 0 R),
and R = gas constant (1.9872 Btu/lb 0 mole R).
The constant-pressure specific heat of air is calculated from (Table D of ref. 7)
C = 0.2331 + 1.6309x10 T + 3.9826x10 T pa r r 1.6306x10 T (A-4) r 0
where T r is compartment temperature in K.
Similarly, the specific heat of water vapor is obtained from (Table D of ref. 7)
C = 0.4278 + 2.552x10 T pv Z
-7
+ 1.402x10 T 2
Z
- 4.77lx10 -11 T r
3 (A-5)
pphL Form 245'043)
Cat. 4973401
$ F. -B N A.-04 6 Rev.pg Dept. PENNSYLVANIAPOWER 8c LIGHT COMPANY ER No.
CALCULATIONSHEET Date 19 Designed by PROJECT Sht. No. ~of Approved by where the units of Cpv are Btu/ibm 0 F, and T r is compartment temperature 0
in K.
The mixture specific heat is taken as the molar-average value for the air and water vapor; (A-6) where g and a
III v are the mole fractions of air and water vapor respectively, and Ma and Mv are the molecular weights of air and water vapor respectively.
A.3 Saturation Pressure of Water The saturation pressure of water, as a function of temperature, is calculated from the saturation-line function given in Section 5 of Appendix 1 of ref. 14.
o pp&L Form 2454 nN83)
Cat. rQU401 SE -g- g A=04 6 Rev.og Dept. 'PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of A.4 Saturation Enthal y of Li uid Water and Va or The saturation enthalpy of liquid water and vapor, as a function of pressure, is calculated from the property routines used in the RETRAN-02 thermal-hydraulics code (Section 1II.1.2.1 of ref. 9). These routines are simplified approximations to the functions given in the ASME 1967 steam tables.
A.S Saturation Tem erature of Water The saturation temperature of water, as a function of saturation pressure and saturation enthalpy, is calculated from the RETRAN-02 property routine (Section ZZI.1.2.2 of ref. 9).
A.6 S ecific Volume of Saturated Water and Va or The specific volume of saturated liquid and vapor is calculated from the RETRAN-02 property routines (Section IZI.1.2.3 of ref. 9). The routines give saturated specific volume as a function of saturation pressure and enthalpy.
PPAL Form 245'10rLO Cot. N973l01 Dept. PENNSYLVANIAPOWER 8r LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by PROJECT Sht. No. LB 0 of Approved by A.7 Coefficient of Thermal Ex ansion for Air/Water-Va or Mixture The coefficient of thermal expansion, 8, for the air/water-vapor mixture is defined as 9=1 Bv (A-7) v BT r r P
where v = specific volume of air/water-vapor mixture, P = compartment pressure',
r and
= compartment temperature 0 T
Z ( R).
Evaluation of eq. (A-7) with the assumption of ideal gas behavior for the air/water-vapor mixture gives 9=1 (A-8)
T Z
A.S Viscosit of Air/Water-Va r Mixture The viscosity of the air/water-vapor mixture is calculated from (ref. 13 p.3-249) u = (V iri +u P ]/[HM1/2 +9M1/2 ] (A-9)
PP&L Form 245'$ 83)
Cal. t973i0r Sf, -Q-. IS A =04 6 ReV.P g Dept. PENNSYLVANIAPOWER 8c LIGHT COMPANY ER No.
Date 19 CALCULATIONSHEET Designed by PROJECT Sht. No. ~3 of Approved by where a' m viscosity of air and water vapor respectively
( ibm/hr- ft),
III,ftI a' = mole fraction of air and water vapor respectively, M
a
= molecular weight of air (28.8 ibm/lb mole),
and M
v
= molecular weight of water vapor (18 ibm/lb mole).
a and p v are determined by fitting straight lines to the data given in Tables A.l and A.2. The equations which give u and p as functions of a v temperature are p
a
= 0.0413 + (7.958x10 )(Tr-32), (A-10) and p
v
= 0.0217 + (4.479xl0 )(Tr-32), (A-11) where p and p have a v units of ibm/ft hr and T r is compartment temperature in 0 F.
ia PPKL Form 2454 <1182)
C41. 4023401,,
$ E . N A=04 6 Rev.PZ Dept. PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET Designed by Approved by PROJECT Sht. No. ~of Table A.l Viscosity of Air Viscosity of Air* Temperature (ibm/ft hr) ( F) 0.0413 32 0.0519 165.2
- Data from ref. 12, p. F-56 Table A.2 Viscosity of Water Vapor Viscosity of Water Vapor* Temperature (ibm/ft hr) ( F) 0.0217 32 0.0290 195
- Data from ref. 14 p. 294.
PP&L Form 24&4 (l(VN)
Ctt. t973401 B g <.-04 6 Rev.0g Dept. PENNSYLVANIAPONER & LIGHT COMPANY ER No.
Date CALCULATIONSHEET 19 Designed by PROJECT Sht. No. 333 of Approved by A.9 Thermal Conductivit of Air/Water-Va or Mixture The thermal conductivity, k, of the air/water-vapor mixture as a function of temperature and composition is calculated from (ref. 13, p. 3-244)
(A-12) where ka',k = thermal conductivity of air and water vapor respectively, g a',Izi = mole fraction of air and water vapor respectively, M
a
= molecular weight of air (28.8 ibm/lbmole),
and M
v
= molecular weight of water vapor (18 ibm/lbmole) .
The component conductivities are determined from linear curve fits of the data given in Tables A.3 and A.4. The curve-fit equations for the component thermal conductivities are ka = 0.0140 + (2.444x10 ) (T-32) g (z -13) and k-a = 0.010 + (2.00x10 )(T-32), (A-14) where k a
and k v have units of Btu/hr ft 0F and T is in 0 F.
A PPE 1 Form 2454 n0/N)
Cat. N973401
$ F. -8 N A=04 6 Rev.01 Dept. PENNSYLVANIAPOWER Sc LIGHT COMPANY ER No.
Date 19 CALCULATION SHEET DesIgned by PROJECT Sht. No. ~l~ of Approved by Table A.3 Thermal Conductivity of Air Thermal Conductivity of Air Temperature (Btu/hr ft F) ( F) 0.0140 32 0.0184 212
pp&L Form 24s4 n0/s3)
Cat. t973401
$ Q N A =04 6 ReV.Qg Dept. PENNSYLVANIAPOWER 8 LIGHT COMPANY ER No.
CALCULATIONSHEET Date 19 Designed by PROJECT Sht. No. /~~of Approved by Table A.4 Thermal Conductivity of Water Vapor*
Thermal Conductivity of Water Vapor Temperature (Btu/hr ft F) ( F) 0.010 32 0.0136 212
- Values from Appendix 12 of ref. 15 and p. 296 of ref. 14.
ATTACHMENT 8 "C,i C~
,gi a
~ 4' a h ae 1