ML17157B097
| ML17157B097 | |
| Person / Time | |
|---|---|
| Site: | Susquehanna  |
| Issue date: | 11/05/1990 |
| From: | Chaiko M, Murphy M PENNSYLVANIA POWER & LIGHT CO. |
| To: | |
| Shared Package | |
| ML17157B098 | List: |
| References | |
| NUDOCS 9203230299 | |
| Download: ML17157B097 (143) | |
Text
COTTAP-2, REV.
1 THEORY AND INPUT DESCRIPTION MANUAL Prepared by:
H. A. Chaiko aIld H. J.
murphy NOVEMBER 5, 1990 9203230299 920313 PDR ADOCK 05000387 P
l
pp<<t. Form 2<<54 no/831 Cat. <<973401 8-N A-0)6 Rev.01:
Dept.
Date ~//
> 19 +~
Designed by Approved by PROJECT r
Sht. No.
4 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET CONTENTS 1.
INTRODUCTION 2.
METHODOLOGY 2.1 Model Description 2.1.1 Mass and Energy Balance Equations 2.1.1.1 2.1.1.2 Balance Equations without Mass Transfer Between Compartments Balance Equations with Mass Transfer Between Compartments 2.1.2 Slab Heat Transfer Equations 12 2.1.2.1 Conduction Equation and Boundary Conditions 2.1.2. 2 Film Coefficients 2.1.2.3 Initial Temperature Profiles 13 17 23 2.1.3 Specihl Purpose Models 24 2.1.3.1 2.1.3.2 2.1.3.3 2.1.3.4 2.1.3.5 2.1.3.6 2.1.3.7 2.1.3.8 2.1.3.9 2.1.3.10 Pipe Break Model Compartment Leakage Model Condensation Model Rainout Model Room Cooler Model Hot Piping Model Component Cool-Down Model Natural Circulation Model Time-Dependent Compartment Model Thin Slab Model 24 25 28 33 34 35 39 41 43 43 I
2.2 Numerical Solution Methods 3.
DESCRIPTION OF CODE INPUTS 53 3.1 Problem Description Data (Card 1 of 3) 3.2 Problem Description Data (Card 2 of 3) 3.3 Problem Description Data (Card 3 of 3) 3.4 Problem Run-Time and Trip-Tolerance Data 54 55 59 60
pp&L Form 2454 nor831 Cat. rr9ncOr SE -B-N A-04 6 Rev.o 1 Dept.
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CALCULATIONSHEET 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 Error Tolerance for Compartment Ventilation-Flow Mass Balance Edit Control Data Edit, Dimension Data Selection of Room Edits Selection of Thick-Slab Edits Selection of Thin-Slab Edits Reference Temperature and Pressure for Ventilation Flows Standard Room Data Ventilation Flow Data Leakage Flow Data Circulation Flow Data Air<<Flow Trip Data Heat. Load Data Hot Piping Data Heat-Load Trip Data Pipe Break Data Thick Slab Data (Card 1 of 3)
Thick Slab Data (Card 2 of 3)
Thick Slab Data (Card 3 of 3)
Thin Slab Data (Card 1 of 2)
Thin Slab Data (Card 2 of 2)
Time-Dependent Room Data (Card 1 of 2)
Time-Dependent Room Data (Card 2 of 2) 61 61 62 63 63 64 64 65 66 67 68 69 70 71 73 74 75 78 79 80 81 82 84 4.
SAMPLE PROBLEMS 85 4.1 4.2 4.3 4.4 4.5 4.6 Comparison of COTTAP Results with Analytical Solution for Conduction through a Thick Slab (Sample Problem 1)
Comparison of COTTAP Results with Analytical Solution for Compartment Heat-Up due to Tripped Heat Loads (Sample Problem 2)
COTTAP Results for Compartment Cooling by Natural Circulation (Sample Problem 3)
COTTAP Results for Compartment Heat-Up Resulting from a High-Energy Pipe Break (Sample Problem 4)
COTTAP Results for Compartment Heat-Up from a Hot-Pipe Heat Load (Sample Problem 5)
Comparison of COTTAP Results with Analytical Solution for Compartment Depressurization due to Leakage (Sample Problem 6) 85 96 98 103 112 117
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F -B-g $.-.0 4. 6 Rev.Q 1";
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CALCULATIONSHEET 5.
REFERENCES APPENDIX A THERMODYNAMIC AND TRANSPORT PROPERTIES OF AIR AND WATER 122 126
1 I
1
pp4L Form 2454 ttttr83}
cat. rr97340 1
$F -B-N A.-04 6 Rev.OO Dept.
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CALCULATIONSHEET 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.
PPl C Form 2454 (10/83)
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CALCULATIONSHEET The scale of this problem is rather large in that a model of the Unit 1 and Unit 2 secondary containments consists of approximately 120 compartments and 800 slabs.
Tn 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.
It 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.
Xn 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.
Zt 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.
PP&t. F0~m 2454 (1083)
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of
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CALCULATIONSHEET 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 mass-tracking parameter MASSTR (see problem description'data cards in section 3.2).
2.1.1.1 Balance Equations without Mass Transfer between Com artments If MASSTR=O, 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
PPAL Form 2454 n$ 831 Co 1. N913401 SE -B-N A-046 Rev.O>
Dept.
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of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET rates are held constant at their initial values'hus, 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.
In 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 3.32 ) is only used to calculate the film heat transfer coefficients for thick slabsr 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 PC VdTQ.+0
+0+Q a
va r light Qpanel Qmotor cooler Qwall Qmisc piping dt N
+ P W
(T
. +a)
C (T.)
j=l vj vj o
pa vj where T
compartment (room) temperature
( F),
0 r
t time (hr),
p
~ density of air within compartment (ibm/ft ),
3 a
C
~ constant-volume specific heat of air (Btu/ibm F),
0 va V ~ compartment volume (ft ),
3 Q1 h
compartment 1ighting heat 1cad (Btu/hr) light Q
~ compartment electrical panel heat load (Btu/hr),
panel
= compartment motor heat load (Btu/hr),
otor (2-1)
OI'l
PP&L Form 2<<5<<nOI831 Cat. <<913<<01 SE -B-N A -0 4 6 Rev.Q
>'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET cooler piping wall compartment cooler load (Btu/hr),
heat load due to hot piping (Btu/hr),
rate of heat transfer from walls to compartment air (Btu/hr),
Msc Nv miscellaneous compartment heat loads (Btu/hr),
number of ventilation flow paths connected to the compartment, WVj TVj C
(T.)
pa vj ventilation flow rate for path j (ibm/hr),
air temperature for ventilation path j
( F),
0 specific heat of air evaluated at T
. (Btu/ibm F),
0 Vj 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
PPAL Form 2454 nar83)
C<<t, <<973401 SE N A -0 4 6 Re.'.0 p Dept.
Date 19 Designed by Approved by PROJECT Sht. No.
4 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 tempe'rature 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.
Xf this should occur a
positive piping heat, load would be computed in the usual manner.
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
h.A.(T
. - T ),
w wall j j surfj r
'~1 (2-2) where N
= the number of'walls (slabs) surrounding the room, w
h.
= film heat transfer coefficient (Btu/hr ft F),
2 0 j
'I
PP4L Form 2<<5<<(10/83)
Cat, <<97340 t SE -B-N A-046 Rev.Qy:
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of pENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET and A. = surface area of wall (ft ),
2 j
T
- f. = wall surface temperature
( F).
0 surfj 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 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 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.
pphr. Form 2454 no/83)
C~r. rreracO1 SE -B-N A -0 4 6 Rev.0 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of
.PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Temperature changes within compartments generally occur at essentially constant pressure because leakage paths such as doorways and ventilation ducts allow mass transfer from one compartment to another.
The leakage path model in COTTAP allows sufficient mass transfer between two compartments so that pressure equalization is maintained during a transient.
The leakage path model is discussed in section 2.1.3.2.
The circulation path model allows for mixing between two adjacent compartments which are connected by flow paths at different elevations.
The driving force for. the circulation flow is the difference in air density between the two compartments.
Further discussion of this model is given in section 2.1.3.8.
The pipe break model in COTTAP accounts for leakage from a steam pipe or a pipe containing saturated liquid water.
The total mass flow out of the break must be specified as input.
Xn the case of a pipe containing liquid, the amount of liquid that flashes to steam is calculated by the code.
As a conservative approximation, any liquid that does not flash to steam is cooled to compartment temperature and the heat given off by the liquid is deposited directly into the air/water-vapor mixture.
COTTAP allows for condensation of steam on compartment walls and for vapor rainout.
Details of this model are given in sections 2.1.3.1, 2.1.3.3, and 2.1.3.4.
ppQ. Form 2454 n0r83)
Cat. <<913401 SE -B-N g -0 4 6 Rev.0 gI Dept.
Date 19 Designed by Approved by PROJECT PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Sht. No. ~of The air and vapor mass balance equations that are solved by COTTAP for the case of MASSTR=1 are N
VQP
=E W
Y dt 3=1 Nl
+
E W
Y 3
3 N
+
E
[W..
Y..
-W Y
],
j=l cj,in cj,in cj,out cj,out (2-3)
N VdP
=
E W
. (1Y.)
dt 1
vj vj N
+
E W
(1 Y.)
lj lj N
+
E
[W..
(1-Y..
) -W (1-Y
)J 3=1 cj,in cj,in cj,out cj,out
+W
-W
-W bs cond ro'2-4) where p
= compartment air density (ibm/ft ),
3 a
3 p
~ compartment water vapor density (ibm/ft ),
v N
~ number of ventillation flow paths connected to the v
compartment,
ppCL Form 2454 (10/83)
Car. rr9rmi SE N A -0 4 6 Rev.Q g>
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~Oof PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET N
~ number of leakage paths connected to the 1
compartment, N
= number of circulation paths connected to c
the compartment, W
~ total mass flow through leakage path j (ibm/hr),
lj W
. i total inlet mass flow through circulation cj,in Wcg,out path j (ibm/hr),
m total outlet mass flow through circulation path j (ibm/hr),
Y
. ~ air mass fraction for ventilation path j, vj Y
. ~ air mass fraction for leakage path j, lj Y..
~ air mass fraction of inlet flow for cj,in circulation path j, Y
~ air mass fraction of outlet flow for cj,out circulation path j, W
steam flow rate from pipe break (ibm/hr),
bs W
~ water vapor condensation rate (ibm/hr),
cond W
~ water vapor rainout rate (ibm/hr).
ro The compartment energy balance for MASSTR~l is V[(T +a )p dC (T
)
+ p C
(T ) + p dh (T
)
r o atda r
a pa r
v~
r r
r
PPKL Form 2454 (I$83)
Cat, <<973401 SE -B-N A -0 4 6 Rev.0 g
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET
- p R
p R
] dT
= -V(T
+ a )C (T )dp vv a
a r r
o pa r
a dt dt
- V h (T )dp
+
(T +a
) (R dp
+ R dp )V v r~
r o
v~d a
a dt
+Q
+Q
+O
+Q
+ Q light panel motor cooler piping
+0
+0.
+Q
+W h
Qwall Qmisc break bs v,break
- W h
(T
) -
W h
(T )
ro f r cond f r N
+ g W.[Y.(T.+a )C (T.)
+ (1-Y.)h (T.)]
j=l vj vj rj o
pa vj Vj V
Vj N
+QW1[Y1(T1+a)C(T1)+(1Y1)h(T1)]
j=l lj lj 1j o
pa 1j lj v lj N
+g W.. [Y.. (T..+a)C (T..)
j=l cj,in cj,in cj,in o
pa cj,in
+ (1-Y.. )h (T
)]
cj,in v cj,in N
W
[Y (T+a)C (T) cj,out cj,out r o
pa r
j=l
+(1-Y
)h (T )]<<
cg <<out v
7 (2-5) where hv hv,break Pr P
P saturated water vapor enthalpy (Btu/ibm),
enthalpy of steam exiting break (Btu/ibm)
= h (P
) if pipe contains liquid, v r
= h (P
) if pipe contains
- steam, V
P compartment pressure (psia),
pressure of fluid within pipe (psia),
PPlLL form 2<<5<<(10/83)
Ca<. <<9uco>
~~ -B-N A -0 4 6 Rev.'P g'ept.
Date 19 Designed by Approved by PROJECT Sht. No. I~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET R
= ideal gas constant for steam (0.1104 Btu/ibm R) 0 v
R
~ ideal gas constant for air (0.0690 Btu/ibm R),
0 a
Qb k
heat transferred to air and water vapor from break liquid exiting break as it cools to compartment temperature (Btu/hr),
W
= steam flow rate exiting pipe break (ibm/hr),
bs h
= saturation enthalpy of liquid water (Btu/ibm).
f 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 Trans fer E
ations The slab model in COTTAP describes the transient behavior of relatively thick slabs which have a significant thermal capacitance.
For each thick I
- slab, the one-dimensional unsteady heat conduction equation is solved to I
I
ppa,L Form 2454 t l0/83)
Cat. I973401 SE -B" N A -0 4 6 Rev.0 g'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~3of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 pat - ~
a T sax 2
2 s
s (2-6) subject to the following boundary and initial conditions:
8T 3X XaaO t)T 3X X~L
= h
[T (t) - T (oit)] I
1 r1 s
k
- h
[T (Lit) - T (t)] I
2 s
k 12 (2-7)
(2-8) where T (xo) ax+ b, s
(2-9)
T (xit) = slab temperature
( F)i 0
s t
~ time (hr),
ppd L Form 2<<5<< Lrors3L Car. <<923401 SE N A-046 RLVOT Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET x
m spatial coordinate (ft),
thermal diffusivity of slab
= k/(p C
) (ft /hr),
2 s ps thermal conductivity (Btu/hr ft F),
P s Cps h
slab density (ibm/ft ),
3 specific heat of slab material (Btu/ibm F),
film coefficient for heat transfer between thy slab and the room on side 1 of the slab (Btu/hr ft F),
h film coefficient for heat transfer between thy slab and the room on side 2 of the slab (Btu/hr ft F),
T (t)
Temperature of room on side 1 of slab
( F),
and T 2(t)
= Temperature of room on side 2 of slab
( F).
r2 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 (oat)
T (t) J <<
1 s'l (2-10)
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Cat. S91340t SE N A-046 RevQ Dept.
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CALCULATIONSHEET ql (t)
~q tt)
Room on side 1 of slab at temperature T.l(t) rl Slab Temp f T (x,t) s Room on side 2 of slab at temperature T
(t) r2 Side l of slab Film coefficient, hl Heat Transfer Area, A
~Side 2 of slab Fil coefficient, h2 Heat Transfer Area, A
X=O X=L Figure 2.1 Thick slab and adjacent rooms
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CALCULATIONSHEET 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)],
(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 set equal to zero.
Zf side 1 of the slab is in 2
contact with ground then h is set to zero.
pplLL Form 2454 n0/83) car. rrencor B
N A 0 4 6 Rey.o Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 r
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. 23.3r note that the radiative heat transfer component is already included in these coefficients.
pp81. Form 2454 n0/83)
Cat. <<973401 SE -B-N A -0 4 6 Rev.'0
>'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of
.PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 cl C
0.825
+
0.387 Ra
[1+(0.492/Pr)9/16)8/27 (2-12) where h
= natural convection film coefficient for vertical cl slab (Btu/hr ft F),
2 0 k = thermal conductivity of air (Btu/hr ft F),
raJ C
= characteristic length of slab (slab height in ft).
The Rayleigh and Prantl numbers are given by Ra g8(3600)
(T f-T )CL/(jjn) 2 3
(2-13)
Pr aa IjC /k, P
(2-14) where g ~ acceleration due to gravity (32.2 ft/sec ),
2 o -1 8 ~ coefficient of thermal exp'ansion for air
( R
),
v = kinematic viscosity of air (ft /hr),
2
PP3t. Form 2t54 (10/83)
Cat. <<97340 t SE -B-N A -0 4 6 Rpv.O ]I Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET u ~ thermal diffusivity of air (ft /hr),
2 p
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 Ra '/5 c2 L
(2-15) and for the case of upward heat flow the correlations are (ref. 8, p.445) h
~ 0 54 k Ra1/4 c3 L
(Ra<10
)
7 (2-16) h
~015k Ra1/3 c3 L
(Ra>10
)
7 (2-17)
The characteristic length for horizontal slabs is the slab heat transfer area divided by the perimeter of the slab (ref. 18).
PPAL Form 2i54 (10/83)
Cat. <<973401
~E -B-N A -0 4 6 Re".0 1
Dept.
~
Date 19 Designed by Approved by PROJECT Sht. No. 40 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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
~
(c +1)
(4+a+b-c) e oT a<n 3
s w,av av 2
(2-18) where a
Tav Stetan-Boltzman constant (0.1712x10 Btu/hr ft R ),
([(T +a
) +(T
+a
)
J/23
( R) 4 4
1/4 o
compartment air temperature
( F),
0 T
= slab surface temperature
( F),
0 surf es e w,av
~ slab emissivity
~ water vapor emissivity evaluated at Tav a
= 459.67 F.
0 Only the water vapor contribution to the air emissivity is included in ecgxation (2-18) because gases such as N
and 0
are transparent to therma 2
2
ppht. Form 2454 t 10/83)
Cat. rr973401 SE -B-N A -0 4 6 Rev.o 1'ept.
Date
'I9 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET radiation (ref. 11, p.3.11),
and the effect due to CO is negligible 2
because of its small concentration (0.03tit 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 e (T,P,P,P L )
= A (1-exp(-A X
) ]
1/2 w
m o
1 (2-19)
X(TgP gP gP L )
P L
] 300%
a
m w m L T 3 P + [5(300/T)
+ 0.5]
P a
w (101325)
(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 0
1 I
purposes of this work, they are represented by the following polynomial expressions:
Ppkl Form 2454 n0/83)
Cat. t9r3co>
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. 22 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET and A (T)
~ 0.6918 2.898x10 T 1.133x10 T
0 (2-21)
A (T) = 1.0914
+ 1.432xl0 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),
c has the value 0.45, and a and C are defined by n
ging (TgP gP gP L )]
a w
m Bln(P L )
w m (2-23) and b = Bin[a (T,P
,P
,P L )]
w
m 3ln (T)
(2-24)
Values of a and b are obtained through differentiation of the Cess-Lian equations.
The average mean beam length L for a compartment is m
calculated from L
= 3.5V/A m
(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.
PPAL Form 2l54 na/83)
Ca~. sermon SF- -B-N A -0 4 6 Rev.0
],
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~ of
.PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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, d T (x 0)/dx 0,
2 2
s (2-26) dT (x,0) dx
-h
[T (0) - T (0,0) ],
kl rl s
(2-27) and dT (x,o) dx 2
s r2
-h
[T (L,O)
T (0) ].
x=L (2-28)
The solution is where T (xO) =ax+b, s
(2-29) h2
[T 2(0) - T 1( )]
k+hL+kh/h (2-30) b~T (0) +kh
[T (0) - T (0)].
r1 2
r2 rl h [k+hL+kh/h]
(2-31)
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.
PP8 L Form 2454 {1N83)
Gal. N97340i SE N A -0 4 6 Rev.'0 f Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~>of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET 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). If 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 h
(P
) =W h
(P
) +
[W
-W
]h (P ),
bt f p
bs v r bt bs f r (2-32) where Wb
~ total mass flow existing the break (ibm/sec.),
W
= steam flow exiting break (ibm/sec.),
bs h
= enthalpy of saturated liquid (Btu/ibm),
f h
~ enthalpy of saturated vapor (Btu/ibm),
v P
~ fluid pressure within pipe (psia) g P
P
~ compartment pressure (psia).
r As a conservative approximation, the liquid exiting the break is cooled to room temperature and the sensible heat given off is deposited in the
ppAL Form 2lsl (ro/83)
Cat, rr913401 SE -B-N A -0 4 6 Rev.o 1'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET compartment air space.
This heat source is represented by the term, Q, in eq.
(2-5) and is calculated from break'
(~
~
)
(h (P
) h (T )] ~
(2-33) where T is the compartment temperature.
r The total mass flow out the break and the pipe fluid pressure are specified as input to the code.
I In the case where the pipe contains high-pressure steam, all of the mass 0
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 Leaka e Model Inter-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 ID number, flow area, pressure loss coefficient, TD numbers of rooms connected by the leakage path, and the allowed directions for
pphL Form 2454 n0/83)
Cot. rr973l01 SE -B-N A-0 4 6 Rev.0 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET 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
= C (A /A
)
DP 1
pl 1
max (2-34) where W
= leakage flow rate (ibm/hr),
cpl A1 proportionality constant (ibm-in /hr-lb ),
2 leakage path flow area (ft ),
2 A
= max flow area for all leakage paths (ft ),
2 hP = pressure differential between compartments (psia).
The constant C 1 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.
ppbL Form 2a5w (IO/83)
Cat. e97%0>
SE -B-N A -0 4 6 Rev.0 1'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~
of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET A leakage model suitable for calculation of compartment pressure transients can be selected by setting the associated loss coefficient.
equal to a positive quantity.
In this case the leakage rate is computed by balancing the intercompartment pressure differential with an irreversible pressure loss:
1 1 I 1 I (3600)
= hP i 2g Pl 1 144) 2 (2-35) where Kl = loss coefficient for leakage path (based on Al),
2 A
= leakage area (ft ),
1 W
= leakage flow rate (ibm/hr),
1 p
= density within compartment which is the source of the leakage 1
flow (ibm/ft ),
3 hp = pressure difference between compartments associated with leakage path (psia).
A maximum leakage flow rate for each path is calculated from N
=pmin (V,V) C 1 tlIlax 1' p2'2-36)
ppAL Form 2454 n0/83) car. rr973lo1 SE -B-N A-046 Rev01 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~4 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET where V
and V are the volumes (ft ) of the compartments connected by 3
3 the leakage path, p (ibm/ft ) is the average of the gas density
-1 for the two compartments, and C
(hr
) is a user specified p2 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
<T (P
)
surf sat v
(2-37) where T (P
) is the saturation temperature of water evaluated at the sat v
partial pressure of vapor within the compartment.
T f is the slab surf surface temperature.
PPdL Form 2454 (f0/83)
Gal. a973401 SE -B-N A -0 4 6 Rev.O
]'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET In 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'
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.
PPlLL Form 2L54 (10/83)
CS1, 11973401 SE -B-N A-0 4 6 Rev:0 1
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~Oof PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET Table 2.3 Uchida Heat Tranfer Coefficient*
Mass Ratio (Air/Steam)
Heat Transfer Coefficient (Btu/hr<<ft - F)
(0. 10 0.50 0.80 1.30 1.80 2.30 3.00 4.00 5.00 7.00 10.00 14.00 18.00 20.00
>50.00 280.25 140.13 98.18 63.10 46.00 37.01 29.08 23.97 20.97 17.01 14.01 10.01 9.01 8.00 2.01
- Values from ref. 16, p.
65
PP((L Form 2454 (1883)
Cat. N91~(
SE -B-N A-04 6 Rev.0 1:
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~ j of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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.
In 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
)
u w
r surf (2-38) where q
. = rate of heat transfer to the wall (Btu/hr),
h
= Uchida heat transfer coefficient (Btu/hr-ft - F),
2 0 A
= wall surface area (ft ),
2 w
T compartment air temperature
( F),
0 r
T
= wall surface.temperature
( F).
0 surf
pp&L Form 24&i n0/83)
Cat, %73401 SE -B-N A-04 6 Rev'0 P Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET The corresponding condensation rate at the wall surface is calculated from W
~
(h - h)A (T
T cond u
w r
surf h
(2-39) where and h ~ natural convection/radiation heat transfer coefficient, h
+ h,
c r'Btu/hr-ft F),
2 0 h
= natural convection coefficient (Btu/hr-ft - F),
2 0 c
h
= thermal radiation coefficient (Btu/hr-ft - F).
2 0 r
Ecyxation (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 ecgxal to the slab surface temperature, i.e., the major resistance to condensation heat transfer is associated with the diffusion layer rather than the condensate film.
pphL Form 2454 na/83)
Car. eonei SE. -B-N A-O4 6 a v.Or'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~
of
.PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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%. It is activated when the relative humidity reaches 99%.
The rain out of vapor is calculated from and W
= (200.0 RH 198.0) max(W C
)
(RH > 0.99),
ro vap,in'l (2-40)
W
= 0.0 ro (RH < 0.99),
(2-41) where W
= rate of vapor rainout (ibm/hr),
ro C
= user specified constant (see section 3.2),
r'1 W
= net vapor mass flow into the compartment (ibm/hr),
vap,in RH
= relative humidity.
PP8 1. Form 245'10I83)
C4t rr973401 SE, -B-N A -0 4 6 Rev.'0 1:
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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:
=C(T
-T),
Qcool c,avg r
(2-42) where Q
= cooler load (Btu/hr),
cool o
C
=
Q
/ (T
- T...
),Btu/hr F,
cool initial c,avg initial r initial 0
T
= average coolant temperature
( F),
c,avg
=
(T
+T
)/2 c,in c,out and o
T
= compartment temperature
( F).
r The inlet cooling water temperature, T
, is supplied as input, and the c,in'utlet cooling water temperature, T
, is calculated from the cooling cgout water energy balance, where Q
=C(T T) =W C
(T
- T
)g cool c,avg r
cool pw c,in c,out (2-43)
W
= cooling water flow rate (ibm/hr),
cool
PPd t. Form 2454 (10/83)
Cat. 4973401 SE -B-N A-0 4 6 Rev.0 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~Sof PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET C
= specific heat of water (1 Btu/ibm F).
0 pw The code checks to ensure that the following condition is maintained throughout the calculation:
W C
(T - T
)
cool
cool pw r c,in (2-44) 2.1.3.6 Hot Pi in 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,
r= U'OLD (T - T ),
piping f
r (2-45)
PPE L Form 2454 (10/83) car. rr973l01 SF -B-N A "0 4 6 Rev.'0 1 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. +4 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET where U = Overall heat transfer coefficient (Btu/hr-ft - F),
2 0 D = outside diameter of pipe or insulation (ft),
L pipe length (ft),
T
= Pipe fluid temperature
( F),
0 f
T
= Compartment temperature
( F).
0 r
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 insulated
- pipes, the overall heat transfer coefficient is calculated from D. ln (Di/D ) +
1 2k.
H +H i
c r (2-46) where D. = Insulation outside diameter (ft),
i D
= Pipe outside diameter (ft),
P 0
- k. ~ Insulation thermal conductivity (Btu/hr ft F),
i 2 0 H
= Convective heat transfer coefficient (Btu/hr ft F),
c H
~ Radiation heat transfer coefficient (Btu/hr ft F).
2 0 r
PP8 L Form 2454 (lor83)
Cat. rr973a01 SE -B-N A-046 Rev.o):
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. 37 of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET For uninsulated pipes, U = H
+ H c
r (2-47)
The convective heat transfer coefficient, H, is calculated from the c
following correlation for a horizontal cylinder (ref. 8, p. 447):
c air 0
0.60 +
0.387 Ra 9/16 8/27
[1+(0.559/Pr)
)
(2-48) where k
= thermal conductivity of air (Btu/hr-ft-F),
o air D
= pipe outside diameter for uninsulated pipes (ft),
0
= 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 is calculated from (ref. 10, pp. 77-78)
Z H
CG(T
- T
)/(T -T )
4 4
r r
surf r
s (2-49) where E
pipe surface emissivity,
ppa,L Form 2454 nOI92) ca1. <<912401 SE -B-N A -0 4 6 Rcv'.0 g
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. +~
of
.PENNSYLVANIAPOWER &LIGHTCOMPANY
. ER No.
CALCULATIONSHEET and
-8 2o4 0 = Stephan Boltzman constant (0.1712x10 Btu/hr-ft R ),
0 T
= compartment ambient temperature
( R),
r T
= pipe surface temperature
( R) for uninsulated pipes 0
surf 0
m insulation surface temperature
( R) for insulated pipes.
The Rayleigh number is given by:
R
= (3600) g (T
-T )D 2
3 a
surf r o
VG (2-50) where g = 32.2 ft/sec 2 g
m volumetric thermal expansion coefficient (1/ R),
2 kinematic viscosity (ft /hr),
a Tsurf thermal diffusivity (ft /hr),
2 4
0 pipe surface temperature
( F) for uninsulated pipe, 0
insulation surface temperature
( F) for insulated pipe, 0
T
= compartment ambient temperature
( F),
r D
m pipe outside diameter (ft) for uninsulated pipe, 0
= insulation outside diameter (ft) for insulated pipe.
The Prandtl number is calculated from Pr = C 4/k, P
(2-51)
pal Form 2454 n0/83>
Car. s973401 SE -B-N A-046 Rev.0],
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET where C
= specific heat (Btu/ibm F),
0 p
ll = viscosity (ibm/ft hr),
k = thermal conductivity (Btu/hr ft F).
0 2.1.3.7 Com onent Cool-Down Model In 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) T (t) ],
P dt r
(2-52) with T(t )
= T 0
0 (2-53) where T is the component temperature, p,
C
, and V are the density, P
specific heat and volume of the component.
U is the overall heat transfer coefficient, A is the heat transfer area, T is the ambient room r
temperature, and t is the time at which the component starts to cool 0
down.
pp8.L Form, 245'ols3)
Car. II9r24O1 Sf -B-Z A =0 4 6 Rev.O 1
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~Oof PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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, T (t) is fairly constant during the r
cooldown process of the component.
With this assumption, T (t) can be r
replaced with T (t ) in equation (2-52) to obtain r
o VPC d UA[T-T (t )1
= -UA[T(t)-T (t )l.
UA dt (2-54)
Rewriting (2-45) in terms of the heat loss from the component, Q, gives
~d
= -Q(t),
dt (2-55) where Y is the thermal time constant of the component and is given by Y = pC V/UA.
P The solution to (2-46) is Q(t) = Q(t
) exp[-(t>>t )/Y].
0 o
(2-56)
(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 constant may be calculated by the code.
For pipes filled with liquid, th i
ppaL Form 2454 n0/831 Cat. rr970l01 SE N A-046 RevO)
Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET volume average density and the mass average specific heat of the liquid 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
= ((U (T
) - U (T )]/(T -T
)
+
M C
)/(M+M ),
p f
fo f
ro fo ro mpm f
m '2-58) where U
Tro Mm total internal energy of the fluid (Btu),
the initial fluid temperature
( F),
0 the initial room temperature
( F),
mass of metal (ibm),
M m mass of fluid (ibm),
f C
= specific heat of the metal (Btu/ibm F).
0 PIll 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;
ppct. Form 2459 notmt Gal, 9973401 SE -B-N A -0 4 6 Rev.O g'ept.
Date 19 Designed by Approved by PROJECT Sht. No. +W of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET W
= 3600 2g(P
-P
) (E -E
)
c a2 al u
1 (2-59) where W
= circulation flow rate (ibm/hr),
c P,p
= air densities in compartments connected by circulation a1 a2 path (P
2 P 1), ibm/ft3 E,E elevations of lower and upper flow paths respectively (ft),
1' K,K
= pressure-loss coefficients for lower and upper flow paths 1'
respectively, A,A
~ flow areas of lower and upper flow paths respectively 1'
(ft ),
and g = acceleration due to gravity (32.2 ft/sec ).
2 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.
PPaf. Form 2<<5<< <for83f Caf. <<9ncaf SE -B-N A -0 4 6 Rev.Q y'ept.
Date 19 Designed by Approved by PROJECT aht. No. ~8 of
.PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 2.1.3.9 Time>>De endent Com artment Model As many as fifty time-dependent compartments can be modeled with COTTAP.
In 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 (sinusoidal) 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 It 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 capacitance.
Slabs of this type have nearly linear temperature profiles, and thus, the heat flow through the slab can be calculated by using an overall heat transfer coefficient.
The rate of heat transfer through a
thin slab is obtained from
PAL Form 295'IO/83>
Cat, 997340 l SE -B-N A -0 4 6 Rev.Q y'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET
= UAtT (t) T (t) i I (2-60) where q
= rate of heat transfer from the room on side 1 of the slab to 12 the room on side 2 (Btu/hr),
U
~ overall heat transfer coefficient for the thin slab (Btu/hr ft F),
20 A
= heat transfer area of one side of the thin slab (ft ).
2 Overall heat transfer coefficient data is input to COTTAP for each of the 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 II 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
+ Nt ordinary sr tdr differential equations and N partial differential equations, where N
is s
sr the number of standard
- rooms, N d is the number of time-dependent
- rooms, tdr
ppdl Form 2c5c n0r83>
Cat, rr973401 SE -B-N A-046 Rev.0)
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET and N
is the number of thick slabs.
An energy balance and two mass s
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'he DSS/2 software package which was purchased from Lehigh University (ref. 2).
Before LSODES can be applied to the solution of the governing equations in COTTAP, the N partial differential equations describing heat flow through s
thick slabs must be replaced with a set of ordinary differential equations.
This is accomplished through application of the Numerical Method of Lines (NMOL) (ref.
- 3).
In the NMOL, a finite difference I
approximation is applied only to the spatial derivative in equation (2-6),
PP3l Form 2<<5<<(lOI83)
C<<t, <<973<<01 SE -B-N A -0 4 6 Rex'.0 ]
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET thus approximating the partial differential equation with N coupled ordinary differential equations of the form dT
=
T i=1,2<<...)N,
~i SXX3.
(2-61) where N is the number of equally spaced grid points within the slab, TSi is the temperature at grid point i, and T
. is the finite-difference SXX1 approximation to the second-order spatial derivative at grid point i.
Fourth-order finite difference formulas are used within COTTAP to calculate the T These formulas are contained within subroutine sxxi 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 TSXX1 T
~
1 f-T
+16T
-30T
. +16T T
]
SXXi 2
Si-2 126 si-1 Si si+1 si+2
+O(~ )<<
(2-62) where i m 3,4,...,N-2, and b is the spacing between grid points.
A six-point slopping difference formula is used to approximate T
. at i SXX3.
equal to 2 and N-lr
!I Ili
ppdt. Form 245a n0/83l Gal. a97340)
SE -B-N A -0 4 6 Rev.O Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET T
=
1
[10 T 15 T
- 4 T
+ 14 T 6 T
+ T
]
sxx2
2 sl s2 s3 s4 s5 s6
+ 0(~ )a (2-63) and T
1
[10 T 15 T 4 T
+ 14 T
- 6 T
+ T
]
sxxN-1 2
125 sN sN-1 sN-2 sN-3 sN-4 sN-5
+ o(h ).
(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
=
1
[-415 T
+ 96 T 36 T
+ 32 T sxxl 2
~s1 126 6
s2 s3 s4 3
4
-3 5 - 508T
] +O(b ),
2 (2-65) and T
~
1
[-415 T
+ 96 T 36 T
+ 32 T sxxN 2 sN 126 6
sN-1 sN-2 sN-3 3
4
-3T 4+508 T]+O(h),
2 (2-66) where T
and T
are given by sx1 sxN T
-h
[T (t)
T (t) ]
k (2-67)
PP&1. Form 24&i u0,'831 Car. e 973401 SE N A -0 4 6 Rev.'Q P
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET and T
= -h
[T (t)
T (t)) ~
k (2-68)
The total number of ordinary differential equationsg N
r to be solved is I
ql now given by N
N
=3N
+N
+
N s
eq sr tdr
.~
gj'=l (2-69) where N
. is the number of grid points for slab j.
Note that at least six gj 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),
dt (2-70) where T is the time-dependent room temperature and g(t) is the time tdr 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 Ir
PP2 L Form 2454 (10/83>
Cat. 4973401 SE -B-N A -0 4 6 Rev 0 I Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 1
yn = Z yn 3
j=1 "2
S.
F 0
3 73 (2-71) where h is the step size, and the constants a.,'nd 8. are given in j'
ref. 1, pp.113 and 217.
The system of differential equations being solved are of the form d
y = F(y,t),
dt (2-72) with y(0)
= y
~
0 (2-73)
PPbL Form 24ba n0'M)
CaL a97bao>
SE N A -0 4 6 Rev'.0 y
Dept.
Date 19 Designed by Approved by PROJECT Sht. No.
$ 0 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Equation (2-71) describes two basic solution techniques, Adam's method and Gears method (ref.
5 and 6),, depending upon the values of k and k. If 1
k =1, eq.
(2-62) corresponds to Adam's method, and if k =0 it reduces to 1
2 Gear's method.
In both cases, the constant 9
is non-zero.
0 I
Since 8 go, the finite-difference equations comprise an implicit algebraic 0
I system for the solution y In LSODES, the difference equations are n'olved 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 n'ubstituted into the right-hand-side of eq.
(2-71) and a new value of yn is obtained.
Successive values of y are calculated from eq.
(2-71), by n
iteration, until convergence is attained.
MF=10 corresponds to Adam' method with functional iteration, and MF=20 corresponds'to Gear's method il 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
pp2,L Form 2454 n0r83)
Car. s92340l SE N A -0 4 6 Revo
)'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~+
of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 (k =0) only; the procedure is similar when applied to 2
the Adam's method equations.
The conventional form of Newton's iteration scheme. applied to Gear's difference equations is described by
~[s+1]
~ [s]
h g
~ t
~ [s]
WB k
Ea.
y
. -hB F(t,y
)),
1
'+
[s]
i n-i o
n'n i=1 (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-h8 Bf/By].
For large systems of equations this procedure is very time 0
consuming.
In LSODES, the Jacobian is evaluated and the subsequent inversion of
[I-h8 BF/By] is carried out only when convergence of the finite difference 0
equations becomes slow.
This technique is called chord iteration (ref.
5)
I
ppd r. Form 2454 r10/83)
Car. rr97340r SE -B-N A-04 6 R-..o y'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 2454 n0/83)
Cat, <<en<0>
SE -B-N A "0 4 6 Rev.0
>'ept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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.
PPCL Form 2<<54 nor82)
Cat. <<913<<01 SE N A-04 6 Rev:0 f Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
, 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).
ppbL Farm 2s5c nar83>
Car. %73401 SE -B-N A-046 R
0>'ept.
Date 19 Designed by Approved by PROJECT Sht. No. W~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET WS-I NPZPE
= Number of hot pipes (maximum value is 750).
W9-I NBRK
= Number of pipe breaks (maximum is 20).
W10-Z NLEAK
= Number of leakage paths (maximum is 500).
Wll-I NCZRC
= 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 NFTRZP
= 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 solved; the total mass in each compartment is held constant.
In cases where this option can be used, it results in large savings in
pp6 4 Form 2454 (10r83)
Gal. 0973401 SE -B-N A -0 4 6 Rev.0 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~
of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET computer time.
Zn order to use this option, the following input variables must be specified as:
NBRK=NLEAK=NCZRC=NFTRZP=O
~1~> Mass tracking is on; mass balances are solved for each compartment.
W3-Z MF
~ Numerical solution flag.
MF=222 should only be used if MASSTR 0.
Zf 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 arid larger computation times than MF~13 and MF=23.
=10~> Zmplicit 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
PPdr. Form 245a (10/83)
Car. <<9nrror SE -B-N A -0 4 6 Rev.Q g'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~S of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET internally generated diagonal approximation to the Jacobian matrix is used.
=20=> Implicit method based on backward differentiation formulas (Gear's method).
Difference equations are solved by functional iteration; Jacobian matrix is not used.
=23=> Implicit 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~> Implicit 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.
PP3,L Form 2454 (10/83)
Cat, rt97340t SE -B-N A-0 4 6 Rev.Q >,
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~S of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET W4-R CP1
= Parameter used in calculation of leakage flows.
Zncreasing CP1 increases the leakage flow rate for a given pressure difference.
The recommended value of CP1 4
is lx10.
Larger values of CP1 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.
Zncreasing CP2 increases the maximum leakage flow rates.
W6-R CR1
= Parameter used in rain out calculation.
Zncreasing this parameter increases the rain-out rate when rain out is initiated.
The recommended value of CR1 is 10.
L W7-Z ZNPUTF
= Flag controlling the printing of input data.
=0=> Summary of input data will not be printed.
1
> Summary of input data will be printed.
ppaL Form 2454 nOI83)
Cat. <<973l01 SE N A -0 4 6 Rev.0 I'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~S of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET WS-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's lxl0 3.3.
Problem Descri tion Data (Card 3 of 3)
Wl-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.
ppa L Form 2454 (10/83)
Gal. <<973401 8< -B-N A -0 4 6 Rev.'0 y'ept.
Date 19 Designed by Approved by
. PROJECT Sht. No.
40 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEETS 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
-5 calculation.
A recommended value for TFC is 10
-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 24& (ror83)
Cal. rr92340i SE -B-N A -0 4 6 ri.. 0 1'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~4of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 3.5 Error Tolerance for Com artment Ventilation-Flow Mass Balance Omit this card if NFLOW=O.
Wl-R DELFLO The maximum allowable compartment ventilation flow imbalance (cfm), i.e., the following condition must be satisfied for each compartment:
Net Ventilation Flow (cfm) into Compartment
< DELFLO.
-5 The recommended value of DELFLO is lx10
. It is particularly important to ensure that there are no ventilation flow imbalances when the mass-tracking option is not used (MASSTR~O) because in this case the code assumes that the mass inventory in each compartment remains constant throughout the transient.
3e6 Edit Control Data NEC edit control data cards must be suppliedt on each card the following three items must be specified.
PP8 1 Form 2i54 (10r83)
C4I. 4973401 SE -B-N A-046 Rev.01 Dept.
Date 19 Designed by Approved by PROJECT Sht. No.. 4~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Wl-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 W2-I NS1ED will be printed.
This includes both, standard rooms and time-dependent rooms.
~ Number of thick slabs which will be edited.
Associated heat transfer coefficients are edited along with the slab temperature profiles.
PPdL Form 2454 n0183)
Cat. 197340l
~E N A -0 4 6 Rev.Q gI Dept.
Date 19 Designed by Approved by PROJECT Sht. No.
~~
of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET 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
pp&L Form 245a (10/83) car. a973401 SE -B-N A -0 4 6 Rev'.0 1'-
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~
of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET the locations do not correspond to grid points.
Omit this card if NS1ED=O.
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 NFLOW=O.
Wl-R TREF
= Temperature
( F) used by code to calculate a reference 0
air density.
The reference density is used by the code to convert ventilation flows from CFM to ibm/hr.
W2-R PREF
~ Pressure (psia) used to calculate the reference density
PPd r. Form 2td4 (r0/83) car. rr973401 SE -B-N A -0 4 6
F'ev 0 >
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. 4'~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 3.12 Standard Room Data Wl-I IDROOM
= Room ID number.
The ID numbers must start with 1 and must be sequential.
3 W2-R VOL
= Room volume (ft ).
In order to maintain constant properties in a compartment throughout the calculation, 15 enter a large value for VOL (e.g.
1x10
).
W3-R PRES
= Initial room pressure (psia).
W4-R TR
= Initial room temperature
( F).
0 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.
PPdL Form 2154 (10/83)
Col, rr97340l SE -B-N A -0 4 6 Rev.'0 Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 3.13 Ventilation Flow Data Omit this card(s) if NFLOW~O.
Wl-I IDFLOW
= ZD number of the ventilation flow path.
Values must start with 1 and be secgxential.
W2<<Z ZFROM
= ID number of room that supplies ventilation flow.
This can be a standard room or a time-dependent room.
W3-I ITO
= ID number of room that receives flow.
This can be a standard room or a time-dependent room.
W4-R VFLOW
= Ventilation flow rate (ft /min).
This volumetric flow is 3
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.
PPSt. Form 2454 (1883)
Cat rr9134rt1 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~7ot PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 3.14 Leaka e Flow Data Omit this card(s) if NLEAK=O.
Wl-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 ).
2 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 r
Section
- 2. 1.3.2.
W4-I LRMI
= ID number of room to which leakage path is connected.
This can be a standard room or a time-dependent room.
h W5-I LRH2
= ID number of the other room to which the leakage path is connected.
This can be a standard room or a time-dependent room.
W6-I LDIRN
= Allowed direction for leakage flow.
PPIL L Form 2454 110/83)
C<<1. <<9%401 SE -B-N A-046 Rev.P f Dept.
Date 19 Designed by Approved by
'PROJECT Sht. No. ~@of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 NCIRC=O.
Wl-I IDCIRC
= 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 ID 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 m Elevation of the lower flow path (ft).
W5-R ELVU
~ Elevation of the upper flow path (ft).
pprL( Form 2454 (10/83)
Car. rr9ruoi SE -B-N A -0 4 6 R<< o Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET W6-R ARL
= Flow area of the lower flow path (ft ).
2 W7-R ARU
= Flow area of the upper flow path (ft ).
2 WB-R AKL
= Loss coefficient for lower flow path referenced to ARL.
W9-R AKU
= Loss coefficient for the upper flow path referenced to 3.16 Air-Flow Tri Data Omit this card(s) if NFTRIP=O.
Wl-I IDFTRP Trip ID number.
The ID numbers must start with 1 and must be sequential.
W2-I KFTYP1
= Type of flow path.
= 1 => Ventilation
= 2 ~> Leakage
= 3 ~> Circulation
PP8 L Form 2454 (1 0/83)
Car, r97040r SE -B-N A -0 4 6 Rev.-0 ]I Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~
of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 4
Omit this card(s) if NHEATmO.
Wl-I IDHEAT
= Heat load ID number.
ID numbers must start with 1 and must be sequential.
W2-I NUMR
= ID number of room containing heat load.
W3-I ITYP
= Type of heat load.
m 1 ~> Lighting m 2
> Electrical panel
pp6L Form 245< ttar83)
Cat. l973401 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. 2l of PENNSYLVANIAPOWER & LIGHT COMPANY ER No.
CALCULATIONSHEET
= 3 => Hotor
= 4 => Room Cooler
= 5 => Hot piping 8 => Hiscellaneous W4-R (DOT
= Hagnitude of heat load (Btu/hr).
heat load
( ITYP=5) enter 0.0 for value of (DOT will be calculated (DOT should be negative.
If this is a piping r
this parameter; the by the code.
If ITYP=4, W5-R TC
= Temperature
( F) of cooling water entering cooler if ITYP=4. If ITYP is not equal to 4 enter a value of -I.
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 I and must be sequential.
PPEL Form 2954 tt0/831 Cat. tt07340 1 SE N A -0 4 6 Rev.o r
I Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET W2-Z ZPREF 1D number of associated heat load.
W3-R POD
~ Outside diameter of pipe (in).
W4-R PZD Inside diameter of pipe (in).
W5-R AZNQD Outside diameter of pipe insulation (in).
Zf the pipe is not insulated set AZNOD equal to POD.
W6-R PLEN Length of pipe (ft).
W7-R PEM
~ Emissivity of pipe surface.
WB-R AZNK
~ Thermal conductivity of pipe insulation (Btu/hr ft F).
If the pipe is not insulated set AZNK 0.0.
W9-R PTEMP
~ Temperature
( F) of fluid contained in pipe.
0 W10-I IPHASE
~ 1 if pipe is filled with steam.
II
~ 2 if pipe is filled with licgxid.
ppdt. Form 2a54 (lor83)
Cat. <<9nao>
SE -B-N A -0 4 6 Rev.0
>~
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET 3.19 Heat Load Tri Data Omit this card(s) if NTRIP=O.
W1-I ZDTRIP
= Trip ID number.
IDTRIP must start with 1 and all values must be sequential.
W2-I IHREF
= ID 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.
=2=> Heat load is initiallyoff 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:
~ If TCON=O.O, the entire heat load is tripped off at
PPAt. Form 2454 ($ 183)
Cat. 9973401 SE -B-N A -0 4 6 Rev.Q 1 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
~ If the heat load is a piping heat load (ITYPm5), 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).
When the heat load is tripped off, it will exponentially decay with the user-supplied time constant.
This option can be used with any heat load; it is'ot restricted to just piping heat loads.
= 0.0 if ITMD=2.
3.20 Pi e Break Data Omit this card(s) if NBRK 0.
Wl-I IDBK
~ ID number of break.
IDBK must start with 1 and all values must be sequential.
PPLL Form 2454 (10/83)
Car. 0973401 SE -B-N A -0 4 6 Rev.o 1'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~5 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET W2-I ZBRM
=
ZD number of room in which pipe break occurs.
W3-R BFZPR
= Fluid pressure within pipe (psia).
W4-I IBFLG
= Fluid State flag.
= 1 => fluid in pipe is steam
=
2 => fluid in pipe is liquid water W5-R BDOT
= Total mass flow exiting the break (ibm/hr).
W6-R TRIPON
= Time at which break occurs (hr).
W7-R TRIPOF
= 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 t=TRZPON 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.
PPtt t. Form 2454 (10/83)
Cat( rr973401 SE -B-N A -0 4 6 Rev.'0
>~
Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET Wl-I IDSLB1
= Slab XD number.
IDSLB1 must start with 1 and all values must be sequential.
W2-I IRMl
= ZD number of room on side 1 of slab.
A standard room or a time-dependent room can be specified.
Zf side 1 of the slab is in contact with ground enter a value of zero.
W3-I IRM2
= ID number of room on side 2 of slab.
A standard room or a time-dependent room can be specified.
Xf side 2 of th slab is in contact with ground enter a value of zero.
W4-I ITYPE
= 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.
Zf the specified value of NGRIDF causes the total number of grid points for the
pp6L Form 2454 (10r83)
C41. 4973401 Dept.
Date 19 Designed by Approved by PROJECT Sht. No.
I 7 of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET 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.
ppaL Form 2454 (10/831 Cat. /1073401 SE -B-N A -0 4 6 Rev.0 1'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Allow the code to calculate film coefficients for slab surfaces in contact with ground.
W7-R CHARL characteristic length of the slab (ft).
= height of the slab if ITYPE=1.
= the heat transfer area divided by the perimeter if ITYPE=2 or 3.
If the value of CHARL is set to 0.0, the code will calculate a value for the characteristic length.
In this
- case, the code assumes that the slab is in the shape of a square.
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).
},
ppa,L Form 2454 n0/83) car. <<97uot SE -B-N A -0 4 6 Rev;0 y Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET W3-R AREAS1
= Slab heat transfer area (ft ).
This is the surface area 2
of one side of the slab.
W4-R AKS
= Thermal conductivity of slab (Btu/hr ft F).
W5-R ROS
= Density of slab (ibm/ft ).
3 W6-R CPS
= Slab specific heat (Btu/ibm-F).
W7-R EMZSS
= Slab emissivity 3.23 Thick Slab Data (Card 3 of 3)
If ZHFLAG=O for a slab, then do not supply a card in this section for that particular slab.
Zf IHFLAGml or 2, only supply the required data; leave the other entries blank.
Zf ZHFLAG=12, supply all the heat transfer
'I coefficient data for that slab.
Omit this card(s) if NSLB1=0.
Wl-I IDSLB1
~ Slab ID number.
W2-R HTC1(1)
~ Heat transfer coefficient for side 1 of slab if ITYPE=1 (Btu/hr-ft - F).
2 0
PP41. Form 2454 (10/83)
Ca1. SerSC01 SE -B-N A -0 4 6 Ftev.'0 1'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~Oof PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
= Heat transfer coefficient for upward flow of heat between slab and room IRMl if ZTYPE 2 or 3 (Btu/hr-ft - F).
2 0 W3-R HTC2(1)
Heat transfer coefficient for side 2 of slab if ZTYPE=1 (Btu/hr-ft - F).
2 0
= Heat transfer coefficient for upward flow of heat between slab and room IRM2 if ZTYPEm2 or 3 (Btu/hr-ft - F).
2 0 W4-R HTC1(2)
= Heat transfer coefficient for downward flow of heat between slab and room ZRM1 if ZTYPEm2 or 3 (Btu/hr-ft - F).
Do not supply a value if ITYPE=1.
2 0 W5-R HTC2(2)
~ Heat transfer coefficient for downward'low of heat between slab and room ZRM2 if ITYPEm2 or 3 (Btu/hr-ft - F).
Do not supply a value if ITYPE=1.
2 0 3.24 Thin Slab Data (Card 1 of 2)
Omit this card(s) if NSLB2=0.
pprt L Form 2454 n0r83)
Cat. rr9nao>
SE -B-N A-0 4 6 Rev.0 gt Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET Wl-I ZDSLB2
= Slab ID number.
IDSLB2 must start with 1 and all values must be secpxential.
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 ground, i.e.,
do not specify JRM1 or JRM2 equal to zero.
W3-Z JRM2
= ZD number of room on side 2 of slab.
A standard room or a time-dependent room can be 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 (ft ).
This is the surface area 2
of one side of the slab.
3.25 Thin Slab Data (Card 2 of 2)
Omit this card(s) if NSLB2 0.
pP&L Form 2454 (10/83) car. <<9ruoi SE N A -0 4 6 Rev.'Q Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Wl-I IDSLB2
= Slab ZD number.
W2-R UHT(1)
= Overall heat transfer coefficient for slab is JTYPE=l (Btu/hr-ft F).
2 0 Overall heat transfer coefficient for upward flow of heat through slab if JTYPE~2 or 3 (Btu/hr-ft - F).
2 0 W3-R UHT(2)
= Overall heat transfer coefficient for downward flow of heat through slab if JTYPE~2 or 3 (Btu/hr-ft - F).
Do 2 0 not supply a value of JTYPE~1.
3.26 Time-De endent Room Data (Card 1 of 2)
I Omit this card(s) if NTDR~O.
Wl-I ZDTDR
= ZD number of time-dependent room.
ZDTDR must start with
-1 and proceed secgxentially (i.e.,
ZDTDR 1 r 2 t 3 r ~
~ r NTDR) ~
W2-I IRMFLG
~ 1 if temperature,
- pressure, and relative humidity data will be supplied.
ppa r. Form 2<<54 (10/83)
Car. <<973401 SE -B-N A -0 4 6 Rev. 0 g'ept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET
= 2 if a sinusoidal temperature variation will be used for this room. If 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 IRMFLG=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 IRMFLG=2.
W4-R TDRTO
= Initial room temperature
( F) if IRMFLG=2.
0
= 0.0 if IRMFLG~1.
W5-R AMPLTD
= Amplitude
( F) of temperature oscillation if IRMFLG=2.
0
~ 0.0 if IRMFLG=1.
W6-R FREQ
= Frequency (rad/hr) of temperature oscillation if IRMFLG~2.
0.0 if IRMFLG~1.
PPIL Form 2454 n0r83>
Car. rr913401 SE -B-N A -0 4 6 Rev.'0 y'ept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 ZRMFLGml.
Omit this card(s) if NTDR=O.
Wl-I ZDTDR
~ ZD number of time-dependent room W2-R TTIME
= Time (hr).
W3-R TTEMP Temperature
( F).
o W4-R TRHUM
= Relative humidity (decimal fraction).
W5-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.
pp3L Form 2454 n$ 831 Cat. N973401 B-N.A=04 6 ReV-G.O Dept.
Date 19 Designed by Approved by PROJECT Sht. No. S~ of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 A0 and frequency'.
There are no heat loads or coolers within the standard room; heat is only transferred to or from the room by conduction through the slab.
The equations describing this problem are aT /at = aa T /ax 2
2 s
s BT
= hl [T 1(t)
T (0 t) ],
Bx x=0 k
BT 1
= -h
[T (L,t) T (0) - A sin(et)],
gs l
=L k2 s '2 0
(4-1)
(4-2)
(4-3) and T (x 0)
= ax+b, s
(4-4)
I3 C V
dT Ah
[T (Ort)
T (t) ]
dt (4-5)
PP6L Forrtt 245<< (10/83>
Cat. <<973401 SE -B-N A -0 4 6 RemQ y Dept.
Oath t<<
Designed by Approved by Sht. No. Q6 of I
PROJECT PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Room 1 Standard Room Room 2
Time-Dependent-Room Room temp, T
(t) rl Volume, V Air density, p
Specific heat, Cvl Initial pressure, P
Film coefficient, hl Slab Temp<<
T (x,t) s Room temp, 2()- 2(o)+Oi
(
)
r2 r2 Film coefficient, h
Side 1 of slab Side 2 of slab X=O X=L Figure 4.1 Description of Sample Problem 1
PAL Form 2454 ttN83)
Cat. N7340t SE
-B N A -04 6 Rev.00 Dept.
Date 19 DesIgned by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET where a and b are given by equations (2-30) and (2-31).
Zt 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 hours0.0231 days <br />0.556 hours <br />0.00331 weeks <br />7.61e-4 months <br />, 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 4.4g again, the results show good agreement.
PPttt. Form 2454 (tttt83)
Cat. 4973401 SE -B-N A-04 6 Rev.og Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET Table 4.1 Values of Parameters used in Sample Problem 1
Parameters Value T
0) r1 T
(0)
A0 h
h Vl 80 F
200 F
100 F
0.5 rad/hr 1.46 Btu/hr ft F
2 0 6.00 Btu/hr ft F
2 0 0.0325 ft /hr 2
1.0 Btu/hr ft F
800 ft 300 ft 2 ft 10 14e7 psia
~ 111 TSO FOREGROUND HARDCOPY 1 1 1 1 PRINTED 89284. 1100 JSNAME=EAMAC.COTTAP.SAMPLI.DATA JOL=OSK533 COTTAP SAMPLE PROBLEM 1 --
RUN 1
a ~ 1 ~ Off ~ Offff111 ~ ~ ~ 11 ~ 1 ~ ~ 1 ~ 11
~ 1 ~ 1 ~ ~ 11 ~ ~ ~ ~ 11111111111
~ Offfffffff~
11 ~ 1111 ~
PROBLEM DESCRIPTION DATA
(
CARD 1
OF 3
)
NROOM NSLAB1 NSLAB2 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NCIRC NEC 1
1 0
0 0
I 0
0 0
0 0
1 f1111111111111111111 '1111111111111111111111111111111111t111111111111111 PROBLEM DESCRIPTION DATA
(
CARD 2
OF 3
)
~ 1 1 p
1 NFTRIP MASSTR MF CP'I CP2 CR1 INPUTF 0
0 222 2.04 2.0 10.
1 1 ~ 1 ~ 1 ~ 1 1 1 ~ ~ 1 1 ~ 1 1 1 ~ ~ 1 1 ~ ~ 1 ~ 1 ~ ~ 1 1 ~ ~ 1 1 1 1 ~ 1 1 O 1 ~ ~ ~ ~ 1 1 1 1 ROBLEM DESCRIPTION DATA
(
CARD 3 OF IFPRT RTOL 1
- 1. 0-5 111 ~ ~ 1 ~ ~ ~ ~ 1 ~ ~ ~ ~ 1 1 ~ ~ 1 NSH 0
~ 111111 1
TFC 1.0-5
~ 11 ~ ~ 1111111
~ 1 ~ 1 ~ ~ ~ ~ 11 ~ ~ OOOOOOO
~ Offtfff~ ~ ~ Offffffftt
~ 11111
~ 111111 PROBLEM TIME AND TRIP TOLERANCE DATA T
0.0 f 111111 TEND TRPTOL TRPENO 2000.0 10.00 O.DO 1 ~ ~ tftf ~ 1 ~ ~ 1 ~ ~ Offf ~ 1 ~ Offffff~ ~
Off ~ 111111 ~ 1 ~ ~ ~
TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALA
(
OMIT THIS CARD IF NFLOW
=
0
)
1 1 1 1 t 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 NCE DEL 1.D f 111 111 t
I DEC TLAST TPRNT 1
2000.
100.
~ 111111111111
~ 11 ~ ~ Offff~ 1 ~ ~ ~ 11111111ftf1111
~ 11111 EDIT DIMENSION CARD 1 1 1 ~ 1 1 ~ f f 1 1 1 f 1 f f 1 1 FLO
-5 1 1 1 1 1 1 1 ~ 1 1 1 ~ ~ ~ 1 ~ ~ 1 ~ 1 1 1 1 1 1 1 1 t 1 1 1 1 1 1 1 1 1 1 ~ 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 f 1 1 1 1 1 1 1 1 1 1 EDIT CONTROL DATA CARDS NRED NS LEO NS2ED 2
1 0
1 11 ~ Of 1111 111 ~ ~ ~ ~ ~ 1 ~ ~ ~ 1 ~ 1 ~ Offfff111 ~ ~ 1111 ~ ~ 111 ~ 1 1 ~ tf 1 1 1 1 1 11'11 1 tf 1 11 f 1 ROOM EDIT DATA CARO(S)
-1 O 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 ~ tf ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 EDIT CARO(S)
FOR THICK SLABS 1 11111111
~ 1 ~ 11 ~ 1 ~ 11 11 ~ 11 f 111111
~ 11 ~ 11111 1111111
~ 111 ~ Of 111111tf tftfOtf 111 DI T CARDS FOR THIN SLABS f 11111111 1 11 ~ 111 ~ ~ 1 Otf 1111 ~ Offf1 ~ ~ 11tf 1 1 1 ~ Of 1 1 ~ 1111 Of 11 Of 11111111 REFERENCE PRESSURE FOR AIR FLOWS (OMIT THIS CARD IF NFLOW=O)
TREF 100.
PREF
- 14. 7
~
~ 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 t 1 ~ 1 ROOM DATA CARDS (00 NOT INCLUDE TIME-DEPENDENT ROOMS)
~
I DROOM 1
1 1111
~ tf 1 VOL PRES TR RELHUM RM HT 800.
14.7 80.0 0.5 10.0 1 11 1 1 11111 1111111 11111111 Of 111111 1 ~ 1 1t 1 1 1 AIR FLOW DATA CARDS
(
OMIT THIS CARD IF NFLOW
=
0
)
~ 1 ~ 1 1 ~ 1 1111 tf ~ 11 1111 IDFLOW IFROM ITO VFLOW
~ ~ 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 ~ ttt LEAKAGE PATH DATA
(
OMIT THIS CARD IF NLEAK =
0
)
IDLEAK ARLEAK AKLEAK LRMI LRM2 LOIRN
~ t ~ t t t ~ t ~ ~ ~ t t ~ ~ t ~ t t ~ ~ ~ t ~ ~ t t ~ t t ~ t ~ ~ t t t t ~ tt tt t t t t t t t 1 t t t ~ t t ~ t t t t t t t t AIR FLOW TRIP DATA IDFTRP KFTYP1 KFTYP2 FTSET IDFP sttttttt ~ ~ tt HEA
~
IDHEAT NUMR
~ 0000 ~tttttt QOOT ITYP TC WCOOL t ~ t t t ~ t t ~ t t t ~ t t t t ~ t t t t ttt ~ tt t t ttt 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 ~ ~ ~ ~ ~ ~ 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 I.OAD DATA CARDS C
~I
~
IDPIPE ttttttttt IPREF POO PIO AIODN PLEN PEM A1NK PTEMP IPHASE t ~ t t t ~ t t ~ ~ ~ ~ t ~ t ~ ~ tttt 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 HEAT LOAD TRIP CARDS I OTRI P IHREF ITMD TSET TCON
~tttttttt
~
IOBRK
~ttttttt ~
IOSL81 I
~tttttttt 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 ~
STEAM LINE BREAK DATA CARDS IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP 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 THICK SLAB DATA CARD (CARO 1
OF 3)
IRM I I Rhl2 I TYPE NGRIO IHFLAG CHARL 1
-1 I
IS 12 10.
~ ~ 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 THICK SLAB DATA CARD (CARD 2
OF 3)
IOSL81 1
ttttttttttt~
ALS AREAS1 AKS ROS CPS EMI S 2.0 300.
1.00 140.
0.22 0.8
~ ~ ~ttttttttt~ tt ~ttttttttttttt~ttttttttt~ ~ ~ tt ~ ~ ~ 0004 ~tttttt THICK SLAB DATA CARO (CARD 3 OF 3)
IDSL81 1
~ t ~ttttttttt t
IDSL82
~ttttttt ~ttt JRM1 JRM2 JTYPE AREAS2
~ ~ 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 THIN SLAB DATA CARD (CARO 2
OF HTC1(1)
HTC2(1)
HTC1(2)
HTC2
'1.46 6.00 ttttttttttttttttttttttttttttttttttttt
~ t THIN SLAB DATA CARD (CARD 1
OF 2)
(2) tt ~ttttt ~ttttt ~ t ~ t ~ t ~
t ~ ~ t t t t ~ ~ t t t t ~ t t t t t t t 2)
IDSL82 UHT(1)
UHT(2) o ~ ~ttttttttt~ 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 TIME-DEPENDENT ROOM DATA 4
I OTDR
-I
~ tt
~ ttttt ~ t ~
IRMFLG NPTS TDRTO AMPLTD 2
0 200.0 100.0 t ~ ~ t ~ ttt ~ ~ ~ ~ ttttt ~ ttttttt ~ ttt ~ ~ t ~ t ~ t ~ ~ ~
TIME VERSUS TEMPERATURE DATA FRED 0.50 tt ~ tt ~ ~ ~ ~ tt ~ ~ttttttt
~
I OTOR TTIME TTEMP TT IME TTEMP TTIME TTEMP oo
~
~ ~ t ~ et ~ ~
~ ttttt ~ t ~ tt tttt t tt tttttt ~
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 ~
~ ~ ti~ ~ ~ t ~ ~ttttttt ~ttttttttttttt~ ttt ~ t ~ ttt ~ tt
TSO FOREGROUND HARDCOPY
~ ~ 11 PRINTED 89284.1045
>SNAME=EAMAC.COTTAP.SAMPLI.DATA OL=OSK533 COTTAP SAMPLE PROBLEM I --
RUN 2
ft ~ 11111 ~ 111111111
~ 1111 ~ 1 ~ ~ 111 ~ 1111111111111tfffffffff PROBLEM DESCRIPTION DATA
(
CARD I
OF 3
)
tf 1 1 1 1 ~ 1 ~ Of ~ 111 NROOM NSLAB I NSLA82 NFLOW NHEAT NTDR NTRIP NPIPE NBRK NLEAK NCIRC NEC I
I 0
0 0
I 0
0 0
0 0
2
~ 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 t 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 f PROBLEM DESCRIPTION DATA
(
CARD 2
OF 3
)
NFTRIP MASSTR MF CPI CP2 CRI INPUTF IFPRT RTOL 0
0 222 2.04 2.0 10.
I I
1.0-5 1 11 11111 ~ ~ t 11111111
~ ~ t 1 ~ 1 ~ ~ ~ 1 ~ 11111 1111111111
~ tf1111 ~ 11 1 1 1 1 t 1 1 1 1 1 1 1 ~ 111 PROBLEM DESCRIPTION DATA
(
CARD 3 OF 3
)
NSH 0
~ 111 11111 TFC I. D-5 1111 ~ ~ 11 ~ 11 1 ~ ~ ~ ~ ~ ~ ~ ~ 11 ffttf1 1 1 1ff11111111
~ 11 111 ~ 1 111 1 Of 11111t PROBLEM TIME AND TRIP TOLERANCE DATA T
TEND TRPTOL TRPEND 0.0 1520.0 IO.DO O.DO 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 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE
(
OMIT THIS CARO IF NFLOW
=
0
)
1 1 1 1 111111111111 1
OELFLO 1.0-5
~ 1 ~ 1 1 11 ~ 111 11 1 ~ 1 11 ~ ~ ~ ~ ~ ~ ~ 1 ~
~ 1 ~ 11111111111
~ 1111111111 11111 1111 ~ 1 ~ ~ ~ ~ ~ ~ 1 EDIT CONTROL DATA CARDS IOEC I
2
~ f ~ 1111111 TLAST TPRNT 1500.
1500.
1520.
I.
1 1 1 111111111 t ~ ~ 1 ~ ~ 1 ~ 1 ~ 11 ~ 11111111111111111 11 111 EDIT DIMENSION CARD 11 f 111 11 ~ 11 ~ ~ 1 ~
NRED 2
~ f ~ 1 1 ~ 1 ~ ~ ~ 11111 NS I ED NS2EO I
0 11111 1 1 1 1 1 1 11 ~ 1 1 ~ 1111111111111111 11111 1111 1111 ~ f ~ 111111 11 ROOM EDIT DATA CARD(S)
~ 1 1
-I
~ 1 1 1 1 ~ tf 1 1 11111
~ t111 Of ~ 1 ~ ~ 111 ~ ~ 1111 ~ Of 11 1 f ~ 11111 1 tf 1 1 1 111 11 f 1 1 ~ 1 f 11 ~ 1 EDIT CARD(S)
FOR THICK SLABS
~ ~ 11 ~ 1 ~ 11111111 111111 1 1111 ~ 1 ~ ~ 11111 111111111f Otf 1 11 1 1 1 1 tff Off 1 11 1 ~ ~ 1111 1 EDIT CARDS FOR THIN SLABS f 1 1 1 1111 ~ f 1111 1 11111 111 ~ ~ 1 1 111 ~ 11 ~ 111 ~ 1111 f 1 111 1 tf 1 111 111 1 tf 1 1 1 1 ~ 1 ~ 111 1 1 REFERENCE PRESSURE FOR AIR FLOWS (OMIT THIS CARD IF NFLOW=O)
TREF 100.
~
~ 111
~ 11
~ ft ~ 1 ~ ~
(00 PREF
- 14. 7
~ 1 1 1 1 tf 1 ~ 1 1 ~ 1 1 t 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t 1 1 1 1 1 1 ROOM DATA CARDS NOT INCLUDE TIME-DEPENDENT ROOMS) 1 1111
~ 111 Of 1
~
I IiROOM I
~
~ 1 11 f f f f ~
VOL 800.
11111 PRES TR RELHUM RM HT 14.7 80.0 0.5 10.0
~ ~ ~ 1 ~ 11 ~ 11 ~ 1 1 ~ 1 ~ 1 ~ 1 11 11 ~ 11 111111111111
~ 1I1 A I R FLOW DATA CARDS OMIT THIS CARD IF NFLOW
=
0
)
1111 tf ~ ~ 11 1 1 11 ~
IUFLOW IFROM ITO VFLOW
TSET TCON BOOT TR IPON TRIPOF RAMP JRM2 IDSL82 UHT(1)
~ eeet
~ ~ 1 ~ ~ 1 ~ ~ 11 ~ ~ ~ 0 ~ ~ 01 000000
~ 0 ~ 1100 ~ ~ 01 ~ 1 ~ 0 ~ 011 ~ 01000111111f f000000101
~
LEAKAGE PATH DATA
(
OMIT THIS CARD IF NLEAK =
0
)
IOLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN i ee 1 1 00 0 1 ~ 1 111 101 ~ 0 ~ ~ f 00000 ~ ~ ~ 0 ~ ~ 0001000000000000
~ ~ ~ 00 ~ ~ ~ ~ 0 ~ 1 0 ~ ~ 1 ~ 11 ~ 01 1 AIR FLOW TRIP DATA e
IDFTRP KFTYPI KFTYP2 FTSET IOFP e 1 1 1 0 0 0 0 0 1 0 0 0 0 ~ 0 ~ 0 0 ~ 0 0 0 ~ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ~ ~ 0 1 ~ 1 0 0 0 0 1 1 0 1 0 0 0 0 0 ~ ~ ~ 0 ~ ~ 0 e
HEAT LOAD DATA CARDS IDHEAT NUMR ITYP QDOT TC WCOOL
~ e 1 1 1 1 1 1 1 1 1 1 1 1 ~ 0 ~ 1 ~ 1 ~ ~ 0 1 ~ ~ ~ ~ 1 ~ ~ ~ ~ ~ 0 0 0 0 0 0 0 0 ~ 0 ~ ~ ~ 1 1 0 ~ 1 1 1 1 ~ 0 ~ 0 1 ~ ~ 0 0 ~ ~ ~ 1 ~ 1 0 0 PIPING DATA CARDS IDPIPE IPREF POD PID AIOON PLEN PEM AINK PTEMP IPHASE
~ 11 1 00110101f 00 0 tf0 ~ 000 ~ 0000000000f OfffOf ~ 00000000
~ 000101000011ff 00 011 ~ 0 1
HEAT LOAD TRIP CARDS e
I OTR IP IHREF I TMO
~ 1 1 1 0 0 1 1 0 t 1 0 ~ ~ 1 0 ~ ~ t 1 1 ~ 0 ~ 0 1 0 t 0 0 0 0 0 0 0 1 1 ~ 1 0 1 0 1 1 0 1 0 1 ~ ~ 0 0 0 1 0 1 0 0 1 0 0 0 0 ~ 0 1 0 1 1 1 1 1 e
STEAM LINE BREAK DATA CARDS
~
IDBRK IBRM BFLPR IBFLG e
~ 1111110
~ 1 f 11000 ~ 000 ~ 11 ~ f 0000 1 1100000 000 000000001 0 ~ 0100 0101 1 tf 1 1 1 1 1 11011 4
THICK SLAB DATA CARO (CARO I
OF 3)
IDSI 81 IRMI IRM2 I TYPE NGRIO IHFLAG CHARL 1
I
-I 1
'I 5 12 10.
~ e 1 1 1 ~ 1 ~ 1 1 ~ 1 ~ 1 1 1 0 0 0 ~ 1 ~ 0 0 0 1 ~ 0 0 ~ 1 1 ~ 0 0 ~ 0 0 0 0 0 0 0 0 f 0 0 ~ ~ ~ 0 1 0 0 0 0 0 0 1 ~ 0 0 0 1 0 ~ 0 1 0 1 0 0 e
. THICK SLAB DATA CARO (CARD 2
OF 3)
IDSL81 ALS AREAS1 AKS ROS CPS EMI S I
2.0 300.
1.00 140.
0.22 0.8
~ 1 1 1 1 1 1 ~ 1 0 1 0 1 ~ 1 0 ~ ~ 0 1 ~ 0 1 0 1 1 ~ ~ 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 ~ 1 ~ 1 ~ ~ 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 ~ ~ 1 0 THICK SLAB DATA CARD (CARD 3 OF 3) e ID&LBI HTCI (I)
HTC2(1)
HTCI (2)
HTC2(2)
I 1.46 6.00
~
~ e ~ e 1 1 ~ 1 e 1 1 t 1 1 ~ ~ ~ 1 1 ~ 1 1 0 ~ ~ 0 0 0 t 1 1 0 1 1 ~ ~ ~ 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 ~ ~ 1 1 1 1 1 1 1 0 0 1 '1 1 1 ~ 1 0 THIN SLAB DATA CARO (CARD I
OF 2) e e
I OSL82 JRMI JTYPE AREAS2 e
1 1 1 1 0 1 1 1 1 1 f 1 0 1 ~ 0 ~ 1 1 t ~ ~ ~ 1 0 0 0 0 0 0 f 0 0 0 0 0 ~ 0 0 1 0 1 0 0 0 0 1 1 1 ~ 0 1 ~ ~ 0 1 0 ~ 1 0 1 0 1 1 1 0 0 1 0 '1 1 1 e
THIN SLAB DATA CARO (CARO 2
OF 2) e UHT(2) i ~ i e 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 0 0 1 1 1 1 ~ 1 1 1 ~ ~ \\ 1 1 ~ ~ 1 1 1 ~ 1 ~ 0 1 1 1 1 1 TIME-DEPENDENT ROOM DATA
~
I UIOR
- I IRMFLG NPTS TDRTO AMPLTO FREQ 2
0 200.0 100.0 0.50
~ ~ 1 ~ ~ 1 ~ ~ 11 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ ee
~ ee
~ eee
~ eee
~ 11 ~ 1 ~ 1 ~ ~ effete
~ ee
~ eeeeeeef tee TIME VERSUS TEMPERATURE DATA
~
I DTDR see
~ eeet oeeeeeee T
E TTEMP tee
~ 1 1 TTIME TTEMP TTIME TTEMP
~ ~ 1 1 1 1 1 1 t ~ 1 ~ 1 1 1 1 1 ~ 1 1 1 1 1 ~ 1 1 0 ~ 0 1 ~ ~ 1 1 1 ~ 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1eeetef 01 ~ 11111
~ 1 111111111
~ 1 ~ 01 111101
~ 1111111111
~
FIGURE 4.2 COMPARISON OF COTTAP CALCULATEDTEMPERATURE PROFILE WITH ANALYTICALSOLUTION (t=900 hr)
FOR SAMPLE PROBLEM I 220 210 Ql Q) 200 I~
190 I
180 Legend ANALYTICAL
~ COTTAP 170 0.5 x (tt) 1.5
FIGURE 4.3 COMPARISON OF COTTAP CALCULATEDTEMPERATURE PROFILE WITH ANALYTICALSOLUTION (t2000 hr)
FOR SAMPLE PROBLEM t 250 240 U) 230 LIJ 220 l~
210 200 Legend ANALYTICAL 0 COTTAP 190 180 0.5 x (tt) 1.5
RGURE 4.4 COMPARISON OF COTTAP CALCULATEDTEMPERATURE OSCILLATION WITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 1
I Ill O
LJJ Ci M
K O
OO CL O
W 4JI 200.6 200A 200.2 200 199.8 199.6 199.4 150 1505 1510 TIME (hr)
Legend ANALYTICAL
~ COTTAP 1515 1520 c
C)
PAL Form 2l5l 00t83)
Ca<. N973401
$F N A -04 6 <<V 0m Dept.
Date 19 Designed by
, Approved by PROJECT Sht. No. ~9 of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET 4.2 Com arison of COTTAP Results with Anal tical Solution for Com artment Heat U
due to Tri ed Heat Loads (Sam le Problem 2)
This problem consists of two compartments separated by a thin wall.
One of the compartments is maintained at a constant temperature (COTTAP time dependent room); the temperature in the other compartment is calculated by the code.
The compartment for which the temperature is calculated contains 4 heat loads and 5 associated heat load trips.
The timing of these trips matches the plot in figure 4.5.
The analytical solution for the room temperature is T (t) =T (0)e 8
+T (1-e
)
Z Z
con
.t
-tB/a J y8/a 0
a (4-6) where the constants a and 8 are defined in Appendix B, T is the con compartment temperature on the opposite side of the thin wall, and Q is the function shown in Figure 4.5.
PPd 1. FO m 2t54 <10 831 Cdt, 091%01
~
SE -g N A.-04 6 ReV.PX Dept.
Date 19 Designed by Approved by PROJECT Sht. No. 27 of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET n
C 0 0 D o g
Q a
A I-IIt 0
o 6
4'1 4
Z I
0 00 4)
Q Q
0 Q
Q 0
0 C$
(+H/ ~d Q) $'nd wZ.
pal Form 2454 nOI83)
Col. l913401 SF g
tu p.-04 6 Rev:ox Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET 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)
In this problem, a compartment containing a heat source of 10 Btu/hr is 5
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); 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.
TSO FOREGROUND HARDCOPY
'1000 PRINTED 89284. 1412 SNAME=EAMAC:COTTAP.SAMPL2.DATA
~
OL=DSK534 COTTAP SAMPLE PROBLEM 2
iiiti~ 1 ~ f ~ 000 ~ 0 ~ ~ ~ 0 0 ~ ~ ~ ~ ~ ~ 00 ~ 0 1t0it 0 tfiiiiitiiiiiii 0 0 tfit 0 ~ ~ 0000 ~ 0 1 111 t PROBLEM DESCRIPTION DATA
(
CARD 1
OF 3
)
NROOM NSLAB1 NSLAB2 NFLOW NHEAT NTDR NTRIP NPIPE NBR 1
0 1
0 4
1 5
0 0
if000001 000011
~ ~ ~ ~ ~ ~ 00 ~ ~ ~ 00 ~ 0 ~ 0 ~ 00 ~ ~ 0 ~ ~ ~ 000 ~ 00 ~ 00000 ~
PROBLEM DESCRIPTION DATA
(
CARO 2
OF 3
)
K NLEA 0
00 ~ 000 K NCI RC NEC 0
1 000000110000 NFTRIP MASSTR MF CP1 CP2 CR1 INPUTF IFPRT RTOL 0
0 222 2.04 2.0 10.
1 1
I. 0-5 1 ~ 1 1 0 0 0 0 0 ~ 0 0 0 ~ ~ 0 ~ ~ ~ ~ ~ 0 1 0 0 0 ~ ~ ~ 0 0 0 0 0 0 1 0 \\ 1 0 0 0 0 0 0 0 0 0 ~ 0 0 ~ 0 ~ 0 ~ 0 ~ ~ ~ 0 ~ ~ ~ 0 0 0 1 0 t 1 PROBLEM DESCRIPTION DATA
(
CARD 3
OF 3
)
NSH TFC 0
I. 0-5
~ 11 ~ 00 ~ 0 ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 0 ~ ~ 1 ~ ~ ~ ~ 0 ~ 00 ~ 0 t ~ 0 ~ ~ 0 ~ ~ ~ 0 10 t ~ ~ ~ ~ 0 ~ ~ ~ 0 ~ 1 1 0 1 ~ ~ ~ ~ ~ f J 0 0 1 00 PROBLEM TIME ANO TRIP TOLERANCE DATA T
TEND TRPTOL TRPEND 0.0 40.0 0.005 40.0 000001 11 ~ 0 0 ~ ~ ~ 01 ~ 1 ~ ~ ~ ~ 0 ~ ~ ~ 0 ff1 ~ f 0101 1 Jf 0001 0 0 f 00010 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANC
(
OMIT THIS CARO IF NFLOW
=
0
)
111 ~ 01110000
~ 11 ~ ~ 1 OELFLO
~ 1 101 ~ ~ 111 1 1 1 ~ ~ ~ ~ ~ ~ 1 ~ ~ ~ ~ f ~ 11 00 ~ 01 ttitfif001000101 0011011 01 1 ~ 11 ~ 1 1 01 100 f 0 EDIT CONTROL DATA CARDS I DEC TLAST TPRNT 1
60.
2.0
<1001000000000
~ 0000 ~ ~ ~ 11100
~ 00000 ~ fffffiiiiiittttttt00000000010000001011 EDIT DIMENSION CARO
~ iit NRED NSIED NS2ED 2
0 1
~ 111 1110 1 1 0 ~ 0 ~ ~ ~ ~ ~ ~ 0 ~ ~ 1 ~ 000 ~ 00010 ~ 00111010001
~ 01100
~ ~ 11 ~ ~ ~ ~ 0110 10011 ROOM EDIT DATA CARD(S) 1
-1
~ 11001000 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 0 0 0 '1 0 0 0 0 0 0 0 t 0 0 0 t 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 EDIT CARD(S)
FOR THICK SLABS 1
~ 111 1 0000 00J ~ 100 ~ 00000001
~ 01 ~ ~ 00 ~ 1 10000101010000000000100111100010tiiiif EDIT CARDS FOR THIN SLABS
~ 111 0 0000 0 ~ ~ ~ 1 ~ 011001 10 ~ ~ ~ ~ 0 f 0 1 0 0 10 10 iff t010100 Jf REFERENCE PRESSURE FOR AIR FLOWS (OMIT THIS CARD IF NFLOW=O) 01101 1 111111 1 ~ 11f 000011 TREF PREF y J 0 0 J 0 00 0 ~ 11111
~ 111 ~ ~ 11111
~iii~ 110111
~ ~ 1110110110
~ 00 ~ ~ 1111111111111011
~ 0 ROOM DATA CARDS (00 NOT INCLUDE TIME-DEPENDENT ROOMS)
IDROOM 1
1
~ 1 tif VOL PRES TR RELHUM RM HT 0000.
14.7 100.0 0.5 10.0
~ 1 ~ ~ 1 ~ 1 10 ~ ~ 01 ~ 11 ~ 11110
~ JiiffJifiiiiiiiii A IR FLOW DATA CARDS
(
OMIT THIS CARD IF NFLOW
=
0
)
~ 11111 1 Jit ~ 011 0 11 0 01011 IDFLOW f
IFROM ITO VFLOW
LRMI ARLEAK IOFTRP KFTYPI 0 0 1 ~ 1 1 0 ~ t 0 1 0 0 0 0 0 0 0 1 s 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 ~ t 0 0 0 t 1 1 0 1 1 t 1 ~ 1 1 1 1 ~ ~ 1 ~ ~ 0 1 1 0 0 0 0 0 0 0 ~ 0 1 1 0 ~ ~ ~ 1 1 0 1 1 ~ 1 1 1 0 0 1 1 ~ 0 LEAKAGE PATH DATA
(
OMIT THIS CARD IF NLEAK =
0
)
0 IOLEAK AKLEAK LRM2 LDI RN 0
~ t 0 1 0 0 1 1 0 0 0 0 1 t 1 0 1 0 0 0 0 0 ~ 0 0 0 0 1 1 0 0 0 0 0 0 t 0 0 ~ 0 0 0 0 0 0 0 0 0 t 0 0 1 1 1 0 0 1 0 1 ~ 1 0 0 0 ~ 1 0 0 ~ 1 0 ~
AIR FLOW TRIP DATA KFTYP2 FTSET IDFP s 1 1 1 1 1 0 ~ ~ 0 0 t 0 t ~ 0 1 ~ ~ 0 0 ~ 0 0 0 ~ 0 ~ ~ ~ ~ ~ 0 0 0 0 ~ 0 0 0 0 0 ~ ~ 0 1 ~ 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 ~ ~ 0 0 1 1 0 ~ 0 HEAT LOAD DATA CARDS IDHEAT NUMR ITYP QDOT TC WCOOL I
I 2
1000.
-1.
0.
2 I
3 1000.
1.
0.
3 I
3 3000.
-1.
0.
4 I
8 2000.
- I.
0.
0 1 1 e ~ 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 1 0 1 0 0 0 0 0 0 0 0 10 0 0 1 0 1 PIPING DATA CARDS IDPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE s 1 0 0 1 0 1 0 ~ 1 ~ 0 0 1 1 1 1 0 ~ ~ 1 1 1 0 1 ~ 0 ~ ~ 1 0 ~ 0 0 1 0 0 0 1 0 0 0 0 0 00 0 1 ~ 0 0 0 0 ~ 1 1 ~ ~ 1 0 1 1 1 1 0 1 0 0 1 1 1 0 HEAT LOAD TRIP CARDS IHREF ITMO TSET TCON I
2 1.0 0.
0 TRIP ON I
I 5.0 0.
0 TRIP OFF 2
I
- 10. 0 0.
1 TRIP OFF 3
2
- 15. 0 0.
1 TR I P ON 4
I 20.0 5.
0 EXPON DECAY 0 1 0 0 0 01 0 0 0 t 1 1 0 1 0 1 0 ~ 1 ~ 0 ~ 0 0 0 1 0 0 0 0 0 ~ ~ 0 ~ 0 0 0 0 0 0 1 ~ 1 1 0 0 t ~ 0 0 1 1 0 STEAM LINE BREAK DATA CARDS
~
I DTR I P I
2 3
4 5
111111000010 0
0 IDBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP t11110110 e
IDSLBI IRM2 0i 1 1 1 1 1 1 ~ 0 0 ~ ~ 0 1 ~ ~ ~ 0 0 0 ~ 0 1 ~ 0 0 ~ ~ 0 0 0 ~ 0 ~ t 0 0 0 0 0 0 0 0 0 1 ~ 0 0 0 ~ 1 1 1 0
THICK SLAB DATA CARD (CARO 2
OF 3)
IDSLB1 AREAS I AKS 1eeteetee 0
0 IDSLB I HTC2(2) 11111111 1
e IDSL82
'I 10110 1 0 0 0 1 0 0 1 1 0 0 t t 0 ~ 0 0 ~ ~ ~ 1 0 ~ ~ 1 ~ ~ ~ ~ 1 ~ ~ 1 1 1 0 0 0 0 1 0 1 1 ~ 0 0 ~ 0 1 ~ 1 1 0 0 t 0 0 ~ 0 THICK SLAB DATA CARD (CARD I
OF 3)
ITYPE NGRID IHFLAG CHARL IRMI
~ ~ 0 ~ 1010101000 ROS CPS EMIS ALS 1 0 1 1 0 1 0 0 1 0 ~ 1 1 ~ 1 1 1 t ~ ~ ~ ~ 1 1 ~ t ~ 0 0 0 0 0 0 0 0 0 0 ~ 0 0 1 0 0 t t 1 0 1 t 1 1 0 1 ~ 1 ~ 0 0 0 1 0 ~
THICK SLAB DATA CARD (CARD 3 OF 3)
HTCI (I)
HTC2(1)
HTCI (2)
JRMI JRM2 JTYPE AREAS2 I
-I I
500.
~
~ 1 0 1 1 1 ~ 1 ~ ~ 1 1 ~ ~ ~ 1 1 1 1 ~ 1 ~ 1 1 ~ ~ ~ ~ ~ ~ 1 1 1 1 1 0 0 1 ~ 1 1 ~ 1 1 1 ~ ~ ~ 0 0 0 0 0 0 0 0 0 I~ 1 1 0 THIN SLAB DATA CARO (CARO 2
OF 2) 1eetttteee 1 1 0 1 1 0 0 0 0 ~ 0 0 ~ 1 ~ 1 ~ 0 1 0 1 1 ~ 1 0 t 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 ~ 0 1 0 0 ~ 0 1 0 ~ 1 1 1 0 1 ~ ~ ~ 1 0 0 ~
THIN SLAB DATA CARD (CARO I
OF 2)
UHT(2)
~
IOSL82 UHT( I )
I 0.33 1 ~ 11111111
~ 1 ~ 1 ~ ~ ~ ~ 1 ~ ~ ~ ~ 1 ~ 1 ~ ~ 1 ~ 1 ~ 11 ~ 11 ~ ~
TIME"DEPENDENT ROOM DATA 0
IDTDR MFLG NPTS TDRTO
-I 1
3 0.0 teteeeeeeee
~ 11 ~ 11 ~ ~ ~ 1 ~ 1 ~ 0111111
~ ~ 1 AMPLTD 0.0
~ ~ 1 ~ ~ ~ 11 ~ 0 ~ 110 FREQ 0.00 01111
~ 1 ~ 01111 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 1 I II I DR IT I ME I ~ERS~ls vEMPg+URF+f A T1EMP RHUM PRES
-1 0.00 100.0 0.50
- 14. 70 50.00 100.0 0.50
- 14. 70 100. 00 100. 0 0.50
- 14. 70 I 0 0 4 0 4 4 t 4 4 4 0 4 4 4 4 t 4 4 0 t 4 t 4 4 4 4 4 4 4 ~ 4 0 0 0 4 0 4 ~ 0 4 4 4 0 4 4 4 4 0 4 0 4 0 0 4 4 4 4 0 0 4 4 0 4 4 0 4 4 4 4 0 4 l ~ 0 ~ i ~ 1 0 ~ ~ ~ 0 4 l 1 t 1 4 4 0 4 0 4 4 0 4 4 4 ~ ~ ~ ~ ~ ~ ~ 0 i ~ 0 0 4 0 4 4 4 4 4 ~ i ~ 0 0 4 1 ~ 4 t 0 ~ 1 ~ i f ~ 0 1 f 4 1 1 1 I
FIGURE 4.6 COMPARISON OF COTTAP CALCULATED COMPARTMENT TEMPERATURE WITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 2 135 130 OO O
IJJ
~l 125 120 115 110 105 Legend ANALYTICAL
~ COTTAP 100 10 20 TIME (hr) 30 40
pp&L Form 24&a n Dry)
Cat. a973401
$F. -Q N A =04 6 Rev.0g Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET The walls of the compartment consist of 3 slabs:
a vertical wall (slab 1),
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 High Energy 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 1100 PRINTED 89304.0951 OSNAME=EAMAC.COTTAP.SAMPL3.DATA VOL=OSK533 COTTAP SAMPLE PROBLEM 3
400140 ~ 0000 ~ t000040404001100
~ 40 ~ 0000 ~
0000 ~
PROBLEM DESCRIPTION DATA
(
CARO 1
OF 3
I NROOM NSLA81 NSLA82 NFLOW NHEAT NTDR NTR 1
3 0
2 1
1 1
I I I ~ ~ I 4 4 I IIII 4 ~ IIII ~ 4 4 ~ 4 I 4 4 I ~ I ~ I I ~ I ~ IIIII 4 I
PROBLEM DESCRIPTION DATA
(
CARD 2
OF 3
I I I I ~ I 4 4 II I 0 0 II II I ~ I I I IIIII 4 4 4 I IP NPIPE NBRK NLEAK NCIRC NEC 0
0 1
1 8
I 4 I 4 II 4 I III ~ 4 ~ I I I 4 4 4 I 4 ~ 4 4 4 4 4 I 4
)
1 INPUTF IFPRT RTOL 1
1 1.0-5
~ IIII ~ I 4 II ~ II 4 IIII 4 4 I ~ IIII ~ I I
)
I NFTRIP MASSTR MF CPI CP2 CR 5
1 10
- 2. 04 150.
5 I I I I IIII ~ I I ~ I ~ I ~ It t I ~ 0 ~ II ~ II IIIII 0 IIIII 4 I 0 PROBLEM DESCRIPTION DATA
(
CARD 3 OF 3
4 NSH 10 1010000 044 4
TFC 1.D-5 I I IIIIt I ~ 4 ~ I ~ II ~ I 4 I 4 0 0 II 4 II ~ t ~ IIIII ~ II 4 IIII 4 ~ I 4 I ~ I 4 ~ ~ II 4 4 I I III PROBLEM TIME AND TRIP TOLERANCE DATA 114 4
I 4
T TEND TRPTOL TRPENO 0.0 3.0 0.005 3.0 4 4 I I I I ~ I I I I ~ ~ I 'I I ~ I 4 I 4 I ~ 4 II ~ I ~ I I ~ 4 ~ I ~ II ~ 4 ~ ~ ~ I 4 ~ 4 II ~ I 4 I ~ 4 I I 4 4 I 4 4 4 4 I 4 I I ~
TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE
(
OMIT THIS CARD IF NFLOW
=
0
)
,DELFLO 1.0-5 I I I~ II ~ 4 4 ~ II ~ I I ~ I I ~ ~ I I~ II 4 I I I~ ~ I I 4 ~ ~ I ~
I~ ~ ~ I I~ II ~ ~ ~ II ~ ~ III ~ ~ ~ I I ~ III 4 I~ 4 4 I II ~
EDIT CONTROL DATA CARDS 414 I
I 044 I
4 1
104 4I 1
444 I
4I 111 1I TLAST 0.1 1.0 I.
1 2.2.2
- 10. 0 24.0 500.0 00014014 TPRNT 0.01
- 0. 10 0.01
- 0. 10 0.01
- 0. 10 0.20 5.00 I 4 4 I 4 ~ ~ I II I ~ I ~ ~ IIIII 4 I III 4 ~ I I ~ 4 4 I ~ III 4 ~ I I II I 4 I 4 I I 4 III 4 EDIT DIMENSION CARD IOEC 1
2 3
4 5
6 7
8 4110000 NRED NS IED NS2EO 2
2 0
4 ~ I 4 t I 4 I 4 1 II I I 0 ~ ~ I 4 I It I 4 I ~ ~ III I I ~ ~ 4 I I I 4 ~ I ~ IIII ~ I I ~ 4 I I 4 I ~ I I I 4 II I I ~ II 4 I ROOM EDIT DATA CARO(S) 2I I I ~ ~ ~ ~ I ~ I ~ I t 4 t I I I I ~ I I 4 4 I 'I I I II 4 I I 4 I I I I ~ I t I ~ I 4 I I I ~ I I ~ I t II 4 I 4 I I ~ III I 4 II EDIT CARDS FOR THIN SLABS
~ ~ I I ~ I I I I ~ I ~ I I I I I ~ 4 I ~ I I I I I I ~ I I I ~ I I I 4 I ~ I I ~ I ~ I I I ~ I ~ I I I I I I I ~ I I I I I I I I I 4 I ~
REFERENCE PRESSURE FOR AIR FLOWS (OMIT THIS CARD IF NFLOW=O)
-1 I ~ I ~ ~
I~ I I 4 I 4 ~ ~ ~ ~ I ~ I 4 4 I ~ I 4 I I I ~ ~ ~
I~ ~ I 4 4 4 4 I 4 I I ~ II ~I ~ 4 4 I I I ~ II ~ ~ I I I I I III 4 4 I 4 I I I EDIT CARD(S)
FOR THICK SLABS (g) A A
'0 p
I CO I
TREF 100.
00 ~ 1000001 NOT INCLUDE TIME-DEPENDENT ROOMS)
NIOM
)L ~ 'IUM HT PREF 14.7 I II 4 I I I I I I I II ~ 4 I I I I I t I ~ I I 4 0 I ~ 4 I I 4 I I I I ~ 1 I I ~ ~ I I 4 4 I I I I ROOM OA1'A CARDS
ttt tt t
ttt tttt IDFLOW "I FROM I TO VFLOW 1
-1
" 1.04 FAN 2
1
-1 1.04 FAN ttttttttttt~tttttttttttttttttttttttttttttttttttttttttt hatt LEAKAGE PATH DATA
(
OMIT THIS CARO IF NLEAK =
0
)
tttttttttttt IDLEAK ARLEAK AKLEAK LRM1 LRM2 LDIRN 1
1.0
-1. 0 1
2 ttttttttttttttttttttttttttttttttttttttttttttttttt
~ttttttttttttttttttt CIRCULATION PATH DATA 30000.
14.7 80.0 0.5 27.5 tttttttt~ ttt ~tttt ~ttttt ~ttttt ~ ~ t ~ tt ~ttttttttttttt~tttttttttttfttttttt AIR FLOW DATA CARDS
(
OMIT THIS CARO IF NFLOW =
0
)
IOCIRC KRM1 KRM2 ELEV1 ELEV2 ARIN AROUT AKIN AKOUT 1
1
-1 3.
12.
50.
50.
5.
5.
t t t t t t t t t t t ~ t t t t t t t tttt t t t t t t t t t t t tttttttt tttttt t t t ttt t t t t t tt t t t t t t t t AIR FLOW TRIP DATA ET IDFP 0
1 t TRIP CIRC FLOW OFF AT START 0
1 t TRIP FAN OFF 0
2 t TRIP FAN OFF 0
1 t TRIP LEAKAGE PATH OFF 0
1 t START NATURAL CIRC tttttttttttttttttt~tttttttttttttttttt TC WCOOL
-1.
0.
t t t t t ttttt tttt t t t t t t ~ t t t t t t t t t t t tt tt t DS PTEMP IPHASE t t t t t t t t t t tt t tt t ~ t ~ ~ t t t t t t t t t t t t t t t t t CARDS IDFTRP KFTYP'I KFTYP2 FTS 1
3 1
0.
2 1
1
'I.
3 1
1 1.
4 2
1 2.
5 3
2 2.
t t t t t t t t t t t t t t t t t t t 1 t t t t t t t t t t t t t t t t
HEAT LOAD DATA CARDS t
IDHEAT NUMR ITYP QOOT 1
1 3
100000.
ttttttttttttttttttttttttttttttttttt t
PIPING DATA CAR IOPIPE IPREF POD PID AIOON PLEN PEM AINK t t t t tt 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 HEAT LOAD TRIP tt IOTR 1
t IDBRK tttttttt IDSL81 1
2 3
tttttttt t
IOSL81 1
2 3
tttttttt t
IDSL81 1
2 t t tt t t IP IHREF ITMD TSET TCON 1
1
- 10. 0 0.
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 STEAM LINE BREAK DATA CARDS t t t t ~ t t t t t t t t t t t t t t t t t IBRM BFLPR IBFLG BDOT TRIPON TRIPOF RAMP t t ttt t t t t t t t t t t t t ~ t t t t t ~ t t t t t t tttttttttt t t THICK SLAB DATA CARD (CARO 1
OF 3 tt t t t t tt t t t t t t t t t t t t t t IRM1 1
1 1
tttttttt ALS 3.0 2.0 4.0 ttttttt ~
AREAS1 AKS ROS CPS EMIS 3800.
1.0 140.
0.22 0.80 960.
1.0 140.
0.22 0.80 960.
1.0 140.
0.22 0.80 ttttttttttt~ ~ t ~ t ~ ~ ttttt ~tttttttttttttttttt~tttt ~tttttt THICK SLAB DATA CARO (CARD 3
OF 3)
HTC1 (2)
HTC2(2)
HTC1
(
'I )
HTC2( I )
3.7 3.7 tt ~ ~ ttt ~ t ~ t ~ ~tttttttttttt~ tt ~
THIN SLAB DATA CARD 3.
t t t t t t t t t t tt t (CARD 1
OF 2) t t t t t t t t t t t t t t t t t t t t t t I RM2 ITYPE NGRID IHFLAG CHARL
-1 1
10 2
30.
-1 3
10 2
30.
0 2
10 0
30.
ttttttttttttt~ tt ~ ~ ~ ~ tt ~ tt ~ ~ t ~ttttttttt~ t ~ttttt ~ttttttttt THICK SLAB DATA CARO (CARD 2
OF 3) 1RM1 JRM2 JTYPE AREAS2
444444 4
4 44444 4
IDT
-1 44444 4
4 IOT-I 44444 44444 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 4 4 4 4 THIN SLAB DATA CARD
(
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 4 4 4 CARO 2
OF 2)
IOSL82 UHT(1)
UHT(2)
DR 44444444 IRMFLG NPTS TDRTO AMPLTD FREQ 1
4 80.0 0.0
- 0. 00 4
OUTSIDE AIR 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 4 4 4 4 4 4 4 ~ ~ ~ ~ 4 ~ 4 ~
TIME VERSUS TEMPERATURE DATA OR TT 0
1 2
5 44444 44444 I ME TTEMP RHUM
.00 80.0 0.50
.00 80.0 0.50
.00'0.0 0.50
.00 80.0 0.50 44444444444444444444 '
444444 '
~ 4444444444444
~ ~ 4 ~ 4 ~
PRES
- 14. 70
- 14. 70
- 14. 70 14.70
~ 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 4 ~ 4
~ 4 ~ 4 4 4 4 44 4 ~ 4 ~ 4 4 ~ ~ 4 4 4 4 ~ 4 4 4 4 4 ~ 4 4 ~
444444444444444444 '44 '
~ 4444444444444444444444444444444444444
'444 TIME-DEPENDENT ROOM DATA
figure 4.7 COTTAP TEMPERATURE PRORLE FOR SAMPLE PROBLEM 5 100 U)
I I
OO O
LLI CL I
EL LIJ CL LLI I
95 90 85 80 0
0.5 1.5 TIME (hr) 2.5
TSO FOREGROUND HARDCOPY 0 0 0 0 PRINTED 89285. 1301 DSNAME=EAMAC.COTTAP.SAMPL4.DATA YOL=DSK540 COTTAP SAMPLE PROBLEM 4
0000000000000 '
0000 '
~ 0000000
~tttt ~ 000000 '00000000000000000000000000000 PROBLEM DESCRIPTION DATA
(
CARO 1
OF 3
)
NROOM NSLABI NSLA82 NFLOW NHEAT NTOR NTRIP NPIPE NBRK NLEAK NCIRC NEC I
3 0
0 0
1 0
0 1
1 0
6 0 0 0 0 0 0 0 t 0 0 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 0 0 0 0 ~ 0 0 0 0 0 0 ~ 0 PROBLEM DESCRIPTION DATA
(
CARD 2
OF 3
)
NFTRIP MASSTR MF CP1 CP2 CR I INPUTF IFPRT RTOL 0
I 13 5.D4 150.
50.
I I
1.0-5 tttttttttttttttttttttttttttttttttttttttt~ 0 '0000000000000000000000000000 0
PROBLEM DESCRIPTION DATA
(
CARD 3
OF 3
)
0 NSH 0
0 00000000 0
TFC 1.0-5 0000000000000000000000tttttt0'0000 F 000000000000 F 0000000000000 PROBLEM TIME AND TRIP TOLERANCE DATA T
0.0 0000000000 F 000 TOLERA
(
OM 0
OELFLO I.D-5 0000000000000
'END TRPTOL TRPEND 6.0 0.005 6.0 0000000
~ 0 ~ 0 ~ ~ 0000000000 'ttttttttttttttttttttttttttttttttt NCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE IT THIS CARO IF NFLQW
=
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 0 0 0 0 0 0 0 0 0 0 0 0 EDIT CONTROL DATA CARDS
'p t
IDEC I
2 3
4 5
6 000000000 0
TLAST TPRNT 0.5
- 0. 10 0.6 0.005 2.5
- 0. IO 2.6 0.005 6.0 0.20 25.0 0.50 00 ~ 0 ~ttt ~ 00000000
~ 00 F 0000000000000000'0000000000000000000000000
'DIT DIMENSION CARD NRED NS I ED NS2ED 2
3 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 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 0 0 0 0 0 t 0 0 0 0
ROOM EDIT DATA CARD(S)
I
-I 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 0 0 0 0 0 0 ~ ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 EDIT CARD(S)
FOR THICK SLABS I
2 3
000000000000000000 F 0000 '00 F 000000000000
~tttttttttttttttttt~ ~ 00000000000 0
ED I T CARDS FOR THIN SLABS 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 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 0 0 0 0 0 0 0 0 t 0 0
REFERENCE PRESSURE FOR AIR FLOWS 0
(OMIT THIS CARD IF NFLOW00) 0 TREF PREF 0
100.
- 14. 7 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 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 0 ROOM DATA CARDS NOT INCLUDE TIME-DEPENDENT ROOMS)
CD CD CD C
C)
4 4
I DFLOW VFLOW 44444444444444444444444tttt
~ 444444444444444tttt
~ 44444444444444444444444 4
LEAKAGE PATH DATA
(
OMIT THIS CARD IF NLEAK =
0
)
4 I FROM I TO ITMD TSET AREAS I AKS 1000.
1.00 800.
1.00 800.
IDLEAK ARLEAK AKLEAK LRMI LRM2 LDIRN 1
1.0
-1.0 I
-I 2
4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 ttt 4 t 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 4 4 4 4 4 4 4 4 t t 4 4 tt CIRCULATION PATH DATA 4
IOCIRC KRMI KRM2 ELFV1 ELEV2 ARIN AROUT AKIN AKOUT 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 t t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 4 t 4 4 t 4 4 4 4 t 4 4 4 4 4 4 4 4 t 4 4 4 4 t 4 4 4 4 4 4 4 ~
AIR FLOW TRIP DATA 4
IDFTRP KFTYP1 KFTYP2 FTSET IOFP 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ t 4 4 4 4 4 t 4 ~ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ ~ 4 4 4 4 4 ~
4 HEAT LOAD DATA CARDS IDHEAT NUMR ITYP QDOT TC WCOOL 4 4 4 4 4 4 4 4 4 4 4 4 4 t t 4 4 4 t 4 t 4 4 4 t 4 4 4 4 t4 4 4 4 4 4 4 4 4 4 t 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4
PIPING DATA CARDS 4
IOPIPE IPREF POD PID AIOON PLEN PEM AINK PTEMP IPHASE 4
4 4 4 S 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 t 4 4 4 4 4 4 4 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 4 4 4 4 4 4 t 4 4 4 4 4 4
HEAT LOAD TRIP CARDS I DTRIP IHREF TCON 4
4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 t 4 t 4 4 4 ~ 4 4 4 4 t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 t 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 t t 4 4 4 STEAM LINE BREAK DATA CARDS IOBRK IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP I
I 1000.
2 1800.
0.5 2.5 0.5 44444444444444 '4444444tttttttt
~ 444444444444ttt44
~ 444444444t4444444444t4 THICK SLAB DATA CARO (CARO 'I OF 3)
IDSLBI IRMI IRM2 I TYPE NGR ID IHFLAG CHARL I
I
-I I
15 2
0.
2 1
0 2
15 D
0.
3 I
-1 3
15 2
0.
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 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 4 4 4 \\ 4 4 4 4 4 4 4 4 THICK SLAB DATA CARO (CARO 2
OF 3)
IOSLBI ALS ROS I
2.75 140.
2 4.00 140.
3 2.75 140.
HTC2(2)
IDSL82 t tt tt tt tt t t t tttttttt 't t 't t t tttt t t t ~ tttt t t t tt 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
THICK SLAB DATA CARO (CARO 3
OF 3)
IDSL81 HTC1 ( 1)
HTC2
( 1)
HTC1 (2) 1 0.6 3
0.9 0.4 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 tt t t t t t t t ttt t t t t t t tttt t t t ~ t t t ~ t t t THIN SLAB DATA CARD (CARD 1
OF 2) t I DSL82 JRM1 JRM2 JTYPE AREAS2 ttttt t t tt t t tttt t t t t t t t t t t t t t t t ttt t t t t t t t t ~ ~ t t t t tt t t t t t t t t ~ t t t ~ t t t t t tt tt t t THIN SLAB DATA CARO (CARO 2
OF 2) t UHT( I )
UHT(2) t tt t t t t t ~ t t t t ~ t ~ t t ~ t t t ~ t ~ ~ ~ t t t ~ t t ~ t ~ t ttttt t t t t t t ~ ~ t t ttt ~ tt t ttt t ~ ~ t t t tt t t t
TIME-DEPENDENT ROOM DATA t
I DTDR IRMFLG NPTS TDRTO AMPLTD FREQ
-I 1
3 0.0 0.0 0.00 t OUTSIDE AIR tttt ~ ttt ~ tttttttttttttttttttttt~ ttttttttt
~tttttttttttttttttttttttttttttt t
TIME VERSUS TEMPERATURE DATA J
t I OTDR TTIME TTEMP RHUM PRES
-1 0.00 95.0 0.60 14.7 10.00 95.0 0.60
- 14. 7 50.00 95.0 0.60 14.7 ttt ~ tttttttttttttttt ~ tttttttttttttttttttttt ~ttttt ~ ~ttttttttttttttttttttt I t t t t t ~ t t t tt tt ~ tt ~ t t t t ~ t t t t t t ~ t t tt t t t t t t t t t ttt t tttt t ~ t ~ t t t t t t t ttttt t ~ t t t t
FIGURE 4.8 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 4 180 CA I
I CL OOz Ld CL I
EL Lxl CL 160 140 120 100 80 3
TIME (hrs)
PP4L Farm 2wR {10r83)
CN. l973401
$E N P-0 4 6 Rev. OJ.
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. LLg of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 r
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 hour1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br />.
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 F.
0 The input file for this run is listed in Table 4.6 and results are shown in figure 4.9.
TSO FOREGROUND HARDCOPY 4444 PRINTED 89285.1403 OSNAME=EAMAC.COTTAP.SAMPLS.DATA VOL=OSK536 COTTAP SAMPLE PROBLEM 5
444444444444ftff44444444444444444444444444444444 PROBLEM DESCRIPTION DATA
(
CARD 1
OF 3
)
NROOM NSLABl NSLAB2 NFLOW NHEAT NTOR NTRIP NPIPE 2
0 0
0 2
0 1
1 44 4 4 ~ 4 4 4 ~ 4 4 t t444 4 ~ 4 tf ~ ~ 4 4 4444444444444444 tf ~ 4 ~ 4 4 4 4 PROBLEM DESCRIPTION DATA
(
CARO 2
OF 3
)
4 NFTRIP MASSTR MF CP1 CP2 CR1 INPU 0
I 23
- 5. 04 150.
10.
1 4 4 44 4 4 4 4 4 4 4 4 4444 4 4 4 4444 4 4 4 4 t4 4 t44 4 44 t4 4 4 4 444444444 PROBLEM DESCRIPTION DATA
(
CARO 3
OF 3
)
4 44444 4 444444444444 4 44 NBRK NLEAK NCIRC NEC 0
1 0
1 4 44 4 4 44 444% ~ 44444
~ ~ 4 4 t TF IFPRT RTOL 1
- 1. D-5 4444444444t44t4444444 NSH 0
444 4 4 444 ~ ~
TFC
- 1. D-5 4 444444 444 4 44 44 4 44 4 44 4 4 44 444 44 44444 44444 PROBLEM TIME AND TRIP TOLERANCE DATA 4 4 44 4 4 4 4 4 ~ ~ 44 4 44 444 44 ~
T 0.0 4 4 44 ~ tf 4 4
TO 4
DELFLO 1.0-5 44444444
~ ~
4 TEND 4.0 44444fffftft LERANCE FOR
(
OMIT THIS 4 4 ~ 4444444 44 EDI TRPTOL TRPEND 0.05 4.0 44444444444444444444444
'ftf444444444444 COMPARTMENT-AIR-FLOW MASS BALANCE CARD IF NFLOW
=
0
)
4 4 4 4 4 4 4 4 4 4 ~ ~ f 4 4 4 4 t t4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 t 4 ~ t 4 4 4 4 T
CONTROL DATA CARDS TLAST TPRNT 25.0
- 0. 10 4 4 4 4 4 4 4 4 4 4 4 4 4 ~ 4 4 4 4 4 4 4 4 4 4 tf 4 4 4 4 4 4 4 4 4 ~ 4 4 ~ 4 ~ 4 4 4 4 4 4 4 4 t 4 4 t 4 4 4 4 4 4 4 4 4 EDIT DIMENSION CARO IDEC 1
44 44 444 4 4 4 4
4 NREO NS1ED NS2ED 2
0 0
4 4 4444 44 ~ 4 ~ 4 f 444 4 4444 ttftfttf4 4 4 4 4 44 4 444ttf 4444 ROOM EDIT DATA CARD(S) 4 4 t44444 ~ 4 4 44444444
~ ~ 4 4 44 1
44 4 4
4 444 44 4 4
4 4
4fft 4
4 I
444 4 444 f 4444 44 4444444 444 44444444444444 444 4 4 4444 4 ~ 44t4444444444 4444444 EDIT CARDS FOR THIN SLABS 4 4 4 ~ 4 44 444 44444 4 4 t4 4 4 4 44444444 444 4 4 4 4 44444444 4 444 4444 444 4 4 4 444444 4 4 4 4 REFERENCE PRESSURE FOR AIR FLOWS (OMIT THIS CARO IF NFLOW=O)
PREF 14.7 4 4 4 ~ 4 4 4 4 4 4 4 4 44 4 4 4444444 4 4444
~ 4 4 44 44 44 44 ~ 4 ROOM DATA CARDS (00 NOT INCLUDE TIME-DEPENDENT ROOMS)
TREF 100.
~fffff
~ ~ 4 4 4 4 4 ~ ~ 444 4 4 444444 44 DROOM VOL PRES TR RELHUM RM HT
\\
10000.
14.7 100.0 0.5 10.0 2
1.015 14.7 100.0 0.5 10.0 4444 4 4 4 44 4t 4 4 t444 4 t f 4 444 t4444 4 4 4444 44 44 4 4 44 444 4 AIR FLOW DATA CARDS
(
OMIT THIS CARO IF NFLOW =
0
)
444444444444ffffffffff 414 4
4 1 OF LOW I FROM I TO VF LOW 2
4 4444 444 ~ 4 444444 tf444ttf 4 4 4 44 4 4 444444tf 44 44444 4 ~ 4 44444444 44 4 4 444444f 4 EDIT CARO(S)
FOR THICK SLABS
AREAS2 I RMF LG TDRTO TTEMP PRES IDSLB2 JRMl JRM2 JTYPE tt t t t t t t t t t t t ttttt t tt ~ t t t t t t t t ~ t t t t t tt t ~ t ~ t t t t t t t t tt t t t t t tt t t t t t t t t t t t t tt THIN SLAB DATA CARD (CARO 2
OF 2) t IDSLB2 UHT (
1 )
~
UHT (2) tttttt ~ttttttttttttttttttttt~ ~tttttttttttttttttttttttt~ttttttttttttttttt t
TIME-DEPENDENT ROOM DATA IDTDR NPTS AMPLTD FREQ tt t ~ t t t t ~ t t t t t t ~ t t t t t t t t ~ ~ t ~ t t tt ~ ~ t ~ ttttt t t ~ tt tt t t ~ ~ t ~ t t t t \\ ~ t t t tt t t t t t ~ t t t
TIME VERSUS TEMPERATURE DATA t
I OTDR TTI ME RHUM tt t t t t t t t t t t t t t t t t t t t t t t t ttt t t t t t t tt t ttt 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 tt 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 0 t ~ t ~ t t t ~ ~ t 1 t t t t
K ARLEAK AKLEAK LRMI LRM2 LOIRN
'I. 0
-1.0-I 2
I
~ t t ~ t ~ ~ t t t t t ~ ~ t tt ~ t t t ~ ~ t t t ~ t t ~ tt ~ t ~ t ~ t ~ ~ t t t ~ t t t t t t ~ ~.t ~ t t ~ t t ~ ~ t ~ ~
CIRCULATION PATH DATA I OLEA Ittttt t t t t tt t t t t t t t t t t t t ~ t tt t ~ tt t t t t t t t ~ t t tttt t t t t t tt t ttt t t t t ~ ~ t t t t t t t t t t t t t t t LEAKAGE PATH DATA t
(
OMIT THIS CARD IF NLEAK =
0
)
t IDCIRC KRMI KRM2 ELEVI ELEV2 ARIN AROUT AKIN AKOUT ttt tt ttt tt I
IDFTRP KFTYPI KFTYP2 FTSET IDFP ttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt HEAT LOAD DATA CARDS DHEAT NUMR ITYP QDOT TC I
1 4
-20000.
75.
2 I
5
- 0. DO
-1.
t t t t t t t t t t t t t t t t t t t t t t t t ~ ttt t t t tt ttttt PIPING DATA CARDS WCOOL 2000.0.
t t ttt t t t tt t ~ t ~ t t t t ~ t t t t t t t tt t t t t t t ~ ~ t ~ t t t tt ~ ~ t t t t t t t t ~ tt t tt t t tttt t t t t t t t t t t t t t ~ t t t tt t t t t t t t t t t tt t t AIR FLOW TRIP DATA OPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE I
2 20.
19.
24.
50.
.85
.05 550.
I ttt ~ ~ ~ ~ ~ ~ ~ ~tttttttttttttttttt~tttttttttttt ~ ~ t ~ t ~ ttt ~ tt ~ ttttt ~ ~ ~ ttt ~ tt HEAT LOAD TRIP CARDS IOTR I
ttttttt~
IDBRK tttttttt t
IDSLB I ttttttttt tt I OSLB I tttttttt t
t IDSLB I tttttttt IBRM BFLPR IBFLG BOOT TRIPON TRIPOF RAMP tttttttttttttttttttttttttttttttttttttttttt
~ttttttttttttttttttttt THICK SLAB DATA CARD (CARD I
OF 3)
IRMI IRM2 ITYPE NGR ID IHFLAG CHARL t t t t t t t t t t t t t t t t t ttttt t t tt t t t tt t t t ttt t tt t t t t t t t ~ t t ~ t t t t t t t ~ tt t t t THICK SLAB DATA CARO (CARD 2 OF 3)
ALS AREASI AKS ROS CPS EMI S t t t tttt t t ~ ~ t t t ~ ~ ~ t ~ ~ t t t t t t t t t t tt 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 ~
THICK SLAB DATA CARD (CARD 3 OF 3)
HTCI(I)
HTC2(1)
HTCI(2)
HTC2(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 tt 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 THIN SLAB DATA CARD (CARO I
OF 2)
IP IHREF ITMD TSET TCON 2
I l.
-I t ~ ~ t t tttt 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 ~ tt t t t t t t t ~ t t STEAM LINE BREAK DATA CARDS I
oa CD C)
FIGURE 4.9 COTTAP TEMPERATURE PROFILE FOR SAMPLE PROBLEM 5 120 115 110 I
CL LIJ CL EJJI 105 100 2
TIME (hr)
ppdL Form 2454 n0/831 C<<L <<913401 SE -B-N A:-0 4 6 RL".0 >
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. JL7 of I
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 of 150 F.
The initial relative humidity is set to 0.001 so that the 0
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 and the 2
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 0000 PRINTED 89286.1008 DSNAME=EAMAC.COTTAP.SAMPL6.DATA VOL=DSK532 TFC 1.D-5 0 0 ~ 4 1 ~ 0 4 ~ 1 1 0 t 0 ~ 0 0 ~ 4 0 0 ~ ~ ~ ~ 0 ~ 0 ~ t 0 1 ~ ~ 1 4 0 4 0 4 ~ 0 ~ t 0 ~ 1 ~ 0 4 PROBLEM TIME AND TRIP TOLERANCE DATA 444 ~ ~ 101 ~ 1 ~ 014 04140040 4
COTTAP SAMPLE PROBLEM 6
0 ~ 1 0 4 1 1 4 1 0 0 0 1 0 ~ 0 t 0 0 11 ~ 1 0 ~ 1 ~ ~ 4 ~ 0 ~ ~ 1 0 t 0 0 0 4 0 0 4 0 4 4 0 0 4 ~ 0 4 0 0 4 ~ 0 ~ 0 1 0 4 0 0 0 0 0 0 0 tt 4 PROBLEM DESCRIPTION DATA
(
CARD 1
OF 3
)
0 NROOM NSI.AB1 NSLAB2 NFLOW NHEAT NTDR NTR IP NP IPE NBRK NLEAK NCIRC NEC I
0 0
0 0
1 0
0 0
I 0
3 0 0 ~ 0 0 0 ~ 0 0 0 \\ 0 0 0 4 1 4 0 t t 0 0 t 0 0 1 0 0 0 0 t 0 0 ~ 0 0 0 0 ~ 0 0 0 0 0 4 0 1 4 ~ 0 4 t 0 0 0 0 4 4 1 ~ ~ ~ 1 ~ ~ 0 0 0 0 0 0 0 PROBLEM DESCRIPTION DATA
(
CARO 2
OF 3
)
0 NFTRIP MASSTR MF CPl CP2 CR1 INPUTF IFPRT RTOL 0
1 23
- 5. D4 150.
10.
1 1
- 1. 0-5 0 1 1 0 0 0 4 0 0 0 0 1 0 0 0 0
' 4 0 0 0 0 0 0 4 '0 0 0 0 0 ~ 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 4 0 4 0 4 0 1 4 0 ~ 4 0 0 0 0 4 0 0 0 4 0 0 0 4 0 0 PROBLEM DESCRIPTION DATA
(
CARD 3
OF 3
)
4 NSH 0
T 0.0 01441010 4
4 OELF
~
1.D-440144
~ ~
1 TEND TRPTOL TRPEND 0.2 0.005 4.0 0 0 4 4 4 4 1 4 4 1 4 4 0 4 1 1 4 4 0 0 0 1 0 4 4 0 0 0 1 0 4 0 4 0 0 4 4 0 4 1 4 4 1 0 4 0 1 0 ~ 4 TOLERANCE FOR COMPARTMENT-AIR-FLOW MASS BALANCE
(
OMIT THIS CARD IF NFLOW
=
0
)
4 ~ ttt01440t044 LO 5
4 0 ~ 4 4 0 4 4 4 4 0 4 0 4 1 0 ~ 1 ~ 4 4 0 0 ~ 0 ~ ~ ~ 0 10 0 0 0 0 4 4 4 4 0 ~ 0 1 ~ 4 4 0 ~ 1 0 4 1 4 ~ 0 ~ ~ ~ 1 1 t 0 4 4 EDIT CONTROL DATA CARDS TLAST 0.5 0.6 5.0 4 4 4 0 4 4 4 4 4 0 1 4 0 IDEC 1
2 3
44044144 0
4 NRED 2
~ ~ ~ ~ 4 ~ 14004 0
1
-1 4 1 00 4 0 0 0444 0
4 404014000
~ 0 ~
11444444441 1
TREF 100.
1 ~ 11 ~ 444101 0
IORQOM 1
1 000001014 TPRNT 0.01
- 0. 01
- 0. 10 0 0 1 1 4 1 0 0 0 4 1 0 0 0 4 0 0 0 0 4 4 4 4 0 4 1 4 4 4 4 1 4 4 0 4 4 0 EDIT DIMENSION CARD 4 0 0 1 0 4 4 4 4 4 4 0 0 4 NS I ED NS2ED 0
0 0 4 0 t 0 0 0 0 0 t 0 4 0 ~ 0 ~ 0 1 0 0 4 4 0 0 0 0 4 0 ~ 4 0 0 ~ 0 4 4 4 4 0 4 0 0 1 0 ~ 0 0 0 4 0 4 4 4 0 0 4 0 4 4 4 4 ROOM EDIT DATA CARD(S)
~ 1 0 0 0 0 ~ 0 ~ 4 0 4 ~ 1 4 4 1 0 0 ~ ~ 4 ~ 1 0 0 0 0 0 4 ~ 1 0 1 4 1 0 4 4 4 1 0 4 4 0 0 ~ 0 0 0 0 0 4 1 0 ~ 0 4 0 4 0 EDIT CARO(S)
FOR THICK SLABS 0 4 0 4 0 4 t t t 0 t 0 1 1 0 0 0 0 ~ 1 1 0 1 0 4 0 4 4 4 0 4 4 0 0 0 4 4 1 4 4 4 4 4 4 ~ 0 0 4 4 0 4 0 0 0 0 0 0 0 1 0 0 EDIT CARDS FOR THIN SLABS 0 1 0 4 0 0 1 4 0 1 1 ~ 4 0 0 1 1 0 4 1 t 4 0 4 '4 0 1 0 4 ~ 0 1 4 t 1 0 1 4 0 0 0 4 1 ~ 1 1 1 0 4 ~ 0 1 0 1 1 0 1 1 REFERENCE PRESSURE FOR AIR FLOWS (OMIT THIS CARD IF NFLOW=O)
PREF
- 14. 7 0 ~ 1 0 4 0 4 1 4 0 0 0 t 1 1 ~ ~ 1 0 1 1 0 0 ~ 1 1 \\ 0 0 10 0 1 0 ~ 1 4 4 0 t ~ 1 1 0 0 ~ 0 ROOM DATA CARDS (DO NOT INCLUDE TIME-DEPENDENT ROOMS) 4 ~ 44414t144401 L
PRES TR RELHUM RM HT 14.7 150.0 0.001 10.0
~ 0 0 0 4 t 4 1 0 1 0 4 4 1 1 1 ~ t 0 1 0 4 ~ 4 0 0 4 0 0 0 1 4 4 0 4 4 4 t 4 1 4 4 1 0 1 4 0 ~ 1 0 O
CD CD 0
AIR FLOW DATA CARDS
(
TH~RO~FL~ 0
I OFLOW I FROM I TO t tttttttt t t
t
,VFLOW ttt t
t t
t I
tttt t
I ttt tttttt I
tttt t
t tt tttt t
t t t t t ttt 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 ~ tt t tt t t t t t t t t t ~ t t LEAKAGE PATH DATA
(
OMIT THIS CARD IF NLEAK =
0
)
ARLEAK AKLEAK LRM1 LRM2 LDIRN 0.01 4.0 1
-1 1
t t t t t t t t t t t t ~ t t t t t t t t t t ttttt 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 IDLEAK 1ttttt IDCIRC KRM1 KRM2 ELEV1 ELEV2 ARIN AROUT AKIN AKOUT t ~ t t t t t t t t t t t ~ ~ t ~ t t t t t t ~ t ~ t tt tt t tt ~ ~ t t t tt t t t t t tt t t t ~ t ~ t t t t t t t t t t t t t t ~
AIR FLOW TRIP DATA IOFTRP KFTYP1 KFTYP2 FTSET IDFP ttt t t t t t t t tttt t t t t t t t t tttt t t tt t t t tt t t t t t ~ t t t t t t t t t t tt t t t t t t t t tt t t t t t t HEAT LOAD DATA CARDS ITYP QDOT TC WCOOL DHEAT NUMR tt t t t t t t tt t t t t t t t t t t t t t t t t t t t t ttt ttt t t t t tt 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 OPIPE IPREF POD PID AIODN PLEN PEM AINK PTEMP IPHASE 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 tt t t t t t t t t t t t t t t t HEAT LOAD TRIP CARDS I TMD TSET TCON I DTR IP IHREF 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 tt t t t t t ~ t t t ~ ~ t t STEAM LINE BREAK DATA CARDS DBRK IBRM BFLPR IBFLG BDOT TRIPON TRIPOF RAMP t t t t t tt t tt t ~ t t t t t t t t t t t t t t t t t t t t tttt t ~ t t t t t t t t t t ttt t t t t ttt t t t t t t t t t t THICK SLAB DATA CARO (CARD 1
OF 3)
DSL81 NGR IO IHFLAG CHARL IRM2 ITYPE IRM1 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 tt t t t tt t t t t t ~ t t t t ~ t t t t t t tt t t t t t t t t t t t t t t THICK SLAB DATA CARD (CARD 2
OF 3)
AREASl AKS ALS ROS CPS DSL81 EMI S t t t t t t t ~ t t t t 1 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 ~ ~
THICK SLAB DATA CARD (CARO 3
OF 3)
HTC2(2)
HTC1(1)
HTC2(1)
HTC1(2)
DSL81 t t t t ~ t t ~ t t t t t t t t t tt t t t tt t t t tt 't 't t t t t ttt t t t t 't tt ttt t t t t t t t t t t t t t t t t t tt THIN SLAB DATA CARD (CARD 1
OF 2)
CA I
Q3 CD O
CD
4 404 4
4 0
040 4
~ I 004 4
I jj4 bib IDSL82 JRMI JRM2 JTYPE AREAS2 0ii01ii\\i40i0iiF 00 'i4ii4044404ii00 ~ ii004i0440i04 THIN SLAB DATA CARD (CARO 2
OF 2
4 4 0 4 4 4 4 4 0 4 4 4 4 4 4 4 4 4 0 4 IDSLB2 UHT(1)
UHT(2)
DTDR IRMFLG NPTS TDRTO AMPLTO
-I I
3 0.0 0.0 44404444
~ 4440i440444444
~ 4 ~ 4 ~ 00 ~ 40014i044440i4j404 TIME VERSUS TEMPERATURE DATA FREQ 0.0 4 4 4 4 4 4 4 4 4 4 4 4 0 4 '0 4 4 TTI ME 0.0 10.0 20.0 4441i4 ~ 40 j04444 ~ 0 4 4 0 4 4 4 4 4 t ~ 0 0 0 4 4 0 4 DTDR
-I TTEMP RHUM PRES 150.
0.01
- 1. D-5 150.
- 0. 01 I. D-5
'I 50.
0.01 I. O-S i 0 ~ ~ 0 0 0 0 ~ ~ 4 i 4 ~ 0 4 4 4 ~ 0 4 4 ~ 0 4 4 0 0 ~ 4 4 0 ~ 4 0 0 4 ~ 0 4 4 ~ ~ ~ ~ 4 ~ 4 4 i ~ 4 Oi ~ 040 ~ ~ 004 ~ ~ 4444l ~ OOii440i ~ 4040004
~ i ~ ~ fti4 ~ 044f 1404
~ ~ ~ 4 4 4 ~ ii 0 ~ 4 4 4 0 i ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ 0 0 0 00 4 ~ 4 4 4 4 ~ 4 ~ 4 4 0 ~ ~ 4 ~ ~ ~ 4 4 i 0 I~ 1 ~
IO ~ ~ 4 4 i 0 ~ 4 i 1 0 ~
TIME-DEPENDENT ROOM DATA
FIGURE 4.IO COMPARISON OF COTTAP CALCULATED COMPARTMENT AIR MASS WITH ANALYTICALSOLUTION FOR SAMPLE PROBLEM 6 700 CQ I
LJ I
OOz V)
V)
Q 650 600 550 500 450 400 Legend ANALYTICAL
~ COTTAP 350 0.00 0.05 0.10 TIME (HR) 0.15 0.20
pp&L Form 2454 nOIS3)
Cdt. 4913401 SE -B-N A.-o 4 6 Rev.6 1
Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of s
PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 5.
REFERENCES 1.
- Gear, C.W., Numerical Initial Values Problem in Ordinar Differential
~Eations, Prentice-Hall, Englewood Cliffs, HJ, 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 Ordinar Differential Equations, 1973.,
Chapter E.
5.
Hindmarsh, A.C.,
"GEAR:
Ordinary Differential Equation System Solver," Lawrence Livermore Laboratory report UCID-30001, Rev.l,
- August, 1972.
ppd L Form 2454 na/83) car. <<orxm
$F..-B-. Is A.-04 6 Rev.PZ Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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.
PP3,L FOrm 2454 n0r83)
Cat. 1973401
$E -B-N A =0 4 6 Rev.0 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of
. PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 12.
CRC Handbook of Chemistr and Ph sics, 56th Edition, R.C. Weast,
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.
Pujii, T., and Imura, H., "Natural convection Heat Transfer, from a Plate with Arbitrary Inclination," Znt. J. Heat Mass Transfer, 15, 755 (1972).
ppaL Form 2asa no/N)
Gal. a973401 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. IZ5 of PENNSYLVANIAPOWER 8 LIGHTCOMPANY ER No.
CALCULATIONSHEET 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.
PAL Form 245'10182)
Ca(. tQT2401 g p,.-04. 6 Rev.og Dept.
Date 19 Designed by Approved by PROJECT Sht. No. lg6 of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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
a a'here P
= partial pressure of air (psia),
p
= density of air (ibm/ft ),
3 a
T
= compartment temperature
( F),
0 and M
= molecular weight of air = 28.8 ibm/lb mole.
a The partial pressure of water vapor, P, is also calculated from the v
ideal gas equation of state.
The total pressure with in the compartment, P, is then obtained from r'
P=P+P r
a v
(A-2)
PPEL Form 2iSi (lN83) cat. rr913401 N A.-04 6 Rev Ql Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET A.2 S ecific Heat of Air/Water-Va or Mixture The constant-volume specific heat of air C is given by va and C
= C R/M (A-3) va pa a
C
= constant-pressure specific heat of air (Btu/ibm R),
0 pa R = gas constant (1.9872 Btu/lb mole R).
0 The constant-pressure specific heat of air is calculated from (Table D of ref.
7)
C
= 0.2331
+ 1.6309xl0 T
+ 3.9826x10 T
pa Z
Z 1.6306x10 Tr where T is compartment temperature in K.
0 r
(a-4)
Similarly, the specific heat of water vapor is obtained from (Table D of ref.
7)
C
= 0.4278
+ 2.552x10 T
pv r
+ 1.402x10 T
4.771x10 T
Z Z
(A-5)
ppd L Farm 2454 (fCr83)
Gal. %73401 SF B
N A04 6 ReV01 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. Ijgg.of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 0
where the units of C are Btu/ibm F, and T is compartment temperature pv r
0 in K.
'The mixture specific heat is taken as the molar-average value for the air and water vapor; p
aMa'pa+
v"v'pvl/'aa 'vv (A-6) where g
and gi are the mole fractions of air and water vapor a
v respectively, and M
and M
are the molecular weights of air and water a
v 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.
pp!1. Form 2<<5<<n0/80)
Cat. <<973<<01 SF g
g g.-p4.
6 Rev.pt Dept.
Date 19 Designed by Approved by PROJECT Sht. No.~ of
'PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET 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 ZZZ.1.2.1 of ref. 9).
These routines are simplified approximations to the functions given in the ASME 1967 steam tables.
A.5 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 ZI1.1.2.2 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 ZII.1.2.3 of ref. 9).
The routines give saturated specific volume as a function of saturation pressure and enthalpy.
PPN. Form 2i54 (10I83)
Car, N973401
$Q 8
Ig g.-04 6 Rev 01 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~~0 of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET A.7 Coefficient of Thermal Ex ansion for Air/Water-Va or Mixture The coefficient of thermal expansion, 9, for the air/water-vapor mixture is defined as Il=1 Bv v
3T P
r r where v = specific volume of air/water-vapor mixture, (A-7) and P
= compartment pressure, r
T
= compartment temperature
( R).
0 Z
Evaluation of eq.
(A-7) with the assumption of ideal gas behavior for the air/water-vapor mixture gives 8=1 TZ (A-8)
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)
I1= [uH +I'll]/[IlIM +PM 1/2 1/2 (A-9)
PPLL Form 24K (1N83)
Cat. 4973401 Sp.. w A=.0.4. 6 Reaox Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~8of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET where It
,I3
= viscosity of air and water vapor respectively a'
(ibm/hr-ft),
and 9
,III
= mole fraction of air and water vapor respectively, a'
M
= molecular weight of air (28.8 ibm/lb mole),
a M
= molecular weight of water vapor (18 ibm/lb mole).
v and It are determined by fitting straight lines to the data given in a
v Tables A.1 and A.2.
temperature are The equations which give It and It as functions of a
v It
= 0.0413
+ (7.958x10
)(T -32),
a r
and
= 0.0217
+ (4.479x10
) (T -32),
v r
(A-11) where It and It have units of ibm/ft hr and T is compartment temperature a
v r
0 in F.
ppdL Form 2454 t'rar82)
C4t. 4972401 SF g
N A=04 6 Rev01 Dept.
Date 19 Designed by Approved by PROJECT Sht. No. ~of PENNSYLVANIAPOWER & LIGHTCOMPANY ER No.
CALCULATIONSHEET Table A.1 Viscosity of Air Viscosity of Air*
(ibm/ft hr)
Temperature
( F) 0.0413 0.0519 32 165.2
- Data from ref. 12, p. F-56 Table A.2 Viscosity of Water Vapor Viscosity of Water Vapor*
(ibm/ft hr)
Temperature
( F) 0.0217 0.0290 32 195
- Data from ref.
14 p. 294.
PPE,L Form 2454 nor83)
Ca1. 1F12XO1 8
N A.-04 6 Rev.oz Dept.
Date 19 Designed by Approved by PROJECT Sht. No. 333. of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
r.
CALCULATIONSHEET 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) where k,k
= thermal conductivity of air and water vapor a'
respectively, g,g
= mole fraction of air and water vapor respectively, a'
M
= molecular weight of air (28.8 ibm/lbmole),
and M
= molecular weight of water vapor (18 ibm/lbmole).
v 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 and k
= 0. 0140 + (2. 444x10
) (T-32),
a (A-13) k
= 0.010
+ (2.00x10
)(T-32),
where k and k have units of Btu/hr ft F and T is in F.
0 0
a v
(A-14)
pp4L Form 2454 n$83)
Cai. t913401
$ F. N A =04 6 "ev Qf Dept.
Date 19 DesIgned by Approved by PROJECT Sht. No. ~l PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET Table A.3 Thermal Conductivity of Air Thermal Conductivity of Air (Btu/hr ft F)
Temperature
( F) 0.0140 0.0184 32 212
PAL Form 2iQ n0/83)
Gal. //97340'/
SE 8
N A=04. 6 Rev.PZ Dept.
Date 19 Designed by Approved by PROJECT Sht. No. i~~of PENNSYLVANIAPOWER &LIGHTCOMPANY ER No.
CALCULATIONSHEET Table A.4 Thermal Conductivity of Water Vapor*
Thermal Conductivity of Water Vapor (Btu/hr ft F)
Temperature
( F) 0.010 0.0136 32 212
- Values from Appendix 12 of ref.
15 and p.
296 of ref. 14.
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NRCAN END BATCH NAN10004431 X BOX LABEL: LJ-97-SM-55839 Segment Inventory: Christine. williams on US06WHC102 at 2016-10-28 12:04 a c onro ee
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